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Supernova / Acceleration Probe: A Satellite Experiment to Study the Natureof the Dark Energy

G.Aldering1, W. Althouse2, R. Amanullah3, J. Annis4, P. Astier5, C. Baltay6, E. Barrelet5,S. Basa7, C. Bebek1, L. Bergstrom3, G. Bernstein8, M. Bester9, B. Bigelow10, R. Blandford2,

R. Bohlin11, A. Bonissent12, C. Bower13, M. Brown10, M. Campbell10, W. Carithers1,E. Commins9, W. Craig2, C. Day1, F. DeJongh4, S. Deustua14, T. Diehl4, S. Dodelson4,

A. Ealet7,12, R. Ellis15, W. Emmet6, D. Fouchez12, J. Frieman4, A. Fruchter11, D. Gerdes10,L. Gladney8, G. Goldhaber9, A. Goobar3, D. Groom1, H. Heetderks9, M. Hoff1, S. Holland1,

M. Huffer2, L. Hui4, D. Huterer16, B. Jain8, P. Jelinsky9, A. Karcher1, S. Kent4, S. Kahn2,A. Kim1, W. Kolbe1, B. Krieger1, G. Kushner1, N. Kuznetsova1, R. Lafever1, J. Lamoureux1,

M. Lampton9, O. Le Fevre7, M. Levi1∗, P. Limon4, H. Lin4, E. Linder1, S. Loken1, W. Lorenzon10,R. Malina7, J. Marriner4, P. Marshall2, R. Massey17, A. Mazure7, T. McKay10, S. McKee10,R. Miquel1, N. Morgan6, E. Mortsell3, N. Mostek13, S. Mufson13, J. Musser13, P. Nugent1,

H. Olus.eyi1, R. Pain5, N. Palaio1, D. Pankow9, J. Peoples4, S. Perlmutter1†, E. Prieto7,D. Rabinowitz6, A. Refregier18, J. Rhodes15, N. Roe1, D. Rusin8, V. Scarpine4, M. Schubnell10,

M. Sholl9, G. Smadja19, R. M. Smith15, G. Smoot9, J. Snyder6, A. Spadafora1, A. Stebbins4,C. Stoughton4, A. Szymkowiak6, G. Tarle10, K. Taylor15, A. Tilquin12, A. Tomasch10, D. Tucker4,

D. Vincent5, H. von der Lippe1, J-P. Walder1, G. Wang1, W. Wester4

ABSTRACT

The Supernova / Acceleration Probe (SNAP) is a proposed space-based experiment designed to studythe dark energy and alternative explanations of the acceleration of the Universe’s expansion by perform-ing a series of complementary systematics-controlled astrophysical measurements. We here describe a

1Lawrence Berkeley National Laboratory2Stanford Linear Accelerator Center3University of Stockholm4Fermi National Accelerator Laboratory5LPNHE, CNRS-IN2P3, Paris, France6Yale University7LAM, CNRS-INSU, Marseille, France8University of Pennsylvania9University of California at Berkeley

10University of Michigan11Space Telescope Science Institute12CPPM, CNRS-IN2P3, Marseille, France13Indiana University14American Astronomical Society15California Institute of Technology16Case Western Reserve University17Cambridge University18CEA, Saclay, France19IPNL, CNRS-IN2P3, Villeurbanne, France

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self-consistent reference mission design that can accomplish this goal with the two leading measurementapproaches being the Type Ia supernova Hubble diagram and a wide-area weak gravitational lensing sur-vey. This design has been optimized to first order and is now under study for further modification andoptimization. A 2-m three-mirror anastigmat wide-field telescope feeds a focal plane consisting of a0.7 square-degree imager tiled with equal areas of optical CCDs and near infrared sensors, and a high-efficiency low-resolution integral field spectrograph. Theinstrumentation suite provides simultaneousdiscovery and light-curve measurements of supernovae and then can target individual objects for detailedspectral characterization. The SNAP mission will discoverthousands of Type Ia supernovae out toz = 3and will obtain high-signal-to-noise calibrated light-curves and spectra for a subset of> 2000 supernovaeat redshifts betweenz = 0.1 and1.7 in a northern field and in a southern field. A wide-field survey cover-ing one thousand square degrees in both northern and southern fields resolves∼ 100 galaxies per squarearcminute, or a total of more than 300 million galaxies. Withthe PSF stability afforded by a space obser-vatory, SNAP will provide precise and accurate measurements of gravitational lensing. The high-qualitydata available in space, combined with the large sample of supernovae, will enable stringent control ofsystematic uncertainties. The resulting data set will be used to determine the energy density of dark en-ergy and parameters that describe its dynamical behavior. The data also provide a direct test of theoreticalmodels for the dark energy, including discrimination of vacuum energy due to the cosmological constantand various classes of dynamical scalar fields. If we assume we live in a cosmological-constant-dominatedUniverse, the matter density, dark energy density, and flatness of space can all be measured with SNAPsupernova and weak-lensing measurements to a systematics-limited accuracy of 1%. For a flat universe,the density-to-pressure ratio of dark energy or equation ofstatew(z) can be similarly measured to 5% forthe present valuew0 and∼ 0.1 for the time variationw′ ≡ dw/d ln a|z=1. For a fiducial SUGRA-inspireduniverse,w0 andw′ can be measured to an even tighter uncertainty of 0.03 and 0.06 respectively. Note thatno external priors are needed. As more accurate theoreticalpredictions for the small-scale weak-lensingshear develop, the conservative estimates adopted here forspace-based systematics should improve, al-lowing even tighter constraints. While the survey strategyis tailored for supernova and weak gravitationallensing observations, the large survey area, depth, spatial resolution, time-sampling, and nine-band opticalto NIR photometry will support additional independent and/or complementary dark-energy measurementapproaches as well as a broad range of auxiliary science programs.

Subject headings:Early universe—instrumentation: detectors—space vehicles: instruments—supernovae:general—telescopes

1. Introduction

In the past decade the study of cosmology has takenits first major steps as a precise empirical science,combining concepts and tools from astrophysics andparticle physics. The most recent of these results havealready brought surprises. The Universe’s expansionis apparently accelerating rather than decelerating asexpected due to the gravitational attraction of matter.This implies that the flat, matter-dominated model forthe Universe does not apply and that our current funda-mental physics understanding of particles, forces, andfields is likely to be incomplete.

This evidence for a vacuum energy, or more gen-erally a negative-pressure component called “dark en-

∗Co-PI, email: melevi@lbl.gov†PI, email: saul@lbl.gov

ergy”, comes from the supernova measurements ofchanges in the Universe’s expansion rate that directlyshow the acceleration. Figure 1 shows the results ofKnop et al. (2003) (see also Tonry et al. (2003)) whichcompare the standardized brightnesses of ground andspace-observed high-redshift (0.18 < z < 0.863)Type Ia supernovae (SNe Ia) with a large sample oflow-redshift SNe Ia (Hamuy et al. 1996b; Riess et al.1999). The data implies that for a flat universe a frac-tion ΩΛ = 0.75 ± 0.07 of the critical density wouldreside in a cosmological constant. More generally,these measurements indicate the presence of a new,unknown energy component with energy densityΩw

that can cause acceleration, hence having an equationof state (ratio of pressure to energy density (Turner &White 1997)) withw ≡ p/ρ < −1/3.

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The evidence for dark energy has received strongcorroboration from cosmic microwave background(CMB) results (Balbi et al. 2000; Lange et al. 2001b;Spergel et al. 2003) which are sensitive to the totalenergy density, combined with galaxy power spec-trum and cluster abundance measurements (Bahcallet al. 1999; Efstathiou et al. 2002; Percival et al. 2002;Allen et al. 2003) which probe the matter densityΩM ,or with anH0 prior (see Figure 1). Two of these threeindependent measurements would have to be in errorto make dark energy unnecessary in the cosmologicalmodel.

The dark energy might be due to the cosmologicalconstant term in Einstein’s equations, which impliesvacuum energy withw = −1. Alternatively, it couldbe due to a dynamical scalar field withw 6= −1 and/ortime-varyingw. The fundamental importance of a uni-versal vacuum energy has sparked a flurry of activityin theoretical physics with several classes of modelsbeing proposed (e.g. quintessence (Ratra & Peebles1988; Caldwell et al. 1998; Ferreira & Joyce 1998),Pseudo-Nambu-Goldstone Boson (PNGB) models(Frieman et al. 1995; Coble et al. 1997), cosmic de-fects (Vilenkin 1984; Vilenkin & Shellard 1994), andmodified gravity (Dvali et al. 2000; Carroll et al.2003).

All these models explaining the accelerating Uni-verse have observational consequences for the super-nova Hubble diagram (Weller & Albrecht 2002). Theluminosity distance as a function of redshift can forconvenience be parameterized to first order with effec-tive dark-energy parameters, e.g.wconst, or w0, wa.A constantwconst can represent dark-energy modelssuch as the cosmological constant whilew = w0 +wa(1 − a) is successful at describing a wide varietyof both scalar field and more general models (Lin-der 2003a, 2004). Predictions of dark-energy modelscan be either compared directly to supernova Hubblediagrams or to the dark-energy parameters as fit bythe data. Placing some constraints on possible dark-energy models, Perlmutter et al. (1999b); Garnavichet al. (1998); Perlmutter et al. (1999a); Knop et al.(2003) find that for a flat universe, the data are con-sistent with a cosmological-constant equation of stateand0.2 <

∼ΩM <

∼0.4 (Figure 2), or generallywconst <

−0.6 at 95% confidence level. When combining su-pernova with other results, such as from a varietyof CMB experiments and large-scale-structure mea-surements(Hawkins et al. 2003; Spergel et al. 2003),Knop et al. (2003) findwconst = −1.05+0.15

−0.20 (±0.09

Fig. 1.— There is strong evidence for the existenceof a cosmological vacuum energy density. Plotted areΩM —ΩΛ 68% and 95% confidence regions for super-novae (Knop et al. 2003), cluster measurements (basedon Allen et al. (2003)), and CMB data withH0 pri-ors (outer counters from Lange et al. (2001a), innercontours from Spergel et al. (2003)). These resultsrule out a simple flatΩM = 1, ΩΛ = 0 cosmol-ogy. Their consistent overlap is a strong indicatorfor dark energy. Also shown is the expected confi-dence region from just the SNAP supernova programfor ΩM = 0.28, ΩΛ = 0.72.

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systematics) and Riess et al. (2004) getwconst =−1.02+0.13

−0.19. Cosmic strings (w = −1/3) are alreadyruled out as dark energy, while the domain walls (w =−2/3) and tracking quintessence models (w & −0.7)are disfavored.

Fig. 2.— Best-fit 68%, 90%, 95%, and 99% confi-dence regions in theΩM–w plane for an additionalenergy density component,Ωw, characterized by anequation-of-statew = p/ρ using supernovae alone(Knop et al. 2003). The fit is constrained to a flat cos-mology (ΩM +Ωw = 1). Also shown are the expected68% and 95% confidence regions allowed by just theSNAP supernova program assuming the fiducial valuesw = −1 andΩM = 0.28.

Current and upcoming ground-based supernova ex-periments will continue to improve measurements ofthe dynamical effects of the dark energy. For exam-ple, the Nearby Supernova Factory (Aldering et al.2002) will produce a photometrically calibrated spec-tral time-series for hundreds of0.03 < z < 0.08supernovae, providing a rich data set for refining ourunderstanding of SN Ia behavior. The SNLS1 and

1http://snls.in2p3.fr/

Essence2 projects will discover and follow hundredsof supernovae to∼ 0.03 − 0.05 mag accuracy in therangez = 0.3 − 0.7, giving significantly tighter con-straints on the value ofwconst. Unfortunately oncethe assumption thatw is constant is relaxed, these ex-periments are not able to provide strong constraints onw0 nor w′ (Perlmutter & Schmidt 2003). Testing thenature of dark energy will thus be difficult with theseexperiments.

A new experiment is then necessary to study theproperties and possible models for the dark energy,and refine the measurement of the matter and dark en-ergy densities of the Universe. Since the discovery ofcosmic acceleration in 1998, many observational ap-proaches to dark energy have been proposed (see Kujatet al. (2002); Tegmark (2002); Linder (2003b); Coorayet al. (2004) for recent reviews). The most well devel-oped and understood method of constructing the ex-pansion history of the Universe is the same one thatled to the discovery of dark energy: the measurementof the supernova Hubble diagram. The systematic andstatistical uncertainties in current SN Ia measurementsare on the same order of magnitude: any new experi-ment to perform precision cosmology must eliminateor significantly reduce the influence of the systematicuncertainties while discovering and measuring high-quality light curves and spectra of a statistically largenumber of supernovae.

In this paper we describe the Supernova/AccelerationProbe (SNAP), a dedicated satellite mission designedto measure the properties of dark energy. Originallyconceived in 1999 (Perlmutter 1999), the SNAP con-cept has progressed through a series of refinements allstarting with science requirements and then derivingobservational, instrumental, and mission requirements.The SNAP reference mission is presented in this paperin the form of a spacecraft, orbit, telescope, imager,spectrograph, and observation strategy. This missionserves as a reference from which future optimizationstudies will be performed and is a demonstration ofa design that can realistically accomplish the sciencegoals. It is self-consistent, technically feasible, re-duces risk, and is specifically designed to provide datathat strictly control statistical and systematic uncer-tainties for supernova and weak gravitational lensingscience.

SNAP can run as a complete supernova experi-ment providing discovery, and photometric and spec-

2http://www.ctio.noao.edu/essence/

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troscopic followup of a full sample of supernovae overthe target redshifts. SNAP is also an excellent platformfor performing deep wide-field surveys with space-quality imaging providing crucial complementary con-straints to study dark energy from weak lensing andother studies. SNAP’s full potential is realized whenused in conjunction with complementary results thatare anticipated by the time SNAP launches: a largesample of well-measured low-redshift SNe Ia and pre-cise measurements of the distance to the surface of lastscattering from the Planck satellite.

In §2 we describe the precision cosmology that canbe achieved using Type Ia supernovae. The neededsupernova data set is based on the identification ofknown or plausible systematic uncertainties that fun-damentally limit measurement accuracy, and on thenumber and redshift range of supernovae necessaryto probe precisely the dark-energy parameters. Thepower of weak gravitational lensing surveys in mea-suring cosmological parameters is discussed in§3 andthe added complementarity of lensing and other dark-energy probes made possible with SNAP data is de-scribed in§4. We present in§5 the observing strate-gies and instrumentation suite tailored to provide thedata that satisfy both the statistical and systematic re-quirements for the supernova and lensing surveys. TheSNAP calibration program is described in§6. The re-sults of detailed simulations of the SNAP mission aregiven in§7. In §8 we discuss the general properties ofthe SNAP surveys and the science resources they willprovide.

