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Wide-Field InfraRed Survey Telescope 

WFIRST 
Interim Report 

Science Definition Team 


J. Green', P. Schechter^ 

C. Baltay^ R. Bean'', D. Bennett^ R. Brown®, C. Conselice^ M. Donahue®, S. GaudP, 

T. Lauer'®, S. Perlmutter", B. Rauscher'®, J. Rhodes’®, T. Roellig'^ D. Stern'®, T. Sumi’®, A. Tanner’®, Y. Wang'^ 

E. Wright'®, N. Gehrels’®, R. Sambruna’®, W. Traub’® 

Consultants 

J. Anderson®, K. Cook®®, P. Garnavich®’, L. Hillenbrand®®, C. Hirata®®, Z. Ivezic®®, E. Kerins®'', J. Lunine'', 

M. Phillips®®, G. Rieke®®, A. Riess®', R. van der Marel®, D. Weinberg® 


Project Office 

R.K. Barry’®, E. Cheng®®, D. Content’®, K. Grady’®, C. Jackson’®, J. Kruk’®, M. Melton’®, N. Rioux’® 





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Paul Schechter 


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James Green, SDT-Co-Chair 


Date 


Paul Schechter, SDT Co-Chair 


Date 



1 Univereity of Colorado/Center for Astrophysics and Space Astronomy 

2 Massachusetts Institute of Technology 

3 Yale University 

4 Cornell University 

5 University of Notre Dame 

6 Space Teiescope Science Institute 

7 University of Nottingham 

8 Michigan State University 

9 Ohio State University 

10 Nationai Optical Astronomy Observatory 

1 1 University of California Berkeiey/Lawrence Berkeley National Laboratory 

12 NASA/Goddard Space Flight Center 

13 Jet Propulsion Laboratory/California Institute of Technology 

14 NASAJAmes 


15 Osaka University 

16 Georgia State University 

1 7 University of Oklahoma 

18 University of California Los Angeles 

19 NASA Headquarters 

20 Lawrence Livermore National Laboratory 

21 Johns Hopkins University 

22 California Institute of Technology 

23 University of Washington 

24 University of Manchester 

25 Las Campanas Observatory 

26 University of Arizona 

27 Conceptual Analytics 


WFIRST 


EXECUTIVE SUMMARY 

The Wide Field Infrared Survey Telescope 
(WFIRST) is the highest ranked recommendation for a 
large space mission in the recent New Worlds, New Ho- 
rizons (NWNH) in Astronomy and Astrophysics 2010 
Decadal Survey. The most pressing scientific questions 
in astrophysics today require a very wide-field survey in 
order to be answered, and existing telescopes such as 
the Hubble Space Telescope (HST), James Webb 
Space Telescope (JWST) or the Keck telescope cannot 
make these kinds of observations due to their optical 
designs and narrow fields of view. The first generation 
of digital wide-field surveys from the ground (e.g. Sloan) 
have resulted in significant advances in astronomy and 
astrophysics, and their value is recognized by the addi- 
tional decadal recommendation for continuing devel- 
opment of new ground-based telescopes designed for 
survey work (e.g. LSST). Bringing these wide-field de- 
sign principles into space will revolutionize astronomical 
surveys in much the same way that the Hubble Space 
Telescope revolutionized imaging of individual astro- 
nomical objects and galaxies. The absence of atmos- 
pheric distortion and absorption, and the darkness of 
space enable space-based surveys to cover the near 
infrared band and go deeper, with more precision and 
accuracy, than can ever be possible from the ground. 
WFIRST will be the most sensitive near infrared space 
telescope designed for wide-field survey work, and will 
produce the most powerful and informative astronomi- 
cal data set for probing the nature of dark energy, cata- 
loguing the variety of exoplanet systems, and mapping 
the distribution of matter across cosmic time. The mis- 
sion addresses the most fundamental issues in astro- 
physics utilizing existing, proven technologies, and 
could move into design and development immediately if 
a new start were to be approved. 

The WFIRST Science Definition Team (SDT) was 
formed to refine the science case for the mission, op- 
timize the design and implementation scheme, and, 
with the WFIRST Project, develop a Design Reference 
Mission (DRM) to serve as the basis for further pro- 
grammatic and technical review. This document is the 
interim report of the SDT and Project; accordingly, the 
interim DRM (IDRM) presented herein does not 
represent the final or only mission concept that could 
meet the requirements of the decadal recommenda- 
tions. However, it does serve as an “existence proof” 
that an in-scope mission can be developed which suc- 
cessfully addresses all of the scientific objectives impli- 
cit in the decadal recommendation. 


The WFIRST IDRM uses an unobscured, non- 
cryogenic, 1.3m three mirror anastigmat to feed a single 
instrument. The instrument contains three channels, an 
imager and two identical, slitless spectrometers. All 
three channels use Mercury-Cadmium-Telluride 
(HgCdTe) near-infrared sensor devices. The imager 
covers 0.60-2.0 |am with a pixel scale of 0.18 arcsec 
and the spectrometers cover 1. 1-2.0 |am with a scale of 

0.45 arcsec/pixel. An L2 orbit minimizes concerns with 
stray light from the Earth or Moon, provides an unob- 
structed view of the sky and a thermally stable envi- 
ronment. No new technologies are required to build 
WFIRST, which can be ready for launch in 2020. The 
IDRM design example has a simpler, more robust over- 
all design with increased field of view than the JDEM- 
Omega design. 

The SDT has refined the scientific objectives of 
WFIRST to three cornerstone goals, of equal impor- 
tance: 

1. Complete the statistical census of planetary sys- 
tems in the Galaxy, from habitable Earth-mass 
planets to free floating planets, including analogs 
of all of the planets in our Solar System except 
Mercury. 

2. Determine the expansion history of the Universe 
and the growth history of its largest structures in 
order to test explanations of its apparent accele- 
rating expansion including Dark Energy and 
modifications to Einstein's gravity. 

3. Produce a deep map of the sky at near-infrared 
(NIR) wavelengths, enabling new and fundamen- 
tal discoveries ranging from mapping the Galac- 
tic plane to probing the reionization epoch by 
finding bright quasars at z>10. 

In the following sections, the science case for each 
of these questions is detailed, and the scientific gain 
relative to our current understanding is quantified 
through the use of metrics, “Figures of Merit”, or FOM. 
These broadly accepted metrics, coupled with 
WFIRST’s ability to test dark energy with all of the three 
main probes using multiple consistency checks for sys- 
tematic control, demonstrate that WFIRST is unparal- 
leled in its capacity to address the fundamental science 
issues listed above, and is the next logical step in the 
advancement of space-based astronomical research. 

The SDT also studied the broader aspects of the 
mission implementation, including the question of 


Executive Summary 


1 


WFIRST 


whether the mission should be reduced in scope or re- 
designed in response to a decision by the European 
Space Agency (ESA) to fly the Euclid mission. Consid- 
eration was given to the appropriate response to any 
potential NASA/ESA collaboration on a joint mission. 
The SDT has reached the following conclusions on 
these matters: 

1. Any implementation of WFIRST should include 
all of the science objectives and utilize all of 
the techniques outlined in the NWNH decadal 
recommendation: 

Baryon Acoustic Oscillation Survey with Red- 
shift Space Distortion information 
Exoplanet Microlensing Survey 
Supernova la Survey 
Weak Lensing Survey 

Near Infrared Sky Survey - including a sur- 
vey of the Galactic Plane 
Guest Investigator Program 

2. Due to the importance of the scientific ques- 
tions, and the need for verification of the re- 
sults, WFIRST should proceed with all of its 
observational capabilities intact regardless of 
the ESA decision on Euclid. The actual obser- 
vation program and time allocations may be 
re-optimized in light of Euclid’s selection or in 
response to any Euclid or ground based re- 
sults prior to WFIRST’s launch. 

3. Should NASA and ESA decide to pursue a 
joint mission or program, all of the capabilities 
currently included in WFIRST must be in- 
cluded in the joint effort. 

WFIRST represents an opportunity to re-write the 
text books by performing the first space-quality near 
infrared astronomical surveys over very wide fields. The 
most pressing questions in astrophysics today require 
observation of tens of millions of objects over a signifi- 
cant fraction the total available sky. Telescopes such as 
HST and JWST were not designed for these types of 
observations, and could never address the scientific 
questions addressed by WFIRST. No other planned or 
existing instrumentation, including non-US planned 
missions, can address the breadth of science, nor ap- 
proach the quality of the data, that WFIRST provides. 
WFIRST will be the pre-eminent space astronomical 
science machine of the 2020’s if approved for develop- 


ment. The cost of WFIRST is anticipated to be similar to 
the NWNH cost estimate, a fraction of the cost of its 
sister telescopes, HST and JWST. It is the unanimous 
recommendation of the WFIRST SDT that the prelimi- 
nary studies we have begun be allowed to proceed to 
development and flight as rapidly as programmatic real- 
ities allow. The SDT affirms the NWNH decision that 
development of WFIRST is the highest priority for 
space astronomy in the coming decade. 


Executive Summary 


2 


WFIRST 


1 INTRODUCTION 

The New Worlds, New Horizons (NWNH) in As- 
tronomy and Astrophysics 2010 Decadal Survey priori- 
tized the community consensus for ground-based and 
space-based observatories. Recognizing that many of 
the community’s key questions could be answered with 
a wide-field infrared survey telescope in space, and that 
the decade would be one of budget austerity, WFIRST 
was top ranked in the large space mission category. In 
addition to the powerful new science that could be ac- 
complished with a wide-field infrared telescope, the 
WFIRST mission was determined to be both technolo- 
gically ready and only a small fraction of the cost of 
previous flagship missions, such as HST or JWST. In 
response to the top ranking by the community, NASA 
formed the WFIRST Science Definition Team (SDT) 
and Project Office. The SDT was charged with fleshing 
out the NWNH scientific requirements to a greater level 
of detail. NWNH evaluated the risk and cost of the 
JDEM-Omega mission design, as submitted by NASA, 
and stated that it should serve as the basis for the 
WFIRST mission. The SDT and Project Office were 
charged with developing a mission optimized for 
achieving the science goals laid out by the NWNH re- 
port. The SDT and Project Office opted to use the 
JDEM-Omega hardware configuration as an initial start- 
ing point for the hardware implementation. JDEM- 
Omega and WFIRST both have an infrared imager with 
a filter wheel, as well as counter-dispersed moderate 
resolution spectrometers. 

The primary advantage of space observations is 
being above the Earth’s atmosphere, which absorbs, 
scatters, warps and emits light. Observing from above 
the atmosphere enables WFIRST to obtain precision 
infrared measurements of the shapes of galaxies for 
weak leasing, infrared light-curves of supernovae and 
exoplanet microlensing events with low systematic er- 
rors, and infrared measurements of the Ha hydrogen 
line to be cleanly detected in the Kz<2 redshift range 
important for baryon acoustic oscillation (BAO) dark 
energy measurements. The Infrared Astronomical Sa- 
tellite (IRAS), the Cosmic Background Explorer 
(COBE), Herschel, Spitzer, and Wide-field Infrared Sur- 
vey Explorer (WISE) are all space missions that have 
produced stunning new scientific advances by going to 
space to observe in the infrared. 

This interim report describes progress as of June 
2011 on developing a requirements flowdown and an 
evaluation of scientific performance. An Interim Design 
Reference Mission (IDRM) configuration is presented 
that is based on the specifications of NWNH with some 


refinements to optimize the design in accordance with 
the new scientific requirements. Analysis of this 
WFIRST IDRM concept is in progress to ensure the ca- 
pability of the observatory is compatible with the 
science requirements. The SDT and Project will con- 
tinue to refine the mission concept over the coming 
year as design, analysis and simulation work are com- 
pleted, resulting in the SDT’s WFIRST Design Refer- 
ence Mission (DRM) by the end of 2012. 


Box 1 


“WFIRST is a wide-field-of-view near-infrared 
imaging and low-resolution spectroscopy obser- 
vatory that will tackle two of the most fundamen- 
tal questions in astrophysics: Why is the expan- 
sion rate of the universe accelerating? And are 
there other solar systems like ours, with worlds 
like Earth? In addition, WFIRST’s surveys will 
address issues central to understanding how 

galaxies, stars, and black holes evolve 

WFIRST will settle fundamental questions about 
the nature of dark energy, the discovery of 
which was one of the greatest achievements of 
U.S. telescopes in recent years. It will employ 
three distinct techniques— measurements of 
weak gravitational leasing, supernova distances, 
and baryon acoustic oscillations— to determine 
the effect of dark energy on the evolution of the 
universe. An equally important outcome will be 
to open up a new frontier of exoplanet studies 
by monitoring a large sample of stars in the cen- 
tral bulge of the Milky Way for changes in 
brightness due to microlensing by intervening 
solar systems. This census, combined with that 
made by the Kepler mission, will determine how 
common Earth-like planets are over a wide 
range of orbital parameters. It will also, in guest 
investigator mode, survey our galaxy and other 
nearby galaxies to answer key questions about 
their formation and structure, and the data it ob- 
tains will provide fundamental constraints on 
how galaxies grow.’’ 

From the New Worlds, New Horizons Decadal 
Survey in Astronomy and Astrophysics 


Section 1: Introduction 


3 


WFIRST 


1.1 SCIENCE REQUIREMENTS 

The SDT and Project have developed a require- 
ments flowdown matrix for the mission. The three top- 
level scientific objectives for WFIRST are: 

• Complete the statistical census of planetary sys- 
tems in the Galaxy, from habitable Earth-mass 
planets to free floating planets, including analogs 
of all of the planets in our Solar System except 
Mercury. 

• Determine the expansion history of the Universe 
and the growth history of its largest structures in 
order to test explanations of its apparent accele- 
rating expansion including Dark Energy and 
modifications to Einstein's gravity. 

• Produce a deep map of the sky at NIR wave- 
lengths, enabling new and fundamental discove- 
ries ranging from mapping the Galactic plane to 
probing the reionization epoch by finding bright 
quasars at z>10. 

These objectives then drive the requirements for 
the observatory capabilities and design. A top-level 
flow-down of the WFIRST requirements is given in Fig- 
ure 1. The Science Objectives above are the highest 
level science requirements and appear at the top of the 
page. The derived scientific survey capability require- 
ments of the observatory are listed in the left-hand box- 
es and data set requirements in the middles boxes. 
The top-level Observatory design/operations parame- 
ters are listed in the right-hand boxes. A more detailed 
discussion of the basis for the requirements is given in 
Appendix A and Appendix B. 


Section 1: Introduction 


4 


WFIRST 


WFIRST Science Objectives: 

■ 1 ) Complete the statistical census of planetary systems in the Galaxy, from habitable Earth-mass planets to free floating planets, including analogs of all of the planets in 
our Solar System except Mercury. 

2 ) Determine the expansion history of the Universe and its growth of structure so as to test explanations of its apparent accelerating expansion including Dark Energy and 
modifications to Einstein's gravity. 

— 1 3) Produce a deep map of the sky at NIR wavelengths, enabling new and fundamental discoveries ranging from mapping the Galactic plane to probing the reionization 
epoch by finding bright quasars at z>10. 


WFIRST Survey Capability Rqts 


WFIRST Data Set Rqts 


Exoplanet (ExPl Microlensinq Survey 

Planet detection capability to -0.1 Earth mass (M®) 

Detects > 125 planets of 1 M© in 2 year orbits in a 500 day survey, 
with the masses of > 90 of these planets being determined to better 
than 20% * 

Detects > 25 habitable zonet planets (0.5 to 10 M®) in a 500 day 
survey * 

Detects > 30 free floating planets of 1 M® in a 500 day survey * 

* Assuming one such planet per star 
t 0.72-2.0 AU, scaling with the square root of host star luminosity 


Exoplanet Data Set Rqts 

Observe > 2 square degrees in the Galactic Bulge at < 15 minute sampling cadence 

S/N >100 for J-band magnitude <20.5 sources 

<0.3" imaging angular resolution 

Sample light curves with filter W149 

Monitor color with filter F087, 1 exposure every 12 hours 

Minimum continuous monitoring time span: -60 days 

Separation of >4 years between first and last observing seasons 


Dark Energy Surveys 
BAO/RSD Galaxy Redshift Survey 

• >11 ,000 deg2 sky coverage per dedicated year (“WIDE" Survey 
mode) 

• Goal of >2,700 deg^/yr “DEEP” Survey acquired during the WL 
Survey 

• A comoving density of galaxy redshifts at z=2 of 4.9xl0'5 Mpc'^ 
(WIDE) or 2.1x10 “I Mpc-^ (DEEP). [The source density is higher at 
lower redshifts, peaking at z=l at 2.2x10 Mpc ^ (WIDE) or 5.9x10^ 
Mpc-3 (DEEP)] 

• Redshift range 0.7 < z < 2 

• Redshift errors uzSO.001 (1 +z), equivalent to 300 km/s rms 

• Misidentified lines <TBD% per source type, <10% overall; conta- 
mination fractions known to 0.2% (TBR) 

Supernova SNe-la Survey 

• >100 SNe-la per Az=0.1 bin for most bins for 0.4 < z < 1.2, per 
dedicated 6 months 

• Redshift error a s 0.005 per supernova 

• Relative instrumental bias <0.005 on photometric calibration across 
the wavelength range 

• Distance modulus error (from lightcurve) SO.02 per Az=0.1 bin 

WL Galaxy Shape Survey * 

• > 2,700 deg2 sky coverage per dedicated year (in a “DEEP" Survey 
mode) 

• Effective galaxy density >30/amin^ shapes resolved plus photo-zs 

• Additive shear error <3x1 O '! 

• Multiplicative shear error <1x10'^ 

• Photo-z error distribution <0.04(1 +z), error rate <2% 

• Goal: The WL Galaxy Shape Survey shall be taken in a manner such 

that concurrent spectroscopy also meets the BAG survey requirements 

on source density, redshift errors and fraction of misidentified lines. 


-{> 


Near Infrared Survey 

Identify >100 quasars at redshift z >7 

Extend studies of galaxy formation and evolution to z > 1 by making 
sensitive, wide-field images of the extragalactic sky at near-infrared 
wavelengths, thereby obtaining broad-band spectral energy distribu- 
tions of > le9 galaxies at z>l 

Map the structure of the Galaxy using red giant clump stars as trac- 
ers 

Enable a robust Guest investigator (Gl) program, with at least 10% 
of the mission lifetime available to the community through peer- 
reviewed, open competition 


Dark Energy Data Sets 
BAO/RSD Data Set Rqts 

Spectrometer 
Slitless prism 

Dispersion Re= 195 (TBR) - 240 arcsec 

S/N >7 for reft = 300 mas for Ha emission line flux at 2.0 pm >1 .5x1 0 “ erg/cm^-s 
(DEEP) or 3.1x10“ erg/cm^-s (WIDE) 

Bandpass 1.116pm <A.< 2.0 pm 
Pixel scale < 450 mas 

System PSF EE50% radius 400 mas at 2 p m 
>3 dispersion directions required, two nearly opposed 
mager (for redshift zero reference) 


S/N>10for Hab<23.5 

Approximately equal time in filters F141 and F178 

Supernova Data Set Rqts 

Minimum monitoring time-span for an individual field: ~2 years with a sampling cadence 
<5 days 

Cross filter color calibration <0.005 
Four filters: F087, Fill, F141, F178 

Slitless prism spec (P130) 0.6-2 pm XlhX -75 (S/N > 2 per pixel bin) for redshift/typing 
Peak lightcurve S/N >15 at each redshift 
Dither with 15 (TBR) mas accuracy 
Low Galactic dust, E(B-V) <0.02 

WL Data Set Rqts 

From Space: 2 shape/color filter bands, F141 and F178, and 1 color filter band. Fill 
S/N >18 per shape/color filter for galaxy reft = 250 mas and mag AB = 23.7 
PSF second moment (l« + lyy) known to a relative error of < 9.3x10“* rms (shape/color 
filters only) 

PSF ellipticity (ixx-lyy, 2*lxy)/ (Ixx + lyy) known to < 4.7x10“* rms (shape/color filters only) 
System PSF EE50 radius <170 mas for filter F141, and <193 mas for filter FI 78 
5 random dithers required for shape/color bands, and 4 for Fill at same dither exposure 
time 

From Ground: 4 color filter bands -0.4 <7, < ~0.97pm 

Provide an unbiased spectroscopic Photo-z Calibration Survey (PZCS) training data set 
containing > 100,000 galaxies < mag AB = 23.7 for F141 and F178 and covering at least 
4 uncorrelated fields: redshift accuracy required is cTz<0.01(l-rzJ 


Near Infrared Data Set Rqts 

Image > 2500 deg^ of high latitude sky in three near-infrared filters to minimum depths of 
mag AB = 25 at S/N=5. Fields must also have deep (ground-based) optical imaging 
Image > 1500 deg^ of the Galactic plane in three near-infrared filters 


Section 1: Introduction 


5 


WFIRST 


WFIRST IDRM Design/Operations Overview 


Key WFIRST IDRM Observatory Design Parameters 

• Off-axis focal telescope; 1.3m diameter telescope aperture 

• <240 K telescope optical surfaces 

• Bandpass 0.6 - 2.0 pm 

• Pointing jitter <40 mas rms/axis 

• Coarse Pointing Accuracy <~3 arcsec rms/axis 

• Fine (Relative/Revisit) Pointing Accuracy <~25 mas rms/axis [TBR] 

• ACS telemetry downlinked for pointing history reconstruction 
Imager Channel (ImC): No re-imager; -180K Pupil Mask 

• ImC Pupil Mask stop diameter: 1.275 m 

• ImC Effective Area: 0.811 m^ (avg for all filters including QE and roll off) 

• 5 band parfocal filter set on wheel, driven by ExP, SNe, WL 

• R=75 (2-pix) parfocal, zero deviation prism -r “dark" (TBD) position in same wheel 

• ImC R75 Slitless Prism Effective Area: 0.782 m^ 

• ImC FPA: 4x7 HgCdTe 2kx2kSCAs, 2.1pm, <120K, 180 mas/pix 

• FOV (active area) = -0.291 deg^; Bandpass 0.6 - 2.0 pm 

• 4 Outrigger FGS SCAs mounted to ImC Focal Plane Assy (FPA) 

• WFE is diffraction limited at Ip m 

• TBD requirement on Intrinsic PSF ellipticity ... relate to knowledge rqt 
Slitless Spec Channels (SpCs): -180K Pupil Mask 

• 2 oppositely dispersed SpCs provided, othenwise -identical 

• Optical Path: pupil mask stop, focal prism, refractive focal length reducer 

• Bandpass 1.1-2. 0pm; R© = 160 (TBR) - 210 arcsec 

• SpC Pupil Mask stop diameter: 1.27 m 

• SpC Effective Area: 0.731 m^ (average including QE) 

. SpC FPA (1 of 2): 2x2 HgCdTe 2kx2k SCAs, 2.1pm, <120K, 450 mas/pix 

• FOV (active area) = -0.260 deg^ (per SpC) 

Aux FGS: 2 SCAs: controls Pitch/Yaw when ImC prism is in use 


Key WFIRST IDRM Operations Concept Parameters 

• 5-year mission life, but consumables required for 10 yrs 

• Science Field of Regard (FOR): 54 ' to 126" pitch off the Sun, 360‘ yaw 

• Roll ±10'; SNe observations inertially fixed for -90 days for viewing near the ecliptic pole(s) 

• Gimbaled antenna allows observing during downlinks 

• Slew/settle times: -16 s for dithers, -38 s for -0.7‘ slews 
SNe-la Survey (-11.5 deg^-yrs to z = 0.8, -2.9 deg^-yrs to z = 1.2) 

• A sample 2-tiered survey capability (given 6 months dedicated time) is shown, each tier optimized for a different z range 

• All tiers monitored on a 5-day cadence in selected filters + prism 

• -Square SNe fields are inertially fixed for -90 days 

• Tier 1 (to z=0.8): 5.76 deg^; Fill, F141, F178 (300 s @), P130 (1300 s) 

. Tier 2 (to z=1.2): 1.44 deg^. Fill, F141, F178 (1100 s @), P130 (5300 s) 

• SNe dedicated time is distributed in a 5-day cadence over -2 years to provide suitable light curve tracking and accurate host galaxy references (e.g. if 6 months are 
dedicated SNe, 30 hrs of SNe field monitoring would be done every 5 days for -2 years) 

• SNe fields are monitored from end of one ExP Galactic Bulge season until the start of the 4“' following ExP season (-1.8 yrs) 

• Fields located in low dust regions <20‘ off an ecliptic pole (N and S fields not required) 

• 4-9 sub-pixel dithers, accurate to -15 mas, performed at each pointing 
ExP Survey (-2.04 deg^ monitored every 15 min, 144 days/yr) 

• The Galactic Bulge is observable for two 72-day seasons each year 

• The short revisit cadence impacts other observing modes while exoplanet data sets are being acquired. This, in combination with the field monitoring time span re- 
quired for SNe and the 60 days required for ExP, limits the max number of Galactic Bulge seasons useable for exoplanet observations to seven (over 5 yrs) 

• In each season 7 fields are revisited on a 15 min cadence, acquiring 88s exposures (filter W149) for light curve tracking except for one visit every 12 hours that uses 

filter F087 for color 

• Fields are revisited to an accuracy of 1 pixel rms; no precise dithers 

“DEEP” Galaxy Shape + Galaxy Redshift Survey (-2,700 deg^/yr) 

• 3 smooth-filled ImC maps are acquired, each rolled ( Goal) by -5' relative to each other to meet BAO/RSD survey roll requirements 

• 5 ImC random dithers are acquired over the full field for the shape/color bands, and 4 random dithers for the color-only band 

• 800 s (160 s per dither) integration time in each of 2 shape/color bands 

• 640 s (160 s per dither) integration time in one color-only band 

• SpC integrations are acquired simultaneously during ImC exposures, and more than meet BAO/RSD requirements 

• -7 deg2 are completed each day (ground observations also required) 

• -5 ImC or SpC dispersed fields, observed at multiple roll angles over 1-2 weeks meet the PZCS training data set requirements. Ground observations of these fields 
are required, and locations accessible to both N and S hemisphere telescopes will be chosen 

“WIDE" Galaxy Redshift Survey (-11,000 deg^/yr, -30 deg^/day) 

• 8 SpC maps are acquired during 4 separate passes (2 oppositely-dispersed maps are acquired each pass, one from each of two SpCs) 

• The first two passes are offset from each other to rough fill both SpC and ImC SCA gaps, and the same is done for the next two passes at an -5‘ different roll angle 
and with a different ImC filter 

• Each pass consists of a series of eight 150s exposures, yielding a total SpC exposure time of 1200s. But the rough-filled nature of the exposures results in only 6 ex- 
posures being accumulated over -96% of the observed sky, so only 6xl50s = 900s of SpC time is creditable 

• -30 deg2 are completed each day, with good N/S hemisphere flexibility 


Figure 1: WFIRST Requirements Flowdown Overview 


ImC Filter 

Bandpasses (|im) 

F087 

0.76-0.97 

Fill 

0.97 - 1.24 

F141 

1.24-1.57 

F178 

1.57 - 2.00 

W149 

0.97 - 2.00 

ImC Prism 


P130 

0.60-2.00 


Section 1: Introduction 


6 











WFIRST 


2 SCIENCE 

2.1 Dark Energy Science 

Primary Dark Energy Science Objective: Determine the 
expansion history of the Universe and the growth histo- 
ry of its largest structures in order to test possible ex- 
planations of its apparent accelerating expansion in- 
cluding Dark Energy and modifications to Einstein's 
gravity. 

The dramatic progress in astronomy of the past 
two decades has included several unexpected results. 
Nothing has been more surprising than measurements 
that indicate that the expansion of the universe (discov- 
ered by Edwin Hubble nearly a century ago) is accele- 
rating. The apparent accelerating expansion could be 
due to: (1) a constant energy density (the “cosmological 
constant”) that may arise from the pressure of the va- 
cuum, (2) an evolving universal scalar field, or (3) a 
flawed or incomplete understanding of gravity as de- 
scribed by Einstein’s General Theory of Relativity. Any 
of these possibilities has profound consequences for 
our basic understanding of physics and cosmology. 
The future of the universe will be determined largely by 
whatever force or property of space is causing the ac- 
celeration, making the nature of the accelerating ex- 
pansion one of the most profound and pressing ques- 
tions in all of science. The imperative is to distinguish 
between these possibilities by carrying out a careful set 
of measurements designed to characterize the underly- 
ing source of the so-called “dark energy” that drives the 
accelerated expansion of the universe. Recent mea- 
surements reveal that about 75% of the total mass- 
energy of the universe is dark energy. In other words, 
dark energy is most of our universe today, yet we do 
not know what it is. One of WFIRST’s primary mission 
goals is to understand the nature of the dark energy: 
“WFIRST will settle fundamental questions about the 
nature of dark energy, the discovery of which was one 
of the greatest achievements of U.S. telescopes in re- 
cent years.” [NWNH] 

Dark energy affects the universe in two significant 
ways. First, the expansion history (or geometry) of the 
universe is determined by the energy density of dark 
energy over cosmic time. The growth of cosmic struc- 
tures from the density perturbations we see in maps of 
the Cosmic Microwave Background (CMB) to the galax- 
ies and galaxy clusters we see today is governed by the 
attractive force of gravity and the repulsive dark energy, 
which inhibits the structure growth. Within the confines 
of General Relativity, measurements of the expansion 
history and growth of structure will give consistent re- 


sults. Discrepancies between these two types of mea- 
surements might indicate a breakdown of General Rela- 
tivity. Only by measuring both the expansion history 
and the growth of structure can we distinguish between 
the three broad classes of explanations for the accele- 
ration outlined above. WFIRST has been designed to 
measure each of these with multiple independent tech- 
niques. As described in NWNH, WFIRST “will employ 
three distinct techniques— measurements of weak gra- 
vitational leasing, supernova distances, and baryon 
acoustic oscillations— to determine the effect of dark 
energy on the evolution of the universe”. In addition to 
these three methods, WFIRST adds a fourth method, 
redshift space distortion (RSD), which provides an al- 
ternative measure of the growth of structure. The inde- 
pendence of these four techniques is crucial to verifying 
the accuracy of the measurements. 

Box 2 


“Why should WFIRST employ all three me- 
thods? Supernovae (in particular, type SNe la) 
give the best measurements of cosmic accelera- 
tion parameters at low redshift due to their 
greater precision per sample or per object. BAG 
excels over large volumes at higher redshift. 
Together SNe la and BAG provide the most 
precise measurements of the expansion history 
for 0 < z < 2 and place significant constraints on 
the equation of state. Weak leasing provides a 
complementary measurement through the 
growth of structure. Comparing weak-lensing 
results with those from supernovae and BAG 
could indicate that “cosmic acceleration” is ac- 
tually a manifestation of a scale-dependent fail- 
ure of general relativity. Combining all three 
tests provides the greatest leverage on cosmic- 
acceleration questions. WFIRST can do all 
three.” 