2. Cosmology with Supernovae

Type Ia SNe have already proved to be excellentdistance indicators for probing the dynamics of theUniverse. However, the current supernova cosmologymeasurements are limited by systematic uncertainties(which occur for all cosmological probes). In orderto move toward the era of precision cosmology, a newdata set must both address potential systematic uncer-tainties and provide sufficient statistical power to accu-rately determine dark-energy properties, especially thetime variation of the equation of state. Because con-trol of systematic uncertainties is so central we beginwith aspects of the data set necessary for their con-trol. We proceed by listing the sources of systematicuncertainty, strategies to reduce their effects, and theresulting improvements that can be obtained in mea-suring the supernova Hubble diagram. We then deter-

mine which supernova observations give a statisticaluncertainty comparable to the systematic uncertainty,leading to requirements on the number of supernovaewe need to find, their distribution in redshift, and howprecisely we need to determine each one’s peak bright-ness.

2.1. Control of Systematic Uncertainties

2.1.1. Known Sources of Systematic Uncertainties

High-redshift supernova searches have been pro-ceeding since the late 1980’s (Norgaard-Nielsen et al.1989; Couch et al. 1989; Perlmutter et al. 1995, 1997,1998, 1999b; Schmidt et al. 1998; Riess et al. 1998;Tonry et al. 2003; Knop et al. 2003; Riess et al. 2004).Particularly since the discovery of the accelerating ex-pansion of the Universe, the high-redshift supernovamethodology for measuring cosmological parametershas been critically scrutinized for sources of system-atic uncertainty. Below are identified systematic ef-fects which any experiment aiming to make maximaluse of the supernova technique will need to recognizeand control. We also give a rough estimate of the ex-pectedsystematicresidual in supernova magnitude af-ter statistical correction for such effects with the SNAPdata set or from independent data sets from other as-trophysical studies.

Extinction by Host-galaxy “Normal” Dust:Extinc-tion from host-galaxy dust can significantly reducethe observed brightness of a discovered supernova al-though typically Type Ia supernovae suffer only mod-est extinction (Hatano et al. 1998). Cross-wavelengthflux-calibrated spectra and multi-band photometry willidentify the properties of the obscuring dust and gasand the amount of extinction suffered by individualsupernovae. There will remain a residual uncertaintyproportional to the calculated extinction due to dust-model dependence. This can be minimized by ex-cluding highly-extincted supernovae from the anal-ysis. Stringent requirements on the SNAP calibra-tion system are needed to control uncertainties in thephotometric-system zeropoints, particularly since theuncertainties are correlated from supernova to super-nova. Our calibration program is being designed tocontrol extinction uncertainty to 1%.

Gravitational Lensing by Clumped Mass:Inhomo-geneities along the supernova line of sight can gravita-tionally magnify or demagnify the supernova flux andshift the mode of the supernova magnitude distributionby ∼1 – 10% depending on redshift (Holz & Wald

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1998; Mortsell et al. 2001; Amanullah et al. 2003).Since flux is conserved in this process, averaging largenumbers of supernovae per redshift bin will give thecorrect mean brightness. Deviations from a Gaussiandistribution for the brightness of supernovae at similarz can be used to determine the clumpiness of the inter-vening mass distribution (Kim et al. 2004). The largeSNAP supernova sample will reduce the distance mod-ulus uncertainty per redshift bin to∼ 0.5%. SNAPweak gravitational lensing measurements, and micro-lensing studies can further help distinguish whether ornot the matter is in compact objects.

K-Correction and Cross-Filter Calibration:Broad-band photometry of supernovae at different redshiftsis sensitive to differing supernova-rest-frame spectralregions. K-corrections are used to put these differingphotometry measurements onto a consistent rest-framepassband (Kim et al. 1996; Nugent et al. 2002). Ap-plying K-corrections with only today’s methods andcalibration sets could produce errors of several per-cent. Using the currently available spectra, we tune theSNAP filter-set specifications to give the target system-atic uncertainty< 0.02 mag. (The situation will im-prove even further as the spectral library of supernovaegrows and SNAP itself will add to this library.) Fur-thermore, strict requirements are placed on the SNAPcalibration program to ensure accurate transformationsof fluxes between filters.

Galactic Extinction: Extinction maps of our ownGalaxy are uncertain by∼ 1–10% depending on di-rection (Schlegel et al. 1998). Supernova fields canbe chosen toward the low extinction Galactic caps.Future Spitzer observations will allow an improvedmapping between color excesses (e.g. of Galactic halosubdwarfs in the SNAP field) and Galactic extinctionby dust. Galactic-extinction uncertainty can then becontrolled to< 0.5% in brightness.

Non-SN Ia Contamination:Other supernova types areon average fainter than SNe Ia and their contamina-tion could bias their Hubble diagram. Observed super-novae must be positively identified as SN Ia. As someType Ib and Ic supernovae have spectra and bright-nesses that otherwise mimic those of SNe Ia, a spec-trum covering the defining rest frame Si II 6150A fea-ture for every supernova at maximum will provide apure sample. This systematic would then be elimi-nated.

Malmquist Bias:A flux-limited sample preferentiallydetects the intrinsically brighter members of any pop-ulation of sources. The amount of magnitude bias

depends on details of the search but can reach thelevel of the intrinsic magnitude dispersion of a stan-dard candle. Directly correcting this bias would relyon knowledge of the SN Ia luminosity function, whichmay change with lookback time. A detection thresh-old fainter than peak by at least five times the intrin-sic SN Ia luminosity dispersion ensures sample com-pleteness with respect to intrinsic supernova bright-ness, eliminating this bias (Kim et al. 2004).

2.1.2. Possible Sources of Systematic Uncertainties

A systematics-limited experiment must account forspeculative but reasonable sources of uncertainty. Thefollowing are sources of systematic uncertainty forwhich there is no direct evidence but which cannot yetbe discounted.

Extinction by Gray Dust

As opposed to normal dust, gray dust is postulated toproduce wavelength-independent absorption in opticalbands (Aguirre 1999; Aguirre & Haiman 2000). Al-though models for gray-dust grains dim blue and redoptical light equally, the near-infrared (NIR) light (∼1-2 µm) is less affected. Cross-wavelength calibratedspectra extending to wavelength regions where “gray”dust is no longer gray will characterize the hypothet-ical large-grain dust’s absorption properties. Armedwith the extinction – color excess properties of thegray dust, broadband near-infrared colors can provide“gray” dust extinction corrections for supernovae outto z = 0.5; Goobar et al. (2002a) have explored the ob-servations necessary to be sensitive to 0.02 mag gray-dust extinction.

Gray dust will re-emit absorbed starlight and thuscontribute to the far-infrared background; current ob-servations indicate that the FIR flux is attributable topoint sources (Borys et al. 2002; Scott et al. 2002).Quasar colors in the SDSS sample as a function ofredshift give an upper limit to the possible dimmingdue to gray dust at the level of 0.2 mag (in the rest-frame B-band) atz = 1 (Mortsell & Goobar 2003).Deeper SCUBA and Spitzer observations should fur-ther tighten the constraints on the amount of gray dustallowed.

Uncorrected Supernova Evolution

Supernova behavior itself may have systematic vari-ations depending, for example, on properties of the

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progenitor systems. The distribution of these stellarproperties is likely to change over time—“evolve”—in a given galaxy, and over a population of galaxies.Supernova heterogeneity manifests itself through ob-served signatures in their spectral light emission (thebulk emitted in optical wavelengths), and the time-evolution of that emission. Signs of supernova diver-sity are thus captured in observations of multi-bandlight curves and/or spectral time-sequences that be-gin shortly after explosion and extend to the nebularphase of the event. This has been done using op-tical measurements of nearby SNe Ia drawn from awide range of galactic environments that provide anobserved evolutionary range of SNe Ia (Hamuy et al.1996a, 2000). The photometric and spectral differ-ences that have been identified in these data are wellcalibrated by the SN Ia light curve width-luminosityrelation, leaving a 10% intrinsic peak-brightness dis-persion. There is currently no evidence for system-atic residuals after correction, for example with galaxytype or supernova location (Sullivan et al. 2003).

High signal-to-noise (S/N ) multi-band light curvesand spectra over optical wavelengths can provide pre-cise control over additional general supernova variabil-ity. Efforts are underway to expose additional effectsusing larger, more precise and systematic, low-redshiftsupernova surveys (Aldering et al. 2002). These high-quality data are also necessary to control possible evo-lution effects when performing precision cosmologywith high-redshift supernovae.

Theoretical models can identify observables thatare expected to display heterogeneity. These key fea-tures, indicative of the underlying initial conditionsand physical mechanisms controlling the supernova,will be measured with SNAP, allowing statistical cor-rection for what would otherwise be a systematic un-certainty. The state of empirical understanding of theseobservables at the time SNAP launches will be ex-plicitly tested by SNAP measurements (Branch et al.2001). At present, we perform Fisher matrix analyseson model spectra and light curves to estimate the statis-tical measurement requirements, and to ensure that wehave necessary sensitivity to use subsamples to test forresidual systematics at better than the 2% level. Thisapproach reveals the main effects of — as well as thecovariance between — the following observables:

Rise time from explosion to peak:This is an indicatorof opacity, fused56Ni mass, and possible differencesin the 56Ni distribution. A 0.1 day uncertainty corre-sponds to a 1% brightness constraint at peak (Hoflich

et al. 1998). Achieving such accuracy requires discov-ery within ∼2 days of explosion, on average,∼30×fainter than peak brightness. Current constraints onrise-time differences are two days (Aldering et al.2000).

Plateau level 45 days past peak:The light-curveplateau level that begins∼45 days past — and morethan 10× fainter than — peak is an important indicatorof the C/O ratio of the progenitor star, and fused56Ni.In models, a 5% constraint on this plateau brightnesscorresponds to a 1% constraint on the peak brightness(Hoflich et al. 1998).

Overall light-curve timescale:The “stretch factor”(Goldhaber et al. (2001), see also Riess et al. (1996);Perlmutter et al. (1997); Phillips et al. (1999)) that pa-rameterizes the light-curve timescale (Phillips 1993)is affected by almost all of the aforementioned param-eters since it tracks the SN Ia’s light-curve develop-ment from early to late times. It is correlated with risetime and plateau level and it ties SNAP’s controls forsystematics to the controls used in the current ground-based work. A 0.5% uncertainty in the stretch fac-tor measurement corresponds to a∼1% uncertainty atpeak (Perlmutter et al. 1999b). Stretch distributionsare quite consistent between the current sets of lowand high-redshift supernovae (Perlmutter et al. 1999b;Knop et al. 2003).

Spectral line velocities:The velocities of several spec-tral features throughout the UV and visible makean excellent diagnostic of the kinetic-energy injec-tion in SNe Ia. In models, velocities constrained to∼250 km s−1 constrain the peak luminosity to∼1%(Hoflich et al. 1998), given a typical SNe Ia expansionvelocity of 15,000 km s−1. Current data show smoothvelocity development for a given supernova, but alsoclear differences between supernovae which have notyet been found to correlate with supernova luminosity(Branch & van den Bergh 1993; Hatano et al. 2000).

Spectral features:The positions of various spectralfeatures in the restframe UV are strong metallicityindicators of the SNe Ia. By achieving a sufficientS/N and resolution on such features (Bernstein & Kim2004) SNAP will be able to constrain the metallicityof the progenitor to 0.1 dex (Lentz et al. 2000). Thisspectral region has only recently begun to be exploredwith UV spectroscopy of nearby supernovae with HST.Spectral features in the restframe optical (Ca II H&Kand Si II at 6150A) provide additional constraints onthe opacity and luminosity of the SN Ia (Nugent et al.1995).

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Figures 3 and 4 show the particular light-curve andspectral parameters that can serve as indicators of su-pernova evolution. By measuring all of the abovefeatures for each supernova we can tightly constrainthe physical conditions of the explosion. This makesit possible to recognize subsets of supernovae withmatching initial conditions, ensuring a small luminos-ity range for each subset.

Days from Maximum (Observer Frame)

Norm

aliz

ed F

lux

-50 0 50 100

Search

Early discovery

Fmax, Tmax & stretch

Host extinction (V-band)

Host extinction (R-band)

Opacity, Fused 56Ni

Carbon/oxygen

Decouple parameters

0.0

0.2

0.4

0.6

0.8

1.0

S/N=20

S/N=30

S/N=15

S/N~3S/N=10

S/N=30

S/N=30

Fig. 3.— Sample B-band light curve for az = 0.8Type Ia supernova. Signal-to-noise targets are shownat different epochs for identification of possible sys-tematic effects.

Fig. 4.— Type Ia spectra at maximum light showingline features associated with possible Type Ia super-nova variation. The horizontal axis shows observerframe wavelengths forz = 0 andz = 1.7 supernovae.

In addition to these features of the supernovaethemselves, we will also study the host galaxy of the

supernova. We can measure the host galaxy luminos-ity, colors, morphology, and the location of the super-nova within the galaxy, even at redshiftsz ∼ 1.7. Thelast two observations are difficult or impossible fromthe ground for high-redshift galaxies. These galaxyproperties can provide clues to any shifts with redshiftin the supernova progenitor population.

2.1.3. Systematic-Error Model

The behavior of systematic uncertainties are com-plicated and the determination of their propagated ef-fects on cosmology requires rigorous analysis (Kimet al. 2004; Huterer et al. 2004). Particularly impor-tant systematic effects for supernova-cosmology ex-periments are those that put a floor on how well thedistance modulus can be measured in a certain red-shift bin. For example, supernovae at similar redshiftswhose rest-frame flux regions lie in common observerpassbands can share completely correlated calibrationuncertainty. An increase in the statistical sample ofsupernovae cannot decrease this uncertainty. In ad-dition, these uncertainties could be correlated acrossredshift bins. Again taking calibration as an example,a temperature uncertainty in a blackbody fundamentalcalibrator propagates into correlated flux and magni-tude zeropoint uncertainties. Correlated errors acrossredshift bins can lead to a bias in the determinationof the cosmological and dark-energy parameters. Wedo not further consider correlated bias in this paper asKim et al. (2004) find that the systematic bias inw0

andw′ lies well within the 68%-error contours due tocomparably-sized irreducible systematic uncertainties.

For convenience we adopt in this paper a systematic-uncertainty model of0.02(1.7/zmax)(1+z)/2.7 mag-nitude irreducible uncertainty per redshift bin of width0.1 as proposed by Linder & Huterer (2003), wherezmax represents the depth of the survey. The sys-tematic uncertainty introduced in the comparison ofhigh-redshift supernovae with the local sample is anincreasing function of redshift. Systematic uncertaintywill exist at some level even for the local sample, duefor example to uncertainty in the Galactic-extinctionzeropoint and spatial correlations inE(B − V ) maps.

2.2. Comparing Defined Subsets of Supernovae

The subtyping strategy employed for evolutionbased on observables tied to the explosion character-istics can be more generally applied. The data (super-nova risetime, early detection, light-curve peak-to-tail

8

ratio, identification of the Type Ia-defining Si II spec-tral feature, separation of supernova light from host-galaxy light, and identification of host-galaxy mor-phology, etc.) make it possible to study each individualsupernova and measure enough of its physical proper-ties to recognize deviations from standard brightnesssubtypes. Only the change in brightness as a functionof the parameters classifying a subtype is needed, notany intrinsic brightness. Supernovae cannot changetheir brightness in one measured wavelength rangewithout affecting brightness somewhere else in thespectral time series — an effect that is well-capturedby expanding atmosphere computer models.

As a precision experiment SNAP is designed to dis-tinguish supernovae “demographics” by detecting sub-tle variations in light-curve and spectral parameters.By matching like to like among the supernova sub-types we can construct independent Hubble diagrams,each with systematic biases reduced to the level of 1%in distance. This procedure is described and tested inKim et al. (2004). Comparison within a redshift binreveals possible systematics, while comparison withina subtype over the redshift range cleanly probes thecosmology.

The targeted residual systematic uncertainty fromeffects such as Malmquist bias,K-correction, etc. to-tal ∼2%. Thus, a subset, or “like vs. like”, analysisbased on physical conditions should group supernovaeto within <2% in luminosity. This is in addition to apurely statistical correction for any second-parametereffects beyond the stretch factor.

2.3. Supernova Sample to Probe Dark Energy

The statistical supernova sample appropriate for ex-periments with the presence of systematic uncertaintyhas been considered in the Fisher-matrix analysis ofLinder & Huterer (2003). (Their results have beenvalidated with our independent Monte Carlo analy-sis.) They assign a statistical uncertainty of 0.15 mag-nitudes to each supernova, which combines statisti-cal measurement uncertainty and intrinsic supernovadispersion. The systematic-error model described in§2.1.3 is included.

The importance of using SNe Ia over the full red-shift range out toz ∼ 1.7 for measuring the cosmo-logical parameters is demonstrated in Figure 5, whichshows the uncertainty in measuring the equation ofstate parameter variation,w′, as a function of max-imum redshift probed in distance surveys (Linder &

Huterer 2003). (Note that the results look very sim-ilar whether one definesw′ in terms of a linear ex-pansion ofw(z) in redshift or in scale factor, andwhether one uses a prior on matter density or on dis-tance to the CMB last scattering surface.) This cal-culation considers 2000 SNe Ia measured in the range0.1 ≤ z ≤ zmax, along with 300 low-redshift SNe Iafrom the Nearby Supernova Factory (Aldering et al.2002). A flat universe is assumed. Three types ofexperiments were considered. The first is an ideal-ized experiment subject only to statistical uncertain-ties, free of any systematics, and with extremely tightprior knowledge of the matter density. The second twoare more realistic models which assume both statisti-cal and systematic uncertainties and different priors onΩM .

Fig. 5.— From Linder & Huterer (2003), accuracyin estimating the equation of state variation parame-ter, w′, as a function of maximum redshift probed insupernova distance surveys. The lower two curves as-sume priors inΩM good to 0.01, while the upper twocurves are for the case where systematic uncertaintiesare present. The top, heavy curve corresponds to themost realistic case. It is clear that even with modestsystematic uncertainties good accuracy requires prob-ing to high redshift. In all cases a flat universe is as-sumed.

From this figure we conclude that a SN Ia sampleextending to redshifts ofz > 1.5 is crucial for realis-tic experiments in which some systematic uncertainties

9

remain after all statistical corrections are applied. Ig-noring systematic uncertainties can lead to claims thatare too optimistic. Similar conclusions apply for theother dark-energy parameters, includingw0 and an as-sumed constantw (Linder & Huterer 2003).

The sample of∼2000 SNe Ia is enough to providesystematic-uncertainty limited measures of the dark-energy parameterw′. These supernovae represent asubset of SNe Ia that can provide robust cosmologi-cal measurements (e.g. non-peculiar, low-extinction),culled from an even larger set of discovered super-novae. This large sample is necessary to allow model-independent checks for any residual systematics or re-fined standardization parameters, since the sample willhave to be subdivided in a multidimensional parame-ter space of redshift, light curve-width, host properties,etc. The large number of lower signal-to-noise lightcurves from supernovae atz > 1.7 will provide an ex-tended redshift bin in which to check for consistencywith the core sample.

Expected parameter measurement precisions for theSNAP supernova program withzmax = 1.7 are sum-marized in Table 1. We determine precisions for twofiducial flat universes withΩM = 0.3, one in whichthe dark energy is attributed to a Cosmological Con-stant and the other to a SUGRA-inspired dark-energymodel. The parameter precisions then depend on thechoice of data set, priors from other experiments, as-sumptions on the flatness of the universe, and themodel for the behavior ofw. (Parameter determina-tion from Monte Carlo analysis of simulated data fromthe reference SNAP mission is given in§7.)

If the universe is taken to be spatially flat, the SNdata (with Planck prior) determineΩM to 0.01. Thepresent value of the dark energy equation of state isconstrained within 0.09 and the physically crucial dy-namical clue of the equation of state time variation isbounded to within 0.19. Note that these constraintsaresystematics limited; much tighter constraints wouldbe obtained if systematics were ignored. (In§4 wediscuss the tighter constraints obtained by combiningthe supernova results with the other SNAP measure-ments.)

The precise, homogeneous, deep supernova data setallows for robust interpretation in more general termsthan w0 and w′. The functionw(z) can be imple-mented in a nonparametric, uncorrelated bin, or eigen-mode method (Huterer & Starkman 2003; Huterer &Cooray 2004). One can also obtain the expansion his-tory a(t) itself, e.g. Linder (2003a).

We can also obtain constraints on flatness of theuniverse, rather than assuming it. Current data aremostly sensitive to one linear combination ofΩM andΩΛ (roughly their difference). SNAP is designed toobtain sufficient brightness-redshift data for a widerange of redshifts (0.1 < z < 1.7), and to enablean extraordinarily accurate measurement ofΩM andΩΛ separately (see Figure 1), the culmination of anapproach originally proposed by Goobar & Perlmutter(1995). Assuming that the dark energy is the cosmo-logical constant, the supernova experiment can simul-taneously determine the mass densityΩM to an accu-racy of0.02, the cosmological constant energy densityΩΛ to 0.05. Propagating this through one obtains a0.06 measurement uncertainty of the curvature of theuniverse,Ωk = 1 − ΩM − ΩΛ.

3. Cosmology with Weak Lensing

Gravitational weak lensing provides an independentand complementary measurement of the dark-energyparameters through the mapping of galaxy-shape dis-tortions induced by mass inhomogeneities in the Uni-verse. Weak gravitational lensing of backgroundgalaxies by foreground dark matter (large-scale struc-ture) provides a direct measurement of the amount anddistribution of dark matter (see§8.2 for details on theimpact SNAP can have on these measurements). Thegrowth of these dark matter structures with cosmictime is determined by the dark energy. Thus, preciseweak lensing observations can provide significant andindependent constraints on the properties of dark en-ergy. For a review of the techniques used to measureweak lensing and the current status of weak-lensingmeasurements, see Refregier (2003).

3.1. Weak Lensing as a Probe of Dark Energy

Dark energy modifies the weak-lensing observablesby altering the distance-redshift relation as well as thematter power spectrum. These two, in turn, determinethe weak-lensing shear power spectrum (Kaiser 1998).Specifically, dark energy will modify the normaliza-tion and nonlinear part of the matter power spectrumand redshift evolution. Weak lensing measurementswith a wide-field space telescope such as SNAP canthus achieve an accurate measurement ofΩw, andthe dark-energy parameters (Hu 1999; Huterer 2002;Abazajian & Dodelson 2003; Refregier et al. 2004).

In Figure 6 we show the expected measurement ofthe shear power spectrum possible with 100 million

10

TABLE 1

SNAP 1-σ UNCERTAINTIES IN DARK-ENERGY PARAMETERS, WITH CONSERVATIVE SYSTEMATICS FOR THE

SUPERNOVA AND A 1000SQ. DEG. WEAK-LENSING SURVEY. NOTE: THESE UNCERTAINTIES ARE

SYSTEMATICS-LIMITED , NOT STATISTICS LIMITED.

σΩMσΩw

σw0σw′

Fiducial Universe: flat,ΩM = 0.3, Cosmological Constant dark energy

SNAP SN;w = −1 0.02 0.05 · · · · · ·SNAP SN + WL;w = −1 0.01 0.01 · · · · · ·

SNAP SN;σΩM= 0.03 prior; flat;w(z) = w0 + 2w′(1 − a) · · · 0.03 0.09 0.31

SNAP SN;Planck prior; flat;w(z) = w0 + 2w′(1 − a) · · · 0.01 0.09 0.19SNAP SN + WL; flat;w(z) = w0 + 2w′(1 − a) · · · 0.005 0.05 0.11

Fiducial Universe: flat,ΩM = 0.3, SUGRA-inspired dark energy

SNAP SN;σΩM= 0.03 prior; flat;w(z) = w0 + 2w′(1 − a) · · · 0.03 0.08 0.17

SNAP SN; Planck prior; flat;w(z) = w0 + 2w′(1 − a) · · · 0.02 0.09 0.13SNAP SN + WL; flat;w(z) = w0 + 2w′(1 − a) · · · 0.005 0.03 0.06

NOTE.—Cosmological and dark-energy parameter precisions for two fiducial flat universes withΩM =0.3, one in which the dark energy is attributed to a CosmologicalConstant and the other to a SUGRA-inspired dark-energy model. The parameter precisions thendepend on the choice of data set, priors fromother experiments, assumptions on the flatness of the universe, and the model for the behavior ofw. In thispaper we adopt the non-standard definitionw′ ≡ dw/d ln a|z=1

galaxies over 300 square degrees divided into 2 red-shift bins. The upper curve represents a measurementusing resolved source galaxies withz > 1 while thelower curve representsz < 1 galaxies. The powerof space-based observations is most apparent at smallscales (highℓ), where the shot noise is small dueto the large surface density of resolved galaxies. InFigure 7 we show the joint constraints onΩM andassumed-constantw using 10 million galaxies, 100million galaxies, and 100 million galaxies divided intotwo redshift bins with additional skewness informa-tion. Note that the constraints from weak lensing arelargely orthogonal to the constraints from supernovae.Thus, weak lensing complements the supernova tech-nique in deriving constraints onw.

Takada & Jain (2003) have demonstrated that bycombining additional information on non-Gaussianityfrom the lensing bispectrum in the moderately non-linear regime with the power spectrum, cosmologicalconstraints can be improved significantly (about a fac-

tor of three over the results shown in Figure 7). Atpresent the ability to exploit this information is limitedby computationally intensive numerical predictions fornon-linear growth, but the gravitational physics in-volved is well understood and work on obtaining ac-curate predictions is already underway.

At still smaller (arcminute) angular scales, the lens-ing signal is very strong, but the non-linear growth pre-dictions become very difficult. New statistical treat-ments of weak-lensing data have recently been pro-posed (Jain & Taylor 2003; Bernstein & Jain 2004)which measure the cosmic geometry while cancelinguncertainties in the non-linear growth. This is achievedby cross-correlating the lensing signal with an esti-mate of the foreground mass distribution. Figure 8presents an estimate by Bernstein & Jain (2004) ofthe statistical uncertainties onw0 andwa (or w′, re-call wa ∼ 2w′ at z ∼ 1) that could be obtained bythe SNAP surveys using this lensing cross-correlationtechnique. The quality of the measurement is compa-

11

rable to that of the Type Ia SN measurements, as longas the systematic uncertainties are kept below the sta-tistical uncertainties.

3.2. Advantages of Space-Based Measurements

Several conditions are necessary to make possiblehigh signal-to-noise weak-lensing measurements forthese types of analyses. The shapes of millions ofbackground galaxies must be measured to overcomecosmic variance and provide a precise measure of thedark matter power spectrum. It is particularly impor-tant to be able to resolve many small, distant galaxiesbeyond a redshift ofz ≃ 1; the broad redshift range ofsource galaxies provides a powerful lever arm on theconstraint ofw by providing information on the growthof structure. High spatial resolution is necessary toextract statistically powerful shape information fromeach individual galaxy and decrease the size of thesmallest resolved galaxies in a survey. A stable pointspread function (PSF) and a minimal level of internal

Fig. 6.— The dark matter power spectrum in two red-shift intervals. The upper curve represents a measure-ment made with lens galaxies atz > 1 and the lowercurve a measurement withz < 1. Three differentcosmological models are shown. It is clear that theover 100 million resolved galaxies in the SNAP widesurvey will distinguish between cosmological modelseven after being divided into redshift intervals. There-fore, high signal-to-noise measurements of the evolu-tion of the power spectrum will be possible.

optical distortions are essential for the precise mea-surement of galaxy shapes. The high spatial densityof resolved background galaxies afforded by space-based observations allows cross-correlation measure-ments and gives measurements of the mass powerspectrum at scales where non-linearities are most ap-parent. Accurate photometric redshifts are requiredfor the lensing analyses, particularly the lensing cross-correlation, where any systematic biases in photo-z’sabove∼0.001 inlog (1 + z) would dominate the errorbudget. Catastrophic photo-z errors would similarlyneed to be kept below 1 per 1000. It may be possibleuse internal analyses of lensing data to trade precisionon the dark energy parameters for looser constraintson photo-z biases. Reducing the photo-z errors, bi-ases, and catastrophic errors requires high-accuracyphotometry in bands spanning the visible and near-IR.Atmospheric emission lines make it impractical to ac-quire these data in the near-IR and near certain bright

Fig. 7.— Joint constraints onΩM andwconst achiev-able with the SNAP deep and wide surveys usingweak gravitational lensing. The blue contour is forthe SNAP supernova survey and cyan contour for thewide-field survey. After dividing the wide survey intotwo redshift intervals and adding skewness informa-tion, the constraints (the red contour) are similar in sizeto the SN Ia constraints (shown as a yellow ellipse).Since weak-lensing constraints are largely orthogonalto those of SNe Ia, weak lensing plays a crucial role inSNAP’s ability to measure dark energy.