From the Panel Reports-New Worlds, New Ho- 
rizons in Astronomy and Astrophysics 


2.1.1 Supemovae 

Dark energy was first discovered by using distant 
supernova as beacons to measure how the Universe 
has grown. WFIRST will build on this methodology by 
taking it to a significantly higher level of precision than 


Section 2: Science 


7 


WFIRST 


can be done with ground-based observations. These 
measurements are done using a particular form of su- 
pernova, those of Type la, which are the explosions of 
white dwarf stars of a common known mass. These 
supernovae can be seen at vast distances across the 
Universe, with their light travelling to us from a time 
when the Universe was a fraction of its present age. 
From studies of nearby Type la supernovae, we know 
that they all have about the same peak brightness after 
rescaling to the width of the lightcurve (and are there- 
fore called “standard candles”), thus measuring how 
faint a distant supernova is tells us how far away it is. 
When we combine this information with the redshift, 
which tells us how much the Universe has expanded 
since the time the light was emitted, we probe the histo- 
ry of how the Universe expanded with time, see Figure 
2 . 


Supernova Cosmology Project 
Kowalski, et al., Ap.J. (2008) 



Figure 2: The Hubble diagram for SN la observations 
from the ground and space (HST). Plotted is the dis- 
tance modulus, (I = apparent magnitude - absolute mag- 
nitude as a function of redshift. 

In practice, using Type la supernovae as dark 
energy probes requires several kinds of observations, 
all of which will be conducted by WFIRST. The first 
step is to discover the supernova. This will be done by 
repeatedly observing a large patch of sky, every five 
days, looking for new objects that were not seen before. 

Once the supernovae are discovered, they have to 
be classified to sift out the Type la’s from other types of 
supernovae, or even other variable objects. Classifica- 
tion is done both by following how the candidate super- 
novae change in brightness over time (their ‘light 
curves’), but also by verifying the spectral types of the 
candidates. The spectra obtained to confirm the classi- 
fication will also provide the redshifts of the superno- 


vae. All type la supernova that have been observed in 
the infrared exhibit a double peak in their brightness 
with time. No other type of supernova exhibits this be- 
havior. 

WFIRST’s dark energy goals require high and uni- 
form accuracy measurements across the entire time- 
span of the Universe’s history being probed by the su- 
pernovae. A crucial part of this high accuracy comes 
from repeated observations of each supernova over its 
“life span”. While the Type la supernovae have roughly 
the same intrinsic explosion luminosity, there are impor- 
tant variations within this type, with fainter Type la’s 
fading away faster than the brighter ones. WFIRST 
uses the light curve to see how fast they fade, thus pro- 
viding corrections to the peak luminosities. The super- 
novae occur in distant galaxies, which may have dust, 
that dims and reddens the light reaching us; observing 
supernovae over a wide range of colors allows the dust 
to be detected and the light curves corrected for it. By 
observing in the infrared, WFIRST supernova results 
will be less affected by dust- a key advantage of 
WFIRST. 

During the dedicated Supernova Survey, images 
are used both to discover new supernovae and to 
measure the light curves from ones already discovered 
as they rise and fall in brightness. These images are 
interspersed with spectroscopic observations to obtain 
redshift information. The series of images must be 
done with a certain cadence to most efficiently use 
WFIRST’s capability to measure the expansion history 
of the Universe using supernovae. 

2.1.2 Weak Gravitational tensing 

When light from galaxies propagates across the 
Universe, its path is slightly deflected by the gravity of 
other galaxies, an effect called “weak leasing” (WL), 
see Figure 3. Weak gravitational leasing has emerged 
as a unique probe of the growth of structure. Further- 
more, weak leasing observables are sensitive to the 
expansion history as well. Thus, weak leasing plays a 
particularly powerful role in quantifying possible devia- 
tions from General Relativity, and is an excellent com- 
plement to the other dark energy techniques planned 
for WFIRST. Weak leasing has been quantified by sur- 
veys of increasing statistical power over the last decade 
using both ground and space-based telescopes. How- 
ever, well away from massive clusters of galaxies, the 
subtle variations of the measured galaxy shapes (of or- 
der 1%) are difficult to measure using ground-based 
observatories with their large and time-variable instru- 
mental point spread functions (PSFs). WFIRST has 


Section 2: Science 


8 


WFIRST 


been designed to mitigate these effects with a thermally 
stable platform in space, enabling surveys spanning 
thousands of square degrees that will be statistics- 
limited, as opposed to upcoming ground-based surveys 
that may be limited by systematic effects over similar 
areas. The WFIRST weak leasing survey requires 
measurements of galaxy shapes in two filters. This 
second filter is useful for addressing wavelength- 
dependent PSF issues in galaxy shape measurements 
(Voigt et al. 2011; Cypriano et al. 2010) in order to en- 
sure we achieve the low systematic errors needed for 
the WL experiment to succeed. This is an important 
cross check on systematic errors that other proposed 
experiments have not included. The WL signal is ach- 
romatic but possible systematic errors are not neces- 
sarily achromatic, so a second filter will significantly in- 
crease the robustness of a WL result. A third filter is 
required to get an additional photometric band (color 
information) that will then be combined with ground- 
based data to calculate a photometric redshift for each 
galaxy. 



Figure 3: An illustration of weak lensing showing the ef- 
fect of foreground galaxies on the light from distant 
background galaxies. 


2.1.3 Baryon Acoustic Oscillation (BAO) 

Until about 380,000 years after the Big Bang, pho- 
tons and matter interacted frequently. Hot plasma - pro- 
tons, electrons, and photons - sloshed about as sound 
waves in ever-deepening dark matter potential wells. 
When the plasma cooled and formed neutral atoms, the 
photons streamed freely through the universe, and we 
see them today as cosmic microwave background 
(CMB). After this final interaction of photons with elec- 
trons, the sound waves (acoustic oscillations) stopped 
in place, and left their signature on both the cosmic mi- 
crowave background (CMB) (verified by the observed 


acoustic peaks in the CMB power spectrum) and on the 
matter distribution (verified by the BAO signature in the 
galaxy distribution power spectrum). BAO in the ob- 
served galaxy power spectrum (the three dimensional 
galaxy distribution) have a characteristic scale deter- 
mined by the distance sound has traveled since the Big 
Bang by the time the photons last interacted with mat- 
ter, a time which is precisely measured by the CMB 
anisotropy data. Comparing the observed BAO scales 
with the expected values gives the cosmic expansion 
rate in the radial direction, and the angular diameter 
distance dA(z) through an integral in the transverse di- 
rection, see Figure 4. Put another way, the scale of the 
BAO peak in the power spectrum acts as a “standard 
ruler”, expanding along with the Universe from the time 
of the CMB to the present day. By measuring this 
scale, we determine the expansion history of the Un- 
iverse. 



1 

Observer 


Figure 4: A representation of the BAO spherical shell 
with H(z) and Da(z) measurements. 

Baryon acoustic oscillations are just one of several 
physical phenomena that affect the galaxy power spec- 
trum. The same galaxy redshift survey that will be used 
to measure BAO will also be used to study a phenome- 
non called redshift space distortion (RSD) and to locate 
a feature in the galaxy power spectrum due to the tran- 
sition from radiation domination to matter domination 
(TRMD) 100,000 years after the big bang. As effects of 
both of these on the galaxy power spectrum are sensi- 
tive to the assumed cosmology, they provide additional 
leverage, making WFIRST a yet more powerful mission 
for studying cosmic acceleration. In the discussion that 
follows, we distinguish among these different mea- 
surements, reserving the term baryon acoustic oscilla- 
tions for the phenomenon described in the previous 
section. While RSD and TRMD are expected to shar- 
pen WFIRST's dark energy results, they do not drive 
the requirements beyond those for BAO measure- 
ments. 

Astronomers often use Hubble’s law to calculate 
distances from redshifts, but this estimate does not take 
into account peculiar velocities, which are local gravita- 


Section 2: Science 


9 


WFIRST 


tional deviations from the overall expansion of the un- 
iverse. These local velocities will cause galaxies at 
equal distances to have slightly different redshifts. 
These slight differences elongate the redshift distribu- 
tion for galaxies clustered along the line of sight. Gravi- 
ty causes galaxies to fall in towards overdense regions. 
This pattern makes galaxies between us and the over- 
density appear to be farther away, based on distance 
estimates using their redshifts and Hubble’s Law. Ga- 
laxies on the far side of the overdensity appear closer. 
The net effect is to enhance the overdensity. These ef- 
fects are collectively called “redshift space distortion” 
(RSD). This RSD measurement can be obtained from 
the same data required for BAG and used to constrain 
the growth of cosmic structure in a complementary way 
to WL. BAG along with RSD measurements allow us to 
simultaneously measure the cosmic expansion history 
and the growth rate of large scale structure, thus enabl- 
ing precise measurement of dark energy as well as 
testing general relativity. 

2.1.4 Complementary Dark Energy Constraints 

In the local universe (redshift z<0.5), supernovae 
are unparalleled in their ability to constrain dark energy 
for two reasons. First, there is insufficient cosmic vo- 
lume for more statistical techniques (WL & BAG) to 
work. Second, cosmic structure gets increasingly non- 
linear (and hard to model) as the redshift gets small. 
Dark energy was originally discovered using superno- 
vae at relatively modest redshifts. At the highest red- 
shifts (z-llOO), we have the CMB, which establishes 
the BAG ‘standard ruler’ scale. The BAG provide a link 
between the expansion history of the Universe at 
z=1100 and z=0.5. The BAG systematic errors de- 
crease with increasing redshift (due to decreased nonli- 
near effects), while the SN systematic errors increase 
with redshift. Using the SN and BAG connects the 
whole expansion history of the universe. Weak leasing 
fundamentally measures the three-dimensional distribu- 
tion of matter, which can be compared with theoretical 
expectations. It is sensitive to both expansion and 
growth of structure, and has the potential to be the most 
powerful single dark energy technique. However, weak 
leasing measurements are difficult to make because the 
very small shape distortions induced in faint galaxies 
must be deconvolved from the much larger effects of 
the telescope and optics (the so-called Point Spread 
Function, or PSF). Successful measurements require 
high spatial resolution with an excellent quality and sta- 
bility, and a known small-scale PSF combined with very 
large sky areas. In contrast, the BAG data are relatively 


easy to acquire since we only need to measure the po- 
sitions and velocities of galaxies. In addition, we get 
the RSD information on the growth of structure for free. 

The three methods employed by WFIRST to ex- 
plore dark energy, weak leasing, BAG (with RSD), and 
supernovae, together give us three complementary 
probes of the cosmic expansion history, and two com- 
plementary probes of the growth history of cosmic large 
scale structure. WFIRST is an extremely capable dark 
energy probe able to make very robust measurements 
with significant opportunity for cross-checks and verifi- 
cation of results. 

2.2 Exoplanet Science 

Primary Exoplanet Science Objective: Complete the 
statistical census of planetary systems in the Galaxy, 
from habitable Earth-mass planets to free floating pla- 
nets, including analogs of all of the planets in our Solar 
System except Mercury. 

2.2.1 Introduction/Retrospective 

The first discovery of a planetary companion to a 
sun-like star by Mayor & Queioz in 1995 was, along 
with the discovery of dark energy, one of the greatest 
breakthroughs in modern astronomy. In the intervening 
15 years, hundreds of exoplanets have been discov- 
ered, mostly by the radial velocity technique, and over 
1200 candidates have been detected in transit by the 
Kepler space telescope (Borucki et al. 2011). From the 
very first discovery, it has been clear that nature hosts 
an enormous and unexpected diversity of exoplanetary 
systems, containing planets with physical properties 
and orbital architectures that are radically different from 
our own solar system. Theories of planet formation and 
evolution, originally developed to explain our solar sys- 
tem, have struggled to keep up with the flood of new 
planets. This ferment indicates a vibrant research do- 
main, which is drawing talented young researchers to 
careers in astronomy and planetary science. 

A second facet of the explosion of interest in extra- 
solar planets is the search for planets that could host 
life, those similar in temperature and mass to Earth. 
This goal, which is profound in both scientific and cul- 
tural terms, has captured the imagination of research- 
ers, political decision makers, and people around the 
world. Microlensing, combined with transit surveys (see 
below), will tell us whether Earth-mass planets in habit- 
able orbits are a common or uncommon outcome of 
planet formation. The answer will change humankind’s 
view of the cosmos. It will also help determine the fea- 
sibility and scope of future direct detection missions to 


Section 2: Science 


10 


WFIRST 


see such habitable planets around nearby stars and 
search for indications of life with spectroscopy. 

Microlensing in space fulfills the Primary Exoplanet 
Science Objective of WFIRST for the following reasons, 
(a) WFIRST’s exoplanet (ExP) microlensing survey 
“completes the statistical census of planetary systems” 
as a perfect complement to Kepler’s survey. For ex- 
ample, we know that Kepler’s ability to detect planets is 
ten times smaller at separations of 1 AU than 0.1 AU. It 
is also proportionally smaller for Earth-size planets than 
Jupiter-sized planets. As a result, even though Kepler 
is designed explicitly to detect terrestrial-size planets in 
the habitable zones of solar-type stars, this is close to 
the limit of its capabilities. Fortunately, the converse is 
true for ExP on WFIRST, where the region of high sen- 
sitivity runs from roughly the habitable zone outwards. 
Also, the microlensing signal is far less sensitive to the 
mass of the planet than is Kepler’s transit technique to 
planet size. In sum, detecting terrestrial planets is well 
within microlensing’s capability. Thus the sum of Kep- 
ler plus WFIRST’s ExP survey will yield a composite 
census of planets on both sides of the habitable zone, 
overlapping at almost precisely that zone, (b) 
WFIRST’s ExP program can detect “free-floating” pla- 
nets below an Earth-mass in numbers sufficient to test 
planet-formation theory, a task not possible from the 
ground. It is only in space that the statistics of these 
detections will be adequate, (c) Exoplanet microlensing 
from the ground has had well-documented successes, 
but just as is the case for transits, space is a vastly bet- 
ter place to carry out statistically significant observa- 
tions. Space-based microlensing is superior because of 
the steady viewing without interruptions for weeks at a 
time, with high angular resolution, stable images over 
wide-area fields. 

For these reasons, WFIRST’s ExP microlensing 
survey is both the most efficient and affordable tech- 
nique for quantifying the statistical distribution of pla- 
nets over a wide range of masses and semi-major 
axes. Its capabilities have been amply demonstrated 
from the ground through the first discovery of a ’’super- 
Earth”, only six times the mass of our own planet 
(Beaulieu et al. 2006), and the detection of a new popu- 
lation of Jupiter-mass planets loosely bound or un- 
bound to any host star (Sumi et al. 2011). This latter 
study also concluded that “free-floating” planets may 
outnumber the stars in our galaxy by two to one. The 
sheer number of stars in the galactic bulge make it 
possible to tease out those few planetary microlensing 
events from the innumerable, random passages of in- 
tervening stars across the background of stars in the 


Galactic Bulge. But ground-based systems have intrin- 
sic limitations that limit their sensitivity and efficiency. 

Box 3 


Projected WFIRST Exoplanet Discoveries 

If each of the Exoplanet Microlensing Survey 
Requirements in Figure 1 are met, our current 
best estimates of exoplanet prevalence imply 
that WFIRST will detect: 

3250 total bound exoplanets in the range of 0.1- 
1000 Earth masses and separations in the 
range 0.1-40 AU, including 320 sub-Earth-mass 
planets and 1500 sub-ten-Earth-mass planets. 

2080 free-floating exoplanets, including 190 
sub-Earth-mass free-floating planets and 480 
sub-ten-Earth-mass free-floating planets. 

If each star hosts planets with the masses and 
same semi-major axes as those in our Solar 
System, WIFRST will detect 280 terrestrial pla- 
nets (Venus/Earth/Mars analogs), 3200 gas 
giants (like Jupiter/Saturn), and 84 ice giants 
(like Neptune/Uranus). 


Therefore, microlensing in space— from WFIRST— 
is the best prospect we have for gaining critical know- 
ledge on planet formation and evolution, and for learn- 
ing the occurrence and parameter distribution of Earth- 
mass planets. The Exoplanet Task Force (Lunine et al. 
2008) recognized this, embedding into its strategy a 
medium-cost space-based microlensing mission to 
complement the census of close-in planets currently 
underway with spaceborne transit techniques. The De- 
cadal Survey for Astronomy and Astrophysics elevated 
microlensing to an even higher level of importance 
(NWNH, 2011), placing the science of exoplanets in the 
top two or three science areas of importance to astro- 
physics in the next decade. Space-based microlensing 
plays a pivotal role in the Decadal Strategy. As evi- 
denced by the wide range of parameter space it will ex- 
plore (see Figure 5), and the size and diversity of its 
projected exoplanet discoveries (see Box 3), WFIRST 
is the means to understanding the range of planetary 
system architectures (masses, orbital parameters) and 
to determining how many Earth-mass worlds inhabit the 
crucially important region from the inner portion of the 


Section 2: Science 


11 


WFIRST 


classic habitable zone outward. It will also extend the 
search for free-floating planets down to the mass of 
Earth and below, addressing the question of whether 
ejection of planets from young systems is a phenome- 
non associated only with giant planet formation (disk 
instability?) or also involves terrestrial planets. It is also 
the only technique available to detect planets as small 
as the mass of Mars. Since Mars-mass bodies are 
thought to be the upper limit to the rapid growth of pla- 
netary “embryos”, determining the planetary mass func- 
tion down to a tenth the mass of the Earth uniquely ad- 
dresses a pressing problem in understanding the for- 
mation of terrestrial-type planets. 

2.2.2 WFIRST Exoplanet Science Motivation 

Exoplanet Survey Question #1: How do planetary 
systems form and evolve? 

In the most general terms, planet formation theo- 
ries should describe all of the relevant physical 
processes by which micron-sized grains grow through 
13-14 orders of magnitude in size and 38-41 orders of 
magnitude in mass to become the terrestrial and gas- 
giant planets we see today. These physical processes 
are ultimately imprinted on the final distributions of pla- 
net frequencies, compositions, and orbits. Thus by 
measuring these distributions, i.e., by determining the 
demographics of exoplanets, it is possible to gain in- 
sight into the physical processes that drive planet for- 
mation. 

The discovery of gas giant planets orbiting at pe- 
riods of only a few days, as well as evidence for the mi- 
gration of the giant planets in our own solar system, 
have highlighted the fact that planet formation theories 
must also account for the possibility of large-scale rear- 
rangement of planet positions through gravitational and 
gas dynamical effects during and after the epoch of 
planet formation, and thus must also track the planets 
through billions of years of evolution. Many of these 
theories also predict a substantial population of “free- 
floating” planets that have been ejected from their pla- 
netary systems through interactions with other planets. 
Indeed, evidence for such a population was recently 
found using microlensing (Sumi et al. 2011). The inter- 
pretation of the final exoplanetary system architectures 
that we observe today must account for these dynami- 
cal processes. 

The exoplanet microlensing survey of the WFIRST mis- 
sion will provide an integral and essential component of 
a coordinated plan by the exoplanet community to an- 
swer Exoplanet Survey Question #1. In particular. 


WFIRST will provide the only way to complete the sta- 
tistical census of planets begun by Kepler, by measur- 
ing the demographics of planets with masses larger 
than that of Mars and separations of greater than 0.5 
AU. This includes analogs to all the Solar System’s 
planets except for Mercury, as well as most types of 
planets predicted by planet formation theories thus far. 
The number of such discoveries will be large with > 
3000 bound and 2000 free-floating planet discoveries 
expected. Whereas Kepler is sensitive to close-in pla- 
nets but is unable to detect the more distant ones, 
WFIRST is less sensitive to close-in planets, but sur- 
veys beyond 0.5 AU better than Kepler. WFIRST is 
sensitive to unbound planets with masses as low as the 
Earth, offering the only possibility to constrain the fre- 
quency of these planets, which may have been ejected 
during the planet formation process. Thus, WFIRST 
and Kepler complement each other, and together they 
cover the entire planet discovery space In mass and 
orbital separation (See 

Figure 5j and provide the comprehensive under- 
standing of exoplanet demographics necessary to fully 
understand the formation and evolution of planetary 
systems. 

Exoplanet Survey Question #2: How common are 
potentially habitable worlds? 

The age-old question of whether or not there is life 
on other worlds has gained even more relevance and 
immediacy with the discovery of a substantial popula- 
tion of exoplanets. The first step in determining how 
common life is in the universe is to determine the fre- 
quency of potentially habitable worlds, commonly de- 
noted 7 / 0 . While of course interesting in its own right, 
an accurate measurement of 779 also provides a crucial 
piece of information that informs the design of direct 
imaging missions intended to characterize potential ha- 
bitable planets around nearby stars and search for bio- 
markers. Indeed, the primary goal of Kepler is to pro- 
vide a robust measurement of 77 ®. Early results from 
Kepler indicate that terrestrial planets are likely to be 
very common, at least for short periods of <50 d (Bo- 
rucki et al. 2011, Howard et al. 2011), thus bolstering 
the case that 77 ® might be high. However, these data 
also indicate that a robust measurement of 77 ® with 
Kepler will require an extended mission, primarily be- 
cause of larger-than-expected intrinsic stellar variability 
(Gilliland et al. 2011). Furthermore, it will be difficult or 
impossible to measure the masses of the potentially 
habitable planets detected by Kepler because of the 
faintness of the host stars. 


Section 2: Science 


12 


WFIRST 


Exoplanet Discovery Potential 



Figure 5: The distribution of known exoplanet masses 
and semi-major axes is compared to the expected final 
sensitivity of the Kepler mission and the sensitivity of a 
500-day WFIRST Exoplanet survey. Ground based micro- 
lensing planets are show as red circles, radial velocity 
planets are brown inverted T's, planets discovered via 
their transits are blue squares, and planets found by tim- 
ing and direct imaging are green and magenta triangles, 
respectively. The cyan region shows the expected sensi- 
tivity of Kepler, and the small darker cyan squares are 
Kepler's candidate planets. The purple curve shows the 
sensitivity of a 500-day WFIRST exoplanet program as- 
suming 20% of stars have a planets of indicated mass 
and semi-major axis, and the dashed "free-floating pla- 
nets" line indicates the sensitivity limit for free floating 
planets. Some planets beyond 10 AU will be discovered 
without a microlensing signal of their host stars. 

The exoplanet survey of the WFIRST mission will 
directly address Exoplanet Survey Question #2 by pro- 
viding an independent and complementary determina- 
tion of 77e. In particular, WFIRST will detect 27 //e ha- 
bitable planets orbiting solar-type stars, similar to the 
number from Kepler. In contrast to Kepler, however, 
WFIRST is sensitive to planetary mass, rather than pla- 
netary radius, thus enabling the statistical determination 
of the densities and surface gravities of habitable terre- 
strial planets. Furthermore, while Kepler is most sensi- 
tive to planets in the inner part of the Habitable Zone, 
and begins to lose sensitivity to planets in the outer ha- 
bitable zone, WFIRST is most sensitive to planets in 
outer part of the habitable zone. Thus, the combination 
of WFIRST and Kepler data will make it possible to ro- 


bustly interpolate into the habitable zone from regions 
just outside of it, even if the frequency of habitable pla- 
nets turns out to be small. 

In summary, WFIRST will provide crucial empirical 
constraints on planetary systems that will allow us to 
address the two fundamental questions: “How do plane- 
tary systems form and evolve?" and “How common are 
potentially habitable worlds?". Of course, these two 
questions are not independent. In particular, it is likely 
that the habitability of a given planet cannot be consi- 
dered in isolation. The suitability of a planet for life de- 
pends on the average surface temperature, which de- 
termines if the planet resides in the habitable zone. 
However, there are many other factors that also may be 
important, such as the presence of sufficient water and 
other volatile compounds necessary for life (Raymond 
et al. 2004; Lissauer 2007). Therefore, the habitability 
of a planet likely depends on the formation and evolu- 
tionary history of its planetary system, and a reasonable 
understanding of planet formation is an important foun- 
dation for the search for nearby habitable planets and 
life. 

2.3 Surveys and Guest Investigator Science 

Primary NIR Survey Science Objective: Produce a deep 
map of the sky at NIR wavelengths, enabling new and 
fundamentai discoveries ranging from mapping the Ga- 
lactic piane to probing the reionization epoch by finding 
bright quasars at z>10. 

In addition to dark energy and exoplanet science, 
WFIRST will provide a unique and powerful platform for 
a broad range of compelling infrared survey science. 
Some of these studies will use the data acquired for the 
dark energy and exoplanet surveys. Such legacy 
science is best exemplified by the low redshift Sloan 
Digital Sky Survey (SDSS) where the number of re- 
search papers now published using the archival SDSS 
data - originally collected to study the large-scale struc- 
ture of the Universe - far exceeds the number of journal 
articles written by the original SDSS collaboration. To 
date, thousands of papers have been written using 
SDSS public data making it one of the most successful 
surveys of the Universe ever undertaken. 

Other science will come from separate dedicated 
observations. This latter point is repeatedly empha- 
sized in the NWNH report - e.g., the committee 
considers the guest investigator program to be an es- 
sential element of the mission ...” {NWNH, pg. 207) and 
“As a straw-man example for the first 5 years ... the 
panel imagines ... a galactic-plane survey of one-half 


Section 2: Science 


13 


WFIRST 


year, together with about 1 year allocated by open 
competition ...” (EOS Panel Report, pg. 274). Indeed, 
the Decadal Survey constructed WFIRST out of three 
separate missions with similar hardware but very differ- 
ent scientific goals. One of these missions, the Near- 
Infrared Sky Surveyor (Stern et al. 2010), emphasized 
the vast scientific potential of a space-based, wide-field 
infrared survey observatory for a broad suite of Galactic 
and extragalactic science. We now briefly discuss 
some of this science, beginning with ancillary uses of 
core WFIRST observations and then discussing addi- 
tional (guest) observational programs. 

2.3.1 Ancillary Science from the High Latitude 
Survey (HLS) 

The WFIRST dark energy program is likely to be 
the single largest component of the 5-year mission plan 
with a set of nested surveys. At the widest level, the 
BAG program will obtain shallow observations of 
>10,000 deg2 with relatively uniform spectroscopic cov- 
erage but non-uniform imaging in multiple filters. The 
weak leasing (WL) program will obtain deep, uniform 
three-filter images of > 2500 deg^, and the supernova 
(SN) program will obtain extremely deep, cadenced ob- 
servations of a few square degrees. For this report, we 
focus on the BAG and WL surveys, which together 
comprise the High Latitude Survey (HLS), though we 
note that significant ancillary science is expected from 
both the SN survey and the microlensing survey. 

The HLS will identify unprecedented numbers of 
quasars at very high redshift. Quasars are among the 
most luminous objects in the universe, observable to 
the earliest cosmic epochs. They are thought to be 
supermassive black holes at the centers of galaxies, 
converting mass into energy 20 times more efficiently 
than stars. They provide fundamental information on 
the earliest phases of structure formation in the un- 
iverse and are unique probes of the intergalactic me- 
dium. The discovery of a Gunn-Peterson (1965) trough 
in the spectra of several quasars at redshift z > 6 im- 
plies that the universe completed reionization near that 
redshift (e.g.. Fan et al. 2001), though poor sample sta- 
tistics, the lack of higher redshift quasars, and the 
coarseness of the Gunn-Peterson test make that infe- 
rence somewhat uncertain. Currently, the most distant 
known quasar is at z = 7.1 (Mortlock et al., 2011), and 
only a dozen quasars have been confirmed at z > 6. 
Ambitious surveys will push this number to around 100 
in the next few years, likely identifying one or two qua- 
sars at z ~ 8. WFIRST will fundamentally change the 
landscape of early universe investigations. Based on 


the Willott et al. (2010) quasar luminosity functions, 
WFIRST will identify thousands of quasars at z > 6, 
hundreds of quasars at z > 7, and push out to z ~ 10 
should quasars exist at those redshifts (see Table 1). 
Such discoveries will directly measure the first epoch of 
supermassive black hole formation in the universe, 
probe the earliest phases of structure formation, and 
provide unique probes of the intergalactic medium 
along our line of sight to these distant, luminous 
sources. The large numbers of quasars identified in the 
first Gyr after the Big Bang will enable clustering ana- 
lyses of their spatial distribution (e.g.. Coil et al. 2007, 
Myers et al. 2007). Gptical surveys are not capable of 
identifying quasars above z ~ 6.5 since their optical 
light is completely suppressed by the redshifted Lyman 
break and Lyman-alpha forests. Though JWST will be 
extremely sensitive at near-infrared wavelengths, it will 
not survey nearly enough sky to find the rarest, most 
distant, luminous quasars, which have a surface density 
of just a few per 10,000 degT WFIRST will be the de- 
finitive probe of the first phase of supermassive black 
hole growth in the universe. 

The HLS will also be a very powerful probe of ga- 
laxy evolution, reaching depths comparable to the 
Cosmic Evolution Survey (CGSMGS; Scoville et al. 
2007), but covering a thousand times more sky, enabl- 
ing a breadth of statistical analyses similar to those un- 
dertaken on the low redshift SDSS. In particular, the 
size and scale of the dataset will allow for accurate 
measurements of the clustering of different types of ga- 
laxies (e.g., as a function of stellar mass, size, mor- 
phology, etc.) critical for testing hierarchical models of 
galaxy evolution and probing the details of how galaxies 
trace the underlying dark matter distribution at high red- 
shifts. Though the spatial resolution will not be as ex- 
quisite as that of the Hubble Space Telescope, 
WFIRST is still expected to resolve -80% of galaxies to 
H-25 (AB). These data will provide fundamental infor- 
mation on the formation and evolution of galaxies. In 
particular, near-infrared data is crucial for studying ga- 
laxies at 1 < z < 3, which corresponds to the peak 
epoch of star formation in the universe. Near-infrared 
data is essential for deriving photometric redshifts for 
galaxies at these epochs, redshifts necessary for both 
WL and galaxy evolution science. WFIRST will signifi- 
cantly enhance ground-based optical surveys such as 
LSST, enabling galaxy evolution studies to reach to the 
critical z~2 cosmic epoch. The wide area of the HLS 
will also allow unique studies of distant galaxy clusters, 
which are powerful probes of both cosmology and ga- 
laxy evolution. 


Section 2: Science 


14 


WFIRST 


Survey 

Area 

(deg2) 

Depth 

(5-sigma, A6) 

z>7 QSO’s 

z>10 QSO’s 

UKIDSS-LAS 

4000 

Ks=20.3 

8 

- 

VISTA-VHS 

20,000 

H=20.6 

40 

- 

VISTA-VIKING 

1500 

H=21.5 

11 

- 

VISTA-VIDEO 

12 

H=24.0 

1 

- 

Euclid, wide (5 yr.) 