12

visible lines.

Satisfying all of these requirements simultaneouslyrequires a wide-field space based imaging telescopein a thermally stable orbit. With a high-throughput,space-based 2 meter telescope, an exposure time of2000s will provide the depth to resolve significantnumbers of galaxies in the scientifically interestingrange beyondz ≃ 1. Unhindered by atmosphericemission and absorption, NIR observations from spaceprovide significant redshift depth and improved photo-metric redshift estimates. Avoiding the Earth’s atmo-sphere in a thermally stable orbit gives the fine reso-lution and stable PSF. The PSF and depth give a highgalaxy surface density. A ground-based survey of tensof thousands of square degrees, exploring the masspower spectrum on large angular scales with small sta-tistical errors would be complementary. In particu-lar, such large-angular-scale surveys probe the linearpart of the matter power spectrum while deeper butsomewhat less wide surveys probe the nonlinear re-gion. (For completeness, we discuss the possibility of

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2

-1

0

1

w0

wa

ΛCDM

SUGRA

SNAP WLCCC (stat)

SNAP SNIa

SNAP WLCCC (stat)

SNAP SNIa

Fig. 8.— Constraints on the parametersw0 andwa ≈2w′, wherew(z) = w0 + wa(1 − a) and a is thescale factor (Linder 2003a). Shown are the SNAP con-straints from the supernova survey (filled contours),and those from weak-lensing cross-correlation cos-mography (empty contours; statistics only), as dis-cussed in the text. We show constraints for two mod-els: vacuum energy (“ΛCDM”) and a supergravity-inspired model (“SUGRA”) (Brax & Martin 2000).

a panoramic, wide-field survey with SNAP in§5.1.3.)

4. Joint SNAP Constraints on Dark Energy fromWeak-lensing, Supernova, and other Measure-ments

The two complementary cosmological surveys thatconstitute the leading components of the SNAP pri-mary mission together combined give constraints onthe properties of dark energy significantly strongerthan either one by itself. Table 1 gives the expecteddark-energy parameter uncertainties from the joint re-sults from the deep supernova survey and the com-bination of power spectrum, bispectrum, and cross-correlation cosmography techniques from a 1000square-degree lensing program withngal = 100arcmin−2. A very conservative estimate of the sys-tematics floor on shear calibration of 3% is used.

For a flat universe the present dark energy equationof statew0 can be measured to±0.05, and the timevariation can be bounded within 0.11. Without assum-ing a flat universe, the mass densityΩM , the cosmo-logical constant energy densityΩΛ, and curvatureΩk

can be determined to<∼

0.01. This poses an interestingtest of the cosmological framework by cross-checkingthe curvature measured atz ∼ 1 with current mea-surements out toz ∼ 1000 of Ωk = −0.02 ± 0.02(Bennett et al. 2003). Note thatno priorsare requiredwhen we consider the full SNAP mission of super-novae plus weak lensing. These are significant im-provements over the results from supernovae alone.The constraints are subject to improvement as practicalunderstanding of future weak lensing data develops.

Universes with more dark energy (than the fiducialΩDE = 0.7 assumed here), dark energy possessing amore positive equation of state or a stronger time vari-ation would lead to a measurement with more sensi-tivity to dark-energy properties. We have been conser-vative in taking the cosmological constant as fiducial,the least sensitive of the canonical quintessence mod-els. For example, in a supergravity-inspired model ofdark energy (Brax & Martin 2000),w′ would be moretightly constrained to±0.06. With strong constraintsonw′ we will be able to differentiate between the cos-mological constant and a range of dynamical scalar-field (“quintessence”) particle-physics models (Weller& Albrecht (2001, 2002); Huterer & Turner (2001).)

The SNAP reference mission focuses on the es-tablished methods of Type Ia supernova Hubble di-agrams and weak gravitational lensing to study dark

13

energy. Other less-tested and more model-dependentmethods for measuring cosmological parameters arenow being explored as additional probes of dark en-ergy with SNAP. These include (but are not limitedto) using Type II supernovae as distance indicators(Kirshner & Kwan 1974; Baron et al. 1993; Baronet al. 1995; Leonard et al. 2003), baryon oscillationsas a standard ruler in both transverse and radial di-rections (Seo & Eisenstein 2003), redshift-space cor-relations for the Alcock-Paczynski test (Matsubara &Szalay 2003), strong lensing time-delays and statistics(Holz 2001; Goobar et al. 2002b), and cluster-countingstatistics (Haiman et al. 2001). Attacking dark en-ergy with measurements from independent techniquesthat are subject to differing, but tightly controlled sys-tematic uncertainties will give increased confidence inthe ultimate conclusions made about its nature. Sincethese techniques generally constrain different combi-nations of cosmological parameters, it is important thateach “stand on its own two feet” with systematics con-trol so that they can be combined for studies of darkenergy.

SNAP can naturally study dark energy using manyof these other probes. The necessary measurementscan be made with the SNAP instrumentation suiteas is, or in coordination with ground or other space-based telescopes. A SNAP panoramic-survey observ-ing mode that covers a significant fraction of sky canprovide large number statistics, redshift depth, wave-length coverage, discovery of rare objects, and mea-sures on large angular scales; these are exactly thecharacteristics of the data needed for many of thesecomplementary methods, with all the advantages ofobservations above the distorting and absorbing atmo-sphere.

5. Reference Model SNAP Experiment

Discovery and study of a larger number and of moredistant supernovae (or any probe) is by itself insuf-ficient to successfully accomplish a rigorous investi-gation of the cosmological model. As shown in§2.1we must address each of the systematic concerns whilemaking precise supernova measurements, thus requir-ing a major leap forward in measurement techniques.The requirements placed on the SNAP instrument de-rive directly from the science goals.

The primary requirement is to obtain the correctedpeak brightness vs. redshift of at least 2000 Type IaSNe out to a redshift ofz = 1.7. Identification of

Type Ia SNe requires the measurement of character-istic spectral features near peak luminosity. Host-galaxy redshift is also determined spectroscopically.The corrected peak magnitudes are derived from su-pernova rest-frame optical light curves and spectra.We require a statistical measurement uncertainty forthe peak magnitude corrected for extinction and shapeinhomogeneity roughly equal to the current intrinsicmagnitude dispersion of supernovae,∼ 0.1 mag, anda systematic uncertainty almost an order of magnitudesmaller.

To meet the scientific requirements, the SNAP ref-erence mission has a large, 0.7 square degree instru-mented field of view and an observing cadence of 4days, commensurate with the timescale over whichearly-epoch supernova light curves change. The im-ager’s large field-of-view gives a significant multi-plex advantage; each exposure contains∼ 80 TypeIa supernovae within 5.4 observer-frame months fromthe date of explosion (corresponding to 2 rest-framemonths forz = 1.7 supernovae). Observations inmultiple filters yield multi-color rest-frame opticallight curves. A spectrometer optimized for super-nova spectra is allocated observation time for super-nova type-identification, feature measurements, andspectral-template building. The telescope aperture isconstrained by the photometric and spectroscopicS/Nrequirements and the focal plane must accommodatethe large field of view.

The derived requirements for the SNAP referencemission described here serve as a starting point; theyare subject to change as the mission is further refined.As other subsidiary approaches to measure dark en-ergy are developed as discussed in§4 we can alsoconsider minor detector additions or replacements onthe focal plane with either extended broad-band filtersor with dispersive elements. For example, a band inbetween the reference filter bands could sharpen thephotometric redshift accuracy for a part of the surveyfield. As a general rule, broadband photometry is sig-nificantly faster than slitless spectroscopy by the ra-tio Rspect/Rfilter for equivalentS/N , however, forspecific applications a detector with a small dispersiveelement in place of a filter may be useful. It could pro-vide spectral time series of core-collapse supernovaethat fall in the limited field enabling the determinationof their distance. It could also provide precise redshiftsof field sources that can calibrate photometric redshifts– especially useful for tomographic weak lensing, orfor the baryon-oscillation method.

14

5.1. Reference Model Observation Strategy andData Package

The primary SNAP science program consists of adeep survey and a wide-field survey with individually-designed observing schedules. The repeated scansof the deep-survey field provide supernova discoveryand light curves, and when coadded give a high sur-face density of background galaxies for lensing sur-veys. The wide-field survey is designed for dark-energy measurements using weak lensing and otherw-sensitive techniques. In addition, we explore a pos-sible panoramic survey that extends the weak-lensingdata and provides the general astronomical communitya “legacy” survey of space-quality optical-to-NIR im-ages of a significant fraction of the sky. The programsare described here and summarized in Table 2. Thesurveys are described by the solid-angle of sky moni-tored, the exposure time for each scan of the field, andthe number of times the survey region is scanned.

5.1.1. Supernova Program

A simple, predetermined observing strategy repeat-edly steps through a 7.5 square degree northern zonewith a 4 day cadence continuing for 16 months. Laterin the mission this strategy is repeated for a southernsurvey region. The fields are selected to be perpen-dicular to the Sun, Earth, and Moon and where natu-ral zodiacal light is near minimum, toward the northand south ecliptic caps. This deep-survey strategy al-lows discovery and automatic followup for SNe Ia thatexplode in those regions. Every field will be visitedevery four days for 16 months, with sufficiently longexposures that all relevant SNe Ia in the SNAP surveyregions will have significant signal within a few rest-frame days of explosion. (supernovae at much higherredshifts on average will be found slightly later in theirlight curve rise times although their prior history is inthe data.) The periodic observation of fixed fields en-sures that every supernova atz < 1.7 will have itslight curve followed for at least several months in therest frame as it brightens and fades.

Sixty percent of the SNAP deep supernova surveywill be spent for the pure photometric scan; about120 exposures are possible with a four day cadenceto cover a scan area of 7.5 square degrees. Runningthis survey again in the south yields another 7.5 squaredegrees.

The zodiacal light will be the dominant source ofbackground given SNAP’s fields, orbit, and shielding

of sun and earthshine. The cosmic-ray flux3 contami-nation of 4.5 particles/cm2/s will make multiple expo-sures necessary to eliminate significant contaminationof the images.

Forty percent of the SNAP deep survey will bespent doing targeted spectroscopy of supernovae withparallel imaging (that is, imaging occurs simultane-ously during these spectroscopic observations). Theresulting images will cover random positions and ori-entations within the SNAP field and will be used toincrease the depth of the survey and help with photo-metric and astrometric cross-calibration between de-tectors.

This prearranged observing program will providea uniform, standardized, calibrated data set for eachsupernova, allowing for the first time comprehensivecomparisons across complete sets of SNe Ia. The fol-lowing reference strategies and measurements will ad-dress, and often eliminate, the statistical and system-atic uncertainties described in§ 2.1.

• Blind, multiplexed searching.

• SNe Ia at0.1 ≤ z ≤ 1.7.

• Spectrum for every supernova at maximum cov-ering the rest frame UV and Si II 6150A feature.

• Spectral time series of representative SN Ia, withcross-wavelength relative flux calibration.

• Light curves sampled at frequent, standardizedintervals starting shortly after explosion and ex-tending to 80 restframe days after explosionto obtain a light-curve-width- and extinction-corrected peak rest-frameB brightness to 10%.This requires percent-level peak-magnitude de-terminations in the supernova-frame opticalpassbands.

• Multiple color measurements in a filter set con-sisting of 9 bands approximating rest-frameBat different redshifts.

• Final images and spectra after the supernova isno longer present to enable clean subtraction ofhost galaxy light.

The quality of these measurements is as impor-tant as the time and wavelength coverage, so we re-quire control overS/N for these photometry and spec-troscopy measurements to give high statistical signifi-cance for supernovae over the entire range of redshifts.

3From http://crsp3.nrl.navy.mil/creme96/

15

TABLE 2

REFERENCESNAP SURVEYS.

Program Solid Angle Exposure Cadence # ScansPer Filter (sq. deg.) Per Scan (s) (days)

Deep North 7.5 Optical:4 × 300 4 120NIR: 8 × 300

Wide-field 300 − 1000 Optical:6 × 200 . . . 1NIR: 12 × 200

Deep South 7.5 Optical:4 × 300 4 120NIR: 8 × 300

Panoramic 7000 − 10000 Optical:6 × 67 . . . 1NIR: 12 × 67

We also require control over calibration for these pho-tometry and spectroscopy measurements, by collect-ing monitoring data to measure cross-instrument andcross-wavelength calibration.

Note that to date no single SN Ia has ever been ob-served with this complete set of calibrated measure-ments, either from the ground or in space, and only ahandful have a data set that is comparably thorough.With the observing strategy described here,every oneof > 2000 followed SN Ia will have this complete setof measurements.

The requirements on spectroscopic exposure timesand signal-to-noise are described in detail in Bernstein& Kim (2004). Using an exposure time of 8.5 hours forz = 1.7 supernovae will provide the desired spectral-parameter measurements given the SNAP spectro-graph parameters described in§5.5. Exposure timesfor supernovae at lower redshifts down toz ∼ 1 obeya scaling factor of(1 + z)6. The exact exposure timenecessary will be refined as the library of UV–opticalsupernova spectra continues to grow in coming years.

The number of supernovae that SNAP is expectedto discover is based on the supernova rate per unit vol-ume of Pain et al. (2002) assumed independent of red-shift, which when extrapolated is roughly consistentwith the discoveries of the GOODS/ACS search andSubaru supernova search. This is a conservative as-sumption compared to rates calculated incorporatingthe cosmic star formation rate (Madau et al. 1998).SNAP will be able to spectroscopically observe al-most all the supernovae with deep and good tempo-ral photometric coverage,∼ 4000 supernovae in the32-month survey. Frieman et al. (2003) find that in a

resource-limited survey with systematic uncertaintiestaken into account, using a relatively uniform distribu-tion at high redshift is optimal for providing cosmolog-ical parameter measurements. As a result, SNAP willnot provide spectroscopic followup for a fraction of thehighest redshift supernovae, which are more plentifulthan the lower redshift supernovae. For the cosmologyanalysis, we expect to cull the sample of spectroscop-ically observed supernovae to∼ 2000 events that sat-isfy strict homogeneity and extinction cuts to yield aflat distribution in cosmic time as shown in Figure 9 .