15,000 

H=24.0 

1406 

23 

WFIRST, deep (1 yr.) 

2700 

F3=25.9 

904 

17 

WFIRST, wide (1 yr.) 

(4730) 

F3 = 25.3-25.5 

1148 

21 


Table 1; Number of high-redshift quasars predicted for various ground- and space-based near-infrared surveys, based 
on the quasar luminosity function of Willott et al. (2010). Note: For the WFIRST wide survey, we only consider the 4730 
deg^ (out of 11,000 deg^ total) that are imaged with at least two exposures in both filters. 


Finally, the HLS will also be a powerful probe of 
cool stars and even cooler failed stars (brown dwarfs) 
within the Milky Way. For the coolest brown dwarfs, 
methane absorption in the /.-band makes observatories 
such as the Wide-field Infrared Survey Explorer (WISE) 
(Wright et al. 2010) that are sensitive at 3 to 5 microns 
ideal for identifying objects at the star-planet boundary. 
However, the wide, sensitive, and high spatial resolu- 
tion HLS survey will be a powerful tool for studying cool 
dwarfs in the Galaxy. The HLS will also be sensitive to 
cool white dwarfs (WDs) in the Milky Way halo, particu- 
larly to helium-atmosphere WDs, which become redder 
as they cool. [The formation of molecular hydrogen in 
hydrogen-atmosphere WDs causes such sources to 
become bluer when their temperatures drop below 
5000 K (Hansen 1999).] WFIRST will derive the helium 
WD luminosity function, which provides unique, inde- 
pendent and direct measurements of the age of the Ga- 
lactic halo and disk (e.g., Ferrario et al. 2005). 

Many of the ancillary science objectives will benefit 
from having 3 (or more) filters in the imaging survey. 
With the vast number of objects detected, color infor- 
mation will aid in identifying sources. False positives 
will be reduced allowing the interesting rare new objects 
to be found with higher confidence. 

2.3.2 WFIRST Guest Investigator Science 

Competed guest investigator studies with WFIRST 
will significantly enhance the scientific return of this 
unique platform, providing the flexibility to respond to 
new scientific developments. The Decadal Survey 
suggested that ~6 months of the baseline 5 year mis- 
sion be spent on a near-infrared survey of the Milky 
Way Galaxy. Such a survey would reach ~3 mag dee- 
per than 2MASS (Skrutskie et al. 2006) and -1.5 mag 
deeper than the UKIDSS Galactic Plane Survey (Lucas 
et al. 2008) before reaching the confusion limit. Map- 


ping the entire 360 deg x 2 deg Spitzer GLIMPSE sur- 
vey (Churchwell et. al, 2009) region would only require 
-1 month of observations. Among the various scientific 
goals enabled by such a survey, with the appropriate 
choice of filters, a WFIRST Galactic plane survey could 
map the structure of the Milky Way by locating essen- 
tially all of the luminous red giant stars in the Galaxy, 
thereby identifying the edge of the Galactic disk and 
measuring the shape and the extent of the Galactic 
warp. Two-epoch observations of Galactic clusters, 
separated by -5 years, would identify common proper 
motion members and detect sources well below the 
brown dwarf / free floating planet mass boundary of 10 
- 15 Jupiter masses. 

WFIRST will also be a powerful tool for obtaining 
deep near-infrared images (and spectroscopy) of near- 
by galaxies, complementing many large Trea- 
sury/Legacy programs on Hubble and Spitzer such as 
the Spitzer Infrared Nearby Galaxies Survey (SINGS) 
(Kennicutt et al. 2003), the ACS Nearby Galaxies Sur- 
vey Treasury (ANGST) (Dalcanton et. al, 2009) and the 
Panchromatic Hubble Andromeda Treasury (PHAT) 
survey. Such data are useful for studying stellar astro- 
physics, mapping galaxy interactions and accretion, 
studying galaxy formation, and probing how the stellar 
mass function depends on environment. In a -1 month 
program, WFIRST could resolve the stellar populations 
of -100 nearby galaxies, allowing detailed studies delv- 
ing into their star formation and merger histories. 

The SDT has considered many additional guest in- 
vestigator programs which are beyond the space limita- 
tions of the current report, ranging from exoplanet tran- 
sit studies that would proceed alongside the exoplanet 
monitoring to measurements of the lensing mass pro- 
files and stellar mass content of the most massive ga- 
laxy clusters at high redshift beyond the virial radius. In 


Section 2: Science 


15 


















WFIRST 


summary, operating beyond the reaches of the Earth’s 
atmosphere, free of its limiting absorption and thermal 
background, WFIRST will deeply map the sky at near- 
infrared wavelengths, thereby enabling new and fun- 
damental discoveries that address nearly the full 
breadth of astrophysics, reaching from the local neigh- 
borhood of the Milky Way Galaxy to the epoch of reio- 
nization. 



Figure 6: Sky image from the WISE space telescope of 
the Carina constellation region of the sky. 


Section 2: Science 


16 



WFIRST 


3 FIGURES OF MERIT 

3.1 Figure of Merit (FoM) Introduction 

In a mission with multiple science objectives there 
is competition for finite resources: telescope time, pixel 
size and number, field of view, and filter definitions are 
among the most obvious. As a tool to inform the alloca- 
tion of these resources and to evaluate tradeoffs we 
have adopted a set of quantitative figures of merit 
(FoM) and have used these to allocate resources in a 
balance that closely follows the notional mission de- 
scribed in NWNH. Relative risk and cost will of neces- 
sity enter into the ultimate choice of the WFIRST DRM. 

The decadal survey report describes the JDEM- 
Omega design as being nearly ideal for the mandated 
science, but identified a far broader science case than 
that of dark energy alone. The 2010 report suggested a 
five year mission during which two years were allocated 
to a high latitude survey of imaging and spectroscopy of 
galaxies for weak lensing, BAG and RSD measure- 
ments. Six months were allocated to Type la superno- 
vae identification and follow-up. One and a half years 
were allocated to an exoplanet microlensing study, 
leaving one year for a survey of the Galactic plane and 
Gl programs. 

While the panel suggested a balance between pro- 
grams, it also clearly anticipated the need to adapt to 
evolution in the scientific priorities of the community as 
new discoveries emerge. For example, the RSD me- 
thod has gained substantially more credibility in the 
community in the two years since the community first 
responded to the Astro2010 request for information. 
Future revisions to the proposed strawman time alloca- 
tions are certain. 

Care should be taken when using a FoM as any 
FoM is only as good as the assumptions upon which it 
is based. Additionally, head to head comparisons of 
FoMs are valid only when comparably realistic assump- 
tions are made. 

3.2 Exoplanet FoM 

3.2.1 Exoplanet FoM Description 

The exoplanet FoM provides a quantitative meas- 
ure of the ability of the WFIRST mission to achieve the 
primary exoplanet science goals outlined above. A giv- 
en value of the FoM realized by a given mission design 
is related in a well understood, quantitative way to the 
science deliverables of the mission. The FoM thus pro- 
vides a way to quantitatively assess the impact of 
changes in the mission design to the science return. 


The primary FOM depends on the product of four sepa- 
rate metrics that are tied directly to the four primary 
measurement requirements, and is defined as: 

FoMexp = [N@NffNHzN20%y/^, 
where the terms are: 

• A/e: The number of detected planets with M = 
Me and period P = 2 years, assuming every main 
sequence star has one such planet. This choice is 
designed to be a diagnostic of the overall planet 
sensitivity and yield for the experiment. If the mis- 
sion can detect these planets, it is guaranteed to 
detect more distant planets at the Einstein ring ra- 
dius and beyond. Thus A/e quantifies the ability to 
address ExP survey requirement #2a (see Appendix 
A). This is also a region of parameter space difficult 
to access from the ground. Planets at fixed period 
are considered rather than at fixed semi-major axis, 
a, because P/Re is a weaker function of primary 
mass than bIRe. 

• A/ 200 / 0 : The number of planets detected with M = 
M® and period P = 2 yr for which the primary mass 
can be determined to 20%. Addresses survey re- 
quirement #2b. 

• A/ff: The number of free-floating IM® planets 
detected, assuming one free floating planet per star. 
Addresses exoplanet survey requirement #4. 

• A/hz: The number of habitable planets detected 
assuming every F, G and K star has one, where ha- 
bitable means O.l-IOM®, and [0.7-2 AU](L/LJi ^2 
Addresses exoplanet survey requirement #3. 

These quantities are then multiplied and taken to 
the 3/8 power, so that the FoM is proportional to the 
three halves power of the observing time, all else being 
equal. This was chosen to match the scaling of the 
Dark Energy FoM. 

WFIRST probes regions of parameter space (the 
habitable zone and beyond) that are in large part inac- 
cessible to other methods, and our FoM is designed to 
reflect these unique capabilities. The current and future 
priors on our FoM are likely to be quite weak. We con- 
sider two sets of priors: Stage 1, corresponding to the 
number of planets currently known in each of the four 
categories above, and Stage 2, corresponding to our 
projections for the number of planets known in each 


Section 3: Figures of Merit 


17 


WFIRST 


category at the time of launch, for definiteness taken to 
be 2021, as shown in Table 2. 

With the numbers shown in Table 2, we find that 
FOMexp = 410 without any priors and FOMexp = 539 
with the assumed Stage 2 priors. Without WFIRST, we 
expect FOMexp = 6 (with a significant chance of FOMexp 
= 0 ). 



— 

Nzm 

A/hz 

A/ff 

Stage 1 
(2011) 

0 

0 

~3 

(refl) 

0 


~5 

(ref 2) 

~2 

(ref 2) 

25 

(ref 3) 

-0.5 

WFIRST 

127 

90 

27 

30 


Table 2: Stage 1 and Stage 2 priors and WFIRST results 
for the exoplanet FoM [1. Borucki et al. 2010; 2. Bennett 
et al. 2010: MPF Astro2010 RFI, Figure 4; 3. 
http://kepler.nasa.gov/Science/about/ScienceGoals/expe 
ctedResults/, and Exoplanet task force final report (Lu- 
nine et al. 2008)] 

3.2.2 FoM Evaluation of IDRM Microlensing 
Science Return 

The FoM has been calculated with an updated ver- 
sion of the space-based microlensing simulations de- 
veloped by Bennett and Rhie (2002). Although WFIRST 
takes advantage of the wide-field, high resolution im- 
ages available from space, the stellar density in the 
central Galactic bulge fields observed for the WFIRST 
exoplanet program is high enough that the photon noise 
from the blended images of nearby stars can often con- 
tribute significantly to the photometry noise budget for 
many of the WFIRST target stars. Therefore, it is ne- 
cessary to use simulated images of these crowded 
bulge fields in order to generate simulated light curves 
with the appropriate noise properties. The simulated 
light curves are then searched for planetary signals at 
the appropriate S/N threshold to generate the values for 
A/e, Nn, A/hz, as described above. For A/20%, we also de- 
termine the planet and host star masses using the me- 
thod described by Bennett et al. (2007). Table 2 shows 
the resulting values for the FoMs for WFIRST. When 
these values for the FoMs are achieved, as they are for 
the IDRM, WFIRST will be sensitive to the broad exop- 
lanet discovery space shown in Figure 5. 

The projected numbers of planet discoveries listed 
in Table 2 are also based on these simulations, but ad- 
ditional assumptions regarding the prevalence of exop- 
lanets are also needed. Although there are a number of 
papers that measure the statistical prevalence of pla- 
nets based on the radial velocity and transit methods 


(Gumming et al. 2008; Howard et al. 2010, 2011), it is 
the ground-based microlensing results that are the best 
match to the host stars and range of star-planet separa- 
tions that WFIRST will probe. The combined analyses 
of Sumi et al. (2010) and Gould et al. (2010) give 0.4 
planets per decade of mass and separation centered at 
a mass of ~80 Earth-masses and a separation of ~3 AU 
with a mass function slope that scales as dA//dlog(m) ~ 
m-°\ where m is the planet mass. But, extrapolation to 
lower masses implies a very large number of low-mass 
planets. So, we assume that the mass function flattens 
out to dA//dlog(m) ~ constant for m < 5 Earth-masses, 
which is close to the mass of the lowest ground-based 
detections. For free-floating mass function, we use the 
power-law mass function from Sumi et al. (2011), which 
scales as c/A//dlog(m) ~ Integrating over these 
mass functions yields the bound planet results shown in 
Box 3. 

Most of the updates to the Bennett and Rhie (2002) 
space-based microlensing survey simulations were 
needed because the Bennett and Rhie simulations as- 
sumed CCD detectors instead of the near-IR detectors 
required for WFIRST. This allowed observations slightly 
closer to the Galactic center, with a higher microlensing 
rate but also higher dust extinction, to be used. Another 
change from Bennett and Rhie (2002) was the model 
for the input stellar microlensing rate. Bennett and Rhie 
(2002) used the value measured by observations of 
main sequence stars (Alcock et al. 2000), as these are 
the target stars used by WFIRST. But, observations of 
red clump giant stars consistently found a microlensing 
rate about 10% smaller, for reasons that weren’t un- 
derstood (Popowski et al. 2005; Sumi et al. 2006; Ha- 
madache et al. 2006). As a result, the current simula- 
tions assume a slightly lower microlensing rate than 
Bennett & Rhie (2002). However, recent work (Kerins et 
al. 2009) seems to explain why the rate toward main 
sequence stars should be higher, so the assumed mi- 
crolensing rate is a conservative one. 

3.3 NIR Survey FoM 

3.3.1 NIR Survey FoM Description 

The broad range of science potential for the NIR 
survey aspect of WFIRST presents some challenges in 
terms of defining an FoM. While the dark energy and 
exoplanet science programs have relatively specific and 
well defined questions they are attempting to answer, 
the NIR survey data will be beneficial for science rang- 
ing from studying asteroids in our Solar System to 
measuring the diffuse NIR background due to the first 


Section 3: Figures of Merit 


18 











WFIRST 


galaxies to form in the Universe. Examining galaxies 
and stars in a general NIR survey is also different in 
method from the very specific questions that an exopla- 
net or cosmology program is designed to do. There- 
fore, the goal of the NIR survey FoM is not just to op- 
timize mission design decisions for the handful of spe- 
cific questions detailed below, but also to ensure a ro- 
bust and versatile mission that will enable broad 
science. 

We could define an FoM related to the capabilities 
of the mission, e.g., scaling with the field-of-view, wave- 
length range, aperture to some power, effective spatial 
resolution, number of filters. However, by instead using 
a science-driven FoM, we focus this calculation, and 
ensure that the FoM is related to unique goals of the 
mission with large scientific impact. Similar to the dis- 
cussion in Section 2.3, we focus on two broad catego- 
ries of WFIRST NIR survey in order to span the range 
of potential NIR survey FoM’s. We first define FoM’s 
related to ancillary science from the HLS survey. We 
then discuss defining an FoM to quantitatively assess 
the ability of WFIRST to map the Milky Way Galaxy. 
This approach, followed for the interim report, ignores 
the significant ancillary science potential from other 
core WFIRST observations such as the deep, multi- 
epoch observations obtained for the supernova and mi- 
cro-lensing surveys. For now, we also do not attempt 
to derive an FoM related to guest investigator science. 
The expectation is that design decisions undertaken 
based on the NIR survey FOM’s defined below will also 
benefit such science. 

The HLS will map many thousands of square de- 
grees of high Galactic latitude sky. Such data will ena- 
ble a broad range of investigations that are expected to 
impact a good fraction of the astronomical community. 
As one example, discussed in detail in Section 2.3, the 
sensitive, infrared, wide-field observations are ideal and 
unique for identifying a large census of quasars at the 
highest redshifts. We define two HLS FoM’s related to 
quasar science: 

• Nqsoi- The large number of quasars detected 
at z>7. Such sources allow us to probe the 
environments and clustering of the first black 
holes to form in the universe, as well as the 
evolution of their luminosity functions. 

• Nqso 2 . The number of quasars brighter than 1 
|iJy (corresponding to AB=23.9) at z>10. 
These very rare systems provide the best 
probes of the early universe. 


The HLS data will also be very beneficial for study- 
ing galaxy formation and evolution, particularly at the 
crucial redshift range l<z<2 when much of the stellar 
mass in the Universe forms into stars. Studying galax- 
ies in this redshift range requires sensitive NIR data, 
data that is difficult to obtain over large fields using 
ground-based facilities. We define two HLS FoM’s re- 
lated to this science: 

• Ngxyh The number of galaxies at redshift z>l 
detected down to the 5-sigma point source 
depth of the survey. 

• Ngxy 2 . The fraction of spatially resolved galax- 
ies. 

The HLS is also expected to contribute significantly 
to other science such as cool Galactic sources — e.g., 
both brown dwarfs and white dwarfs — as well as ga- 
laxy clusters and groups out to z>2. Identifying the rare 
Galactic populations will require robust three-band pho- 
tometry, similar to the requirements for the high-redshift 
quasars, while a galaxy cluster FoM would presumably 
scale directly with Ngxyi. Therefore, while we recognize 
and highlight the importance of such science, we do not 
define FoM’s related to such science. 

The Decadal Survey also highlighted that WFIRST 
should spend several months obtaining a sensitive, 
near-infrared Galactic plane survey. One could imagine 
a whole range of FoM's that might come from such a 
survey, such as the accuracy with which WFIRST could 
detect and study specific source populations such as 
brown dwarfs, young stellar objects (YSOs), or red 
giant clump stars across the Galaxy, or the ability of 
WFIRST to measure structural parameters of the Ga- 
laxy such as the pitch angle of spiral arms, the shape 
and extent of the Galactic warp, or the shape, length 
and orientation of the Galactic bar. Since confusion 
will be the limiting factor for WFIRST Galactic surveys 
towards the bulge, evaluation of these FOM's is a non- 
trivial task requiring accurate simulated star catalogs as 
a function of WFIRST pointing, taking into account the 
WFIRST PSF and filter complement. Such work is on- 
going, but was beyond the scope of what could reliably 
be achieved for this interim report. We note, however, 
that the IDRM wavelength coverage ends at 2.0 pim, 
which is likely inadequate for disentangling extinction 
from temperature when studying Galactic populations 
(e.g., Majewski, Zasowski & Nidever 2011). The longer 
wavelength infrared data are also important for studying 


Section 3: Figures of Merit 


19 


WFIRST 


brown dwarfs and YSOs. This issue of extending the 
long wavelength cutoff of WFIRST is discussed in more 
detail in Appendix E. 

3.3.2 FoM Evaluation of IDRM NIR Survey Science 
Return 

We evaluate the HLS NIR survey FoM’s assuming 
one year of a weak-lensing DE survey (e.g., “deep” sur- 
vey) and one year of a BAO DE survey (e.g., “shallow” 
survey). The deep survey covers 2700 deg^ per year to 
a relatively uniform limiting depth of 25.9 mag (AB; 5a 
point source) in all three NIR filters (FI, F2 and F3) and 
will be very useful for a broad range of NIR survey 
science. The current shallow survey strategy has been 
optimized to provide relatively uniform spectroscopic 
coverage. This will be useful for NIR spectroscopic 
survey science (e.g., studying very cold Galactic brown 
dwarfs, to name but one example), though we note that 
the NIR survey science FoMs listed above focus on the 
imaging capabilities of WFIRST and this spectroscopic 
survey science is therefore not captured. The uniform 
shallow spectroscopic coverage leads to very uneven 
imaging coverage that is also only obtained in two of 
the three NIR filters (FI and F3). This diminution of 
NIR color information will have some scientific draw- 
backs in terms of studying source populations. Of 
greatest concern, only a small fraction (<10%) of the 
shallow survey has three or more observations in both 
filters, leading to significant systematic issues with lost 
pixels due to cosmic rays and array defects, particularly 
for studies emphasizing extremely rare source popula- 
tions with unusual colors. We evaluate the HLS FoM’s 
assuming the current IDRM shallow survey strategy 
which covers 11,000 deg^ per year, of which 5456 deg^ 
(49.6%) has only one observation in both filters, 3751 
deg2 (34.1%) has two observations in both filters, and 
979 deg2 (8.7%) has at least three observations in both 
filters. In order to assure robust photometric catalogs, 
we consider three exposures as a strict requirement for 
NIR survey science, though, obviously, significant stu- 
dies would be possible with the less robust, shallower 
imaging data. We therefore evaluate the shallow sur- 
vey FoM’s assuming 979 deg^ is imaged to a depth of 
Fl=25.7 and F3=25.5 (AB; 5a point source). 

We first evaluate the expected number of high- 
redshift quasars that will be detected by the WFIRST 
HLS. We assume the quasar luminosity function (QLF) 
of Willott et al. (2010), which is based on the Canada - 
France - Hawaii Telescope Legacy Survey (CFHTLS). 
The CFHTLS is deeper than the Sloan Digital Sky Sur- 
vey (SDSS), and therefore is preferred to the Fan et al. 


(2001, 2004) high-redshift QLF for this calculation. In a 
single year, the deep survey will detect 904 quasars at 
z>7, of which 4 will be at z>10 and brighter than 1 piJy 
in F3. In a single year, the shallow survey will detect 
261 quasars at z>7, of which 1 will be at z>10 and 
brighter than 1 |aJy in F3. This leads to combined qua- 
sar NIR survey FoM’s of Nqsoi = 1165 and Nqso 2 = 5. 

We evaluate the FoM for the galaxy evolution 
science in the HLS by using data from existing deep 
near infrared surveys from the Hubble Space Tele- 
scope. Our calculations for the number of galaxies are 
done through the use of counts at 1.6 microns, which is 
the middle of the WFIRST filter range. The first FoM 
we consider is the number of galaxies at z > 1 which 
can be detected in the deep survey, which covers 2700 
square degrees, and reaches a depth of 25.9 AB. Here 
we will detect ~10^ galaxies within this magnitude limit 
with roughly half at z > 1. Furthermore 33% of these 
systems will be a z > 2 with most of these at z < 4, al- 
though WFIRST will also find a few very high redshift 
galaxies up to z ~6. For the wider area 11,000 square 
degree BAO survey, which is up to a magnitude less 
deep than the weak leasing survey, we find that the to- 
tal number of galaxies detected will rise to 4x10^, an 
increase solely due to the larger area surveyed. Within 
this number, the fraction at high redshifts, z > 1, is 
slightly lower than the deeper survey, but still just over 
50%. The number of galaxies at z > 2 declines to just 
less than 30%. The faint galaxies between magnitude 
25-26 AB are roughly evenly distributed between red- 
shifts and the wider area survey will not detect the fain- 
ter systems at high redshift. The FoM for the fraction of 
spatially resolved galaxies is calculated using Hubble 
imaging data from previous deep NIR surveys as a ba- 
sis. At -0.2 arcsec resolution, the FoM is 0.85, for a 
slightly less resolved configuration of 0.25 arcsec, the 
FoM drops to 0.77. Note that although the majority of 
the galaxies will be resolved, the ones we miss will be 
typically the faintest and highest redshift systems. 

3.4 Dark Energy FoM 

3.4.1 Scientific Context 

Einstein’s theory of General Relativity states that, 
in general, the effect of gravity depends on both density 
(p) and pressure (P), proportional to pc^-rOP, some- 
thing that is normally positive for matter. If the observed 
accelerated expansion of the universe is interpreted 
using General Relativity it implies this sum of density 
and pressure is negative on cosmic scales. This is 
dramatically at odds with our understanding of the na- 


Section 3: Figures of Merit 


20 


WFIRST 


ture of matter and energy. The missing constituent 
needed to resolve this discord is known as “Dark Ener- 
gy”- 

Einstein described the interaction of gravity (G) 
with matter and energy (T) by means of a deceptively 
simple looking equation = 8nT^y. There are two 
broad classes of explanations for the acceleration of 
cosmic expansion: (1) the first includes a negative 
pressure component in the energy-momentum tensor 
on the right hand side of Einstein’s equation; or (2) the 
second involves a modification of the metric used on 
the left hand side of Einstein’s equation or otherwise 
modifying the form of the left hand side of Einstein’s 
equation to give a new fundamental law of gravity. Dis- 
covering either of these would have profound implica- 
tions for our conception of the universe. In the first 
case, the new component may have a constant energy 
density, s=pc2, in which case it is equivalent to Eins- 
tein's “cosmological constant”. Or, the new component 
may have a time-varying (dynamical) energy density, in 
which case it is called “quintessence”. 

One class of dark energy models posits that there 
is a negative pressure component to the energy density 
of the universe. In general, the pressure is related to 
the energy density by the linear equation of state rela- 
tionship P=i/i/s, where w is a number called the equa- 
tion of state parameter. For radiation, i/i/=l/3.; for nor- 
mal matter or cold dark matter i/i/=0; and for a cosmo- 
logical constant i/i/=-l (i.e., with negative pressure). 
Any component with i/i/<-l/3 leads to a universe with 
an accelerated expansion. 

We do not measure the pressure and energy den- 
sity of matter directly, but rather infer them indirectly 
from their effects on the speed and acceleration of the 
universe’s expansion, and how these affect the dis- 
tances to and between cosmic objects such as super- 
novae and galaxies. As such, seeing a deviation from 
i/i/=-l does not imply a resolution to whether dark 
energy is a new, strange form of matter, or a modifica- 
tion to General Relativity. 

Current measurements are completely consistent 
with a cosmological constant, but a key target of dark 
energy measurements is to test this model by determin- 
ing the value of w more accurately and by seeking evi- 
dence for the potential time-dependence of w. Either a 
deviation from i/i/=-l and/or and deviation from con- 
stancy would invalidate the cosmological constant 
model of dark energy. 

Every technique for studying dark energy is subject 
to systematic errors - shortcomings of either an instru- 


mental or astronomical nature that limit the accuracy 
that can be achieved. When systematic errors are 
present, there is a point beyond which merely acquiring 
more data of the same kind does not improve the accu- 
racy of the result. It is only a slight exaggeration to say 
that the most important task facing the WFIRST project 
is to limit systematic errors. We therefore describe 
these at length in the sections that follow. 

3.4.2 Weak Lensing Considerations 

Weak lensing fundamentally measures the distribu- 
tion of matter (both baryonic and nonbaryonic) in the 
universe. Different cosmological models produce dif- 
ferent mass distributions, so the expected data can be 
used to test models. The principal technical challenge 
for WL is the measurement of galaxy shear with small 
systematic errors (<0.0003) in the presence of the in- 
strument point spread function (PSF). The latter must 
be known very accurately to remove its effects, yet it 
varies as a function of field position, time, and wave- 
length. The data processing must correct for the in- 
strument PSF and reject bad data while not introducing 
any new systematic errors of its own. Finally, WL also 
requires photometric redshifts across the entire range 
of source galaxy redshifts. 

The dependence of the PSF on field position arises 
from aberrations, jitter, detector effects, and (on the 
ground) atmospheric turbulence. All of these effects can 
and often do vary from one exposure to the next, and 
many parameters are required to describe them. There 
are three major advantages to putting the telescope in 
space: (i) the atmospheric turbulence contribution is 
entirely eliminated; (ii) superior temporal stability of the 
PSF can be achieved; and (iii) by making the PSF 
smaller the multiplying factor from PSF ellipticity error to 
galaxy ellipticity error is reduced. As stated previously, 
shape measurement errors arising from PSF deconvo- 
lution rise as the square of the PSF size. With the 
guaranteed absence of adverse atmospheric effects, 
the time dependence of the PSF is dominated by mo- 
tions of the mirrors (primarily, but not only, the second- 
ary mirror). This source of variation will be controlled, 
but not completely eliminated on WFIRST. The resi- 
dual misalignments can be described by a small num- 
ber of displacement and tilt parameters that correspond 
with specific patterns in the wavefront error with known 
field position dependence. This is in contrast to atmos- 
pheric turbulence, where the number of parameters re- 
quired to achieve part in 10,000 accuracy is not known. 
(The full field/time dependence of the wavefront error or 
PSF within an exposure cannot be measured; rather. 


Section 3: Figures of Merit 


21 


WFIRST 


the stellar images provide statistical averages over the 
much more complex instantaneous PSFs). While the 
WFIRST imaging optics and focal plane have 36 rigid- 
body relative-motion degrees of freedom, most linear 
combinations of these are benign and others are re- 
quired to be controlled so that their variations on an ex- 
posure-by-exposure basis are small. A minimum of 7 
telescope degrees of freedom must be taken into ac- 
count (the nondegenerate secondary mirror displace- 
ments and tilts and the tilts of at least one other ele- 
ment) in each exposure, in addition to the jitter pattern 
(measured on all three axes by the fine guidance sys- 
tem, which occupies the same focal plane and looks 
through the same optical path as the science array). 

Wavelength dependence of the PSF can in prin- 
ciple arise from diffraction, aberrations, atmospheric 
turbulence, the complex amplitude transmitted by the 
filter, chromatic aberration induced by refractive ele- 
ments, and detector effects. Removal of these effects 
requires both knowledge of how the PSF depends on 
wavelength and multiband imaging of the source galax- 
ies so that the intrinsic spatial color profile is known. A 
space telescope again provides a unique opportunity to 
address these effects. The size and ellipticity of an ab- 
errated diffraction spot depend on wavelength, but for a 
reflective telescope in space this effect is uniquely de- 
termined by the same low-order aberrations that deter- 
mine the PSF morphology. The WFIRST imaging cam- 
era has no refractive elements except for a flat zero- 
deviation filter substrate and there is no atmospheric 
dispersion. The filter transmission curve will vary across 
the pupil due to e.g. angle of incidence effects, which 
implies a spectral-energy-distribution dependent PSF 
even in the geometric optics approximation. This will be 
a challenge for all Stage IV weak lensing experiments 
but will be most difficult for ground projects with fast 
beams (versus the f/16 WFIRST beam) and where the 
filter effects beat against time-dependent contributions 
to the optical path that may vary across the aperture 
(e.g. turbulence). Detectors used at wavelengths where 
light has a long and strongly wavelength-dependent 
mean free path can exhibit defocus or (in non- 
telecentric systems) lateral shift as the beam passes 
through a thick detector; this is a source of color de- 
pendent PSF for silicon CCDs used in the far red (es- 
pecially z-ry bands) that is eliminated on WFIRST. Fi- 
nally, WFIRST provides fully sampled imaging in two 
shape measurement filters, enabling the color and color 
variation to be measured for each galaxy. This pro- 
vides an important built-in cross check. 