5.1.2. Weak-Lensing Program

The strengths that make SNAP excellent for super-nova observations apply to lensing as well; a wide-field imager in space with stable and narrow point-spread-functions can provide large survey areas, ac-curate shape measurements, and high galaxy angular-surface densities. The nine optical and near infraredfilters are necessary for accurate photometric red-shift determinations. The SNAP deep-survey fieldsin which the supernovae are found will thus serve asa deep lensing field. The SNAP wide-field survey hasbeen tailored to resolve the shapes of∼ 100 galaxiesper square arcminute. Over one year∼ 300 milliongalaxies will be resolved. For source galaxies withan intrinsic ellipticity distributionσǫ = 0.31 (Rhodeset al. 2000), this will achieve a signal-to-noise of unityon the shear measurement in a 1 square arcminute cell,over 1000 square degrees. The reference SNAP deepsurvey will exceed even this density requirement by afactor of three (Massey et al. 2004).

Current plans for the wide-field survey call for each

16

Fig. 9.— Close to 6000 Type Ia supernovae will ex-plode in the SNAP field of view out toz = 1.7 dur-ing the course of the SNAP deep survey (upper blackcurve). A subset of these will be observed in all fil-ters to full depth and early enough during the survey tobe followed photometrically for at least two months inthe supernova frame (middle red curve). Most of theseobjects will be observed spectroscopically. A smallersubset of supernovae with homogeneous light curvesand spectra will be used in the final cosmology anal-ysis; we anticipate using a flat distribution in cosmictime (bottom blue curve).

field to be observed for 1200 seconds in each opticalfilter, and twice as long in each NIR filter. Each point-ing will be divided up into 6 individual 200 secondexposures which are needed to eliminate cosmic raysand cover the spatial gaps between the detectors. Weare engaged in determining the systematic uncertain-ties intrinsic to the SNAP weak-lensing program tofind the optimal survey area and allotted time for thewide-field survey; initial estimates indicate 300-1000square degree field (5–16 months) are appropriate forthe wide-field survey.

The on-board storage space is matched to thetelemetry and these two constraints limit how manyimages can be stored and subsequently sent to Earth. Ifthe telemetry constraints can be eased, either througha higher download rate (and greater on-board storage)or through data compression, the exposure times canbe made shorter, thus increasing the area of the weaklensing survey.

A full description of the SNAP weak-lensing pro-gram can be found in a separate series of papers(Rhodes et al. 2004; Massey et al. 2004; Refregier

et al. 2004).

5.1.3. Panoramic Survey

A extremely wide-field “panoramic” imaging sur-vey is potentially useful for weak lensing and otherprobes of dark energy, cosmology, and astronomy ingeneral. SNAP will provide a unique means for per-forming wide-field optical imaging from space. Wethus explore the depth obtained from a three-yearSNAP survey covering 7000–10000 square degrees.We do not address specific scientific programs madepossible from this survey, considering it as a possiblelegacy dataset that can serve the astronomical commu-nity at large.

5.2. Orbit

The reference mission calls for a halo orbit aboutthe second earth-sun Lagrange point (L2). The L2point is about 1.5 million kilometers from the earthalong the sun-earth line and has a very stable thermalenvironment. There are no eclipses and heat from theearth is constant and negligible. There are ample com-munication contact opportunities from the ground toSNAP. A ground station would communicate from 2-4hours per day with the spacecraft. This orbit is highlyadvantageous from the standpoint of achieving passivedetector cooling; a three square meter radiator that op-erates at 130K provides 45 watts of gross cooling ca-pacity.

Having the SNAP fields near the ecliptic capsplaces the Sun at nearly right angles to the viewingdirection throughout the year. In an L2 orbit, theEarth and Moon will always be nearly at right an-gles to the viewing direction and on the sun side ofthe spacecraft. We utilize this viewing geometry inseveral ways. First, the solar panels can be rigidlybody-mounted on the sunward side of the spacecraft,avoiding the cost, failure modes, and flexure of de-ployed panels. Second, the passive cooling radiatorcan be rigidly located in permanent shadow on the an-tisunward side of the spacecraft. Third, the stray lightbaffling can be optimized for a limited range of solarroll and elevation angles, and for a limited range ofEarth elevation angles.

We plan to have the spacecraft perform 90 degreeroll maneuvers every 3 months during the mission, tokeep up with the mean ecliptic longitude of the Sun.The detector layout in the focal plane has a 90 degreeroll symmetry that allows photometric scans with iden-

17

tical filter coverage from season to season (see§5.4).

5.3. Telescope

The requirements placed on the SNAP telescope de-rive directly from the science goals and the missionconstraints. The wavelength coverage is determinedby the need to observe a number of filter bands acrossthe visible and NIR wavelength range spanning over0.35 µm to 1.7 µm, and to conduct low-resolutionspectroscopy of each supernova near maximum light.This requirement effectively rules out refracting opti-cal trains and drives the telescope design toward all-reflective optics.

The light gathering power is set by the need to dis-cover supernovae early in their expansion phases andto permit photometry and low-resolution spectroscopynear maximum light. These requirements can be metwith a minimum aperture of about two meters. Notethat for a fixed signal-to-noise ratio (S/N ) the ex-posure time for an isolated point source is propor-tional to the telescope aperture to the fourth power withbackground-limited noise and diffraction-limited op-tics.

Image quality is also a factor in determiningS/Nbecause of the effects of natural zodiacal light and de-tector noise. We intend to achieve angular resolutionnear the diffraction limit for wavelengths longward ofone micron. For a two-meter aperture and one-micronwavelength the Airy disk size is 0.11” FWHM. Tomatch this diffraction spot size to the CCD pixel size(∼ 10 µm) one must adopt an effective focal length ofabout 20 meters. This focal length is also matched inthe NIR where HgCdTe detectors with 18–20µm pix-els will observe out to a photon wavelength of 17000A.

A large field of view is needed to obtain multiplex-ing advantage: a single exposure can contain tens ofdifferent supernovae that are in important phases oftheir light curves. The SNAP reference mission has afield of view of the order one square degree, of whichabout 0.7 square degrees will be instrumented by de-tector pixels. The ratio of working field area to diffrac-tion patch area is about 800 million, comparable to thetotal number of detector pixels.

An excellent optical quality and low-level of distor-tion must be maintained over the working focal plane.The image quality of the telescope is driven in partby the S/N requirement, and also by the potentialsystematic supernova spectrum contamination by un-

wanted light from the supernova host galaxy. A sys-tem Strehl ratio of 0.90 at one micron wavelength isbaselined, which corresponds to an RMS wavefront er-ror (WFE) of 0.05µm. At 0.633µm the Strehl ratiois 0.77. (The Strehl ratio is the peak monochromaticimage irradiance divided by the theoretical peak irra-diance for the ideal diffraction limited image.)

5.3.1. Optical Configuration

Prospective launch vehicles (Delta IV, ATLAS V,SeaLaunch) and payload fairing dimensions imposelimits on the telescope size and its mass. An overallpayload length of about 6 meters and a payload diam-eter of about 2.5 meters will accommodate the SNAPobservatory. Through a series of packaging exerciseswe have explored ways to fit the maximum length straylight baffle into available launch fairings, and find thatwith a short optical package,∼ 3 m in length, and atall outer baffle, the required stray light rejection canbe achieved (§5.3.6).

To accommodate dimensional limitations and wide-field optical quality, the three mirror anastigmat de-scribed by Korsch (1977) is used. A schematic view isshown in Figure 10.

Primary

Secondary

Folding

flat

Tertiary

Focal plane

Fig. 10.— Reference model SNAP optics layout. Theentrance pupil is defined by the 2-m primary mirror.The exit pupil is at the folding mirror.

Details of the reference SNAP optical configura-tion have been determined by an iterative process in-volving exploring various alternative choices for fo-cal length, working field coverage, and packaging con-straints (Lampton et al. 2002b, 2003). The optimizedoptical parameters are summarized in Table 3. Theoverall length of the optical train is 3.3 meters. Com-pared with the 21.66 meter effective focal length, thissystem has an effective telephoto advantage of about

18

6.5. The mirrors are pure conic sections of revolutionhaving no polynomial terms. The use of higher poly-nomial terms has not yet been explored. The locationof the vertex of each element is listed in a Cartesian(X,Z) coordinate system whose origin is the vertex ofthe primary mirror and Z is the optical axis.

5.3.2. Mechanical Configuration

The launch environment imposes both stiffness andstrength requirements on the payload. Vehicle aero-elastic stability concerns prescribe the needed payloadstiffness in terms of minimum structural frequenciesin the axial (∼ 25 Hz) and lateral (∼ 10 Hz) direc-tions. The launch environment includes both quasi-steady and random acceleration events that are com-bined to establish the peak loads, or strength require-ments for the payload.

For a space mission it is vital to create a mechan-ical configuration which provides an extremely stablemetering structure that maintains the optical elementalignment during ground testing, launch, and orbit op-erations. The concept adopted for SNAP is to cre-ate three structural components that will be broughttogether during spacecraft/payload integration: a stifflow-precision outer baffle cylinder carrying the exte-rior solar panels and extensive thermal insulation; astiff low-precision spacecraft bus structure that carriesantennas, batteries, and other major spacecraft sup-port components; and a stiff high-precision telescopestructure comprising carbon-fiber metering elements,the kinematically-mounted mirrors, the instrumenta-tion suite, and its own thermal control system. Fig-ure 11 shows the overall payload and spacecraft lay-out, while Figure 12 shows details of the secondaryand tertiary metering structures.

5.3.3. Materials

Space-proven optical mirror technology is largelybased on two approaches: open-back Schott Zerodurglass ceramic composite material and Corning ultra-low expansion ULE glass honeycomb structure. ForSNAP either technology has sufficiently low coeffi-cient of thermal expansion and sufficiently well provenmanufacturing techniques. Studies are underway ex-ploring the detailed fabrication and test flows usingeach process.

The metering structure will utilize a low-CTEcarbon-fiber construction. In particular, the secondarysupport tripod will have to maintain the primary to

Fig. 11.— Cutaway view of the reference SNAP de-sign. The entire telescope telescope attaches to thespacecraft structure by means of bipods. The outerbaffle, shown cut away, also attaches to the spacecraftstructure by means of its separate supporting struts. Adiscardable door, shown open in light gray, protectsthe cleanness of the optics until on-orbit commission-ing begins. Solar panels are fixed, not deployed.

Fig. 12.— Telescope metering structure (carbon fiber,shown in dark gray) provides precision control of op-tical element spacings and orientations. Forward ofthe primary mirror, the secondary is supported on ad-justers within the secondary baffle. Aft of the pri-mary mirror, the tertiary metering structure supportsthe folding flat, the tertiary, and the focal plane instru-mentation. The passive radiator at top is thermally butnot structurally linked to the focal plane instrumenta-tion.

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TABLE 3

OPTICAL SURFACES AND LOCATIONS

Optic Diameter Central Hole Curvature Asphericity X Location, Z Location(m) (m) (m−1) (m) (m)

Primary 2.00 0.5 -0.2037466 -0.981128 0 0Secondary 0.45 none -0.9099607 -1.847493 0 -2.00Folding flat 0.80× 0.48 0.20× 0.12 0 0 0 0.91

Tertiary 0.69 none -0.7112388 -0.599000 -0.87 0.91Focal plane 0.577 0.258 0 0 0.9 0.91

secondary spacing accurate to a few microns. Thistripod, and the other major metering components, willcertainly require a dedicated active thermal controlsystem with passive cooling. We anticipate the needfor five-axis motorized adjustment for the secondarymirror during ground integration, on-orbit observatorycommissioning, and occasionally during science oper-ations. For this reason we plan to include a hexapod orother multi-axis positioner into the secondary-mirrorsupport structure.

The single highest priority bearing on the choice ofmirror coating is the system throughput at the longestwavelengths where rest-frame optical photons fromthe highest-redshift supernova are the most distant andphotons are the most precious. A secondary consid-eration is to establish a low thermal emissivity for themirrors so that operating them at approximately 290Kwill not seriously impair our astronomical sensitivityin the NIR bands. The most common coating for as-tronomical mirrors at visible wavelengths is SiO over-coated aluminum. It offers outstanding durability andunmatched reflectance throughout the visible band, 0.4to 0.7µm. A less common choice is protected silver,which is less efficient in the blue but more efficient inthe red and NIR. The SNAP optical system has four re-flections so its throughput varies as the fourth power ofthe mirror coating reflectivity. We have assumed herethe use of protected silver rather than protected alu-minum owing to its substantially higher total systemthroughput at the photon-starved wavelengths.

5.3.4. Geometric-Optics Performance

In the reference SNAP optical configuration, thecenter of the focal plane is severely vignetted by thenecessary hole in the folding flat which lies near theCassegrain focus. In optimizing the optical perfor-

mance of the system, the useful imaging surface onthe focal plane is taken to have an annular shape.

The optical performance of our reference telescopeis fundamentally limited by aberrations and manufac-turing errors at short wavelengths, and by diffraction atlong wavelengths. Accordingly, our expected perfor-mance figures divide into two areas: geometrical raytraces that quantify the aberrations and pupil diffrac-tion studies. We summarize the key performance itemsin Table 4 and Figure 13.

Fig. 13.— Ray trace spot diagrams. Upper left: 13mrad off axis; upper right 11 mrad; lower left 9 mrad;lower right 7 mrad. Tick marks are spaced 10µm inthe focal plane.

From spot diagrams at various off-axis angles, wehave compiled the statistics on the mean radial cen-troid of ray hits in the focal plane, and the second mo-ments of the spot distributions. These are listed in Ta-ble 5 in the form of the two orthogonal RMS breadths

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TABLE 4

REFERENCE OPTICAL PERFORMANCE

Parameter Value/Performance

Focal Length 21.66 metersAperture 2.0 meters

Final focal ratio f/10.83Field Annular, 6 to 13 mrad; 1.37 sq deg

RMS geometric blur 2.8µm, average 1 dimensionCentral obstruction 16% area when fully baffledVane obstruction 4% area, tripod

(radial RMS and tangential RMS) in columns 2 and 3.The mean breadth is listed in column 4 below as mi-crons on the focal plane, and in column 5 as an angu-lar size on the sky in milliarcseconds. At the inner andouter radii of the image annulus, the FWHM becomesas large as 60 milliarcsec, although in the midrange ofthe annulus it is smaller.