Weak lensing represents a substantial data 
processing and algorithmic challenge. One such chal- 
lenge (one of the few that is more difficult in space) is 
the need to combine multiple undersampled images to 
achieve fully sampled output. This was previously iden- 
tified (both on the JDEM SCO and during the New 
Worlds, New Horizons 2010 Decadal Survey process) 
as a risk for space weak lensing experiments. The 
WFIRST project has supported development of algo- 
rithms that combine undersampled images without in- 
troducing artifacts associated with the pixel grid (Rowe 
et al., 2011). Another challenge is the automated stack- 
ing of several images (ranging from 5-6 for WFIRST 
through hundreds with some of the proposed ground 
projects) while rejecting defects, transients, or poor 
quality data, and avoiding the use of median filters or 
other highly nonlinear algorithms that produce artifacts 
in the PSF of the final data. The least risky approach 
here is to begin with a homogeneous data set that 
meets systematic requirements on an exposure-by- 
exposure basis. 

Providing accurate photometric redshifts requires 
access to the near infrared for galaxies whose Balmer 
or 4000A breaks have redshifted out of the optical (the 
ugriz and possibly the y ) bands, but which do not have 
an accurately identified Lyman break. Deep broadband 
wide-field near infrared imaging is only possible from 
space due to the extremely bright atmospheric OH 
bands. This limits ground-based photometric redshifts 
in a wide-field survey to z ~ 1.3 (except for the ~1 ga- 
laxy per arcmin^ at z > 2 that is resolved from the 
ground). Since weak lensing shear is already an 
integral over the line of sight, this severely restricts the 
redshift baseline over which the evolution of the lensing 
signal can be measured. WFIRST imaging in three near 
infrared filters will complement ground-based optical 
photometry, providing both the break position and at 
least one rest-frame optical filter to z ~ 3. 

3.4.3 Baryon Acoustic Oscillation Considerations 

Primordial density fluctuations seeded all of the 
structure in the universe. In the early universe a tightly 
coupled fluid of photons, electrons, and baryons ex- 
panded from regions of initial over-density (and over- 
pressure). Eventually the photons decoupled from the 
fluid and are now observed as the cosmic microwave 
background (CMB). Small over-abundances of baryons 
were left in spherical shells around the locations of the 
initially over-densities. These appear as ripples on the 
power spectrum of large samples of galaxies, P(k). 
These correspond to a ~1% excess in galaxy correla- 


Section 3: Figures of Merit 


22 


WFIRST 


tions. WMAP measured the size of the horizon at the 
drag epoch shortly following decoupling (the radius of 
the shells) to be 153 co-moving Mpc from the peaks 
and troughs of the power spectrum that are the signa- 
ture of baryon acoustic oscillations. The WMAP data, 
which will be augmented by the currently operating 
Planck satellite, calibrates a “standard ruler" that is use- 
ful for tracing the expansion history of the universe. 

The use of the BAO to investigate dark energy re- 
quires a large galaxy redshift survey over large regions 
of the sky. Observations of the spherical sound wave 
are made radially and transverse to the line-of-sight. 
The transverse measurement yields the angular diame- 
ter distance, which could be measured to an aggregate 
precision of 0.1%. The radial measurement yields the 
Hubble parameter, H{z), a direct measurement of the 
expansion history of the Universe. Most of the power of 
the BAO measurement of dark energy comes from the 
radial measurement of the Hubble parameter. Spec- 
troscopic redshifts are required to extract the radial 
BAO signature, since photometric redshifts unaccepta- 
bly smear the peak in the radial direction (e.g. at z=l, 
even an excellent photo-z quality of az/(l+z)=0.02 pro- 
duces a 100 Mpc radial smoothing of the density map; 
the smoothing of the correlation function is a factor of 
V2 greater. 

Obtaining the three-dimensional positions of galax- 
ies (sky positions and redshifts) is not particularly chal- 
lenging. Achieving maximum sky coverage with uni- 
form instrumental properties is an advantage of a space 
mission. The major limiting factor is sufficient observing 
time to measure the full available sky to a sufficient 
depth to avoid excessive shot noise. 

One potential systematic error arises only when the 
measured structures become nonlinear. Due to the in- 
creasingly non-linear growth of structure with time, this 
is a greater error for the ground-based, lower redshift 
experiments than for WFIRST observation at higher 
redshifts. Even at low redshifts, the acoustic scale of 
153 Mpc is so much larger than the scale of non-linear 
structure formation that the scale remains a robust 
standard ruler. Further, since <1% of the volume is 
non-linear, perturbative corrections for a small degree 
of non-linearity are possible. 

The baryon oscillations are smeared out at low 
redshift (“smearing” here means that the peak in the 
correlation function is widened; the Fourier space de- 
scription is that the amplitude of the wiggles is sup- 
pressed at high k). This is thought to be mostly from 
the effects of large-scale flows: two points that were 
initially separated by 153 Mpc co-moving may at the 


present epoch have a somewhat larger or smaller sepa- 
ration. Simple density-field reconstruction techniques 
can significantly counteract this effect (see e.g. Padma- 
nabhan & White 2009; Noh et al. 2009 for recent stu- 
dies, including studies of clustered haloes as opposed 
to simply the dark matter power spectrum). For the 
large-scale flows to cause the acoustic scale to be 
shifted would require a consistent mean infall on 153 
Mpc scales. This non-linear shift is only 0.2% at z=l 
and smaller at higher redshift. Since these shifts can be 
computed, they can also be corrected. 

The acoustic scale could shift from galaxy bias, the 
offset between the observed baryonic matter distribu- 
tion and the more significant underlying dark matter dis- 
tribution. A linear bias does not change the shape of the 
correlation function, so it cannot shift the scale. Galaxy 
bias can affect how the convergent and divergent large- 
scale flows attain positive or negative weights in the 
two-point function (qualitatively, the source of shift is 
that large-scale flows tend to bring highly biased ob- 
jects that trace large overdensities toward each other). 
The relation between the galaxy field and the large- 
scale velocity field is the quantity that matters here. 
Calculations with simple halo occupation models show 
suggest that this is a small effect (<0.2% at z=l). 
WFIRST’s large galaxy redshift survey should be able 
to constrain the bias model to correct this 0.2% effect at 
z = 1 to < 0.1%. Other, more exotic galaxy biasing ef- 
fects that might affect the BAO position have been pro- 
posed but are not expected to introduce any uncorrect- 
able systematic errors (e.g. Tseliakhovich & Hirata 
2010; Yoo et al. 2011). 

Because the BAO observations give a differential 
signature as a function of scale, most errors cancel out. 
According to the Dark Energy Task Force, “This is the 
method ieast affected by systematic uncertainties..." 
and, “It is less affected by astrophysical uncertainties 
than other techniques." The BAO is the only approach 
that the NRC's Beyond Einstein Program Assessment 
Committee (BEPAC) called “very robust." Well- 
understood cosmological perturbation theory and nu- 
merical simulations provide a solid framework with 
which to control small biases and nonlinearities, espe- 
cially for z > 1. In the end, the BAO measurement may 
well be statistics-limited to the cosmic variance limit. 

3.4.4 Redshift Space Distortion Considerations 

Weak gravitational leasing tests modified gravity 
models by comparing the amplitude of clustering meas- 
ured at two different redshifts to deduce the rate of 
growth of structure. The growth rate can be measured 


Section 3: Figures of Merit 


23 


WFIRST 


directly at a single redshift by recognizing that the rea- 
son that structure grows is because matter flows into 
potential minima (clusters). These flows are directly 
observable as redshift-space distortions in galaxy red- 
shift surveys. While clustering is statistically isotropic, 
peculiar velocities affect the apparent positions of ga- 
laxies only in the line of sight direction. The degree of 
the observed anisotropy on large scales probes the 
growth of structure. Redshift space distortion can 
measure the growth of structure to a level comparable 
to that from weak leasing and cluster counting, but are 
complementary in that they measure velocities whereas 
weak leasing measures the gravitational potential and 
cluster counting identifies the many-a peaks of the 
density field. Moreover the WFIRST redshift space dis- 
tortion measurements will probe out to z = 2, well 
beyond the peak of the weak leasing sensitivity. 

Large galaxy redshift surveys offer the opportunity 
to measure growth of structure to high precision. Unlike 
the more robust BAO, this requires careful modeling of 
the non-linear velocity field and the effects of galaxy 
bias. Cosmological simulations are required to help 
with this modeling. The degree of accurate modeling 
determines how close to the cluster the matter flow can 
be used. The minimum scale implies a maximum wa- 
venumber, kmax. The use of redshift space distortion is 
a relatively young field, but it is rapidly advancing. It is 
difficult to predict with precision what kmax will be 
achievable when WFIRST flies, but the proposed hard- 
ware design is such that the relevant data are captured 
during the course of the BAO survey. 

3.4.5 Type la Supernovae Considerations 

The utilization of Type la supernovae as calibrated 
standard candles led to the original discovery of the ac- 
celeration of the expansion of the Universe. In the past 
decade this technique was used in second generation 
experiments to further refine our understanding of this 
phenomenon. These second generation experiments 
have proven to be very productive, and have performed 
as predicted before the measurements were carried 
out. To this day supernovae represent the most mature 
and predictable method in the study of the acceleration 
of the universe and the nature of dark energy. The 
Dark Energy Task Force similarly concluded that: “The 
SN technique is at present the most powerful and best 
proven technique for studying dark energy.” 

The relative peak brightnesses of Type la superno- 
vae are used to measure relative luminosity distances 
across redshift. This method has the advantage of pro- 
viding a rather direct measurement of the distance. 


This directness also makes it easier to recognize - and 
develop controls for - the important sources of syste- 
matic uncertainties. These have been extensively stu- 
died by the second generation experiments, and sys- 
tematic error budgets can be found in all recent major 
results papers (see, e.g., Guy et al. 2010, Suzuki et al. 
2011). Almost all of the dominant current systematic 
uncertainties have reached or are reaching the limits of 
what can be observed from the ground. To take the 
supernova technique to its next level of precision, and 
take advantage of this powerful cosmological tool, will 
require space. 

As we explore a wide range of redshifts, it is impor- 
tant to ensure that the supernovae we are comparing 
from low to high redshift do not represent different dis- 
tributions among the subpopulations of SNe la, and that 
they are not being dimmed/reddened by different dust. 
These two “evolution” systematics are the most impor- 
tant astrophysics considerations in the systematics 
budget (as opposed to instrumentation/calibration con- 
siderations). The concern about supernova population 
evolution is addressed by measuring identifying charac- 
teristics of each supernova (such as the lightcurve 
timescale/shape and color or specific spectral features) 
and separately calibrating the subpopulation that is so 
identified. It is also possible to find specific SN la mea- 
surements (such as the H band lightcurves) that are 
empirically more similar across subpopulations. The 
systematics due to evolution of dust dimming/reddening 
is also addressed by measuring colors of the superno- 
vae, and by observing in redder bands when possible. 

Space observations are required for these mea- 
surements for several reasons. The range of restframe 
wavelengths used for identifying subpopulations and 
characterizing dust needs to be broad enough to obtain 
a substantial lever arm. By using the 1- to 2-micron 
near-infrared capabilities of a space mission it is possi- 
ble to almost double the rest wavelength lever arm. 
The low sky background and small PSF available in 
space also makes possible observations of SN la spec- 
tral features, providing identification and redshift for 
every supernova used. In fact, these advantages of 
space could even allow spectra with excellent signal-to- 
noise that can further address these systematic uncer- 
tainties (see Appendix E for a discussion of how this 
might be possible with an IFU spectrograph substituting 
for the slitless prism). 

There are also systematics issues related to the in- 
strumentation and the experimental design. Observing 
the supernovae in different restframe bands at different 
redshifts has often been necessary in ground-based 


Section 3: Figures of Merit 


24 


WFIRST 


programs, and the resulting K-correction interpolations 
and extrapolations have contributed significantly to the 
systematics budgets. With the wider range of observer- 
frame wavelengths observable from space, the same 
restframe wavelengths can be observed at every red- 
shift and K-correction extrapolations can be eliminated; 
With time-sampled SN spectrophotometry from space 
the systematics due to K-correction interpolations can 
be addressed, too. 

Perhaps surprisingly, one of the remaining domi- 
nant systematic issues is due to the calibration of the 
photometry. While in principle this systematic can be 
controlled by careful experimental design on the ground 
or in space, in practice the thermal and gravitational- 
load stability of the space platforms, as well as the 
scheduling predictability (without weather) makes it 
easier to achieve in space. 

The excellent final performance of WFIRST’s Type 
la supernova measurements reflects the space-based 
control of all these systematics. By measuring the light 
curves of typically a hundred supernovae in each red- 
shift bin of 0.1, distance errors of 0.8 to 1.5 % can be 
obtained in each bin. (If the optimistic systematics con- 
trol is obtained there will be a motivation for considering 
an additional year of observations, since the additional 
square root of N improvement could then yield strikingly 
smaller uncertainties.) 

3.4.6 The Figure of Merit 

It is useful to be able to estimate the power of dif- 
ferent experiments, or combinations of experiments, 
towards determining or constraining the physical possi- 
bilities for dark energy. This is the idea behind a “figure 
of merit.” Over the last few years, the cosmological 
community, through the JDEM Science Definition 
Team, the Dark Energy Task Force, and by the JDEM 
Figure of Merit Science Working Group (FoMSWG) de- 
veloped the idea of creating a figure of merit to quantify 
the effectiveness of various dark energy measure- 
ments. The figure of merit calculations assume a given 
set of agreed upon prior information (cosmological val- 
ues accepted from existing experiments), and test the 
power of various experiments to distinguish between 
alternative dark energy models. Ideally, an experiment 
would distinguish between two models, say A and B, 
but that is not the case for dark energy, where a very 
broad range of models, with very different implications 
for both structure growth and the expansion history of 
the Universe, are possible. Rather than consider a 
specific dark energy model or a suite of models, the 


DETF opted for testing the ability of experiments to test 
a single representative model. 

The figure of merit devised by the Dark Energy 
Task Force is a simple 2-parameter model, 
w(a)=Wo-hWa(l-a), where a is the dimensionless scale 
factor of the universe with a=l today, and a increasing- 
ly smaller than unity in the past (it is related to the red- 
shift by a=l/l-rz). In this model, the universe then be- 
gan with w= Wa and the current value is w=Wo, with a 
linear change with scale factor in between. The mid- 
point of the transition is at 1-a = or z=l. An experi- 
ment that places limits on dark energy can then be cha- 
racterized by an error ellipse in the Wq versus Wa plane. 
The figure of merit is then inversely proportional to the 
area enclosed by the 95% confidence contour of this 
ellipse; the better the constraining power of an experi- 
ment, the higher the figure of merit. The DETF figure of 
merit may be the most standard one in use today. We 
therefore adopt it for the present purposes, notwith- 
standing such shortcomings as it might have (see Ap- 
pendix C). 

3.4.7 Comparing Figures of Merit 

While the DETF FoM may be used to compare the 
outcomes of different dark energy programs, one must 
do so taking careful account to use identical “priors” 
and identical assumptions about systematic errors of 
astronomical (as opposed to instrumental) origin. 
Priors are previously obtained results that provide addi- 
tional constraints on the interesting quantities. The 
DETF proposed a set of “stage IN' priors that we adopt 
here. 

As described in the preceding sections, each tech- 
nique for studying dark energy has systematic errors 
that result from the method of measurement and others 
that result from imperfect models for the astronomical 
systems being measured. In what follows we have 
adopted two sets of systematic error estimates, a con- 
servative set and an optimistic set. The conservative 
set represents the collective opinion of the SDT as to 
what is likely to be achievable. 

We can reasonably hope for improved astronomi- 
cal understanding and better control of instrumental er- 
rors between the present writing and the launch of 
WFIRST. We have therefore included a second set of 
FoMs for WFIRST that adopt these more optimistic sys- 
tematic errors. The conservative and optimistic as- 
sumptions regarding systematic errors are described 
below. 


Section 3: Figures of Merit 


25 


WFIRST 


WFIRST (conservative) 

+SN 



WFIRST (optinnistic) 

+SN 


370 



Figure 7: DETF FoM calculations for conservative and optimistic WFIRST assumptions. The stage III baseline is a DETF 
FoM = 116. 


In Figure 7, we show the DETF figures of merit 
achieved by each of the three methods called out in 
NWNH, along with the results of combining techniques. 
They are calculated for a straw man allocation of one 
year to a deep, weak lensing plus BAO survey, one 
year to a wide BAO survey, and six months to a super- 
novae survey. The figure on the left was obtained us- 
ing conservative systematic error estimates; the one on 
the right using the more optimistic estimates. 

In Appendix C, we compare the results of this straw 
man program with those for other proposed missions. 
In so doing we have made every effort to treat syste- 
matic errors consistently. It is clear from the figures 
that such comparisons can only be meaningful if the 
systematic errors are treated uniformly. Even then, 
comparisons with different missions is difficult as it 
doesn’t take into account the relative risk of different 
approaches or the likelihood that design goals will be 
met. 

The expected sky coverage and projected number 
density of galaxies for the 3 different weak lensing sur- 
veys we consider (WFIRST, LSST and Euclid) are giv- 
en in Table 3. 

We assume common survey assumptions for each: 

• A galaxy distribution described by 
n(z)Gcz2exp(-z/zo)i^ with Zo=0.64 for 0<z<2. 
We break the galaxies into Nph=10 redshift 


bins, with galaxies evenly distributed between 
them, 

• A photometric redshift uncertainty of a(z)= 
0.04(l+z). 

• A statistical shear measurement uncertainty, 
a,=0.35/V2. 

• 50 logarithmically spaced bins in ell, 
10<l<3000 



WFIRST 

LSST 

Euclid 

Sky coverage (sq. 
deg.) 

2640/yr 

15,000 

15,000 

Project galaxy 
density (per sq. 
arcmin.) 

30 

20 

30 


Table 3: Summary of survey specifications for WFIRST, 
LSST and Euclid weak lensing surveys. 


We consider two scenarios summarized in Table 4: 

• a conservative scenario, in which we consider 
constraints from lensing shear correlations 
alone, and with a number of systematic un- 
certainties included, and 

• an optimistic scenario in which galaxy-lensing 
cross correlation information is also included, 
and in which we assume better control over 
both instrumental and astrophysical systemat- 
ic uncertainties is achievable. 


Section 3: Figures of Merit 


26 









WFIRST 



Table 4; Summary of the systematic uncertainties included in the weak lensing scenarios. 


Conservative scenario details: 

• Intrinsic alignment (lA) contributions to the ob- 
served shear field are modeled using a nonli- 
near alignment model (Hirata and Seljak 2004, 
Hirata et al. 2007). We marginalize over uncer- 
tainties in the amplitude of the lA auto- 
correlation and cross-correlation with galaxy 
position using an analogous approach to ga- 
laxy bias, marginalizing over 5x5 grids for two 
parameters bi and ri (Joachimi and Bridle 
2010). As in the FoMSWG analysis (Albrecht 
et al. 2009) we include a prior on a(biri)= 
0.003NbiasV(Nph-l) 

• A shear calibration (l)=(l-rfi)(l-r fj) 

Cee'i(l) with a prior on a(fi)=0.00lVNph inde- 
pendently in each redshift bin. 

• Photometric redshift offsets with a prior 
a(AZsys) = 0.002(l-rz). 

Optimistic scenario details: 

• We include uncertainties about galaxy bias by 
introducing a bias amplitude, bg , Pgg(k,z)°'’= = 
bg(k,z)2 Pgg(k,z), and cross correlation coeffi- 
cient between galaxy position and shear mea- 
surements, tg, Pge(k,z)*= = bg(k,z) tg(k,z) 
Pge(k,z). 

• The Fisher analysis includes marginalization 
over a NbiasxNbias grid with Nbias=5 logarithmi- 
cally spaced in z and k of bg and tg. The values 
at each scale and redshift the values come 
from interpolating over the grid. 

• Acknowledging that our galaxy bias marginali- 
zation may not be sufficient to describe the ful- 
ly nonlinear regime, we include a cutoff in mul- 
tipole space for each photometric redshift bin, 
lmax(Zi)=0.132zi hMpc'i (Rassat et al. 2008, 
Joachimi & Bridle 2009). Galaxy position cor- 


relations with I > Imax(Zi) are excluded from the 
Fisher analysis. 

For the SN survey, the conservative FoM calcula- 
tions include the following assumptions: 

• Imaging/Slitless prism spectroscopy 6 month 
survey to z=1.2. 

• Error assumptions: supernova intrinsic spread 
in intrinsic luminosity aint= 0.11-r0.033z, sys- 
tematic error asys= 0.02(l-rz)/1.8 

For the SN survey, the optimistic FoM calculations 
include the following assumptions: 

• Same survey time and depth as the conserva- 
tive assumptions 

• Error assumptions: same as conservative ex- 
cept systematic error reduced to asys = 
0.01(l+z)/1.8 

For the SN survey in a five year Dark Energy pro- 
gram, the FoM calculations include the following as- 
sumptions: 

• Survey time doubled to 12 months and redshift 
range increased to z=1.5 

• Error assumptions: same as optimistic calcula- 
tions 

Supernova on other Dark Energy programs 

• Euclid and BigBOSS are not planning on a su- 
pernova program. 

• LSST will get many supernova but no super- 
nova program has been defined that we are 
aware of for which we could calculate an FoM. 
Ground based supernova programs are limited 
to lower redshifts and shorter wavelengths 
than possible from space. 


Section 3: Figures of Merit 


27 











WFIRST 


For the BAO and RSD survey, the conservative 
and optimistic scenarios used in the FoM calculations 
are defined in Table 5. Additionally, the following as- 
sumptions were used in all of the BAO and RSD FoM 
calculations: 

• BAO calculations are done in bins of dz=0.1. A 
0.36% error is added in quadrature to each of 
the H and D_A errors in each bin, representing 
a systematics floor 

• The non-linear smearing of linear signal power 
is modeled following the method of Seo and 
Eisenstein, 2007. 

• The Lagrangian displacement scale that sets 
the width of the Gaussian smearing kernel is 
reduced by 50% to represent reconstruction of 
the linear signal. 

• Redshift space distortion is included by mea- 
suring P P_m(k) marginalizing over bias in the 
linear theory formula P_{red}(k,|a)=(b-rf 
P_m(k), independently each redshift bin. 

• Gaussian smearing of information, as in Seo & 
Eisenstein, again with a 50% reconstruction 
factor 

3.5 Growth of Structure Figure of Merit 

Dark energy may be the most likely explanation for 
cosmic acceleration, but it is not the only possibility. 
One class of alternative explanations involves modifica- 


tions of Einstein's theory of General Relativity. Modified 
theories of gravity can have significantly different pre- 
dictions for how large scale structures, such as galaxies 
and clusters of galaxies, form and grow, as compared 
with the predictions of dark energy models. These sig- 
natures can be detected by weak leasing measure- 
ments and the motions of large scale structure, also 
known as redshift space distortion, imprinted in galaxy 
redshift surveys. 

A simple extension to the DETF FoM was sug- 
gested to include information about large scale struc- 
ture growth. This assesses an experiments ability to 
measure the growth rate of fluctuations in density, 
5=5p/p, that grow to form galaxies and clusters of ga- 
laxies. The growth rate function, f(z)=dln 8/ dina can 
be well modeled by f(z)=Qm(a)^ with y=0.55 for an ac- 
celeration universe with w»-l and obeying General Re- 
lativity. Measuring a deviation from Y=0.55-rAy would 
help determine whether cosmic expansion is due to 
dark energy or to non-Einsteinian gravity. 

A straightforward figure of merit that takes this into 
account is the inverse of the square of the uncertainty 
in y. As with the DETF FoM, we have computed the 
contributions of baryon acoustic oscillations, superno- 
vae and weak leasing to this figure of merit, under our 
conservative assumptions, and show how they combine 
in Figure 8. 



Sky Coverage (sq. deg.) 


Depth Limit 

(ergs/cm^/sec) @ 1.5 urn 


Redshift Range 


Redshift Uncertainty 


Redshift Space Distortion 


kmax (h/Mpc) 


Reconstruction factor 


WFIRST 


13,700 

(1 yr deep & 1 
yr wide) 
2x10-1® (deep) 
4x10-1® (^jde) 


WFIRST 

Optimistic 

WFIRST 5 yr 
DE Program 

Euclid 

BigBOSS 

Same as 

“23,250^^ 

15,000 

14,000 (Northern 

conservative 

(2.5 yr deep & 
1.5 yr wide) 


survey) 


Same as 
conservative 


Same as 
conservative 


4x10-16 


0.7 -2.0 


Same as 
conservative 


Same as 
conservative 


Same as 
conservative 


0.001(l+z) 


Same as 
conservative 


Same as 
conservative 


Same as 
conservative 


No 


Yes 


Yes 


Yes 


N/A 


0.15 


Same as 
optimistic 


Same as 
optimistic 


N/A 


50% 


Same as 
optimistic 


Same as 
optimistic 


N/A 


<1.7 


Same as 
conservative 


Yes 


Same as 
optimistic 


Same as 
optimistic 


N/A 


0.79/D(z) 


Same as 
optimistic 


Same as 
optimistic 


1.7/D(z) for LRGs, 
0.84/D(z) for ELGs 


Table 5: Summary of the conservative and optimistic surveys for the BAO/RSD FoM calculations 


Section 3: Figures of Merit 


28 


















WFIRST 


+SN 



Figure 8: WFIRST conservative y figure of merit = l/(r(y)2. 
The stage III baseline is a Gamma FoM = 46. 


Among the three methods, weak leasing is unique 
in its ability to constrain the growth of structure inde- 
pendent of other measurements. In concert with ba- 
ryon acoustic oscillation measurements, these con- 
straints are yet stronger. 

Opinions vary regarding how much more likely it is 
that dark energy, as opposed to modified gravity, is the 
correct explanation for cosmic acceleration. While 
NWNH discusses the latter alternative, the emphasis is 
on dark energy. What is clear from the above figure is 
that a mission that does not involve weak lensing might 
miss the cause of cosmic acceleration. 


Section 3: Figures of Merit 


29 


WFIRST 


4 IDRM IMPLEMENTATION 
4.1 Overview 

The WFIRST IDRM payload configuration (see 
Figure 9 for an optical path block diagram and Figure 
10 for a fields of view layout) provides the wide-field 
imaging and slitless spectroscopy capability required to 
perform the Dark Energy, Exoplanet and NIR surveys. 
A 1.3 m unobscured aperture, focal telescope feeds a 
single instrument comprised of three observing chan- 
nels: an Imaging Channel (ImC) covering 0.60 - 2.0 
pim, and two identical, but oppositely dispersed. Spec- 
trometer Channels (SpCs) covering 1.1 - 2.0 pim. The 
instrument uses 2.1 pim long-wavelength cutoff 
HgCdTe detectors already developed as part of a 
JDEM Engineering Development Unit (EDU) Focal 
Plane Assembly (FPA). The two SpCs provide the 
faster survey speeds desirable for a BAO/RSD spec- 
troscopic redshift survey mode and, because they are 
dispersed in opposing directions, they also provide red- 
shift measurements unbiased by spatial offsets be- 
tween the line and continuum emission regions, without 
requiring a later field revisit. The ImC covers the NIR 
and is optimized to provide good sensitivity down to 0.6 
pim in the visible. The ImC provides a high quality point 
spread function, precision photometry, and stable ob- 
servations for Exoplanet, SNe, Weak Leasing and NIR 
surveys, as well as the redshift zero reference for 
BAO/RSD. Quality pointing accuracy, knowledge, and 
stability are all required to resolve galaxy shapes and 
precisely revisit both the Exoplanet and SNe fields. 
Pointing to between 54° and 126° off the Sun enables 
the observation of Exoplanet fields for up to 72 conti- 
nuous days during each of the twice yearly Galactic 
Bulge viewing seasons. Additionally, the observatory 
accommodates viewing within 20° of the ecliptic poles 
to monitor SNe fields in fixed inertial orientations that 
can be maintained for ~90 days. 

The Exoplanet survey requires large light gathering 
power (effective area times field of view) for precise 
photometric observations of the Galactic Bulge to 
detect star/planet microlensing events. Seven fields 
are observed repeatedly to monitor the (very common) 
stellar light curves during microlensing events and the 
(relatively rare) planet lensing signals that may be su- 
perimposed on the stellar light curves. Exoplanet moni- 
toring observations are performed in a wide filter span- 
ning 0.97 - 2.0 |am, interspersed ~twice/day with brief 
observations in a bluer, 0.76 - 0.97 pim, filter for stellar 
type identification. 


To accomplish the wide-field slitless spectroscopic 
redshift survey, the BAO/RSD measurement requires 
NIR spectroscopy to centroid Ha emission lines and 
NIR imaging to locate the position of the galaxy image. 
High dispersion spectroscopy enables centroiding the 
Ha emission lines to a precision consistent with meet- 
ing the redshift accuracy. To address completeness 
and confusion issues, prisms are used as the dispers- 
ing element and at least 3 roll angles, two of which are 
approximately opposed, are observed over -96% of the 
mapped sky. The bandpass range of 1.1 - 2.0 jam pro- 
vides the required redshift range for Ha emitters and 
the 0.45 arcsecond pixels in the SpC provide the area 
needed to meet the sky coverage requirements while 
maintaining centroiding accuracy. 

The SN measurement also requires large light ga- 
thering power to perform the visible and NIR deep im- 
aging and spectroscopy needed to classify and deter- 
mine the redshift of large numbers of Type la SNe. 
Precise sampling (S/N of 15) of the light curve every 
five days meets the photometric accuracy requirement 
and the use of three NIR bands allows measurements 
of SNe in the range of 0.4 < z < 1.2, providing better 
systematics at low z than can be achieved by the 
ground and extending the measurements beyond the z 
> 0.8 ground limit. 

The WL measurement requires an imaging and 
photometric redshift (photo-z) survey of galaxies to mag 
AB -23.7. A pixel scale of 0.18 arcseconds balances 
the need for a large field of view with the sampling 
needed to resolve galaxy shapes. Observations in two 
NIR filters, with >5 random dithers each are made to 
perform the required shape measurements to deter- 
mine the shear due to lensing, while observations in an 
additional NIR filter are combined with color data from 
the shape bands and the ground to provide the required 
photo-z determinations. Either the ImC or SpC spec- 
trometers with overlapping ground observations are 
used to perform the photo-z calibration survey (PZCS) 
needed to meet the WL redshift accuracy requirement. 

The three instrument channels along with the aux- 
iliary FGS and the telescope form the payload. The 
payload and spacecraft together make up the Cbserva- 
tory. The Cbservatory mass is 2500 kg, including mar- 
gin. An Earth-Sun L2 libration point orbit has been se- 
lected to provide the passive cooling, thermal stability, 
minimum stray light, and large sky coverage needed to 
make these precise measurements. An Evolved Ex- 
pendable Launch Vehicle (EELV) or Falcon 9, with 
parking orbit insertion and transfer trajectory insertion 
control to enable eclipse-free launch opportunities vir- 


Section 4: DRM Implementation 


30 


WFIRST 


tually any day, is used to place the observatory on a 
direct trajectory transfer orbit to L2. The mission life is 
5 years with consumables sized to allow an extension 


for a total of 10 years. A key requirement is designing a 
low risk mission using components with flight heritage. 
Each of the elements of the mission is described below. 


Telescope 


Instrument 


<240 K 
Unobscured. 

Focal 

Telescope : 

PMandSM 
followed by Tertiary 
Mirrors (TMs) and 
fold flats, that feed 
three Science 
Channels and an 
auxiliary FGS 


1.3 m 
Aperture 



Spec. 

TM 



Cold 



Mask 



Spec. 

TM 


Imager 

TM 



Spectrometer Channels (SpC) 



4-Lens 
Refractive 
Focal Length 
Reducer 

450 mas/pix; 
f/~6.3 


-0.536° X'0.536‘ 
FOV Extent 



3-Element 


4-Lens 

Focal 


Refractive 

Prism 


Focal Length 



Reducer 


i 

ffl 


-0.536'’ X '0.536" 
FOV Extent 


EACHSdC : 

2x2 FPA; 
2kx2kSCAs; 

-16 Mpix; 

<120K; 

11 -2p bandpass; 
-0.26 deg2 
Active Area 


R©= 160-240 a-s 


Auxiliary 

FGS 




250 mas/pix; 


1x2 FPA; 2kx2k SCAs; -8 Mpix; 
<150-170K; 0.6-2[j bandpass; 
-0.04 deg^ Active Area 


Imager Channel (ImC) 


-0.463" X -0.802" 
FOV Extent 


Cold 

Pupil 

Mask 


FilterWheel 


7-positions 
(e g blank, prism, 5 filters) 


4x7 FPA; 

2kx2k SCAs: 
-112 Mpix; 
<120K: 

0.6-2p bandpass; 
-0.29 deg^ 

Active Area 


1 80 mas/pix: 
f/~15.9 


FGS = Fine Guidance Sensor 

Figure 9: Payload Optical Block Diagram 


“Outrigger FGS” SCAs (4, in pink) shown in 
notional positions on ImC Focal Plane 


SpC-B [-0.9275°, 0“] 


0.536- 



0.536- 


ImC: 7x4 @ 0.1 87p; SpC 2(2x2){g0.457p 
[xfield center, yfield center, degrees] 

ImC: [0°, 0°] 


0.463- 


0.802- 

^ Outrigger fine 
guidance sensors 


SpC-A [0.9275°,0' 


0.536' 



0.536- 


0.1 42- 


0.31- 

Auxiliary Fine Guidance 
System: 2@0.25'Vp [0°, -0.6 


Figure 10; Channel Field Layout 


Section 4: DRM Implementation 


31 





WFIRST 


4.2 Telescope 

The science channels are fed by a Three Mirror 
Anastigmat (TMA) unobscured telescope, which offers 
a wide field along with a flat focal surface and good cor- 
rection of low order aberrations. The design uses a 
focal TMA working at a pupil demagnification of 11.8 
(110 mm pupil diameter with cold mask). A 1.3 meter 
diameter primary mirror feeds 3 separate tertiary mir- 
rors for the ImC and two SpCs. The unobscured form 
was selected as the baseline for the IDRM, a change 
from the JDEM-Omega baseline. Shifting the second- 
ary mirror off-axis eliminates the diffraction pattern 
created by the secondary mirror supports. It also elimi- 
nates the need for a large secondary mirror baffle al- 
lowing the primary mirror diameter to be reduced to 
1.3m, from 1.5m on JDEM-Omega, while still providing 
equivalent or better throughput. These improvements 
provide a lower exposure time to the same limiting flux 
as compared to JDEM-Omega. The unobscured tele- 
scope allows for better alignment of the instrument 
fields improving the sky tiling schemes and improving 
the survey speeds. The total field of view extent for all 
three channels is 0.95 deg^ (0.81 deg^ active area). 

The Optical Telescope Assembly (OTA) reflecting 
surfaces are maintained below 240K to limit the NIR 
thermal emissions to< 10% of the minimum Zodiacal 
background. The instrument volume is maintained be- 
low -180K to control thermal emissions. The three ter- 
tiary mirrors are included in the OTA, so the optical in- 
terface for each channel is at a real pupil. The three 
instrument channels are well separated allowing access 
for integration of each channel in any order. 

The secondary mirror has a 6 degree of freedom 
mechanism to adjust focus and alignment. The tele- 
scope mirrors are made from ULE which allows a highly 
lightweighted, thermally stable mirror while the closed 
back design provides the required stiffness. The OTA 
structure is manufactured from low-moisture compo- 
sites to minimize mass and thermal distortions while 


providing adequate stiffness. The telescope structure is 
insulated to minimize heat transfer from the solar array 
into the telescope and to minimize heat transfer to the 
instrument. 

4.3 Instrument 

The WFIRST instrument is divided into three chan- 
nels, an imager channel and two oppositely-dispersed, 
but otherwise identical spectrometer channels. The key 
instrument parameters are shown in Table 6. The ImC 
is designed to a diffraction limit of Ipim as required for 
WL galaxy imaging and SN S/N requirements. The NIR 
SpCs are designed to a 3|am diffraction limit to achieve 
the required dispersion. 

The ImC consists of a cold pupil mask, filter wheel, 
fold mirror, and the HgCdTe FPA. The ImC FPA uses 
2k X 2k HgCdTe detectors, with 18|am pixels and a 
long-wavelength cutoff of 2.1 pim. The FPA is arranged 
in a 7x4 layout with a pixel scale of 0.18 arcse- 
conds/pixel. A 7-position filter wheel provides 5 filters, 
a blank and an R-75 (2-pixel) dispersing element for 
executing the SNe program. A description of the filter 
wheel complement is shown in Table 7. 

The two NIR SpCs have identical, refractive lens 
systems to change the focal length to provide the larger 
pixel scales required for the BAO/RSD spectroscopic 
survey. Each SpC consists of a 3 element focal prism 
of CaF 2 and S-TIHl prisms, four lenses of ZnSe, CaFz 
and Infrasil and the HgCdTe FPA. The fixed prisms 
have a dispersion of R0=16O-24O (TBR) arcsec and 
are arranged to disperse in opposing directions on the 
sky to reduce source confusion without the need to re- 
visit the field later in the mission. The SpCs use detec- 
tors identical to those in the ImC. The FPAs for each 
spectrometer are arranged in a 2x2 layout with a pixel 
scale of 0.45 arcsecs/pixel. Passive cooling is used to 
maintain the FPA temperatures for both the ImC and 
SpCs. 


Channel 

Wavelength 
Range (pim) 

Sky Coverage 
(active area; deg^) 

Pixel Scale 
(arcsec/pixel) 

Resolving 

Power 

FPA 

Temperature 

(K) 

Imager 

0.6 -2.0 

0.29 

0.18 

75 (2-pixel; slit- 
less prism in 
filter wheell 

<120 

Spectrometer 

1.1 -2.0 

0.26 per SpC 

0.45 

160-240 (R0; 
slitless) 

<120 

Auxiliary FGS 

0.6 -2.0 

0.04 

0.25 

N/A 

<150-170 


Table 6: Key Instrument Parameters 


Section 4: DRM Implementation 


32 













WFIRST 


Position 

Name 

Bandpass 
[HID] 

Techniques 

Filter, F087 

0.76-0.97 

SN, ExoDlanet 

Filter, Fill 

0.97 - 1.24 

SN, WL photo-z’s 

Filter, F141 

1.24-1.57 

SN, WL shapes 

Filter, F178 

1.57 - 2.00 

SN, WL shapes 

Filter, W149 

0.97 - 2.00 

ExoDlanet 

Prism, P130 

0.60 - 2.00 

SN, WL PZCS 

Blank 

N/A 

Calibration 


Table 7: WFIRST Filter Positions 


The IDRM instrument design incorporates minor 
modifications from the JDEM-Omega instrument. Two 
detectors from each of the SpCs have been moved to 
enlarge the ImC to a 7x4 array, from 6x4. To compen- 
sate for the reduced number of SpC detectors, the pixel 
scale in each SpC is increased to 0.45 arcsecs/pixel, 
from 0.37 arcsecs/pixel, to provide an equivalent field 
size for the SpCs. The additional four detectors in the 
ImC increase the imaging field size by -17%, benefit- 
ting the Exoplanet, NIR, SNe, and WL surveys. Each 
SpC design is simplified from a collimator, disperser, 
and camera set to a design with prisms in the converg- 
ing telescope beam, followed by focal length reducing 
lenses. This is a more compact and robust design form. 
Additionally, the bluest filter in the ImC filter wheel is 
replaced with a broad filter (0.97 |am to 2.0 pim) for the 
Exoplanet survey. Finally, JDEM-Omega proposed us- 
ing 2.5pim long-wavelength cutoff detectors but also 
recognized that a bluer detector cutoff could simplify the 
thermal and optical system design of the instrument. 
The scientific requirements do not extend longwards of 
2.0 pim, so detectors with sensitivity to 2.5 pim are not 
required. Reducing the long-wavelength detector cutoff 
simplifies the design as the detector operating tempera- 
tures can be at least 20K warmer for equivalent dark 
current, reducing the size of the cryogenic radiator. In- 
stead of creating a 2.0 pim cutoff instrument using a 2.5 
pim cutoff detector, WFIRST has demonstrated detec- 
tors with an intrinsic cutoff of 2.1 |im and these detec- 
tors are the baseline for the WFIRST IDRM. 

The three instrument channels are kinematically 
mounted to and thermally isolated from the telescope 
structure. The instrument optics are maintained below 
180K via radiation off of each of the instrument hous- 
ings. The detectors on the instrument focal planes are 
cooled to below 120K via dedicated radiators. The 
Sensor Cold Electronics (SCEs) that power and readout 
the SCAs are mounted close to, but thermally isolated 
from them, as they can be held at a warmer tempera- 


ture. The SCEs are cooled to -150K via direct radia- 
tion off of their mounting plate. Panels on the side of 
the solar array are used as sunshields to protect the 
payload structure from solar illumination during the -90 
day inertially fixed SNe observations. 

The use of CMOS-multiplexer (readout integrated 
circuit) based hybrids with non-destructive readouts, 
supports noise reduction and permits electronic shutter- 
ing, eliminating the need for a shutter mechanism. 
Sample Up The Ramp (SUTR) processing is used dur- 
ing all observations with the raw frames that are gener- 
ated every -1.3 sec being combined during the course 
of the integration period to produce one output image 
(Offenberg et al., 2005). All detectors in the three in- 
strument channels are identical, simplifying detector 
production and sparing. The baseline design is 2K x 2K 
HgCdTe detectors with a 2.1 pim long-wavelength cu- 
toff and 18 pim pixels operating at <120K. 

Though not formally a part of the scientific instru- 
mentation, there are additional imaging detectors used 
for fine guidance. During normal imaging operation, 
two of the four “outrigger” detectors located on the ImC 
FPA are used for guiding (the other pair provide redun- 
dancy). When the ImC R-75 disperser is inserted by 
the filter wheel, these outriggers will no longer see un- 
dispersed stellar images, so a separate auxiliary Fine 
Guidance Sensor (FGS) with 2 SCAs provides this 
function. 

4.4 Calibration System 

Past experience with space imaging and spectros- 
copic missions leads to the conclusion that WFIRST 
has stringent calibration requirements in a number of 
areas. The general WFIRST strategy is to use ground 
calibration methods to the maximum extent possible, 
reserving on-orbit calibration to verification of the 
ground results and extending the calibrations where 
ground calibration may not be effective. To maintain 
the calibration requirements over the entire mission, not 
only are the calibrations important, but so are mea- 
surements of calibration stability. The latter will deter- 
mine the need for and frequency of on-orbit calibra- 
tions. The WFIRST calibration program will place 
strong emphasis not only on the areas requiring calibra- 
tion, but also on the verification of these calibrations, 
either on the ground or in orbit, using multiple tech- 
niques as cross-checks. The SNe and microlensing 
fields are observed repeatedly over the lifetime of the 
mission, providing excellent opportunities to develop 
and use sky calibration standards. 


Section 4: DRM Implementation 


33 















WFIRST 


All optical and detector components will be cali- 
brated at the component, subsystem, and instrument 
levels. These data will be used to feed an integrated 
instrument calibration model that will be verified using 
an end-to-end payload-level thermal vacuum test. This 
test will involve a full-aperture (1.3 meter) diameter col- 
limated beam that will test for optical wavefront error as 
well as photometry. 

The exoplanet program imposes some constraints 
on photometric calibration, but also provides a unique 
opportunity to meet these calibration requirements. 
Proper measurements of the stellar and planetary light 
curves require stable relative calibration to 0.1% (rela- 
tive to nearby stars in the same detector) over the 
course of the event. These observations use mainly a 
single filter. Over the course of the mission, the fields 
are sampled many lO’s of thousands of times with a 
random dither. Most of these observations will be of 
stars without microlensing events. If the star is not a 
variable star, then the relative calibration will be moni- 
tored during the extensive number of observations to 
establish stability. Slow variations across the field-of- 
view and over time can thus be monitored and cor- 
rected for. The absolute calibration and occasional col- 
or measurements using the bluer color filter have less 
stringent calibration requirements (1%) that will be met 
by the more stringent calibration requirements for Dark 
Energy that are described below. 

The three Dark Energy observational methods 
have different calibration demands on instrument para- 
meters and their accuracy. The SN Survey places the 
most stringent demands on absolute and inter-band 
photometric calibration. White Dwarfs and other suita- 
ble sky calibration targets will be used to calibrate the 
absolute flux as well as linearity of the imager over sev- 
eral orders of magnitude. This linearity will be tested on 
the ground, and verified with an on-orbit relative flux 
calibration system (if necessary). Observations of as- 
tronomical flux standards will be extended across the 
detector by means of the “self-calibration’ techniques 
described by Fixsen, Mosely, and Arendt (2000) and 
employed for calibration of Spitzer/IRAC (Arendt et al. 
2010). The intra-pixel response function (quantum effi- 
ciency variations within a pixel) will be fully characte- 
rized by ground testing. 

For the WL Survey, the requirement for galaxy el- 
lipticity accuracy places significant demands on both 
the optical and detector subsystems. The uniformity 
and stability of the point spread function (PSF) needs to 
be strictly controlled and monitored to ensure a suc- 
cessful mission. This drives the need to characterize 


the detector intra-pixel response and the inter-pixel re- 
sponse (capacitive cross-coupling with nearest neigh- 
bors) for both magnitude as well as spatial and tempor- 
al variations. It is likely that the combined PSF effects, 
including spacecraft jitter, will have some variability on 
time scales of a single exposure. These residual ef- 
fects will be continuously monitored with the observato- 
ry attitude control system and field stars and down- 
linked to provide ancillary information for the scientific 
data analysis pipeline. 

The BAG survey relies primarily on the spectrome- 
ter channels, which are not driving the calibration re- 
quirements for the mission. Established calibration 
techniques used for other space missions should be 
adequate to meet the relatively loose photometric and 
wavelength calibration requirements. The larger plate 
scale in the spectrometers may demand some attention 
to the spatial effects such as intra-pixel response, but 
not to the degree required by the WL Survey. 

4.5 Fine Guidance Sensor 

The fine guidance sensor (FGS) is used to meet 
the fine pointing requirements needed for the Exopla- 
net, WL, and SN surveys. The absolute pointing accu- 
racy requirement of <25 milli-arcseconds is driven by 
SN requirements for returning precisely to previously 
observed objects. WL drives the pointing stability of 
<40 milli-arcseconds over an exposure. The primary 
Outrigger FGS consists of two pair of HgCdTe detec- 
tors, a prime and redundant, located on the ImC FPA 
and fed through the ImC optical train, including the filter 
wheel. This guider is used in all observations that in- 
clude imaging. An additional pair of FGS detectors, the 
Auxiliary FGS, is fed from a separate field at the tele- 
scope intermediate focus via an additional compact ref- 
lective relay. The Auxiliary FGS, along with the star 
trackers, provides pointing control for science observa- 
tions when the ImC is performing spectroscopy. 

4.6 Spacecraft 

The WFIRST spacecraft has been designed to 
provide all the resources necessary to support a payl- 
oad at L2 using mature and proven technology design. 
The design is based on the Solar Dynamics Cbservato- 
ry (SDC) spacecraft, which was designed, manufac- 
tured, tested, and qualified at GSFC. The spacecraft 
bus design provides cross strapping and/or redundancy 
for a single-fault tolerant design. Structures: The 
spacecraft bus is an aluminum hexagonal structure, 
consisting of two modules (bus module and propulsion 


Section 4: DRM Implementation 


34 


WFIRST 


module) that house the spacecraft and payload elec- 
tronics boxes and the propulsion tank. The spacecraft 
bus provides the interfaces to the payload and the 
launch vehicle. It supports a multi-panel fixed solar ar- 
ray and a sunshield to prevent the sun from illuminating 
payload hardware during science observations. The 
structural resonances in the spacecraft and payload are 
tuned to frequencies that do not overlap with reaction 
wheel resonances to minimize jitter in the instrument. 
Attitude Control: The spacecraft is three-axis stabi- 
lized and uses data from the payload fine guidance 
sensor, inertial reference unit, and star trackers to meet 
the coarse pointing control of 3 arcsec, and the fine rel- 
ative pointing control of 25 mas pitch/yaw and 1 arcsec 
roll (all values RMS per axis). There are 2 sets of fine 
guidance sensors. The first is a pair of redundant sen- 
sors (4 total) on the imager focal plane and the second 
is a pair of auxiliary guiders (2 total) for guiding during 
SNe spectroscopy mode. The star trackers are used 
for coarsely pointing to within 3 arcsec RMS per axis of 
a target. After that, the FGS takes over to meet the fine 
pointing requirements for revisits and relative offsets. A 
set of 4 reaction wheels is used for slewing as well as 
momentum storage. The wheels are passively isolated 
to allow stable pointing at frequencies higher than the 
FGS control band. The GNC subsystem provides a 
safe hold capability (using coarse sun sensors), which 
keeps the observatory thermally-safe, power-positive 
and protects the instrument from direct sunlight. Pro- 
pulsion: A hydrazine mono-prop subsystem is required 
for orbit insertion, orbit maintenance, and momentum 
dumping from the reaction wheels throughout the dura- 
tion of the mission. The prop subsystem does not have 
any unique features for WFIRST. This subsystem is 
well within the requirements of other propulsion sys- 
tems that have launched. Electrical Power: Three 
fixed, body-mounted solar array panels provide the ob- 
servatory power. Gallium Arsenide solar array cells 
operate with 28% efficiency and provide 2500 watts of 
output for an average orbit usage of -1400 W. The re- 
mainder of the power subsystem is comprised of an 80 
A-hr battery and power supply electronics that control 
the distribution of power and provide unregulated 28 
Vdc power to the payload. The solar array is currently 
sized to provide full observatory power at EOL with 2 
strings failed at the worst case observing angles. 
Communications: The communications subsystem 
uses S-band transponders to receive ground com- 


mands and to send real-time housekeeping telemetry to 
the ground via 2 omni-directional antennas as well as 
for ranging. A Ka-band transmitter with a gimbaled an- 
tenna will downlink stored science and housekeeping 
data at a rate of 150 Mbps without interrupting science 
operations. Command & Data Handling: The com- 
mand and data handling subsystem includes a 1.1 Tb 
solid state recorder (SSR) sized to prevent data loss 
from a missed contact. The daily data volume is esti- 
mated at 0.9 Tb per day, assuming 2:1 lossless com- 
pression. The data will be downlinked twice daily to the 
NASA Deep Space Network (DSN). The C&DH/FSW 
provides fault management for the spacecraft health 
and safety as well as being able to safe the payload 
when necessary. Thermal: The spacecraft thermal 
design is a passive system, using surface coatings, 
heaters and radiators. 

4.7 Ground System 

The WFIRST Mission Operations Ground System 
is comprised of three main elements: 1) the facilities 
used for space/ground communications and orbit de- 
termination, 2) the Mission Operations Center (MOO) 
and 3) the facilities for science and instrument opera- 
tions and ground data processing, archiving, and 
science observation planning. For each element, exist- 
ing facilities and infrastructure will be leveraged to pro- 
vide the maximum possible cost savings and opera- 
tional efficiencies. The functions to be performed by 
the ground system and the associated terminology are 
shown in Figure 11. 

The DSN is used for spacecraft tracking, com- 
manding and data receipt. It interfaces with the MOO 
for all commanding and telemetry. Tracking data is sent 
to the GSFC Flight Dynamics Facility. 

The MOC performs spacecraft, telescope and in- 
strument health & safety monitoring, real-time and 
stored command load generation, spacecraft subsys- 
tem trending & analysis, spacecraft anomaly resolution, 
safemode recovery, level 0 data processing, and 
transmission of science and engineering data to the 
science and instrument facilities. The MOC performs 
Mission-level Planning and Scheduling. 

The science and instrument facilities maintain in- 
strument test beds, perform instrument & telescope ca- 
librations, assist in the resolution of instrument anoma- 
lies, perform instrument flight software maintenance, 
and generate instrument command loads. 

These facilities are also responsible for science 
planning & scheduling, supporting mission planning ac- 


Section 4: DRM Implementation 


35 


WFIRST 


tivities carried out by the MOC, running the Guest In- 
vestigator (Gl) Program, providing Science Team and 
Gl support, and performing EPO activities for the public 
and the astronomical community. Data handling in- 
volves ingesting Level 0 science and engineering data 
from the MOC and performing Level 1-3 data 
processing for the Science Teams and Gl community 
and transmitting these calibrated data to the data arc- 
hive. All data will be archived. Data search and access 
tools are provided to the science community that enable 
efficient searches and delivery of archival data that en- 
sure interoperability with NASA data archives and the 
Virtual Astronomical Observatory. 

Approximately 5 dedicated Science Teams will be 
funded over a 5-year period to execute the primary dark 
energy, exoplanet, and NIR survey science programs. 
In this period, the Gl program provides funding for ancil- 
lary science. Operations costs and grants for the Gl in 
the primary mission are fully included in the lifecycle 
costs. 

4.8 ENABLING TECHNOLOGY 

The HgCdTe near-infrared detectors baselined for 
WFIRST have extensive heritage from HST, JWST, and 
on-going production of commercial off-the-shelf devices 
for ground-based observatories. WFIRST uses a 7x4 
mosaic of these detectors while the largest near- 
infrared focal plane built for space so far is a 2x2 array 


of detectors. Although scaling of the focal plane from a 
2x2 array to a 7x4 array is not technology development, 
it is considered an engineering challenge so an EDU 
was started on the JDEM project and work continues 
under WFIRST. The EDU FPA includes a 6x3 silicon 
carbide (SiC) mosaic plate incorporating the 2.1 pm 
detectors, the Sensor Cold Electronics (SCE), including 
a repackaged version of the SIDECAR ASIC and asso- 
ciated mounting hardware. The full mosaic plate will be 
populated with flight-like detectors and qualification 
testing of the assembly will be completed prior to Phase 
A, mitigating the technical risk of scaling of a large NIR 
mosaic. 

Anticipating the need to demonstrate acceptable 
detector performance (in order to meet the scientific 
requirements) and yield (at an acceptable cost), the 
JDEM/WFIRST project initiated a detector demonstra- 
tion program over 3 years ago. To date, two lots have 
been built, a more experimental one under the Detector 
Technology Advancement Program (DTAP), and a 
more WFIRST -specific lot under the FPA EDU detector 
build. A third lot is currently in process to demonstrate 
enhanced robustness and margin. These lots have 
provided test data showing improved detector perfor- 
mance over previous designs and these results are be- 
ing used to guide mission design and optimization. 


Mission Operations 

• Spacecraft (S C) and instrument 
health and safety monitoring 

• Real time and stored command 
load generation 

• Perform command upUnk & 
telemetry’ do\Milink 

•SC subsystem trending and analysis 

• Perform S C simulations using 
vendor testbed 

• Support S C FSW maintenance 

• Perform Level 0 Processing 

• Distribute Level 0 data 

♦Archive Level 0 & engineering data 

• \Cssion Planning and Scheduling 

• Perform commissioning planning 
and execution 

• Generate orbital planning products 
& perform momentum management 

• Ground System monitoring 

• Anomaly Resolution & 

Safemode Recoverv 


Instrument Operations/Support 

• Maintain instrument testbeds 

• Support commissioning planning execution 

• Perform instrument FSW maintenance 

• Perform instrument telescope calibration 

• Generate instrument command loads 

• Perform instrument anomaly resolution 

Science Support 

• Perform Science planning & scheduling 

• Support Mission Plaiming & Scheduling 

• Support commissioning planning execution 

• Support Science Teams 

• Develop algorithms for data processing 

• Support instrument & telescope calibration 

• Support Participating Scientists (GO’s) 

Education/Public Outreach 

• Perform EPO activities for public and 
astronomical community 


Space/Ground Communications 
& Orbit Determination 

•SC tracking & orbit determination 

• command transmission 

• data receipt 


Data Processing Pipeline 

• Develop and maintain pipeline 
architectiue and standards 

• Develop and maintain data processing 
pipeline 

• Ingest Level 0 data 

• Perform Level 1-3 data processing 

• Transfer Level 0-3 data 

Data Archive 

• Ingest and archive level 0-3 data products 

• Ingest and archive higher level data 
products 

• Manage proprietary data periods 

• Provide data search and access tools 

• Interoperate wth other archives 


Figure 11: WFIRST Ground System functions and associated terminology 


Section 4: DRM Implementation 


36 



WFIRST 


It was recently discovered that some HgCdTe de- 
tectors are showing degradation after long term sto- 
rage. These are manufactured using similar technology 
to that for WFIRST. This degradation leads to a slow 
increase in dark current and the number of “hot pixels” 
during ground processing and testing. The root cause 
for this degradation has been identified and design and 
process change features have been identified. The cur- 
rent lot of demonstration parts that the JDEM/WFIRST 
project is building already includes these design 
changes. The WFIRST detectors will be tested this 
summer to validate the design change. There is a min- 
imum of 2.5 years available for WFIRST to complete 
the performance and qualification testing to validate the 
design before the procurement process for the WFIRST 
flight detectors will start, assuming a Phase A start in 
FY13. 

The JDEM Omega RFI identified weak leasing as a 
goal and the Decadal Survey EOS panel report identi- 
fied risks associated with weak leasing. Both the SDT 
and the Project are pursuing the Decadal Survey's rec- 
ommendation to address challenges related to weak 
leasing early to mitigate the chances of significant cost 
growth. Among the efforts underway are ensuring that 
the telescope design is compatible with controlling sys- 
tematic effects to the level necessary for weak leasing 
and end to end simulations of galaxy ellipticity mea- 
surements with hardware in the loop. The work leading 
up to this interim report has affirmed that the pursuit of 
weak leasing should continue in the upcoming mission 
development efforts. 


Section 4: DRM Implementation 


37 


WFIRST 


5 OPERATIONS CONCEPT 

The primary focus in designing WFIRST science 
operations is to optimally acquire the datasets for the 
four main surveys (the exoplanet microlensing survey, 
and Dark Energy measurements based on surveys of 
Supernova SNe-la, BAO/RSD galaxy redshifts, and WL 
galaxy shapes), while considering ways to enhance the 
general NIR Survey dataset on a non-driving basis. 
Each survey has its own unique operations concept, but 
in the case of the WL galaxy shape survey, we are able 
to simultaneously acquire a deeper BAO/RSD galaxy 
redshift survey, albeit at a slower than optimal sky cov- 
erage rate. 

Exoplanet microlensing observations require moni- 
toring of high density star fields in the Galactic Bulge for 
periods of> 60 days in order to detect these relatively 
rare but readily observed events. These observations 
will be carried out in 7 campaigns of ~72 days duration 
during the twice yearly periods when the Bulge is in the 
Field of Regard (FOR) of the Observatory, and will pro- 
vide an exoplanet detection yield rate as specified in 
Figure 1, Box 3, and Table 2. These campaigns will 
span the bulk of the planned mission lifetime in order to 
provide long temporal baseline data for stellar typing 
through relative proper motion studies of the source 
and lens stars. Seven fields will be scanned in a conti- 
nuous pattern at a revisit cadence of 15 minutes. Inte- 
grations of 88s with filter W149 will be used to routinely 
sample microlensing event light curves, but -every 12 
hours a revisit cadence will be executed with filter F087 
in place to provide star color information. Revisits to the 
same field during each campaign will be at the same 
pointing, to within a random dithering of -1 pixel rms. 
All the exposures are downlinked and stored to provide 
extensive field monitoring data covering pre-, post-, and 
on-going microlensing signals, as well as to provide rel- 
ative photometric calibration data at the field star loca- 
tions. 

SNe observations require regular monitoring of two 
small fields within 20° of an ecliptic pole over an ex- 
tended period of time (-2 years), and provide a SNe-la 
yield rate as a function of dedicated SNe time as speci- 
fied in Figure 1. As an example, for a dedicated SNe 
time allocation of 6 months, the observatory repeatedly 
(for -30 hours every 5 days for -2 years) monitors 
-square fields of -5.8 deg^ for mid z (to z=0.8; Tier 1) 
SNe-la and -1.4 deg^ for high z (to z=1.2; Tier 2) SNe- 
la. Monitoring consists of observations with filters 
Fill, F141, and F178 (300s @ for Tier 1 and 1100s @ 
for Tier 2) and with R-75 prism P130 (1300s for Tier 1, 
and 5300s for Tier 2). Monitoring revisits to each SNe 


field to within 15 (TBD) milliarcsecs to provide 4 or 9 
(TBD) precise sub-pixel dithers are accomplished via 
the S/C attitude control system (ACS) using the Aux 
FGS and star trackers when the R75 prism is used, and 
the ImC FGS when any filter is used. To enable spec- 
tral monitoring of the SNe and host galaxy in the same 
orientation, the observatory roll angle is inertially fixed 
for -90 day periods, then rotated -90 degrees to main- 
tain field monitoring coverage while keeping the sun 
within 45 degrees of the maximum-power roll angle. 