Distortion is another fundamental optical aberra-tion, but it does not impact theS/N nor does it di-rectly impact the detection of supernovae unlike theother Seidel aberrations distortion. It does howevercause the loci of scanned field objects to depart fromparallel tracks in the focal plane, and does complicatethe weak lensing science. In our reference design, wehave disregarded distortion as a driver, in order to useall available design variables to maximize the workingfield of view and minimize the net geometrical blur. Itis nonetheless important to explore the resulting dis-tortion quantitatively. The telescope mirror assembly(TMA) distortion is axisymmetric owing to the sym-metry of the unfolded (powered) optical train, and inpolar coordinates any off-axis angle maps onto a singlefocal plane radius independent of azimuth angle. Thedistortion is therefore purely radial. Column 6 of Ta-ble 5 lists the radial distance of an off-axis field pointas a function of the sine of the off-axis angle, and thedeparture from proportionality to the sine of that an-gle. The TMA distortion is of the pincushion type,having increased magnification toward the extremityof the field. Compared to a linear mapping ofsin θonto focal plane radius, the distortion amounts to abouttwo percent.

5.3.5. Pupil Diffraction

For a star at infinity and a telescope focused atinfinity, the pupil diffraction pattern is computed us-ing the Fraunhofer formalism. The focal plane irradi-ance is simply the square of the modulus of the two-dimensional Fourier transform of the pupil. We havecomputed this irradiance function and diffracted lightbackground for a variety of prospective metering struc-tures.

5.3.6. Stray Light

A comprehensive stray light control plan has beendeveloped for SNAP. The goal is to keep all stray lightsources far below the natural zodiacal irradiance levelas seen at the focal plane. The primary concern issunlight scattered past the forward edge of the outerlight baffle. This requires a minimum of two succes-sive forward edges, since the light diffracted past a sin-gle edge would exceed the allowable irradiance at theprimary mirror, assuming typical mirror scattering val-ues. Figure 14 shows our treatment of the outer baf-fle interior vane arrangement. The mission referenceL2 orbit simplifies the stray light design by eliminat-ing the possibility of sun and full Earth light enteringthe main baffle from opposite directions. Analysis ef-forts are underway to quantify the effects of both outof band light rejected by the focal plane filters, as wellas ghosting and internal reflections within the filters. Asystems engineering approach is being pursued, alongwith development of a detailed stray light budget forboth solar and stellar contamination sources.

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TABLE 5

OFF-AXIS ANGLE , IMAGE MOMENT, AND RADIAL DISTORTION

Off Axis Radial RMS, Tangential RMS Average RMS Average RMS Radial Distortionsin θ (µm) (µm) (µm) (milliarcsec) (µm)

0.006 3.32 1.60 2.62 24.9 -8380.007 3.33 1.60 2.62 24.9 -7820.008 3.18 1.59 2.53 24.1 -6300.009 2.83 1.51 2.28 21.7 -3730.010 2.28 1.37 1.89 18.0 00.011 1.57 1.35 1.47 14.0 5090.012 1.18 1.89 1.58 15.0 11650.013 2.09 3.23 2.73 26.0 1983

AVERAGE= 2.22 21.0

5.3.7. Tolerances

The departure of any surface from its nominalmathematical conic section or the misplacement ormisorientation of any of the surfaces causes a wave-front error and a degraded image quality. One measureof this degradation is the telescope’s Strehl ratio. TheStrehl ratio can be converted into RMS wavefront error(RMS WFE) through Marechal’s relation. To achievea system Strehl ratio of 0.77 at 0.633µm wavelength,the total WFE must not exceed 0.05 nm RMS. Thisallowed WFE will be apportioned into individual con-tributions as part of the detailed telescope design.

A tolerance budget has been developed based on agroup of exploratory studies of the sensitivity of thegeometrical spot size to variations in element curva-ture, shape, location, and orientation. These calcula-tions show that by far the single most critical param-eters are the primary mirror curvature and the spac-ing between primary and secondary mirrors expectedgiven the fast (f/1.2) primary mirror. A two-microndisplacement of the secondary piston, or a two-microndisplacement in the virtual image created by the pri-mary mirror is found to increase the RMS geometri-cal blur by about 3µm. Similarly, a 15-µm lateraldisplacement or a 15-microradian tilt of the secondarymirror causes a 3-µm growth in the RMS geometricalblur.

The reference model SNAP telescope includes on-orbit mechanical adjustments that permit the reloca-tion and reorientation of the secondary mirror, andpossibly the tertiary mirror as well, to optimize image

quality. By means of these adjustments we anticipateaccommodating small shifts in any of the optical ele-ments locations and orientations, allowing for correc-tion of geometrical blur.

5.4. Imager

The wide field of view of the SNAP imager al-lows simultaneous batch discovery and building of su-pernova rest-frame optical light curves, and over themission lifetime will yield several thousands of super-novae at0.1 < z < 1.7 with the proposed photometricaccuracy. More distant, less precisely measured su-pernovae will also be available in our data set. Themultiplexing advantage with this large field reducesby more than an order of magnitude the total expo-sure times necessary to follow all the supernovae. Fig-ure 3 shows critical points on the light curve and thedesired measurement accuracy that the SNAP imagermust furnish. We note that the statedS/N need not beachieved with a single measurement but can be synthe-sized from multiple measurements, taking advantageof the substantial time dilation for high-redshift super-novae.

Weak lensing by large-scale structure is a statisti-cal study that requires the accurate measurement ofthe shapes of many galaxies. In order to efficientlysurvey a large area in a finite time, a large field ofview covered by detectors with high quantum effi-ciency is necessary. Given a fixed number of pixelsin the focal plane, there are competing desires to havebetter resolution, which requires smaller pixel scalesand wider sky coverage, which requires larger pixel

22

Fig. 14.— Schematic treatment of the outer baffle in-terior vane arrangement. Sunlight is incident from theleft, where the height of the baffle and its angled for-ward edge maintains the baffle interior in darkness.

scales. The theoretical optimum of this trade-off re-quires that the pixel size be roughly matched to thesize of the PSF (Bernstein 2002); further plate scaleand pixel size studies using both simulated and realdata are currently in progress for optimizing photo-metric and shape-measurement accuracy while main-taining a large field of view. For the case of the state-of-the-art SNAP CCDs in which the PSF size is domi-nated by diffusion in the silicon at∼ 8000 A, the the-oretical optimum requires a pixel size of roughly 0.1arcsecond. (Diffusion would be worse in a conven-tional CCD that has a field-free region.) In order tomake precise, bias-free photometric redshift measure-ments, wide spectral coverage for the optical to nearinfrared is needed. Such photo-z measurements arecrucial to interpreting the cosmological implications ofthe wide-field survey. The aforementioned capabilitiesare necessary to measure the shapes of a significantnumber of faint galaxies beyondz = 1 in order tostudy the evolution of structure. Crucially importantsystematic errors in shape measurements arising fromunstable anisotropic PSFs and systematic errors/biasesin photometric redshift determination are significantlyreduced in a space-based imager such as SNAP whencompared to ground-based facilities.

The SNAP imager addresses the above require-ments using two detector technologies to efficientlycover the wavelength range of 3500A to 17000A.The visible region (3500A to 10000A) is measuredwith Lawrence Berkeley National Laboratory new-technologyp-channel high-resistivity CCDs (Hollandet al. 2003; Stover et al. 2000; Groom et al. 2000)which have high (∼80%) quantum efficiency for wave-lengths between 3500 and 10000A. Extensive radia-tion testing shows that these CCDs will suffer little orno performance degradation over the lifetime of SNAP(Bebek et al. 2002a,b). In the reference design a pixelsize of 10.5µm has been matched to the telescope fo-cal length and diffraction limit at 10000A of 0.1 arc-sec. Improved shape measurements and robust PSFphotometry come from a dithered observation strategy.Undersampling, dithering, cosmic ray hits, and manyother effects are included in the exposure time calcu-lator developed by Bernstein (2002).

The NIR range (9000A to 17000A) is measuredwith commercially available HgCdTe arrays. Currentlarge area (2048× 2048 pixel) HgCdTe detector de-vices have a pixel sizes in the range of 18 - 20µm.The telescope optics are designed to give an angularpixel size of 0.17 arcsec, matched to the telescope fo-

23

cal length and diffraction limit at 17000A. The SNAPreference performance specifications require low readnoise and dark current (< 6-8 e− for multiple readsand< 0.1 e−/sec/pix, respectively), high quantum ef-ficiency (>60%), and uniform pixel response. Ref-erence imager detector specifications are given in Ta-ble 6. The evolution of the SNAP focal-plane designis described in Lampton et al. (2002a).

The minimum filter set required is primarily deter-mined by the precision needed for the cross-filterK-correction, that is necessary when reconstructing theprimary restframe band (B-band in the reference de-sign) light from a set of laboratory-frame filter mea-surements. Six visible filters and three NIR filters aresufficient if they are derived from a B-band filter withlogarithmic(1 + z) scaling of their wavelength cen-ters and widths. The reference set that we considerhere consists of nine redshiftedB filters logarithmi-cally distributed in wavelength with effective wave-lengths at4400 × 1.15nA for n ∈ 0, 1, ..., 8. Fur-ther optimization of the filter set for supernova scienceand photometric-redshifts is in progress. In particular,the ultimate SNAP “B” filter will not necessarily bea JohnsonB although it is expected to have a similarcentral wavelength and width.

A fixed-filter design is preferred over a large fil-ter wheel which would be a single point failure risk.Figure 15 shows an array of visible and NIR filtersin the SNAP focal plane. To enhance the amount ofNIR light that is integrated, the individual NIR filtershave twice the area in the focal plane of the individ-ual visible filters. The constraint that the satellite berotated in 90 increments requires the filter pattern toremain symmetric with respect to two orthogonal axes.Consider the filter arrays in Figure 15. Note that the ar-rays can be scanned though an observation field left-to-right, right-to-left, top-to-bottom, and bottom-to-top,and that a given star will be measured with each filterbandpass but not necessarily the same physical filter.Note that any 90 rotation of the filter array can stillmeasure the star field in all filter types.

As shown in Figure 15, underlying each NIR filteris one 2k× 2k, 18 µm HgCdTe device, 36 in total.Underlying each 2×2 array of visible filters is one 3.5k× 3.5k, 10.5µm CCD, with 36 devices in all. The totalnumber of pixels is∼600 million.

The SNAP focal plane will be passively cooled tooperate at 140K, a habitable temperature for the CCDsand sufficiently cold to achieve the noise requirementsfrom the 1.7µm-cutoff HgCdTe devices. Short flex ca-

Fig. 15.— The SNAP focal plane working concept.The two-axis symmetry of the imager filters allowsany 90 rotation to scan a fixed strip of the sky andmeasure all objects in all nine filter types. The im-ager covers 0.7 square degrees. Underlying the filters,there are 36 2k x 2k HgCdTe NIR devices and 36 3.5kx 3.5k CCDs on a 140K cooled focal plane. The sixCCD filter types and three NIR filters are arranged sothat vertical or horizontal scans of the array throughan observation field will measure all objects in all fil-ters. The false colors indicate filters with the samebandpass. The central rectangle and solid circle arethe spectrograph body and its light access port, respec-tively. The spectrum of a supernova is taken by placingthe star in the spectrograph port by steering the satel-lite. The four small, isolated squares are the star guiderCCDs. The inner and outer radii are 129 and 284 mm,respectively.

24

TABLE 6

REFERENCE MISSION SPECIFICATIONS FOR THE IMAGER AND ITS SENSORS

Parameter Visible NIR

Field of View (deg2) 0.34 0.34Plate scale (arcsec) 0.10 0.17

Wavelength (A) 3500–10000 9000 – 17000〈Quantum efficiency〉 (%) 80 60

Read noise (multiple reads) (e−/pixel) 4 6–8 (multiple read)Dark current (e−/s/pixel) 0.002 0.1

Diffusion (µm) 4 5Number of fixed filters 6 3

bles penetrate the focal plane to bring the signals to theelectronics located on the backside. The present ref-erence design envisions an ASIC-based readout thatwould also operate at 140K; this avoids routing low-level analog signals long distances and reduces the sizeof the cable plant between the cold focal plane and thewarm data acquisition electronics located to the side.

A four-channel custom chip will read out each CCD(Walder et al. 2003). It consists of a single-ended todifferential converter followed by a correlated doublesampler and a novel multi-slope integrator. This circuitis designed to operate at room temperature for test pur-poses and at 140 K. The readout speed is 100 kHz. The16-bit dynamic range is covered using 3 gains eachwith a 12 bit signal to noise ratio. A 12-bit pipelineADC digitizes the analog data.

In the deep survey, multi-band exposures of a pointof sky will be achieved by shift-and-stare observationsin which the pointings are shifted by the 2.9 arcminwidth of the optical filters. Each pointing will consistof four 300-second exposures; the multiple exposuresare for cosmic-ray rejection and dithering of our under-sampled pixels. The fixed filters prevent independenttuning of exposure times for different filters. Within ascan, over one hundred pointings are required to coverthe 7.5 square degrees in all filters to the desired depth.A scan of the north (south) field will be repeated everyfour days for 16 months for a total 120 scans.

In the wide (and panoramic) surveys, long adja-cent strips will be observed using the shift and staremethod. Six rather than four dithers will be made perpointing so as to fill the gaps between the detectors andprovide robust galaxy-shape measurements. Observedpatches of sky will not be revisited. The exact shapes

of the fields are under review.

5.5. Spectrograph

The spectrometer is used to make a positive identifi-cation of Type Ia supernovae by observing the charac-teristic SiII feature at 6150A, measure the features as-sociated with supernova heterogeneity, determine theredshift of the underlying host galaxies and super-novae, build a template spectral library of SNe Ia, andlink standard stars with the SNAP photometric system.

The specific signature of Type Ia supernovae is theSiII line at λ = 6150A (rest frame). In models, thestrongest sensitivity to the metallicity in the progeni-tor system lies in the rest-frame UV band. The needfor both supernova-frame UV and Si features definesa broad wavelength range, 4000 - 17000A that mustbe covered by the instrument to observez ≤ 1.7 su-pernovae. The broad features of the supernova spec-tra and the non-negligible detector noise contributionfor the faintest objects make a low-resolution spectro-graph optimal: studies (Bernstein & Kim 2004) find anoptimal resolving powerλ/δλ ∼ 100 at FWHM and1 pixel per FWHM sampling, with constant resolvingpower in the 0.6-1.7µm range. Other types of super-novae, such as II or Ib, have lines of H or He in thesame wavelength range with similar equivalent widths,allowing supernova classification of all possible candi-dates with one spectrograph.