The WL and BAO-RSD surveys require mapping 
large sky areas as rapidly as exposure times permit, 
with two mapping modes being planned. A combined 
WL/BAO-RSD mode, also called the DEEP survey, 
meets requirements for WL shape and photo-z ImC 
measurements and simultaneously provides a deep 
BAO/RSD SpC survey. This mode optimally maps the 
ImC FOV across the sky in 3 NIR filters (Fill, F141, 
F178) with no gaps in the ImC field at a rate of -2,700 
deg2/yr (-7+ deg^/day). Three of these smooth-filled 
passes on a target field are required, each with a differ- 
ent filter and with an -5° roll angle difference (as per 
BAO-RSD roll requirements). The two passes per- 
formed in the two reddest filters are for WL shape/color 
measurements, and deliver 5 randomly dithered obser- 
vations of 160 seconds over the full observed field. The 
third pass is performed with Fill to acquire WL color 
data only, and only four 160 second exposures over the 
full observed field are required. A faster WIDE survey 
mode meets BAO-RSD requirements and also provides 
photo-z colors for ground based WL programs. This 
mode optimally rough-fills the SpC FOV across the sky 
(simultaneously mapping the ImC across the sky in two 
filters) at a rate of -11,000 degVyr (-30+ degVday). 
Two same-filter passes over a target field are com- 
pleted with a slight offset in the passes to rough-fill the 
SCA gaps in the SpC focal planes. A second set of two 
passes are completed with a second filter at a slight roll 
angle (-5”) relative to the first pair of passes to limit 
source confusion. The area covered during the WL 
and/or BAO/RSD surveys is broken into a series of iner- 
tially fixed observations, each comprised of a pro- 
grammed sequence of small slews/settles. The chosen 
inertially-fixed fields are ultimately stitched together into 
a contiguous map, and are selected within the FOR ac- 
cording to a schedule that accounts for availability. Zo- 
diacal brightness, the Galactic plane, and other geome- 
tric/thermal constraints, and possibly operational (mo- 
mentum dumping) considerations. Given the L2 van- 
tage point and the 5 year mission life, the scheduling 
constraints to achieve the WL and BAO/RSD sky cov- 


Section 5: Operations Concept 


38 


WFIRST 


erage are not particularly challenging, but care must be 
taken to ensure that appropriate observable fields are 
available at all times. 

Combining all of the above sky coverage, monitor- 
ing, and cadence requirements with stray light and solar 
array exposure considerations, the observatory is de- 
signed to have a pitch FOR between 54 and 126 de- 
grees off the sun with no azimuthal (yaw) constraint 
about the sun line. Roll about the observatory line of 
sight is constrained to ±10° during all observations with 
the exception of SNe observations, where the require- 
ment is to be able to remain inertially fixed for 90 days 
while pointed within 20° of either ecliptic pole (max 
power to occur at the middle of any 90 day period). 
The WFIRST design provides the flexibility to support 
different observing strategies, and Figure 1 gives the 


sky coverage and exoplanet/SNe-la detection rates per 
unit of dedicated observing time. The observing time 
can be divided in many different ways yet still provide 
large sky surveys, large numbers of SNe-la characteri- 
zations, and large numbers of exoplanet detections. 
Figure 5 illustrates one way in which Exoplanet and 
SNe ops might be accommodated, then blocks out the 
large pieces of observing time that remain available for 
HLS, Gl, and Galactic Plane observations (as well as 
the calibration/training datasets to be defined during the 
remainder of the SDT study). This flexibility is a key 
strength of WFIRST, as this ability to accommodate a 
wide range/order of NIR imaging and spectroscopic 
surveys is critical to the success of any Facility Class 
mission. 



HLS= High Latitude Surveys 
Gl = Guest Investigator Surveys 
ExP= Exoplanets Survey 
SNe = Supernovae Survey 
GP = Galactic Plane Surveys 
GP-Bulge = Galactic Plane, including 

the Galactic Bulge, Surveys 


V 


□ HLS,GI, and/or GP 
■ ExP 

□ SNe plus HLS. Gl, and/or GP 

□ SNe plus HLS, Gl, and/or GP-Bulge 


WFIRST IDRM Ops Flexibility within ExP/SNe Constraints 
(If GP-Bulge Season Ends as IOC Completes) 


Figure 12: WFIRST exhibits excellent observing mode flexibility in sample ops concept meeting ExP and SNe field mon- 
itoring requirements. 


Section 5: Operations Concept 


39 


WFIRST 


6 COST & SCHEDULE 

The current WFIRST DRM has relatively few 
changes from the JDEM-Omega reference mission, and 
thus future independent cost estimates should be very 
comparable to the NWNH Astro2010 independent cost 
estimate. The WFIRST mission was estimated at 
$1.61B by the NWNH independent cost team. These 
WFIRST optimizations or changes are believed to be 
cost neutral or provide minor cost savings. Over the 
summer, the Project will develop a WFIRST LCCE us- 
ing multiple estimating techniques. Project Manage- 
ment, Systems Engineering, Mission Assurance, Inte- 
gration & Test, and Public Outreach will be estimated 
using a grassroots approach and validated against ana- 
logous missions. Pre- and Post-launch Science will be 
projected using guidance from NASA HQ on the ex- 
pected size of the WFIRST Science Announcement of 
Opportunity (AO). This estimate will include support for 
the AO-selected science teams in the mission devel- 
opment phase as well as the 5 years of operations. 
Additional funds for the Guest Investigator (Gl) Program 
will be included in the Science estimate. The payload 
and spacecraft will be estimated primarily using para- 
metric estimates. These estimates will be constructed 
using master equipment lists (MELs) and historical cost 
databases and are adjusted for mass and complexity 
factors. Additionally, NASA HQ has requested that an 
Independent Cost and Schedule Estimate (ICE/ISE) be 
performed by the Aerospace Corporation. The ICE/ISE 
is expected to be completed in September 2011. 

The development phase of WFIRST spans 82 
months, from preliminary design through launch (phase 
B/C/D). This development phase is preceded by 9 
months to fully develop the baseline mission concept 
(Phase A) and several years of concept studies (Pre- 
Phase A). The observing phase (Phase E) of the mis- 
sion is planned for five years. The development sche- 
dule is shown in Figure 13. The estimate is at a 70% 
Joint Confidence Level (JCL) meaning it includes mar- 
gins for cost and schedule risk. The 70% JCL schedule 
allocates ten months of funded reserve to the WFIRST 
development. 

The build-up and integration philosophy of the 
WFIRST observatory is based on the well established 
practice of building small assemblies of hardware, tho- 
roughly testing them under appropriate flight environ- 
ments, and then moving on to the next higher level of 
integration with those assemblies. The WFIRST tele- 
scope and instrument will be developed and individually 
qualified to meet mission environments. The critical 
path of the mission is through the development of the 


instrument. The instrument is qualified prior to integra- 
tion with the telescope. Following ambient check-out, 
the entire payload is tested at temperature and vacuum 
at GSFC to verify the end-to-end optical performance. 
The spacecraft is then integrated to the payload, and 
checked at ambient. Following a successful ambient 
checkout, a complete observatory environmental test 
phase is performed, including a repeat of the optical 
test with the fully integrated observatory. Upon suc- 
cessful completion of the observatory environmental 
test program, the observatory is readied for shipment to 
the KSC, where the launch campaign is conducted. 

The parallel build-up of all of the mission elements, 
allows substantial integration activity to occur simulta- 
neously, increasing the likelihood of schedule success. 
Because all of the major elements of the observatory 
(telescope, instrument, and spacecraft) are located at 
GSFC two years before the planned launch, there is 
considerable flexibility in optimizing the schedule to 
compensate for variation in flight element delivery 
dates. Over the two year observatory l&T period, the 
Project will have flexibility to reorder the l&T work flow 
to take advantage of earlier deliveries or to accommo- 
date later ones. Should instrument or telescope sche- 
dule challenges arise there are options to mitigate the 
schedule impacts by reallocating the payload level envi- 
ronmental test period. Should instrument or spacecraft 
challenges arise, there are options to modify the 
workflow and pull other tasks forward to minimize risk 
and maintain schedule. The WFIRST schedule is very 
achievable. With two years between the delivery of the 
WFIRST instrument and launch, and given the addi- 
tional flexibility that is inherent in the l&T flow, the 
WFIRST observatory l&T program has a high probabili- 
ty of executing within budget and schedule. In sum- 
mary, the proposed WFIRST observatory l&T flow pro- 
posed is very achievable, given the planned schedule 
reserve and the opportunities available for workaround. 

Fifty-one months are allocated to complete the 
WFIRST instrument, from the start of preliminary de- 
sign, thru the delivery of the instrument, not including 
reserve. Additionally, the schedule includes ten months 
of funded reserve, further increasing the likelihood of 
executing the plan. An engineering development unit 
FPA has already been initiated and flight-like detectors 
have already been delivered. Integration of those de- 
tectors into the silicon carbide mosaic plate will occur 
later this summer and integrated testing will be per- 
formed. Thus even before Phase A commences, a 
large mosaic NIR focal plane will have been demon- 


Section 6: Cost & Schedule 


40 


WFIRST 


strated mitigating the risk of the element that this ele- 
ment would drive the mission critical path. 

Early interface testing between the Observatory 
and ground system is performed to verify performance 
and mitigate risks to schedule success. Prior to payl- 
oad integration, interface testing between the space- 
craft and the ground system is performed. Immediately 
following payload integration to the spacecraft, end-to- 
end tests are performed, including the payload ele- 
ments. These tests are performed numerous times 
prior to launch to ensure compatibility of all interfaces 
and readiness of the complete WFIRST mission team. 


Given that WFIRST requires no new technologies, 
can be built today, has an implementation strategy that 
is conservative, proven and amenable to workarounds, 
and has a schedule based on continuously retiring risk 
at the earliest possible opportunity, the WFIRST mis- 
sion is executable within the cost and schedule con- 
straints identified in this report, consistent with the New 
Worlds, New Horizons finding that WFIRST “...presents 
relatively low technical and cost risk making its comple- 
tion feasible within the decade...”. 


Task Name 


12 

2013 

2014 

2015 

2016 

2017 

2018 

2019 

2020 

Q3|Q4 

Q1|Q2|Q3|Q4 

D 

1 

O 

O 

QllQ2lQ3lQ4 

Q1|Q2|Q3|Q4 

01 |Q2|Q3|Q4 

01 |Q2|Q3|Q4 

01 I02l03l04 

01 |02|03|04 


Payload l&T 
Spacecraft Bus 
Observatory l&T 
Launch Services 
Ground Systems 


PNC 


SRR 


A 

SRR 


PDR 


A 

PDR 


CDR 


Spacecraft Bus 

A 

CDR 


PhD 


PhE 


WFIRST 

KDPA 

KDPB 

KDPC 


KDPD 



0 

<T> 

O 

O 

O 

O 


MCR 

SRR 

PDR 

CDR 

SIR 

ORR 

Telescope 




Telescope 





A 

A 

A 

A 

A 1 



SRR 

PDR 

CDR 

PER 

PSR 

NIR Instrument 




NIR Instrument 







''' 


A \ 


A 

PER 


KDPE 

«> 

ERR 


PER 


PSR 



PSR 




Launch Services 
A. A A 

ATP PDR CDR 

Ground Systems 

A.A : ~ 


Obs I It Env Test 

nrrnn lrd 
Launch Ops 

^ LRR 


PDR 


CDR R-1 


R-L 


) Funded Schedule Reserve 


Figure 13; Mission Schedule 


Section 6: Cost & Schedule 


41 


WFIRST 


7 CONCLUSION AND PATH FORWARD 

This report describes the work of the WFIRST 
Science Definition Team and Project Office on defining 
the WFIRST mission. The SDT has found that the mis- 
sion objectives given in the NWNH Decadal Survey re- 
port are achievable and that the science remains highly 
compelling. The top-level science requirements have 
been refined and lower level requirements derived. 
Figures of Merit have been specified for the dark ener- 
gy science, based on previous work of the Dark Energy 
Task Force and the Figure of Merit Science Working 
Group. New FoMs have been derived for exoplanet 
microlensing and for sky surveys. The purpose of 
these FoM's is to provide quantitative means for com- 
paring performance of various mission configurations. 

A significant effort by the Project Office and SDT 
has gone into refining the design concept for the obser- 
vatory. This report contains the latest Interim Design 
Reference Mission. The design is similar to that speci- 
fied in the NWNH report, with a few improvements to 
boost performance and lower cost. The most important 
of these is to change from an on-axis "obscured" tele- 
scope to an off-axis unobscured concept. The imaging 
performance is superior for the off-axis design and 
there is adequate flight heritage to baseline such an 
approach. 

In Europe, the Euclid dark energy mission is in 
Phase A for the M2 competition. It has overlap with 
WFIRST in some of its science objectives, but is a sig- 
nificantly different design with different performance 
characteristics. The WFIRST SDT has compared the 
missions and found that they are synergistic. Several 
science objectives of WFIRST, including exoplanet mi- 
crolensing and supernova dark energy measurement, 
are not part of the baseline Euclid mission. Also, other 
areas of dark energy measurement, including weak 
leasing and baryon acoustic oscillations, are addressed 
in different and complementary ways in the two mis- 
sions. WFIRST has more focus on near IR observa- 
tions and Euclid on visible observations. With this in 
mind, the SDT has concluded that the WFIRST design 
should not change, even if Euclid is selected and is 
launched ahead of WFIRST. However, there would 
likely be changes made to the observing program of 
WFIRST to more complement that of Euclid. Should 
NASA and ESA decide to pursue a joint mission or pro- 
gram, all of the capabilities currently included in 
WFIRST must be included in the joint effort. 


Planned Studies 

The first iteration of an engineering design cycle 
for the WFIRST mission is planned for the coming year. 
Some of the more noteworthy aspects of this study are 
described briefly in this section. These address open 
trades, liens on the present design, and preparations 
for the Phase A study. Some of the items listed here 
are in fact normally addressed in Phase A. However, 
WFIRST is in a more mature state than is common in 
pre-Phase A, as a consequence of prior mission con- 
cept studies. Hence, we are taking advantage of the 
opportunity to begin this work now in order to reduce 
schedule risk downstream. 

Attitude Control The frequent slews needed for a 
large-area sky survey, coupled with fine pointing control 
and the multiple fields of regard, require a capable 
ACS. An integrated model of the observatory structure 
and the attitude control system was begun for the 
JDEM Omega concept, and is now being modified for 
WFIRST. This includes a finite-element model of the 
structure and solar arrays, models of the ACS sensors 
and actuators, and a model of fuel slosh. This serves as 
a test-bed for development of ACS control laws, per- 
forming trade studies of sensor and actuator perfor- 
mance requirements, and providing more accurate in- 
put to operations concept development on issues such 
as settle time following slews. 

Vibration Isolation The structure must be de- 
signed so that vibration modes at frequencies above 
the ACS control bandwidth do not degrade image quali- 
ty. At L2, the primary disturbance is vibration of the 
reaction wheels. The preliminary study of the Omega 
telescope indicated that the following implementation 
strategies are likely to be adequate to meet the stability 
requirements needed for weak leasing galaxy shape 
measurements, which impose the most stringent stabili- 
ty requirements of all of the required science measure- 
ments: 

• Passive mechanical isolation of the spacecraft 
reaction wheels 

• Reaction wheel speed limited to <= 45 Hz. 

• Possible addition of passive mechanical isolation 
of the spacecraft from the telescope. 

• Resonances in the payload structure detuned 
from those of the reaction wheels to prevent 
large jitter motions of the optical metering struc- 
ture. 

This study will be repeated in greater detail for the 
WFIRST S/C bus and optical metering structure. An 


Section 7: Conclusion and Path Forward 


42 


WFIRST 


important component of managing the science impacts 
of vibration present during an exposure is the downlink- 
ing data from the attitude control system to aid the 
science data analysis via pointing history reconstruc- 
tions. 

Thermal Design The thermal environment of the 
metering structure must be controlled so as to maintain 
the positions of the optical elements to within their bud- 
geted tolerances. The JDEM-Omega studies found that 
it was sufficient to provide thermal control of the me- 
chanical structure and mirrors to +I-1C. This is less 
stringent than the stability achieved on Chandra (-0.2 
degrees C), indicating that we should have significant 
design margin given the thermal environment similari- 
ties between Chandra’s highly elliptical orbit and 
WFIRST’s Earth-Sun L2 orbit. The thermal model will 
be updated to the WFIRST design, and ultimately inte- 
grated into a Structural Thermal Optical analysis. 

Optical Design The design meets the image quali- 
ty requirements with comfortable margin over the entire 
field of view. A detailed tolerance analysis will be per- 
formed to allocate fabrication and alignment tolerances 
for all of the components. This tolerance budget will lat- 
er be incorporated into the STOP analysis. 

Wavefront Sensing. The addition of wavefront 
sensors to the imager focal plane is under considera- 
tion. Data from wavefront sensors would aid in the 
analysis of weak lensing observations, and simplify the 
maintenance of optical alignment by the operations 
team. 

Calibration The optimal combination of astronomi- 
cal observations and on-board illumination system 
needed for photometric calibration is still under study. 
The issues range from wavelength-dependent flat- 
fielding to detector linearity and filter stability. 

Data Simulations High-fidelity simulations are re- 
quired: 

1. Cosmological/Science Simulations to verify the 
link between our Science Objectives and our 
Survey Requirements ... if the WFIRST mis- 
sion delivers the required Surveys, can the 
Science Objectives actually be met? 

2. Image Processing Simulations to verify the link 
between our Survey Requirements and our 
Dataset Requirements ... if the mission deliv- 


ers the required Datasets, can those Datasets 
be image processed to produce the required 
Survey information? 

3. Observatory transfer function simulations us- 
ing sky-truth inputs to verify the link between 
our Required Datasets and our Observatory 
Design/Ops Concepts ... if we build/operate an 
Observatory as specified will it in fact deliver 
the required Datasets? 

All of the above levels of simulation are needed to 
derive/validate requirements at the Survey, Dataset, 
and Observatory Design/Ops levels, and are critical to 
giving us the ability to design the right system based on 
well supported, comprehensive trades. Results from the 
JDEM mission concept study teams can, in some in- 
stances, be applied to WFIRST, but in most cases the 
existing tools would need to be modified or new tools 
developed. 

Detector and Focal Plane Assembly This is de- 
scribed in Section 4.8 above, and is included in this list 
for completeness. Additional detector lots would be de- 
sirable to mitigate the yield risk, as resources permit. 

Independent Cost Estimate (ICE) The ICE is de- 
scribed above in Section 6 and is listed here for com- 
pleteness. 

The SDT and Project Office will continue working 
on WFIRST after this Interim Report. Several possible 
modifications to the IDRM have been identified that 
warrant further study. These include extending the wa- 
velength range redward of 2 microns and adding an 
Integral Field Unit (IFU) spectrometer for SN spectros- 
copy. These options are described in more detail in 
Appendix E. Additional science simulation work is 
planned to give more detailed assessment of mission 
performance and aid in further refinement of the mis- 
sion design. After the ESA M2 decision, there may be 
other work related to Euclid. A final report of the SDT is 
due in about 1 year. 


Section 7: Conclusion and Path Forward 


43 


WFIRST 


Appendix A Exoplanet Science Goals & Re- 
quirements 

A.l. Microlensing Exoplanet Detection Method 


Planetary Microlensing 


Galactic Center 


8kpc 


Sun 


1 -7 kpc from Sun 


■"5 





Source star Lens star WFIRST 

and images and planet 


Figure 14: The geometry of a microlensing planet search 
towards the Galactic bulge. Main sequence stars in the 
bulge are monitored for magnification due to gravita- 
tional lensing by foreground stars and planets in the Ga- 
lactic disk and bulge. 


WFIRST finds exoplanets using the technique of 
gravitational microlensing. The physical basis of micro- 
lensing is the gravitational bending of light rays by a 
star or planet. As illustrated in Figure 14, if a “lens star” 
passes close to the line of sight to a more distant 
source star, the gravitational field of the lens star def- 
lects the light rays from the source star. The gravita- 
tional bending effect of the lens star splits and magni- 
fies the images of the source star. The individual im- 
ages are not resolved, so the observer sees a micro- 
lensing event as a transient brightening of the source 
as the lens star’s proper motion moves it across the line 
of sight. Gravitational microlensing events are charac- 
terized by the Einstein ring radius. 


R, = 2.0 AU 

E 






0.5 Mq DJ\ kpc) 


where Ml is the lens mass, and Dl and Ds are the dis- 
tances to the lens and source stars, respectively. Re is 
the radius of the ring image that would be seen with 
perfect alignment between the lens and source stars. A 
microlensing event’s duration is given by the Einstein 
ring crossing time, typically 1-3 months for stellar 
lenses and a few days or less for a planet. 


Planets are detected via light curve deviations that 
differ from the normal stellar lens light curves (Mao & 
Paczynski 1991). Usually, the planet signal occurs 
when one of the two images of the source star passes 
close to the location of the planet, as indicated in Fig. 1 
of Gould & Loeb (1992), but planets are also detected 
at very high magnification where the gravitational field 
of the planet destroys the symmetry of the Einstein ring 
(Griest & Safizadeh 1998). The probability of a detecta- 
ble planetary signal and its duration both scale as Re ~ 
Mpi'2, but given the optimum alignment, planetary sig- 
nals from low-mass planets can be quite strong (many 
tens of percent). The limiting mass for the microlensing 
method occurs when the planetary Einstein radius be- 
comes smaller than the projected radius of the source 
star (Bennett & Rhie 1996), resulting in a suppression 
of the amplitude of the deviation. This suppression is 
stronger for planets located inside Re. For the F, G or 
K-dwarf source stars in the bulge that can be monitored 
with a space-based survey, the sensitivity of the micro- 
lensing method extends down to < O.lMe. 

Microlensing is most sensitive to planets at a sepa- 
ration of ~ Re (usually 2-3 AU) due to the strong stellar 
lens magnification at this separation, but the sensitivity 
extends to arbitrarily large separations. Planets well in- 
side Re have a lower probability of detection. Planets 
in the habitable zones of their parent star tend to be lo- 
cated at separations that are substantially smaller than 
Re, and thus are more difficult to detect. This in turn 
requires the higher photometric precision and higher 
angular resolution afforded by a space based micro- 
lensing mission. 

Well-sampled planetary microlensing light curves 
yield unambiguous planet mass ratios and separations 
in units of Re, but not absolute planetary masses and 
separations in physical units (i.e., AU). However abso- 
lute values are needed to place the microlensing detec- 
tions in the context of the discoveries made by other 
methods. For all but a small fraction of planetary micro- 
lensing events, high-resolution (<0.3”) imaging is 
needed resolve out the dense stellar background in the 
target bulge fields, and so allow for the detection and 
unambiguous identification of the light from the host 
stars. This in turn allows the star and planet masses 
and separation in physical units to be determined (Ben- 
nett et al. 2007). A space-based survey with the requi- 
site resolution will obtain this information naturally for 
the majority of the host stars. 


Appendix A: Exoplanet Science Goals & Requirements 


A-1 


WFIRST 


A.2. Exoplanet Survey Questions and Science 
Requirements 

The WFIRST Exoplanet survey requirements flow 
down from the Exoplanet Survey Questions discussed 
in Section 2.2.2: 

1. How do planetary system form and evolve? 

2. How common are potentially habitable worlds? 

WFIRST can address the first of these questions 
by determining the demographics of planetary systems 
with its sensitivity to virtually all types of exoplanets that 
will not be detected by Kepler. Furthermore, due to its 
sensitivity to planets at substantial distances, WFIRST 
can determine how the properties of planetary systems 
depend on their Galactic environment. WFIRST has the 
unique ability to detect old, free-floating planets of < 1 
Earth-mass, which provide important constraints on the 
dynamical histories of planetary systems. The micro- 
lensing is also able to detect planets that orbit stars, 
which are too dim to be detected. This is an advantage, 
but if all the planets detected by WFIRST fall into this 
category, WFIRST’s contribution to Exoplanet Survey 
Question #1 will be significantly compromised. These 
considerations lead to the following Science Require- 
ments: 

A. Make a definitive measurement of the fre- 
quency of bound and free-fioating pianets with 
masses extending to iess than an Earth-mass 
and separations greater than 0.5 Ail. 

B. Measure the masses of the pianets and host 
stars for the majority of the detected exopiane- 
tary systems. 

Kepler will address Exoplanet Survey Question 2, 
which is critical for the planning of future missions, but 
this is a challenging measurement for Kepler. So, an 
additional measurement with a very different method by 
WFIRST is needed. This implies the final WFIRST 
Science Requirement: 

C. Make a definitive measurement of the fre- 
quency of habitabie pianets. 

A.3. Exoplanet Survey Requirements 

Obtaining a definitive measurement of the frequen- 
cy of exoplanets of a given type with WFIRST, and so 
meeting Science Requirements A and C above, trans- 
lates directly to a requirement on the number of de- 
tected planetary deviations of that type. In general 
terms, inferring the frequency of exoplanets involves 


Appendix A: Exoplanet Science Goals & Requirements 


first detecting the planetary deviations, then inferring 
the planetary parameters from those deviations, and 
finally calibrating the probability of detecting planets of 
the given type for the ensemble of observed microlens- 
ing events. These pieces of information can then be 
simply combined to estimate the intrinsic planet fre- 
quency (e.g., Gould et al. 2010). Calibrating the detec- 
tion probability is a well-understood procedure incurring 
negligible uncertainties (Gaudi & Sackett 2000; Rhie et 
al. 2000), and thus for robustly-measured deviations (as 
specified below) for which the light curve parameters 
well-measured, the fractional uncertainty in the inferred 
planet frequency is due almost exclusively to the Pois- 
son fluctuations in the number of detected planets A/p, 
which we can approximate as A/p-^'T Thus achieving a 
certain precision in the measurement of the exoplanet 
frequency requires a minimum number of planet detec- 
tions. 

Of particular interest are planets with mass less 
than that of the Earth. Microlensing is the only tech- 
nique available to detect planets as small as the mass 
of Mars, which are thought to be the largest bodies that 
can be formed by rapid growth of planetary “embryos”. 
We therefore define: 

Exoplanet Survey Requirement #1: Planet detection 
capability to ~0.1 Earth Mass 

The primary strength of WFIRST’s exoplanet sur- 
vey is the ability to survey a broad region of parameter 
space inaccessible to other techniques or ground- 
based microlensing surveys, and thus there are a large 
number of specific questions that we seek to address 
with the mission products. Fortunately, for most re- 
gions of planet discovery space, the number of detec- 
tions scale self-similarly, such that the ratios of the 
number of detections in different regions remain ap- 
proximately constant (Bennett & Rhie 2002). Thus we 
can specify the minimum number of detections at one 
fiducial set of values of the exoplanet parameters to 
quantify the primary measurement requirement. With 
this in mind, we define: 

Exoplanet Survey Requirement #2a: If every star 
has a planet with a mass of 1 Earth mass and an 
orbital period of 2 years, detect (at a > 160) at 
least 120 of them. 

Here Ax^ is the difference between the of the model 
fit with and without a planet, and the minimum value of 

A-2 


WFIRST 


160 is set by the requirement to detect and characterize 
the planetary perturbation, calibrated from experience 
with ground-based microlensing planet detections. 

Figure 5 shows the WFIRST exoplanet discovery 
potential when this requirement is saturated. In particu- 
lar, WFIRST is sensitive to analogs to every planet in 
our solar system, except for Mercury, clearly demon- 
strating both its broad discovery space, as well as the 
ability to address the question of whether or not our so- 
lar system is unique. When the survey requirements 
above are met, WFIRST will measure the mass function 
of planets with mass >0.1Me and separations in the 
range of 1.5-5 AU with a resolution of 0.2 dex in mass 
and a precision of <10% per mass bin. Determining the 
planetary mass function down to a tenth the mass of 
the Earth will uniquely allow WFIRST to probe the phys- 
ics of the assembly of terrestrial, ice, and gas-giant pla- 
nets. 

Owing to its continuous coverage and high photo- 
metric precision, the overwhelming majority of the pla- 
netary perturbations detected at > 160 by WFIRST 
will yield measurements of the planetary mass ratios 
and projected separations in units of Re at precision of 
<20%. However, measuring host star masses and dis- 
tances, and thus planet masses and separations in 
physical units requires additional measurements, which 
will only be possible for a subset of the detections. 
These measurements place quite different require- 
ments on the survey data. In particular, as mentioned 
above, for most events high-resolution (<0.3”) imaging 
is needed to detect and unambiguously identify the light 
from the host star, which allows for a measurement of 
its mass and distance. Therefore, to ensure that 
Science Requirement B is met we define: 

Exoplanet Survey Requirement #2b: Measure planet 
masses to 20% accuracy for at least 80 planet 
events with mass of 1 Earth mass and a period of 2 
years, assuming one such planet per star. 

Generally, the number of detections of habitable 
planets does not scale simply with the number of detec- 
tions for the fiducial set of values above. This is be- 
cause habitable planets typically perturb demagnified 
images, resulting in smaller amplitude deviations whose 
detectability is more sensitive to the photometric preci- 
sion and the angular source size. Therefore, to ensure 
that Science Requirement C is met, we define: 


Appendix A: Exoplanet Science Goals & Requirements 


Exoplanet Survey Requirement #3: If every F, G, 
and K star has a hahitahle planet, detect (at a > 
50) at least 25 of them. 

When this requirement is met, we can measure the 
frequency of habitable planets, //e, to a precision of 
-20% 770 -i' 2 . This is comparable to the expected preci- 
sion obtained by Kepler assuming an extended mission 
(Lunine et al. 2008). Habitable planets are detected 
with a lower threshold than the other planets be- 
cause they can only be found orbiting relatively bright 
stars, and this means that the lens-source relative 
proper motion can be detected directly from the images. 
This enables an estimation of the angular source size, 
which would otherwise be degenerate with the mass 
ratio in such low signal-to-noise ratio planetary devia- 
tions, and so could prevent characterization of the pla- 
net. 

The number of detections of free-floating low-mass 
planets also may not scale simply with the number of 
detections for the fiducial set of values above. This is 
because the robust detection of a free-floating planetary 
event requires a higher detection threshold than for a 
planetary deviation associated with a stellar microlens- 
ing event, since a much larger number of stars must be 
searched for these events, therefore increasing the 
probability of false positives. These high detection 
thresholds also increase the sensitivity to the photome- 
tric noise and the finite size of the source stars. There- 
fore, to ensure that WFIRST will detect free-floating 
planets as well as bound planets, we define: 

Exoplanet Survey Requirement #4; If there is one 
free floating Earth-mass planet per star in the Ga- 
laxy, detect (at a > 300) at least 30 of them. 

The detection of free-floating planets requires a 
higher A^;^ threshold than is needed for planets de- 
tected with a host star because -lO^ light curves must 
be searched for free-floating planetary events, whereas 
we expect only a few xlO'* stellar microlensing events 
to be searched for the signals of bound planets. 