The silicon feature and other features in the spec-trum of a typical Type Ia supernovae, shown in Fig-ure 4, are to be carefully observed. Their characteris-tics (position, width, height, etc.) are related to the su-pernova peak magnitude through physical parameterssuch as temperature, velocity and progenitor metallic-

25

ity.

The field of view must include the underlyinggalaxy in order to determine its spectrum during thesame exposure. This is necessary for subtraction ofthe host spectrum from the spectrum in the supernovaeregion, and for an accurate determination of supernovaredshift. To avoid single-point failure in the spectro-graph we desire two detectors in each focal plane. Thedetectors cover 3”× 6” split into 40 slices that can eas-ily cover the mean size of galaxies at redshift 1-2. Thelarge field of view allows the pointing requirementsto be relaxed. The main spectrograph specificationsare summarized in Table 7. See Ealet et al. (2003) fordetails on the design process.

5.5.1. Integral Field Unit

The requirement for simultaneous acquisition of su-pernova and host spectra, the ability to subtract off thehost-galaxy spectrum after the supernova has faded,spectrophotometry for calibration purposes, and thehigh object acquisition precision that would be neededfor a traditional long slit spectrograph, make a 3Dspectrograph an attractive option. A 3D spectrographreconstructs the data cube consisting of the two spa-tial directions X and Y plus the wavelength direction.For each spatial pixel, the spectrum is reconstructed.Two principal techniques are indicated for 3D spec-troscopy: first, the use of a Fourier Transform Spec-trometer (FTS), and second, the use of integral fieldspectroscopy.

Trade studies indicate that integral-field spec-troscopy using the image slicer technique is preferredfor SNAP. This technique, developed since 1938 in or-der to minimize slit losses, is very powerful (Bowen1938; Content 1997; Prieto et al. 2002). The new gen-eration of image slicers improves the efficiency andthe compactness of the system and appears to be avery well adapted solution for the SNAP mission.

Figure 16 shows the principle of this technique. Thefield of view is sliced alongN (in the drawingN = 3,for SNAPN = 40) strips on a slicing mirror, consist-ing of a stack ofN plates where the active surface ison an edge. Each of theN slices re-images the tele-scope pupil, creatingN telescope pupil images in thepupil plane. Thanks to a tilt adapted to each individ-ual slice, theN pupil images lie along a line. In thepupil plane, a line of “pupil mirrors” is arranged. Eachpupil mirror is placed on a pupil image and reimagesthe field strip. These images are arranged along a line

and form a “pseudo-slit”. At this stage, therefore, thereis an image of each of theN strips of the field of view.The pseudo-slit is placed in the entrance plane of thespectrograph, acting as the entrance slit. A last line ofmirrors is placed on the pseudo-slit. This line adaptsthe output pupil of the slicer into the input pupil of thespectrograph.

5.5.2. Reference Spectrograph Instrument Concept

The spectrograph components are summarized inthe block diagram shown in Figure 17 with the prin-cipal components described below.

Relay Optics

This unit is the interface between the telescope beamand the instrument. Some telescope aberrations can becorrected within this optical system. A simple three-mirror configuration should be sufficient to allow pick-

Fig. 16.— Principle of the image slicer. The field ofview is sliced alongN (hereN = 3) strips on a slicingmirror. Each slice re-images the telescope pupil ontoa line of “pupil mirrors” which reimages the field stripalong a “pseudo-slit”. The pseudo-slit is placed in theentrance plane of the spectrograph, acting as the en-trance slit (courtesy J. Allington-Smith, Durham U.).

26

TABLE 7

REFERENCE MISSION SPECTROGRAPH SPECIFICATIONS

Property Visible NIR

Wavelength coverage (µm) 0.35-0.98 0.98-1.70Field of view 3.0”× 6.0” 3.0”× 6.0”

Spatial resolution element (arcsec) 0.15 0.15Number of slices 40 40

Spectral resolution,λ/δλ 100 100

Fig. 17.— A schematic spectrograph optical design.The beam is going out from the slicer (on the bot-tom right) to a prism disperser back faced coated bya dichroic. The visible light (blue path) is reflectedand the IR light (in red) continue to a second prismused to reach the required spectral dispersion. Thetwo beams are therefore focused on two detectors.The dimensions of the spectrograph are approximately400 × 80 × 100 mm.

ing off the beam at a point most convenient for thespectrometer.

Slicer Unit

The slicer unit acts as a field reformatting system. Asdescribed above, the principle is to slice a 2D field ofview into long strips and optically align all the stripsto form a long spectrograph entrance slit. The slicingmirror is comprised of a stack of slicers. Each slicerhas an optically active spherical surface on one edge.A line of pupil mirrors does the reformatting. Eachpupil mirror sends the beam to a slit mirror, whichadapts the pupil to the entrance of the spectrograph.

The long thin active surface of each individual

slicer will produce a large diffraction effect. In orderto minimize flux losses to a few percent, the spectro-graph entrance pupil must be oversized. A combinedtheoretical and experimental approach is underway atLaboratoire d’Astrophysique de Marseille to define theoptimum entrance pupil for a JWST application (in theinfrared bands 1-5µm). This will be directly adaptedfor the SNAP concept.

The reference requirements on the slicer unit are anaccuracy of≤ λ/10 RMS on the optical surfaces anda surface roughness of≤ 50 A RMS. Existing proto-types fully meet these specifications.

Optical Bench

Thanks to the moderate beam aperture and field ofview, the spectrograph optics will be straightforward.The reference is a classical dichroic spectrograph: onecollimator mirror, one prism with a dichroic crystal,and two camera mirrors are required. Using sphericalshapes for all the mirrors would provide an adequatelysharp image, but using aspheric mirrors will make itpossible to have a very compact spectrograph. Theprism solution is well matched to the requirement of aconstant resolution over the whole wavelength range.The dichroic crystal allows the coverage of two chan-nels simultaneously: one for the visible (e.g.. 0.35–0.98µm) and one for the infrared (0.98–1.70µm).

Detectors

In the visible, the main goals are high quantum effi-ciency and very low noise. Given concerns over degra-dation due to radiation exposure and the poor perfor-mance of conventional thinned CCDs in the red partof the visible, the fully-depleted LBNL CCDs are thedetectors of choice. Thinned, back-side illuminated,deep depletion, low-noise conventional CCDs of 1024

27

× 1024 pixels are an alternative option. In the NIR,some factors constrain the detector technologies. Theoperating temperature will be dictated by the detectordark current. HgCdTe arrays with cutoff wavelength of1.7µm are currently under consideration which allowoperation in the 130-140 K range. A detailed list ofthe performance specifications for the detectors is pro-vided in Table 8. To achieve the listed performance inread noise and dark current, a multiple sampling tech-nique is required. To optimize exposure time, the im-pact of the rate of cosmic rays on the spectrum qualityis under study.

5.5.3. Efficiency Estimate

Simulations of the efficiency of the instrumentshow a cumulative efficiency of the instrument fromthe relay optic and including the detector at a levelbetter than 50% in the visible and 40% in the infrared.This excellent performance is due to high slicer ef-ficiency and is based on a conservative value for theefficiency of individual mirrors (98%), much lowerthan is expected from a silver coating at these wave-lengths. The principal losses are from the prism (alsoconservatively estimated at 80%), and from the detec-tor.

5.6. Telemetry

During the reference deep survey, the observationtime of SNAP is partitioned roughly 60% to prepro-grammed, stepped photometry and 40% to targetedspectroscopy with parallel photometry. The former isdivided into a sequence of 300s exposures followedby 30s of sensor readout. The latter is comprised ofexposures varying from a few seconds to a thousandseconds. For the longer exposure times, the spec-trograph NIR detector is continuously read in up-the-ramp mode to allow cosmic-ray rejection. Imaging ispossible during spectroscopic exposures; the imageris read as in photometry mode except that the expo-sure times vary, determined by the time to achieve arequiredS/N in the spectrograph for a particular su-pernova. For each imaging exposure, the CCD devicesproduce a single frame of correlated double sampleddata while the NIR devices produce two frames (eachcontaining the average of multiple reads), one for postreset values and the other for post integration values sothat the digital correlated double sampling can be doneon the ground.

The operating concept for processing the raw data

is to perform only lossless compression of the framesin the satellite. A factor of two is easily done; a greatercompression factor is probably achievable. The pri-mary motivations are to be able to look retrospectivelyinto the data to better determine a supernova explosiontime and to be able to co-add many months of data forweak lensing science to extract weak signals from theper frame noise. With this approach we avoid develop-ing flight software for automated acquisition and pro-cessing of reference, dark and flat frames and applyingthem irrecoverably to data frames. The consequenceis that in L2 SNAP will require about 133 Gb of flightdata storage for a 24 hour contact period through theDeep Space Network capacity. We anticipate that DSNwill have the ability to receive 300 Mbit s−1 Ka-banddata by the time SNAP launches.

The current reference weak lensing survey (Rhodeset al. 2004) calls for a 1-year 1000 square degree sur-vey consisting entirely of imaging. At L2, 6 ditheredexposures per optical filter would be taken for a totalof 1900 s. Such a survey would require a daily fourhour download of data and would use only∼ 150 GBof on-board storage. A wider survey could be takenif more time were given to the survey or if the expo-sure time per filter were lowered. The latter optionwould require that the data download time be accord-ingly raised to compensate for more exposures or thatthe on-board compression of the data be increased be-yond the factor of two that can be achieved throughlossless compression.

6. Calibration Program

An important feature of the supernova-cosmologyanalysis is its dependence on therelativebrightness ofType Ia supernovae. Cosmological and dark-energyparameters are determined from the shape, and notthe absolute normalization, of the Hubble brightness-redshift relationship. In order to constrain the possibleeffects of population evolution, SNAP will use homo-geneous subsets of SN Ia. Identification of these SNIa subsets depends in part on the brightness and colorevolution of supernovae. Each supernova redshiftzis plotted against its restframe B band flux which de-pends on the K-correction and the extinction correc-tion, which in turn depend on the color of the super-novae. As a result, the analysis relies on thecolor,where we use this term to mean the flux ratios ofcalibrated passbands. The SNAP calibration programmust thus precisely control the absolutecolor calibra-

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TABLE 8

REFERENCE MISSION SPECTROGRAPH DETECTOR SPECIFICATIONS

Visible NIR

Detector size 1k× 1k 1k× 1kPixel size (µm) 10-20 18-20

Detector temperature(K) 140 130-140〈QE〉(%) >80 >60

Read noise(e−/pixel) 2 5 (multiple read)Dark current(e−/pixel/s) 0.001 0.02

tion, not necessarily the absolute flux calibration, inthe0.35 − 1.7 µm observing window.

The SNAP calibration program will provide fluxesin physical units associated with the same restframepassband for a homogeneous set of supernovae dis-tributed out toz = 1.7. Calibration provides the trans-formation of the measured signal in a given passbandinto a flux associated with a calibrated passband. Cali-bration affects flux-correction for extinction due to theMilky Way, the SN host galaxy, and the intergalac-tic medium, and also the K-corrections which providethe transformation between fluxes in the observed andrestframe passbands.

In the SNAP cosmological-parameter determina-tion, calibration enters early in the analysis and con-sequently the calibration uncertainty propagates non-trivially throughout. Depending on its nature and size,the calibration uncertainty can contribute significantlyto thew0 − w′ error budget. The propagation of theseuncertainties has been explored in Kim et al. (2004)for a simplified blackbody calibration model. Realis-tic calibration uncertainty will be more complex andthe SNAP calibration methodology is being crafted toensure that calibration does not impede achievementof the science goals.

The SNAP reference calibration concept consists ofseveral programs which are subject to ongoing workexamining modifications, extensions, and alternativestrategies. A set of astronomical sources with knownphysical fluxes (or more importantly known physicalcolors) are established as “fundamental standards”. Anetwork of fainter primary and secondary standardstars, accessible to SNAP and larger ground-basedtelescopes, are established with respect to the fun-damental standards. The SNAP observatory has anobservation and analysis program that takes standard

star observations and derives a transformation betweenSNAP signals and fluxes in the instrument passbands.These programs are described in detail in the followingsubsections.

6.1. Fundamental Standards

In the ideal situation, target supernovae would becalibrated directly against a true irradiance standardobserved through the same optical chain. However,because of the unavailability of convenient irradiancestandards observable through the same optical path asthe supernovae, a suitable, calibrated proxy (or prox-ies) must be identified. Consequently SNAP must usestars as irradiance and color standards (standard can-dles). These selected stars may be established as stan-dards using calculations of model stellar atmospheresas a substitute for a NIST-traceable irradiance stan-dard. A few stars may be unreddened and easy tomodel, so that all or part of the standard candle fluxdistributions can be replaced by a suitably normalizedmodel atmosphere calculation. Traditionally in opti-cal astronomy the bright,V = 0 star Vega has beenused as the NIST stand-in. However, Vega itself is fartoo bright to be used for most astronomical programs,so it has been used to calibrate fainter stars e.g. theLandolt standards, Oke standards etc. The SNAP cal-ibration program has identified “fundamental standardstars” to be bright,V ∼ 12, stars whose spectral en-ergy distributions are independently determined. AtV = 12 − 13, the fundamental stars may be observedwith the SNAP spectrograph.

The current Hubble Space Telescope fundamentalflux standards are a set of three WD stars and could bea good choice for the basis of the SNAP flux calibra-tion. These stars have pure hydrogen atmospheres andare too hot for molecular constituents, which means

29

that the physics of the model calculations are relativelystraightforward. The three models are normalized near5500A using Landolt V band magnitudes. The HSTprogram ((Bohlin et al. 2001) also provides three pri-mary solar analog standards, whose optical flux hasbeen measured on the WD flux scale and whose IRflux shape is solar. The stellar model approach is atested method that yields a precision of∼ 1% in theUV and optical, while the near infrared relative fluxesare less well tested. The systematic flux errors in theWD model technique have been estimated by the dif-ference between the two extreme models that still fitthe observations. This uncertainty reaches a maxi-mum in the SNAP wavelength range of 1.8% at 1.7µm,meeting the goals of the reference mission. One possi-bility for further reducing the uncertainties is to verifythat the WD modelTeff andlog g values derived fromthe Balmer line profiles fit uniformly for the Lymanand Paschen lines, as well. A second verification inprogress with NICMOS is to confirm to< 1% the rel-ative IR fluxes of the models and the solar analogs.