A.4. Exoplanet Data Requirements 

Microlensing events require extremely precise 
alignments between a foreground lens star and a back- 
ground source star, and are both rare and unpredicta- 
ble. Furthermore, the probability that a planet orbiting 
the lens star in any given microlensing event will give 
rise to a detectable perturbation is generally much 


A-3 


WFIRST 


smaller than unity, ranging from a few tens of percent 
for a Jupiter-mass planet and a typical low- 
magnification event, to less than a percent for planets 
with mass less than that of the Earth. These planetary 
perturbations have amplitudes ranging from a few per- 
cent for the lowest-mass planets to many tens of per- 
cent for the largest perturbations, but are brief, ranging 
from a few days for Jupiter-mass planets to a few hours 
for Earth-mass planets. Also, the time of the perturba- 
tions with respect to the peak of the primary event are 
also unpredictable. Thus detecting a large number of 
exoplanets with microlensing requires monitoring of a 
very large number of stars continuously with relatively 
short cadences and good photometric precisions of 
~1%. Practically, a sufficiently high density of source 
and lens stars, and thus a sufficiently high microlensing 
event rate, is only achieved in lines of sight towards the 
Galactic bulge. However, these fields are also 

crowded, and this high star density means that high 
resolution is needed to resolve out the individual stars 
in order to achieve the required photometric precisions 
and to identify the light from the lens stars. 

Because the source star density and event rate are 
strong functions of Galactic coordinates, and the detec- 
tion probability of a planet with a given set of properties 
depends sensitively on the detailed properties of the 
event (host star mass and distance, event duration, an- 
gular source size, photometric precision, cadence), 
quantitative predictions for the yields of given realiza- 
tion of exoplanet survey dataset require sophisticated 
simulations that incorporate models for the Galactic dis- 
tribution of lenses and sources to simulate and evaluate 
the detectability of events with realistic photometric pre- 
cision. Such simulations for the WFIRST mission have 
been performed and are described below, updated from 
the simulations of Bennett & Rhie (2002). The planet 
yields from these simulations were ultimately used to 
determine the set of exoplanet survey data require- 
ments necessary to meet the four measurement re- 
quirements listed above. The resulting survey data re- 
quirements are as follows: 

Exoplanet Data Requirements: 

• Monitor 2 square degrees in the Galactic bulge 
for a total of 500 days. 

• Signal-to-noise ratio of >100 per exposure for a J 
= 20.5 star 

• Photometric sampling cadence of 15 minutes or 
better. 


Appendix A: Exoplanet Science Goals & Requirements 


• Better than 0.3" angular resolution to resolve the 
brightest main sequence stars 

• Monitor microlensing events continuously with a 
duty cycle of >95% for at least 60 days to 
measure basic light curve parameters. 

• Measurements in a second filter every 12 hours 
in order to measure the color of the microlensing 
source stars. 

• Separation of >4 years between first and second 
observing seasons to measure lens-source 
relative proper motion. 

We can roughly understand the order of magnitude 
of these requirements. Consider the primary mea- 
surement requirement #2a: If every star has a planet 
with a mass of 1 Earth mass and a period of 2 years, 
detect (at a Ax^ > 160) at least 120 of them. The typi- 
cal detection probability for a planet with iWp=iW® and 
P=2 yrs is -0.5%, and thus -100/0.005 = 2x10'* micro- 
lensing events must be monitored to detect -100 such 
planets. The microlensing event rate in the highest 
density fields accessible by WFIRST is -2x10-5 
events/year, and thus 2xl0'*/2xl0-5-l billion star-years 
must be monitored. The typical stellar density down to 
J=23 is -1085 stars per square degree, and thus at 
least -2 square degrees must be monitored. In order to 
detect, fully sample, and accurately characterize the 
perturbations due to such planets, which typically last a 
few hours and have amplitudes of several percent, pho- 
tometric precisions of <1% and cadences of better than 
15 minutes are needed. Finally, given the areal densi- 
ty of -108 stars per square degree, an angular resolu- 
tion of lO "* degrees or 0.3” arcseconds is needed to re- 
solve the faintest stars. The remaining three require- 
ments above ensure the ability to accurately measure 
the parameters of the primary events, which typically 
last -40 days, and allow one to infer the angular size of 
the source star from its color and magnitude, separate 
the light from the lens and source, and measure the 
relative lens-source proper motion, all three of which 
are required to measure the mass and distance to the 
primary lens (and thus measure the mass and separa- 
tion of the detected planets) for the majority of events. 

These data requirements then provide the con- 
straints within which hardware and operations concept 
designs must operate. 


A-4 


WFIRST 


Appendix B Dark Energy Science Goals & Re- 
quirements 

B.l. Baryon Acoustic Oscillation/Redshift Space 
Distortion Requirements 

The principal requirement for the BAO/RSD pro- 
gram is the measurement of 3D positions 
(RA/Dec/redshift) for a large sample of galaxies with a 
characterizable selection function. Overall one desires 
to do this over a wide range of cosmic history; we re- 
quire observations in the 0.7<z<2 range for WFIRST 
because the lower redshifts can be obtained efficiently 
from the ground. 

Ideally the survey would cover the entire extraga- 
lactic sky (28,000 deg^), and achieve a galaxy density 
that reaches the sample variance limit out to mildly non- 
linear scales (nP > 1 at all redshifts and k~0.2 h/Mpc). 
This is not feasible within programmatic constraints 
(which limit the size of the telescope and detector and 
the available time for BAO/RSD surveys) and so we 
have attempted to come as close as possible. In partic- 
ular, this led to the split of the BAO/RSD survey into a 
DEEP survey (acquired, as a goal only, as a by-product 
of the WL galaxy shape survey) that samples the entire 
redshift range well (reaching nP>l out to z=1.85) and a 
WIDE mode that covers much more of the sky - 11,000 
deg2/yr - but only reaches the sampling variance limit 
at low k. 

The 3D measured positions of galaxies need only 
be accurate enough not to cause significant degrada- 
tion of the large-scale structure measurement at mildly 
nonlinear scales; for Gaussian errors the loss of S/N 
per mode is exp{-kWI2). Thus one needs to know po- 
sitions to an accuracy of better than 1/k. The transverse 
requirement is trivially met, but the radial (redshift) 
measurement requirement is not. We have therefore 
set a redshift error requirement of 300 km/s rms, which 
corresponds to a radial error of 3. 2-3.5 Mpc/h (depend- 
ing on z). The degradation of S/N per mode is 20% at kn 
= 0.2 h/Mpc. 

Misidentified lines have two major effects on the 
power spectrum: there is a suppression of the power 
spectrum due to introduction of a smoothly distributed 
component (proportional to the contamination fraction 
s), and an additional source of power associated with 
clustering of the contaminants (proportional to s^). In 
order to keep the degradation of the signal small we 
require the total misidentification fraction to be Is<0.1 
(TBR). We have to remove the clustering of contami- 
nants from the true signal and hence we need the total 


Appendix B: Dark Energy Science Goals & Requirements 


amount of such power (proportional to Is^) to be small 
enough that there is no significant systematic error after 
it is subtracted. This flows down to a requirement on the 
misidentification fraction per contaminant (TBD). The 
requirement on knowledge of the fraction of misidenti- 
fied lines is driven by the RSD: the ~s suppression of 
power has no effect on the BAG signal but biases the 
RSD measurement by a factor of 1-Is. Therefore the 
RSD drives the requirement on Is to be known to 0.2% 
(TBR). 

The detailed requirements on the BAO/RSD survey 
are as follows (DEEP mode is computed at ecliptic lati- 
tude 45° and WIDE is at 35°; all fluxes are extinction- 
corrected at E(B-V)=0.1 and Rv=3.1): 

• > 11,000 deg2 sky coverage per dedicated 
year (“WIDE” Survey mode) 

• Goal of > 2,700 deg^/yr “DEEP” Survey ac- 
quired during the WL Survey 

• A comoving density of galaxy redshifts at z=2 
of 4.9x10-5 Mpc-3 (WIDE) or 2.1x10-4 Mpc-^ 
(DEEP). [The source density is higher at low- 
er redshifts, peaking at z=l at 2.2x10-4 |y|pQ-3 
(WIDE) or 5.9x10-4 Mpc-3 (DEEP)] 

• Redshift range 0.7 < z < 2 

• Redshift errors Oz s O.OOl(l-rz), equivalent to 
300 km/s rms 

• Misidentified lines < TBD% per source type, 
< 10% overall; contamination fractions known 
to 0.2% (TBR) 

The implementation choice for the BAO/RSD was 
driven by several considerations. A slitless prism ap- 
proach was selected for the spectroscopy as it elimi- 
nates 0*5 order features that otherwise resemble emis- 
sion lines (thus simplifying data processing), and max- 
imizes S/N by putting all transmitted light in 1=* order. 
(Since the SpC is sky-limited, the required exposure 
time degrades by 2X% if X% of the light is in an unde- 
sired order.) The bandpass covers the bright Ha line 
across the redshift 0.7-2.0 range. Since the galaxy red- 
shift survey requires only a detection and not the mor- 
phology of the emitting region, there is no requirement 
to recover full sampling. At fixed detector count it is ad- 
vantageous to reduce the SpC f/ratio relative to the ImC 
so that a galaxy occupies only a few pixels per expo- 
sure. 

At a spectral dispersion R© « 200 arcsec, the red- 
shift accuracy of 300 km/s rms corresponds to a re- 
quirement to centroid the emission line to 0.4 pixels rms 
(including the raw centroiding of the emission line, addi- 


B-1 


WFIRST 


tional issues such as astrometric uncertainties and [Nil] 
or continuum blending, and the mapping from line posi- 
tion to wavelength). This dispersion also supports the 
splitting of the [ONI] doublet (2900 km/s or 4.3 pixels), 
which both reduces the raw contamination fraction (by 
reducing the S/N for [ONI] detections) and makes [ONI] 
directly identifiable if the S/N is high enough to support 
marginal detection of the weaker doublet member. This 
dispersion does not split [Nil] from Ha: the splitting of 
Ha from the stronger [Nil] feature is 900 km/s (1.3 pix- 
els). Such splitting would not be desirable since it would 
reduce the S/N for the combined line detection. (Note, 
however, that our galaxy yields do not assume any [Nil] 
contribution - we have treated it as margin.) 

Oppositely dispersed spectra are advantageous in 
order to disentangle the astrometric center of Ha emis- 
sion from the redshift (otherwise the former becomes 
an irreducible source of noise for the latter). WFIRST 
has considered both options that provide a single dis- 
persion direction in hardware (with the other direction 
acquired 6 months later by rolling the satellite) and op- 
tions that provide both directions near-simultaneously 
(as did JDEM-Omega). Both appear to be viable but the 
dual dispersion provides a greater range of tiling op- 
tions. 

The ImC is used to provide positions of candidate 
galaxies, and to provide the location of the bandpass 
window relative to each emission line (for redshift zero 
reference). 

Variations in the selection function are the principal 
systematic challenge for the galaxy clustering program. 
For WFIRST, these include zodiacal light brightness 
variations. Galactic dust, photometric calibration drifts, 
stellar density, and variations of the SpC PSF across 
the fields of view. Repeated visits to calibration fields 
(e.g. the supernova fields) will track secular changes in 
the photometric calibration as a function of time. The 
sky brightness and stellar density variations are critical 
for WFIRST as they vary by factors of a few over the 
survey area. However, these are effects that can be 
simulated by operations on the actual data (e.g. by add- 
ing sky photons or stellar traces to an image and then 
re-processing it); and so we expect that the associated 
selection function effects will be very well known. More- 
over, even if one did not know the amplitudes of these 
effects, most of their power is in unique patterns on the 
sky (low-multipole modes and features associated with 
the tiling) that are very different from the modes used 
for BAO/RSD, and so removing them via template pro- 
jection provides a backup option. 


Appendix B: Dark Energy Science Goals & Requirements 


Deeper spectroscopic measurements of a small 
subset of the galaxies will be required to measure con- 
tamination fractions. This requirement will be met using 
some combination of tile overlaps, the SN fields, and 
the ground assets used for WL-PZCS observations. 

The BAO/RSD data set requirements are: 

• Spectrometer 

• Slitless prism 

• Dispersion R@ = 195 (TBR) - 240 arcsec 

• S/N > 7 for reff = 300 mas for Ha emission 
line flux at 2.0 |am > 1.5x10-1® erg/cm^-s 
(DEEP) or 3.1x10-1® erg/cm^-s (WIDE) 

• Bandpass 1.116 <?L< 2.0 pim 

• Pixel scale < 450 mas 

• System PSF EE50% radius 400 mas at 2 pim 

• > 3 dispersion directions required, two nearly 
opposed 

• Imager (for redshift zero reference) 

• S/N >10 for HabS 23.5 

• Approximately equal time in filters F141 and 
F178 

B.2. Supernova Requirements 

The supernova technique relies on Type la super- 
novae as distance indicators to measure the expansion 
history of the universe and thus yield information about 
the acceleration of the expansion of the universe and 
the nature of dark energy. Type la’s have an intrinsic 
luminosity spread of around 50%, but can be calibrated 
using the shapes of their lightcurves to between 12 and 
18%, thus providing a measurement of their distances 
to between 6 and 9%. The low end of this range is 
achieved by observations in the infrared for the lower 
redshift supernovae, providing a distinct advantage to 
observations from space, and by other methods using 
spectral features at the higher redshifts. It is expected 
that by the time WFIRST data becomes available, the 
distance precision will be further improved by methods 
using other information, such as spectral features. A 
plot of the calibrated observed luminosity of each su- 
pernova versus its redshift, which we call the Hubble 
diagram, yields the cosmological information. 

The requirements of the supernova technique can 
be divided into four categories, all carried out by the 
WFIRST supernova survey: 

1. Discovery of the supernovae. This is done by 
the WFIRST imager by observing the same 
area of sky with a 5 day cadence and carrying 


B-2 


WFIRST 


out a pixel by pixel subtraction of previous ref- 
erence images from each new observation. 

2. Selection of the Type la ‘s. Typically one third 
to one half of the candidates discovered by the 
imager are good Type la ‘s discovered before 
peak luminosity. The selection of the la’s is 
done by taking a spectrum of each candidate 
using the prism P130 in the ImC filter wheel. 

3. Redshift measurement is obtained from the 
spectra. A final reference spectrum will be 
taken after the supernova has faded away, us- 
ing the narrow lines of the host galaxy for an 
accurate redshift measurement. The final ref- 
erence spectrum will also be used to improve 
the galaxy background subtraction from the 
supernova spectra. 

4. The peak luminosity of each supernova is ob- 
tained from the lightcurves provided by the re- 
peated 5 day cadence images from the 
WFIRST imager. 

The precision of the WFIRST supernova data will 
be further improved by making use of a large, carefully 
calibrated data set of nearby (z<0.1) supernovae ob- 
tained from presently ongoing ground based nearby 
supernova surveys. These nearby surveys are best 
done from the ground since WFIRST will not be able to 
collect a significant number of supernovae below z=0.1 
due to the volume effect. In the estimation of the Fig- 
ures of Merit, a sample of 500 nearby supernovae, as 
projected by the FoMSWG Panel, was used, although 
the expectation is that a larger sample will be available 
by the time WFIRST flies. 

The detailed requirements on the survey capabili- 
ties and the data set are as follows: 

Survey Capability Requirements. 

• >100 SNe-la per Az=0.1 bin for most bins for 
0.4 < z < 1.2, per dedicated 6 months 

• Redshift error a < 0.005 per supernova 

• Relative instrumental bias< 0.005 on photo- 
metric calibration across the wavelength range 

• Distance modulus error (from lightcurve) < 
0.02 per Az=0.1 bin 

Data Set Reqirements 

• Minimum monitoring time-span for an individu- 
al field: ~2 years with a sampling cadence< 5 
days 

• Cross filter color calibration < 0.005 


Appendix B: Dark Energy Science Goals & Requirements 


• Four filters: F087, Fill, F141, F178 

• Slitless prism spec (P130) 0.6-2 |am, XIKK 
~75 (S/N > 2 per pixel bin) for redshift/typing 

• Peak lightcurve S/N > 15 at each redshift 

• Dither with 15 (TBR) mas accuracy 

• Low Galactic dust, E(B-V) < 0.02 

B.3. Weak Lensing Requirements 

The weak lensing technique uses the shear of dis- 
tant galaxies by gravitational lensing, which is deter- 
mined by an integral of the tidal field along the line of 
sight to the source galaxy. The strength of the lensing 
signal as a function of the redshift of source galaxies is 
sensitive to both the growth of cosmic structure at inter- 
vening redshifts 0<z<Zsource, and to the distance-redshift 
relation (since the same amount of mass produces 
more shear on more distant sources). The correlation of 
lensing shear with foreground galaxies of known red- 
shift Zfg probes the relation of these galaxies to the mat- 
ter field and in combination with RSD allows direct con- 
sistency tests of general relativity (e.g. Reyes et al. 
2010). Finally the dependence of the cross-correlation 
signal with the redshift of the source galaxies isolates 
the purely geometrical information from weak lensing 
from the information about perturbations (Jain & Taylor 
2003). 

A weak lensing survey must provide wide angle 
sky coverage, a high density of usable sources across 
a wide redshift range (local to z~2), provide photometric 
redshifts so that the galaxies can be sliced into bins to 
study evolution of the signal and remove “intrinsic” (not 
lensing induced) shape correlations, and achieve ex- 
quisite control over coherent systematic errors in the 
shear signal. The latter includes both “additive” shear 
errors, i.e. apparent shear due to imperfect correction 
for instrument effects (aberrations, anisotropic jitter, 
geometric distortions, etc.) that is not present in the sky; 
and “multiplicative” shear errors where the calibration of 
the observed shear is incorrect. Some sources of error 
(e.g. failure to recover full sampling) can lead to both 
additive and multiplicative errors. 

The detailed requirements on the weak lensing 
survey are as follows: 

• > 2,700 deg2 sky coverage per dedicated year 
(in “DEEP” Survey mode) 

• Effective galaxy density > 30 per arcmin^, 
shapes resolved plus photo-z’s 

• Additive shear error < OxlO '* 

• Multiplicative shear error < IxlO-^ 


B-3 


WFIRST 


• Photo-z error distribution < 0.04(l+z), error 
rate <2% 

• Goal is for the WL Galaxy Shape Survey to be 
taken in a manner such that concurrent spec- 
troscopy also meets the BAG survey require- 
ments on source density, redshift errors and 
fraction of misidentified lines. 

Control over systematic errors in the shear mea- 
surement implies several requirements on the data set, 
in the areas of (i) knowledge of the PSF; (ii) multicolor 
imaging; and (iii) sampling. 

The PSF ellipticity must be known in order to en- 
sure to meet the additive shear error requirement, and 
the PSF second moment (Ixx + lyy) must be known in 
order to meet the multiplicative shear error requirement. 
The data set requirements on PSF knowledge were 
calculated to use 50% (in a root-sum-square sense) of 
the shape measurement error budget (which also in- 
cludes other terms, such as residuals from the data 
processing algorithms and detector effects). In setting 
this requirement, we conservatively assume no decor- 
relation (or “averaging down”) of systematic shear er- 
rors in the 10 exposures used to measure shapes. 

The PSF of any telescope will be color-dependent; 
for WFIRST diffraction will dominate this effect. In order 
to solve it, it is required to know the intraband color var- 
iations of the galaxies and hence fully-sampled imaging 
is required in two filters. 

We also require a sufficient number of dithered ex- 
posures to recover full sampling of the sky image out to 
the band limit set by the optics (D/A). This imposes a 
joint requirement in the space of number of dither posi- 
tions, the dither pattern (ideal vs random), and the 
f/ratio. Given other pressures on WFIRST, we chose to 
implement the shape measurement in the two reddest 
filters (F141 and F178) where the sampling require- 
ments are easiest to meet. Simulations show that 4-5 
random dithers are sufficient (Rowe et al. 2011). Fill 
is strongly undersampled at 0.18”/pix and implementing 
full sampling would have required more dithers or a 
higher f/ratio, either of which would negatively impact 
the survey speed. 

A further advantage of this choice is that due to the 
red spectral shapes of the source galaxies the S/N is 
greater for a redder filter. The principal disadvantage is 
the larger PSF; however the quadrupole moments (e.g. 
Ixx-lyy) of the PSF induced by a given wavefront error 
depend only very weakly on wavelength. 

The photometric redshifts require multi-filter imag- 
ing with coverage across the optical and NIR bands. 


Appendix B: Dark Energy Science Goals & Requirements 


This implies the need for ground-based imaging in griz 
or a similar filter set. It also implies the need for imaging 
in the WFIRST Fill filter to bridge the gap between 
the ground optical filters and WFIRST F141 in order to 
provide photo-z’s for objects whose Balmer or 4000A 
features are in or near this gap (roughly 1.3<z<2.0). 

Finally, the photo-z error distribution needs to be 
calibrated against spectroscopic redshifts for a repre- 
sentative sample of the WL source galaxies. The sam- 
ple should contain > 10^ galaxies (Bernstein & Huterer 
2010) spread over several fields observable from 
WFIRST, the ground-based telescopes that provide 
optical photometry, and any assets needed to complete 
the spectroscopic survey. Bright emission line searches 
(using NIR slitless spectroscopy from WFIRST and an 
optical multi-fiber spectrograph such as proposed for 
low-z BAG on the ground) would likely measure a ro- 
bust redshift for -50% of the source galaxies, with the 
remainder to be done via deeper spectroscopy. The 
detailed trade of how much of the program to do from 
WFIRST before switching to sensitive ground spectro- 
graphs with lower multiplex factors must await deci- 
sions about which ground spectrographs will exist by 
the time WFIRST flies. We have provisionally allocated 
time for WFIRST to cover 5 fields using one arm of the 
SpC to a depth of 3xl0-i^ erg/cm^/s (7a). These fields 
would be at ±20° ecliptic latitude, accessible from 
ground assets either hemisphere. 

In summary, the WL data set requirements are: 

• From Space: 2 shape/color filters, F141 and 
F178, and one color filter. Fill 

• S/N > 18 per shape/color filter for galaxy reft = 
250 mas and mag AB = 23.7 

• PSF second moment (U + lyy) known to a rela- 
tive error of < 9.3x10 '* rms (shape/color filters 
only) 

• PSF ellipticity (Ixx-lyy, 2lxy)/(lxx + lyy) known to < 
4.7x10 '* rms (shape/color filters only) 

• System PSF EE50 radius < 170 mas for filter 
F141, and < 193 mas for filter F178 

• 5 random dithers required for shape/color 
bands and 4 for Fill at same dither exposure 
time 

• From Ground: 4 color filter bands -0.4 < A < 
-0.97|am 

• Complete an unbiased spectroscopic PZCS 
training data set containing > 100,000 galaxies 
with < mag AB = 23.7 for F141 and F178 and 
covering at least 4 uncorrelated fields; redshift 
accuracy required is az<0.01(l-rzj 


B-4 


WFIRST 


Appendix C Shortcomings of and Alternatives to 
the Dark Energy Task Force Figure 
of Merit 

The idea that the performance of a dark energy 
experiment can be boiled down to a couple of numbers 
is overly simplistic. There was considerable discussion 
within the SDT of the shortcomings of the DETF FoM, 
and whether they were so severe as to negate any 
benefit there might be in adopting it. Not everyone 
agreed to its adoption. The shortcomings are spelled 
out here in the interest of representing the range of opi- 
nions held by the members of the SDT. 

• Potential models to be tested are so varied and 
unconstrained that the simple specific DETF model 
form (with its two parameters and linear transition) 
is not generally representative of the full suite of 
potential models. Quoting from the JDEM Figure 
of Merit Science Working Group (FoMSWGj, “The 
FoMSWG finds that there is no singie number that 
can describe the scientific reach of a JDEM.” 

• Figures of merit estimates depend on an accurate 
assessment of the quality of the experimental data 
and associated systematic errors, in many cases 
years before the experiment is even fully defined. 
Figures of merit only reflect the information pro- 
vided so the result is dependent on the accuracy of 
the projected data quality. In particular, systematic 
errors and the performance of instruments play 
central roles. 

• Astrophysical systematic errors must be estimated. 
There can be (and often are) reasonable differenc- 
es of opinion between scientists on how to quantify 
these uncertainties, and it is likely that these esti- 
mates will change with time, understanding, and 
new measurements. These changes could be for 
the better, but also could be for the worse as new 
complexity is discovered. 

• The wide-ranging auxiliary science that could come 
from the survey is given no credit. 

• Prior astrophysical knowledge must be appro- 
priately assumed, but projections of that knowledge 
are both uncertain and changeable as the field 
continues to evolve. As the FoMSWG wrote, “Dark 
energy remains a compeliing astrophysical ques- 
tion (perhaps the most compelling) and the creativi- 


ty and imagination of astronomers and physicists 
will continue to be directed toward investigations 
into the nature of dark energy. Predictions of what 
will be known about dark energy, or what will be 
known about systematic uncertainties associated 
with dark energy measurements, eight years in the 
future are inherently unreliable.” 

• The FoM formalism does not properly reward the 
cross checks on consistency enabled by perform- 
ing multiple measurements of different observables 
with very different systematics that probe the same 
aspects of dark energy (e.g. measuring the expan- 
sion history with both BAG and SN). 

• Redundancy in the data set (e.g. measuring more 
degrees of freedom in a detector than exist on the 
sky) and internal checks within a given technique 
are often the keys to reducing systematic errors. 
This level of detail is generally not present in pa- 
rameteric FoM optimization studies, and conse- 
quently such tests should be considered a factor 
outside the FoM. 

The DETF figure of merit is strongly model- 
dependent, so it provides a test of experiments against 
an assumed form of dark energy evolution, whereas the 
very core of the measurement objective is to test for 
non-standard forms. An improved figure of merit would 
effectively test the ability of experiments to constrain 
the function w(z). This was the motivation for the JDEM 
FoMSWG to define a figure of merit with 36 uncorre- 
lated redshift bins of piecewise continuous parts to 
represent the function w[z). 

A central flaw of the DETF figure of merit for our 
purposes is easily seen by noting that excellent mea- 
surements at only two redshifts purport to determine the 
entire evolution of dark energy over all of cosmic time. 
Additional measurements are rendered irrelevant in this 
framework. The great bulk of dark energy measure- 
ments to date have been made at redshifts z<l so the 
standard figure of merit devalues high redshift mea- 
surements. 

Experiments do not directly measure w(z). Super- 
nova measurements provide a luminosity distance, 
Di(z) (either assuming a value for space curvature, or 
marginalizing over the uncertainty). Baryon Acoustic 
Oscillations provide the angular diameter distance, 
Df{z) as well as the Hubble expansion rate H(z). The 
luminosity distance and angular diameter distance are 
related by Dl = Da(z) (1+z)^ and both the luminosity and 


Appendix C: Shortcomings of and Alternatives to the Dark Energy Task Force Figure of Merit 


C-1 


WFIRST 


angular diameter distances are integrals over the in- 
verse of H(z). The weak gravitational leasing technique 
effectively measures the three-dimensional distribution 
of matter in the universe, from which one can derive the 
evolutionary properties of the universe. 

The measurement techniques all have potential 
systematic effects. These can be entered into the 
Fisher matrix machinery of the figure of merit calcula- 
tions, but this must be done by hand. The machinery 
does not add value, but only reflects the information 
supplied to it. For this reason, and due to the sensitivity 
of the results to the priors and systematic error models, 
it is common for different scientists to arrive at very dif- 
ferent figure of merit vaiues when attempting to calcu- 
iate the power of identicai experiments. 

Due to the reliance on priors, the figures of merit 
are also time-sensitive. As the JDEM FoMSWG wrote, 
“However, we would like to make the important point 
that although considerable effort went into constructing 
the Fisher matrices, they should be used with caution, 
since any data model purporting to represent the state 
of knowledge eight years in the future is highly sus- 
pect." (Joint Dark Energy Mission Figure of Merit 
Science Working Group, Dec 7, 2008). 

In the end, the figure of merit has provided impor- 
tant general lessons on the dependencies and interde- 
pendencies of different methods. Beyond that, it is not 
at all helpful when designing an instrument for minimum 
systematic errors or in estimating the values of those 
systematic errors. It does not replace the need to cal- 
culate, simulate, and innovate. It does not even allow 
for the cross-comparison with different experiments us- 
ing the same “technique” (e.g. SN, WL, or BAG) unless 
the exact same priors, exact same systematic error es- 
timates (or basis for such estimates), the exact same 
astrophysical systematics, and the exact same statistics 
(e.g. emission line luminosity functions or SN la rates) 
are agreed upon. 

Figure of merit calculations for WFIRST alone cov- 
er an enormous range, depending on assumptions 
made about the inclusion or exclusion of various tech- 
niques, the level of systematic errors, and observing 
time allocations. It is important to recognize that the 
figure of merit responds to these inputs and does not 
create new information, so the substantial uncertainties 
in the figure of merit based on the choice of input as- 
sumptions render it less than useful. 

It is a major strength of the WFIRST approach that 
the mission is designed with the capability to execute a 
wide range of possible programs, so that progress in 
dark energy research in the coming decade can influ- 


ence the balance of the observations to be performed. 
In this manner, the WFIRST program can adapt to 
ground-based progress, numerical simulation progress, 
new modeling capabilities and insights, and any other 
knowledge that enhances or casts doubt on various as- 
pects of the program. The WFIRST SDT does not pre- 
tend to have the insight to maximize the dark energy 
impact of the mission from today’s perspective other 
than to design and build in capabilities and to minimize 
instrumental systematic errors. Rather, the SDT opts to 
maximize WFIRST’s dark energy accomplishments at 
launch and even after initial data are captured and ana- 
lyzed. This adaptive approach guarantees a powerful 
dark energy program that is complementary with inter- 
vening dark energy measurements and accomplish- 
ments, whatever they may be. 


Appendix C: Shortcomings of and Alternatives to the Dark Energy Task Force Figure of Merit 


C-2 


WFIRST 


Appendix D WFIRST in the Context of Other Mis- 
sions and Projects 

WFIRST will launch seven years from the begin- 
ning of a new start. We must consider the astronomical 
context in which WFIRST might be operating 7-12 
years hence. At least some of the astronomical ques- 
tions that WFIRST will address might also be ad- 
dressed by another space mission (in particular ESA's 
Euclid) and by ground-based programs (in particular 
DES and LSST for weak leasing and BigBOSS for 
BAO). In this appendix, we briefly consider the extent 
to which these missions might or might not pre-empt 
one or another part of the WFIRST dark energy science 
program. 

It is the great strength of the WFIRST mission that 
it will carry out many different science programs. It was 
precisely for this reason that it ranked more highly than 
more narrowly focused missions in the decadal survey. 
Were one or another piece of the WFIRST program 
were to be pre-empted, more time might be devoted to 
other equally important parts of its program. 

D.l. Weak Leasing 

WFIRST would carry out weak leasing observa- 
tions at the "deep" rate of 2,700 square degrees per 
year. Our straw man allocation devotes one year to this 
mode, not taking possible results from DES, LSST and 
Euclid into account. 

LSST is expected to produce 15,000 square de- 
grees of weak leasing data. Despite the overlap be- 
tween LSST and WFIRST, the decadal survey recom- 
mended LSST as its highest priority ground-based pro- 
gram and WFIRST as its highest priority space mission. 
Weak leasing can constrain both dark energy and alter- 
native theories of gravity, making it especially impor- 
tant. But for weak leasing to constrain dark energy or 
modified gravity, there must be a factor of ten improve- 
ment in accuracy over present day measurements. The 
thermal stability of a space telescope, the absence of 
gravitational stresses, and most importantly, the ab- 
sence of an atmosphere with constantly changing "op- 
tics" makes space the natural place from which to carry 
out weak leasing. 

The LSST PSF will have contributions from tele- 
scope jitter, telescope optics and detector effects, as 
will WFIRST, but in addition will suffer from much larger 
changes in thermal and gravitational stresses, and 
largest yet, contributions from atmospheric seeing. The 
hope for LSST is that these much larger variations can 
be averaged out by observing each field a few hundred 


times. As is shown below, if LSST does as well as is 
hoped, it might do as well as the WFIRST weak leasing 
program. But if not, WFIRST will be positioned to carry 
out a strong program. WFIRST's shape measurements 
would in any event be subject to different instrumental 
systematic errors and, since they are to be carried out 
at longer wavelengths, somewhat different astronomical 
systematics. 

The Euclid mission, a candidate for selection as an 
ESA M-class mission, would carry out weak leasing ob- 
servations of 15,000 square degrees at optical wave- 
lengths (like LSST and unlike WFIRST) over the course 
of a 5 year mission. There are reasons to prefer weak 
leasing observations in the infrared over those in the 
optical. Much more of the galaxy light is emitted in the 
infrared. Galaxies are also less misshapen in the infra- 
red. On the other hand, the diffraction limited PSF is 
bigger in the infrared than in the optical. 

One can therefore measure more galaxies per 
square arcminute in the optical than in the infrared if 
one has enough photons to do so. But if Euclid is to 
take full advantage of its smaller diffraction limit, it must 
satisfy more stringent jitter and optical aberration con- 
straints than the already demanding requirements for 
WFIRST. As is shown below, if Euclid does as well as 
is hoped, it might do a better job of weak leasing than 
WFIRST. But if not, WFIRST will again be positioned to 
carry out a strong program. And WFIRST's shape 
measurements would, again, be subject to different in- 
strumental systematic errors and, since they are to be 
carried out at longer wavelengths, somewhat different 
astronomical systematics. 

D.2. Baryon Acoustic Oscillations 

WFIRST will carry out baryon acoustic oscillation 
observations at the "wide" rate of 11,000 square de- 
grees per year, and also at the "deep" rate of 2,700 
square degrees per year, covering the redshift range 
0.7<z<2. 

The proposed Prime Focus Spectrograph on the 8- 
meter Subaru telescope would carry out a BAO survey 
at 0.7 < z < 1.5 over ~80 nights using the [ON] emission 
feature. The FoMSWG "Stage IN" forecasts already 
assume a survey (WFMOS) very similar to this one. 

The proposed BigBOSS survey (Schlegel et al. 
2011) would use the Mayall 4-m telescope on Kitt Peak 
to carry out BAO observations of galaxies at optical wa- 
velengths over -14,000 square degrees, covering the 
redshift range z < 1.7. It would also obtain observa- 
tions of quasar Lyman-alpha absorption lines in the 
range 2 < z < 3; this will provide a BAO measurement in 


Appendix D: WFIRST in the Context of Other Missions and Projects 


D-1 


WFIRST 


a complementary redshift range to WFIRST as well as 
a wealth of data on the intergalactic medium (IGM). 
(The Lyman alpha forest is also affected by redshift 
space distortion; however unlike for galaxies, there is 
no relation between the bias b, RSD amplitude beta, 
and growth rate f, so determination of the latter relies 
on accurate modeling of the IGM by hydrodynamic si- 
mulations. 

The WFIRST 1 year Deep -r 1 year Wide survey 
covers the same solid angle of sky as BigBOSS. The 
WFIRST Wide survey component achieves the same 
number density of galaxies (and nP) at z=l. BigBOSS 
performs better at lower redshift (in part because the 
BigBOSS luminous red galaxies are available, and 
these contribute more per object to nP than star forming 
galaxies), whereas WFIRST performs better at high 
redshift: by z=1.3 WFIRST -Wide is providing more than 
3 times the source density of BigBOSS. WFIRST -Deep 
provides a source density that is 3-4 times higher, albeit 
over only 2700 deg^'2. 

The Euclid mission under consideration by ESA 
would carry out BAO observations over 15,000 square 
degrees, covering the redshift range 0.7 < z < 1.6. By 
virtue of its smaller aperture and its less efficient spec- 
trometer (including the grism: transmitted 0**1 order light 
adds background but not signal), Euclid fares less well 
per unit time. But by investing more time into BAO, we 
show in Figure 15 that Euclid performs almost as well 
as WFIRST. 

D.3. Supernova 

By virtue of carrying out its supernova program in 
the infrared, WFIRST is likely to be superior to optical 
supernova programs. While LSST will doubtless identi- 
fy many supernovae, in the absence of a coherent pro- 
gram of spectroscopic followup we cannot assign any 
figure of merit to an LSST supernova effort. Additional- 
ly, neither Euclid nor BigBOSS are planning on a su- 
pernova program. 

D.4. Caveats Regarding Comparisons 

As we have emphasized often and at length, the 
accurate characterization of the accelerating expansion 
of the universe hinges critically on limiting sources of 
systematic error. For astronomical sources of syste- 
matic error, it is relatively straightforward to adopt con- 
sistent estimates for different projects. It is more diffi- 
cult to be consistent in estimating instrumental sources 
of systematic error. 

In some cases we can independently estimate 
these from the specifications for the instrument. In oth- 


er cases we must rely upon the numbers reported by 
the different project teams. 

This also applies to the sensitivities adopted. To 
the extent that different projects use different ap- 
proaches to estimating sensitivities, results may not be 
commensurable. Short of carrying out the detailed ana- 
lyses ourselves, we must again accept the numbers 
presented. 

D.5. Systematic Errors 

The systematic errors adopted for Euclid, LSST 
and BigBOSS are given in Table 3, Table 4, and Table 
5 in section 3. We have adopted the optimistic as- 
sumptions in all cases. The BAO figures of merit there- 
fore include both classical BAO measurements and 
redshift space distortion, but not measurement of the 
transition from radiation to matter domination. For 
LSST we have assumed an effective useful galaxy 
density of 20 per square arcminute. A more conserva- 
tive estimate, adopting the same RMS ellipticity re- 
quirement for LSST as for WFIRST and allowing for the 
larger LSST PSF would give 15 galaxies per square 
arcminute. 

D.6. Comparison 

Figure 16 shows 3 different Venn diagrams: one for 
the five year Euclid program, one for the combined pro- 
grams of LSST-rBigBOSS and one for our straw man 
2.5 year program for WFIRST. In each case Stage III 
priors have been assumed. 

D.7. Interpretation 

Restricting attention to the combination of weak 
lensing and baryon acoustic oscillations, Euclid and 
LSST-rBigBOSS, were they to perform as hoped, would 
produce better figures of merit than WFIRST. But with 
the addition of supernovae, WFIRST outperforms them 
both. Supernovae measure the equation of state pa- 
rameter, w, at low redshift, complementing the mea- 
surement of w at higher redshift by BAO and weak lens- 
ing. This leads to a dramatic improvement in the DETF 
FoM. 

D.8. Five Years of Dark Energy with WFIRST 

It might be fairer to compare Euclid's five year dark 
energy program with a five year WFIRST dark energy 
program. We have done that, by increasing the time 
allotted to each of the three methods of measuring dark 
energy (a 2.5 year deep survey, 1.5 year wide survey, 
and a 1 year supernovae survey), again using the opti- 
mistic assumptions. The DETF FoM improves for 
WFIRST improves from 1335 to 1770. As we have not 


Appendix D: WFIRST in the Context of Other Missions and Projects 


D-2 


WFIRST 


tried to optimize such a program one might do yet bet- 
ter by redistributing the observing time. Our purpose in 
carrying out this exercise is not to recommend that 
more time be allocated to dark energy at the expense of 
exoplanet microlensing and IR surveys, but rather to 
emphasize that WFIRST is very well suited to dark 
energy studies. 



Figure 15; The fractional error in the Hubble expansion 
rate, H(z), as a function of redshift, z, driven by the pre- 
cise measurement of the Baryon Acoustic Oscillation 
(BAO) scale in the spectroscopic galaxy redshift survey. 
The constraints for the proposed WFIRST 1 year deep + 
1 year wide survey, are shown alongside those for pros- 
pective Euclid and BigBOSS surveys. Each survey has 
been evaluated per the "optimistic" scenario outlined in 
3.4.7, using the same assumptions about systematic un- 
certainties, and using the stated galaxy yields or limiting 
fluxes estimated by that survey. WFIRST's capabilities in 
the IR allow it to achieve superior measurements at z>l, 
providing strong complementarity with ground based 
observations at z<l. 


Appendix D: WFIRST in the Context of Other Missions and Projects 


D-3 


WFIRST 


EUCLID Optimistic (5 yrs DE) 

+SN 


WFIRST Optimistic (2.5 yrs DE) 

+SN 


426 


+BAO 


1036 



(a) 


LSST WL+ BigBOSS BAO/RSD Optimistic 

+SN 



WFIRST Optimistic 
+SN 



(b) 

Figure 16: FoM comparisons of WFIRST with (a) Euclid and (b) LSST + BigBOSS 


Appendix D: WFIRST in the Context of Other Missions and Projects 


D-4 


WFIRST 


D.9. Exoplanet Microlensing 

The WFIRST Exoplanet survey will complete the 
statistical census of exoplanets begun by the Kepler 
mission with sensitivity extending outward from the ha- 
bitable zone to infinity (unbound planets). In addition to 
Kepler, ground-based radial velocity surveys will extend 
to longer periods with somewhat improved velocity sen- 
sitivity, which will enable the detection of planets below 
a Saturn mass in ~10 year orbits, but the radial velocity 
method is unlikely to be sensitive to lower mass planets 
due to intrinsic stellar velocity noise. A space-based 
astrometry mission could be sensitive to planets down 
to about an Earth mass, but such a mission would not 
be sensitive over nearly as wide a range of orbital sepa- 
rations as WFIRST, and now that the Space Interfero- 
metry Mission (SIM) has been canceled, it is highly un- 
likely that such a mission could fly prior to WIFRST. 

This leaves only other microlensing planet search 
programs that could detect some of the low-mass pla- 
nets that are the primary goal of the WFIRST Exoplanet 
program. As shown in Table 2, the number of detec- 
tions expected from the ground is quite modest. The 
only observing program that could compete with the 
WFIRST exoplanet program is Euclid, as it is a tele- 
scope with a similar size and field-of-view. However, 
the exoplanet program on Euclid is considered second- 
ary science, and neither the thermal design nor the fil- 
ters are optimized for an exoplanet search. As a result, 
Euclid’s exoplanet survey is limited to only a few 
months of observations and less than 10% of the exop- 
lanet yield of WFIRST. Thus, if Euclid is selected, it will 
not contribute significantly to the exoplanet science 
planned for WFIRST. 


Appendix D: WFIRST in the Context of Other Missions and Projects 


D-5 


WFIRST 


Appendix E Possible Modifications to the 
WFIRST IDRM 

The NWNH took JDEM-Omega to be the template 
for WFIRST, saying that JDEM-Omega seemed nearly 
ideally suited for the WFIRST science goals. The SDT 
took JDEM-Omega as the starting point for its design 
reference mission. It heard proposals for changes, 
some of which have been adopted. Other changes are 
still under consideration, in particular the substitution of 
an integral field unit (IFU) for the slitless prism used in 
supernova spectroscopy and the extension of the sensi- 
tivity of the detectors redward of 2 microns. 

Supernova Spectroscopy Option: Substituting an 
Integral Field Unit Spectrograph (IFU) for the Slit- 
less Prism and its Supporting Instrumentation 

The knowledge that can be extracted from any sur- 
vey is limited by the uncertainties in the data. These 
uncertainties can be statistical in nature, in which case 
additional data points (e.g. more SNe ) will reduce the 
final error, or through systematic errors, which, by defi- 
nition, cannot be reduced through the accumulation of 
additional, similar data. WFIRST is a powerful survey 
telescope, and will collect such large and deep surveys 
that we expect the final data products to be systematics 
limited. The only way to increase the science return in 
such a case is to reduce the systematic errors. 

Systematic errors can be created by the instru- 
ment, and these are addressed by design and calibra- 
tion. They can also be astrophysical in nature. For ex- 
ample, it is known that not all Type la SN are identical, 
and that sub-classes exist with different light curves. 
Ignoring this subtlety will eventually limit the strength of 
the scientific conclusions that can be drawn from a 
large data set that cannot remove this systematic un- 
certainty. 

To address this issue, the SDT is considering the 
potential inclusion of an Integral Filed Unit Spectro- 
graph (hereafter, IFU) to more accurately classify the 
observed SNe and reduce the systematic errors in the 
analysis. 

The baseline supernova program uses a prism in a 
filter wheel to obtain slitless spectroscopy of each su- 
pernova. An IFU uses a compact splayed arrange- 
ment of mirrors to slice a small image (including, e.g., a 
supernova, its host galaxy, and some background ga- 
laxies) into separate elements that each get dispersed. 
The resulting data cube of flux at each position and wa- 
velength has many times higher signal-to-noise than a 


Appendix E: Possible Modifications to the WFIRST IDRM 


slitless spectrum with the same exposure time - or, 
equivalently, significantly reduced exposure times for 
the same signal-to-noise. In contrast, a slitless spec- 
trum includes contributions from the full sky in each 
spectral bin, making it more difficult to isolate the faint 
SNe signal. 

While the inclusion of an additional channel clearly 
involves some increases in complexity, there are poten- 
tial practical advantages to using an IFU instead of a 
slitless prism approach. The IFU is expected to be less 
demanding in its pointing and stability requirements 
compared to the baseline slitless approach, and it is 
expected to eliminate the need for certain calibration 
instruments. Whether these advantages outweigh the 
additional complexity will be studied over the coming 
months. 

Science Improvement with an IFU 

From a science perspective, the signal-to-noise 
gain with an IFU is quite important. The supernova 
program that can be accomplished with the lower sig- 
nal-to-noise slitless spectroscopy is only sufficient to 
recognize the supernovae as “Type la” and provide its 
redshift. With the dramatically higher signal-to-noise of 
an IFU the spectral features of the supernova can be 
used to: 

1. Distinguish intrinsic color variations from the 
effects of dust (Chotard et al., 2011). Current- 
ly, these two sources of reddening and dim- 
ming are not distinguished at high redshift, so 
the mix of these two effects is assumed to stay 
constant over the redshifts studied. For the 
precision measurements of i/i/(z) it would be 
important to separate them, since both are im- 
portant corrections in the distance modulus 
calculation. This systematics control remains 
important even in the redder observer wave- 
lengths (out to 2 microns) that WFIRST can 
reach. 

2. Improve the “standard candle” calibration of 
the Type la supernova. Bailey et al. (2009) 
showed that with spectral feature ratios of suf- 
ficient signal-to-noise the magnitude disper- 
sion of SN la distance modulus in the 
restframe optical can be reduced from 0.16 
mag to 0.12 mag dispersion. This is as good 
as the improvement in dispersion using 
restframe H band observations. With IFU 


E-1 


WFIRST 


spectroscopy, however, this distance modulus 
improvement can be obtained over a large 
redshift range (beyond z = 1.7), while the 
restframe H band photometry is only available 
to redshift z = 0.1 (and J band only to z = 0.4) 
even with an instrument observing out to 2 mi- 
crons. 

3. Compare the detailed composition and physi- 
cal state of high-redshift supernovae to that of 
low-redshift supernovae. Type la superno- 
vae are not all identical, but we can find spec- 
troscopic matches of subsets of SNe la. If 
surprising cosmologies are inferred from su- 
pernova distance measurements over a range 
of redshifts it will be important to show that the 
effect is not simply an artifact due to a popula- 
tion of SNe la that is demographically drifting 
from one distribution of these spectroscopic 
subsets to another. With IFU spectroscopy it 
is possible to obtain the signal-to-noise suffi- 
cient to distinguish the different matching 
spectroscopic subsets. 

4. Remove the K-correction systematics from the 
measurement. The slitless grism-based pro- 
gram uses only three filters over the whole 
redshift range studied, introducing the need for 
K corrections. The low signal-to-noise slitless 
grism spectra must then be combined to statis- 
tically remove any systematic biases in these 
K corrections (although this approach has not 
yet been studied to see what systematics will 
remain). With IFU spectrophotometry provid- 


Appendix E: Possible Modifications to the WFIRST IDRM 


ing the lightcurves there would be no K correc- 
tions at all. 

While the control of systematic uncertainties is the 
primary motivation for considering an IFU, its shorter 
exposure times can also be used to improve the depth 
of the survey and therefore the Figure of Merit. An ex- 
ample six-month-observing-time program has been de- 
veloped (similar to the supernova program studied in 
detail by the ISWG) that yields significantly improved 
FoM over the slitless spectrograph six-month- 
observing-time program described as the baseline pro- 
gram above. The systematic uncertainties discussed in 
the FoM section of this document may be significantly 
reduced with the IFS spectroscopy. One study has 
found that the FoM for the supernova measurement 
combined with WL and BAO will increase by 20% (see 
Figure 17). 

SDT Future Studies 

Prior to the conclusion of the final report, the SDT will 
conduct a trade study concerning the utilization of an 
IFU for SNe redshift determination and sub- 
classification instead of the current baseline plan. This 
will involve the development of consensus FoM’s for 
comparison of the potential science gains, as well as 
the programmatic impacts from a cost, integration, sys- 
tem level requirements, and calibration perspective. 
The positive and negative impacts on observational im- 
plementation will also be considered. These will used to 
reach a final SDT consensus recommendation on the 
inclusion of an IFU in the final SDT baseline mission. 


WFIRST 



Figure 17: Projected WFIRST measurements of the expansion history of the universe using Type la supernovae as cali- 
brated standard candles. Approximately 100 SNe la are measured for each redshift bin. The solid lines show the re- 
sults from the current baseline WFIRST supernova program for conservative and optimistic (red) projections of the sys- 
tematic uncertainty control achieved. Also shown (dotted lines) are possible alternative programs using an IFU instead 
of the slitless prism spectroscopy. 


Extended Bandpass Option: Extending the longwa- 
velength cutoff beyond 2.0 p,m: 

In the course of its deliberations, a number of SDT 
members repeatedly expressed the opinion that one or 
another part of the WFIRST science program would be 
carried out more effectively if the WFIRST detectors 
had sensitivity redward of 2.1 microns and filters that 
cut off redward of 2 microns. But the SDT also unders- 
tood that if the DRM calls for hardware that is more ex- 
pensive than for JDEM-Omega, it is less likely to be 
funded. This IDRM adheres to the same wavelength 
cutoffs as in JDEM-Omega. In the year between this 
report and the final DRM, the SDT will consider further 
the tradeoffs associated with incorporating redder de- 
tectors and filters. In what follows we present some of 
the arguments presented by the SDT in favor of redder 
wavelengths. 

Scientific gains from redder response 

The cosmological science return of WFIRST would 
be yet greater were it sensitive beyond 2 microns. The 
zodiacal light foreground is a minimum at 3.5 microns, 
and distant galaxies and QSOs are red sources. For a 
partially resolved galaxy with an exponential scale 
length of 0.05 arc-seconds, and a spiral SED redshifted 


to z=2, the SNR with a 1.3 meter unobscured telescope 
is 2.05 times better at 3.54 microns compared to 1.77 
microns. For a QSO with a constant vF^, which is not 
quite as red as the z=2 galaxy, the SNR is 1.39 times 
better at 3.54 microns. 

Even though shear measurements require resolu- 
tion of sources, the SNR for measuring shear is 1.1 
times better at 2.5 microns than at 1.77 microns for the 
galaxy above. For a larger galaxy with 0.1" exponential 
scale length the optimum SNR for shear is at 3.54 mi- 
crons. Note that for an exponential disk, the half- 
encircled energy diameter is 3.32 times the scale 
length, while for an unobscured circular aperture the 
half-encircled energy diameter is »WD = 0.33” when X 
= 2.1 microns for a 1.3 meter diameter. WFIRST will 
have a better PSF than DES or LSST out to 4 microns, 
both of which are specifically designed to measure 
weak leasing. 

The improved SNR for detecting galaxies will facili- 
tate the detection of high redshift clusters. A wider 
range of wavelengths will ease the separation of QSOs 
from stars. 

A 3.5 micron capability for WFIRST will never suf- 
fer in comparison to ground-based observations. While 
the foreground at 2 microns is 1600 times smaller in 
space than on the ground, the foreground is 2.7 million 


Appendix E: Possible Modifications to the WFIRST IDRM 


E-3 


WFIRST 


times smaller from space in the thermal infrared. Hogg 
et al. 2000 spent 15 hours of integration time on the 10 
meter Keck telescope [many nights with overheads] to 
find 11 sources at 3.2 microns, while the 40 cm WISE 
telescope catalogued 28 sources per second of wall 
clock time in its Preliminary Data Release. 

The advantages of redder response for a survey of the 
plane of the Milky Way 

NWNH and the EOS panel recommended that six 
months of the WFIRST mission should be devoted to a 
galactic plane survey, but did not elaborate on the na- 
ture or goals of that survey. The most important galac- 
tic plane science topics WFIRST could address gener- 
ally fall into two broad categories: 

1) galactic structure (spiral arm geometry and ex- 
tent; disk scale length and scale height; disk warp) 
and 

2) star formation (extent of the star-forming disk; 
star forming efficiency, IMF, and triggering me- 
chanism as function of galactocentric distance and 
metallicity). 

The best tracers for these goals are red-clump 
giants and young-stellar objects (YSOs) with IR ex- 
cesses due to circumstellar dust disks. In the inner ga- 
laxy, source crowding near b = 0 is so large that even 
with WFIRST's small pixel size confusion will limit the 
gains over ground based surveys. However, over 
much of the outer galactic plane, source crowding is a 
small enough effect that WFIRST's great intrinsic sensi- 
tivity can be mostly achieved, allowing a wide area sur- 
vey much deeper than any that currently exist or likely 
could be accomplished from the ground. 

Even in the outer galaxy, however, extinction is still 
a strong impediment to one’s ability to do the desired 
science, because color cannot be directly equated to 
stellar effective temperature. In order to identify the red 
clump giants and YSOs, it is necessary to have a filter 
set that allows one to break the degeneracy between 
effective temperature and reddening. The standard 
JHK filter set accomplishes this goal remarkably well 
for late type stars because J-H remains essentially con- 
stant for Teff < 5000 K, whereas H-K becomes redder 
for cooler stars (yielding the well-known hook-shaped or 
step-shaped locus of stars in the J-H vs. H-K color-color 
diagram). In this color-color diagram, therefore, stellar 
effective temperature (for spectral type > KO) and red- 
dening vectors are well-separated, allowing one to ac- 


Appendix E: Possible Modifications to the WFIRST IDRM 


curately determine the extinction to each star. Similar- 
ly, YSO IR excesses typically begin at K band because 
the inner edge of the disk is set at the dust sublimation 
temperature of about 1300 K. This leads to a distinct 
YSO locus in the J-H, H-K diagram, allowing YSOs to 
be identified in wide-area NIR surveys even in the face 
of large and varying extinction. 

The ability of a JHK filter set to do the desired ga- 
lactic plane science has been well-documented in the 
published literature (see particularly Lucas et al. 2008; 
Meyer et al. 1997). Can one accomplish the same 
goals with a filter set that does not extend to 2.2 micro- 
ns? There are some shorter wavelength color-color 
diagrams that provide some separation between red- 
dening and Teff. However, any such survey will be 
depth limited by extinction to that of the shortest wave- 
length band - limiting the radial depth of the survey and 
diminishing or eliminating the advantage of WFIRST 
over a dedicated ground-based survey. Because the 
current WFIRST longest wavelength filter does not ex- 
tend far enough to the red, it neither samples far 
enough outside the H- opacify minimum to yield a good 
temperature sensitive color, nor is sensitive to the IR 
emission from dust in the inner disk of most YSOs. 
Without a longer wavelength filter, WFIRST’s ability to 
do the unique galactic plane science envisioned by the 
EOS report will be correspondingly limited. 


WFIRST 


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Appendix F: References 


F-5 


WFIRST 


Appendix G 

Acronym List 

2MASS 

A&A 

ACS 

ACS 

AJ 

ANGST 

AO 

ApJ 

ApJL 

ApJS 

ASIC 

AU 

BAO 

BEPAC 

BigBOSS 

C&DH 

CaF2 

CCD 

CDR 

CFHTLS 

CMB 

CMOS 

COBE 

DE 

DES 

DETF 

DOF 

DRM 

DSN 

DTAP 

E(B-V) 

EDU 

EE 

EELV 

ELG 

EOL 

EOS 

EPO 

ESA 

ExP 

FGS 

FoM 

FoMSWG 

FOR 

FOV 

FPA 

FSW 

FY 

2 Micron All Sky Survey 

Astronomy and Astrophysics 

Advanced Camera for Surveys 

Attitude Control System 

Astronomical Journal 

ACS Nearby Galaxies Survey Treasury 

Announcement of Opportunity 

Astrophysical Journal 

Astrophysical Journal Letters 

Astrophysical Journal Supplement Series 

Application Specific Integrated Circuit 

Astronomical Unit 

Baryon Acoustic Oscillations 

Beyond Einstein Program Assessment Committee 

Big Baryon Oscillation Spectroscopic Survey 

Command and Data Handling 

Calcium Fluoride 

Charged Coupled Device 

Critical Design Review 

Canada - France - Hawaii Telescope Legacy Survey 

Cosmic Microwave Background 

Complementary Metal Oxide Simi-conductor 

Cosmic Background Explorer 

Dark Energy 

Dark Energy Survey 

Dark Energy Task Force 

Degree of Freedom 

Design Reference Mission 

Deep Space Network 

Detector Technology Advancement Program 
Extinction (B-V) 

Engineering Development Unit 
Encircled Energy 

Evolved Expendable Launch Vehicle 
Emission Line Galaxy 
End of Life 

Electromagnetic Observations from Space 
Education and Public Outreach 
European Space Agency 
Exoplanet Microlensing Survey with WFIRST 
Fine Guidance Sensor 
Figure of Merit 

Figure of Merit Science Working Group 

Field-of-Regard 

Field-of-View 

Focal Plane Array 

Flight Software 

Fiscal Year 


Appendix G: Acronym List 


G-1 


WFIRST 


GHz 

Gigahertz 

Gl 

Guest Investigator 

GLIMPSE 

Galactic Legacy Infrared Mid-Plane Survey Extraordinaire 

GNC 

Guidance Navigation and Control 

GP 

Galactic Plane 

GSFC 

Goddard Space Flight Center 

HgCdTe 

Mercury Cadmium Telluride 

HLS 

High Latitude Survey 

HST 

Hubble Space Telescope 

l&T 

Integration and Test 

lA 

Intrinsic Alignment 

ICE 

Independent Cost Estimate 

IDRM 

Interim Design Reference Mission 

IFU 

Integral Field Unit 

ImC 

Imager Channel 

IMF 

Initial Mass Function 

IR 

Infrared 

IRAS 

Infrared Astronomical Satellite 

JCL 

Joint Confidence Level 

JDEM 

Joint Dark Energy Mission 

JWST 

James Webb Space Telescope 

KDP 

Key Decision Point 

KSC 

Kennedy Space Center 

L2 

Sun-Earth 2"'^ Lagrangian Point 

LCCE 

Lifecycle Cost Estimate 

LRD 

Launch Readiness Date 

LRG 

Luminous Red Galaxy 

LSST 

Large Synoptic Survey Telescope 

mas 

Milli-Arc-Seconds 

Mbps 

Megabits per Second 

MCR 

Mission Concept Review 

MEL 

Master Equipment List 

MNRAS 

Monthly Notices of the Royal Astronomical Society 

Mpc 

Megaparsec 

MOC 

Mission Operations Center 

MPF 

Microlensing Planet Finder 

NASA 

National Aeronautics and Space Administration 

NIR 

Near Infrared 

NIRSS 

Near-Infrared Sky Surveyor 

NRC 

National Research Council 

NWNH 

New Worlds, New Horizons in Astronomy and Astrophysics 

OTA 

Optical Telescope Assembly 

PASP 

Publication of the Astronomical Society of the Pacific 

PDR 

Preliminary Design Review 

Photo-z 

Photometric Redshift 

PSF 

Point Spread Function 

PSR 

Pre-Ship Review 

PZCS 

Photo-Z Calibration Survey 

QE 

Quantum Efficiency 

QLF 

Quasar Luminosity Function 

QSO 

Quasi-Stellar Object (Quasar) 


Appendix G: Acronym List 


G-2 


WFIRST 


RFI 

Request for Information 

RMS 

Root Mean Square 

RSD 

Redshift Space Distortion 

S/C 

Spacecraft 

S/N 

Signal/Noise 

SCA 

Sensor Chip Assembly 

SCE 

Sensor Cold Electronics 

SCG 

Science Coordination Group 

SDO 

Solar Dynamics Observatory 

SDT 

Science Definition Team 

SDSS 

Sloan Digital Sky Survey 

SED 

Spectral Energy Distribution 

SiC 

Silicon Carbide 

SIM 

Space Interferometry Mission 

SIR 

Systems Integration Review 

SINGS 

Spitzer Infrared Nearby Galaxies Survey 

SN 

Supernova 

SNe 

Supernovae 

SNR 

Signal to Noise Ratio 

SpC 

Spectrometer channel 

SRR 

System Requirements Review 

SSR 

Solid State Recorder 

SUTR 

Sample Up The Ramp 

TBD 

To Be Determined 

Tbits 

Terabits 

TBR 

To Be Resolved 

TMA 

Three Mirror Anastigmat 

TRMD 

Transition from Radiation to Matter Domination 

UKIDSS 

UKIRT Infrared Deep Sky Survey 

US 

United States 

vDC 

Volts Direct Current 

VISTA 

Visible and Infrared Survey Telescope for Astronomy 

WD 

White Dwarf 

WFIRST 

Wide-Field Infrared Survey Telescope 

WISE 

Wide-field Infrared Survey Telescope 

WL 

Weak Lensing 

WMAP 

Wilkinson Microwave Anisotropy Probe 

YSO 

Young Stellar Objects 

ZnSe 

Zinc Selenide 


Appendix G: Acronym List 


G-3