The direct method of determining stellar fluxes isto compare observations of stars, particularly in thenear infrared, with a lamp source. As stated in Bohlinet al. (2001) “In order to improve the accuracy of thestandard star IR flux distributions, some standard starsshould be compared to an actual standard IR lamp todefine a proper absolute flux calibration, just as wasdone for Vega. . . . such fundamental data are lacking. . . ” These authors normalize the flux scale at onebandpass once the spectral shape has been determined,while a lamp comparison determines both the absolutelevel and the shape of the spectral flux distribution.The absolute calibration of Vega (Hayes & Latham1975; Hayes 1985) exemplifies a direct method of es-tablishing a fundamental calibrator. The need and ap-proach for such an experiment is under study by theSNAP calibration team.

6.2. SNAP Standard Star Network

In order to minimize the need for on-orbit calibra-tion time, a ground-based standard star network con-sisting of the fundamental standards linked to primaryand secondary standards will be established. This net-work will provide the preliminary calibration data forthe spacecraft by setting the spectrophotometric zero-points. Further, the network will enable parallel andfollow-on observation from the ground to support on-orbit science observations. The network will establishan all-sky photometric system covering the spectrum

from 3500 to 17000A and spanning approximately 6magnitudes (12 to 18 mag) of brightness.

Primary standards are fainter (V = 15 − 18) thanthe fundamental standards and will be calibrated withrespect to the fundamental standards through spec-trophotometry and photometry. They will be used totransfer the calibration to an “all sky” grid. Some willlie in the SNAP science fields and others around the ce-lestial equator to tie the northern and southern SNAPfields together and provide standards distributed over24 hours. The primary standards will be tied to the sec-ondary standards through spectrophotometry and pho-tometry. Secondary standards will be in the SNAPfields. They will span a wide color and magnitude(V > 18) range, and hence spectral type. Uncertain-ties will be minimized by multiple observations of thefields.

Once in orbit, we will verify the zeropoints for boththe primary and the secondary standard stars. Theplanned repeating observation cadences will allow typ-ically 140 observations of every star in the SNAP-N and SNAP-S fields over the course of the mission,leading to refinement of the brighter secondaries andestablishment and verification of the fainter secon-daries.

6.3. Calibration Transfer

SNAP is developing a flux-based (rather thanmagnitude-based) plan for transferring the funda-mental standard star calibration to the primary andsecondary standards, and ultimately to supernovaethrough a combination of spectroscopy and photom-etry. There are two common choices of calibrationpassbands. Traditionally in observational astronomya set of passbands is associated with a specific mag-nitude system. These (virtual) passbands, when usedto observe the system’s primary standard stars, repro-duce exactly the tabulated magnitudes. Bessell (1990)has produced throughput realizations of the Johnson-Cousins magnitude system. Another approach is to useobservations to infer the actual throughput of the ob-servers optical system (including atmosphere). SNAPcan use both approaches in its calibrations. Further,as the demand for precise calibration is fairly strin-gent, SNAP needs to be able to account for changesin the instrument performance. For example, we in-tend to re-determine the transmission properties of thephotometry filters during the mission by taking advan-tage of the multiple observations of stars in the SNAP

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fields provided by the 4-day observing cadence. Inter-nal calibrated, stable illumination sources may also beutilized.

7. SNAP Simulation

The design of the SNAP reference mission has beenguided by the Fisher-matrix analysis described in§2.3.A detailed simulation of the reference mission nowprovides validation of the scientific reach of the SNAPmission and provides a tool for further mission refine-ment and optimization. We have developed a detailedparameterized simulator of supernova cosmology mis-sions. We describe here its use in projecting the scien-tific yield from the SNAP supernova reference missiondescribed in this paper. A similar but more completepixel-level simulation will be used to test the mission-analysis software.

For the telescope/camera configuration and observ-ing plan described in the previous sections, we gen-erate a list of Type Ia supernovae and their associatedhost galaxies in the observed field of view during thecourse of the survey. The incident flux at the telescopeis calculated for each supernova, accounting for the un-derlying cosmology, magnification from gravitationallensing, and host and Galactic dust. The photometricobservations of the supernovae from the SNAP scan-ning strategy are simulated, resulting in multi-bandlight curves for each event.

The rest-frameB andV light curves are fit to SNIa-class templates while the light curves in other fil-ters are fit to a polynomial, in order to measure themagnitude, color, and light-curve parameters of eachsupernova. Triggered spectroscopic observations aresimulated through Fisher-matrix techniques (Bernstein& Kim 2004) which predict the quality of the spectro-scopic parameter measurements. Supernova observ-ables are related to the intrinsic peak absolute mag-nitude using the models described in Hoflich et al.(2003). In this manner, supernova’s light-curve andspectral parameters are then used to determine its dis-tance modulus, along with host-galaxy extinction (AV

andRV of the Cardelli et al. (1989) dust model) andits individual absolute magnitude.

Given the reference SNAP supernova distributionand expected distance moduli folded with the expectedsupernovae from the Nearby Supernova Factory, we fitthe cosmological parameters. While this can be donefor a general set of parameters, we concentrate on thedark-energy parametersw0 andw′ assuming a flat uni-

verse and a fiducial model withw0 = −1 andw′ = 0(recall we definew′ ≡ dw/d ln a|z=1 ≈ wa/2). Thestandard systematic-error model is adopted. Marginal-izing over all other parameters, we get uncertainties inw0 of 0.07 andw′ of ∼ 0.31 for the prior 0.03 un-certainty inΩM . If we take no prior inΩM but as-sume cosmological constraints expected from Planck,the w′ uncertainty improves to∼ 0.16. These re-sults are somewhat better than those determined in theFisher analysis shown in Table 1 where all supernovaeare assumed to have identical distance-modulus uncer-tainty. By setting exposure times based on light-curverequirements for the highest redshift supernovae, thelower redshift events have betterS/N with the fixedfilter design.

To explore how SNAP will be able to distinguishbetween different dark-energy models, we simulateconstraints onw0 andw′ choosing as fiducial modelsinstantiations of two postulated theories that accountfor an accelerating universe: a cosmological constantand a supergravity-inspired model. Using Monte Carlowe generate 68% confidence contours for SNAP super-novae, in conjunction with the data anticipated fromthe Planck mission, and SNAP supernovae and weaklensing. (Figure 18). We marginalize over the absolutemagnitude andΩM with no prior imposed on either.

Even with just SNAP supernovae, the chosen mod-els are distinct, with the fiducial values lying well out-side the 68% contours of the other model. Inclusionof SNAP weak-lensing power spectrum, bispectrum,and cross-correlation cosmography information pro-vides improved sensitivity. SNAP and complementarydata will provide important guidance to the true natureof dark energy.

We have done the most detailed simulation of aweak lensing survey to date by identifying instrumen-tal aspects of SNAP that will affect the PSF, apply-ing this PSF to simulated images, and calculating thelensing efficiency and subsequent constraints on cos-mological parameters from the SNAP weak lensingsurvey. The results of these studies are in Rhodeset al. (2004); Massey et al. (2004); Refregier et al.(2004). The cosmological reach of the SNAP weak-lensing program presented in this paper is based onthese simulations. We are continuing to develop theimage simulations for more accurate results and to bet-ter identify instrumental factors that might be tweakedfor gains in sensitivity to weak lensing. We also areexploring the impact of new analysis techniques, e.g.bispectrum measurements of the mass distribution and

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Fig. 18.— The 68% confidence region in the dark-energy parameters for fiducial cosmological constant(labeled withΛ) and supergravity (labeled with S) uni-verses. The blue dashed curves show the results of thesupernova simulation with a Planck prior and an as-sumed flat universe. Using Fisher analysis, we findsignificant improvement is obtained using the SNAPsupernova and 1000 square-degree weak lensing sur-veys (black curves). Additional CMB data (dotted redcurves) provides additional constraints for the super-gravity universe, but not for the fiducial cosmologicalmodel. We definew′ ≡ dw/d ln a|z=1.

cross-correlation cosmography, for measuring dark-energy parameters (Bernstein & Jain 2004; Jain & Tay-lor 2003; Takada & Jain 2003).

8. Ancillary Science with the SNAP Survey Fields

The SNAP surveys will have an unprecedentedcombination of depth, solid-angle, angular resolution,temporal sampling, and wavelength coverage from theoptical to the NIR. The wealth of potential sciencefrom deep and wide-field surveys has already beendemonstrated in such surveys as the Hubble DeepFields (Williams et al. 1996, 2000) and the SDSS(Abazajian et al. 2003). In§4 we summarized howthe SNAP data set will contribute to our understand-ing of dark energy. We here explore the properties ofthe surveys and their potential scientific yield in otherareas.

8.1. SNAP Survey Depth

Based on the telescope and camera characteristics,we quantify the expected depth, solid-angle, and timeresolution of the SNAP supernova and weak lens-ing surveys. The telescope and camera properties ofSNAP have been modeled and incorporated into anadvanced exposure-time calculator (ETC) (Bernstein2002). Besides having all the usual capabilities of astandard ETC, our ETC includes unique handling ofthe pixel response function, undersampling, dithering,and probabilistic cosmic-ray rejection. As mentionedin §5.4, SNAP will use dithering to obtain spatial res-olution below the pixel scales.

The high cosmic-ray flux in a space environmentproduces a non-trivial reduction of effective exposuretimes; pixels from a single exposure that are contami-nated by a cosmic ray are recognized through medianand other filtering and dropped in the dithered recon-struction. The expected contamination probability ofa point source is 0.0002 per second. Short individ-ual exposure (plus readout) times limit the contami-nation: four 300 second exposures give better than a99% probability that there will be no cosmic-ray con-tamination at a given position for at least one of thedithers that make up a pointing.

The magnitude depths for individual scans and co-added images of the SNAP supernova fields are cal-culated for each filter. Table 9 shows the limitingS/N = 5 AB magnitude for each filter in the surveys,for point sources that are not contaminated with cos-mic rays. As with the HST, the limiting magnitudefor any given point is probabilistic, due to the ran-dom occurrence of cosmic rays. The probability for agiven level of cosmic contamination (and approximatedegradation in signal-to-noise) can be determined us-ing the binomial distribution. In a single scan of thedeep survey 77% of point sources will have no cosmiccontamination in any of the four dithered images while98% will have one or fewer cosmic-contaminated im-age, only slightly reducing signal-to-noise.

The SNAP observing strategy provides remarkablyeven depth over the range of filters. For a given fil-ter, individual scansof the deep and wide-field sur-veys are only∼ 0.75 magnitudes shallower than theHubble Deep Fields (HDFs) while the deep fields co-added over time are∼ 1.5 magnitudes deeper than theHDFs (Williams et al. 1996) and up to 0.5 magnitudesdeeper than the UDF depending on the filter. SNAPhas the additional advantage of having nine filters ob-

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TABLE 9

THE SNAP AB MAGNITUDE SURVEY DEPTH FOR A POINT SOURCES/N = 5.a

Filter λeff (A) ∆λ(A) Deep Survey (AB mag) Wide-field Survey PanoramicPer Scan Co-added Scans (AB mag)

1 4400 1000 27.9 30.6 28.3 26.72 5060 1150 27.9 30.6 28.3 26.83 5819 1322 27.8 30.5 28.2 26.84 6691 1520 27.8 30.4 28.1 26.85 7695 1749 27.8 30.4 28.1 26.86 8849 2011 27.7 30.3 28.0 26.77 10177 2313 27.5 30.1 27.8 26.68 11704 2660 27.5 30.1 27.8 26.69 13459 3059 27.4 30.0 27.7 26.5

aRandom cosmic-ray hits make theS/N for a given position probabilistic; see text. Thechoice of filter set is currently subject to optimization studies; the filters and depths presentedhere are meant to be illustrative.

serving to this depth, compared to the four filters ofthe HDFs, and 9000 times the area in the deep survey;when these data from all filters are combined, the lim-iting magnitude increases by another 0.6 magnitudes.The wide-field survey has∼ 600, 000 times the area ofthe HDFs.

SNAP fields will contain many faint diffuse galax-ies whose detection is important for the weak-lensingstudies, and for other potential science projects. Thelimiting magnitudes for Gaussian-aperture photometryof an exponential-disk galaxy with FWHM=0.12” areshown in Table 10.

8.2. Ancillary Science

In this section we give a brief outline of additionalscience topics likely to benefit from SNAP survey data.This list is incomplete, and includes only a few of themost obvious ancillary science projects.

The SDSS (York et al. 2000), Hubble Deep Fields(HDFs) (Williams et al. 1996, 2000), and Ultra DeepField4 demonstrate the vast range of science enabledby wide, deep, and precise multi-band surveys. SNAPwill carry this tradition forward as the first wide fieldsurvey in space.

SNAP deep-survey fields will cover more than 9000

4http://www.stsci.edu/hst/udf

times the area of the HDFs, go even deeper, include9 color observations, and provide significant time do-main information. The SNAP wide-survey field iscomparable in size to the Sloan Southern Survey5 andCFHT Legacy Survey6 but includes diffraction limitedimaging, and probes many magnitudes fainter in morefilters. A panoramic survey would cover almost a quar-ter of the full sky at slightly shallower depth. Thecombination of depth, temporal coverage, wavelengthrange, diffraction-limited seeing, and wide field makeSNAP imaging surveys uniquely powerful in the studyof a wide range of objects and phenomena, which weoutline below.

• Galaxies — Within the 15 square degree deepsurvey area, SNAP will make accurate (∆z <0.03) photometric redshift estimates for at least107 galaxies from redshift 0 to 3.5, spanningmore than 90% of the age of the Universe. Sta-tistical studies are possible with such a largesample, e.g. the determination of the galaxy lu-minosity function and color distributions as afunction of redshift. Photometric redshifts canbe estimated from the 4000A break for galax-ies out to aboutz = 3.2. For galaxies at stillhigher redshift, the simplest indicator is the Ly-

5http://www.sdss.org6http://www.cfht.hawaii.edu/CFHLS

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TABLE 10

THE SNAP AB MAGNITUDE SURVEY DEPTH FOR AN EXPONENTIAL-DISK GALAXY HAVING FWHM=0.12”FOR S/N = 10.a

Filter λeff (A) ∆λ(A) Deep Survey (AB mag) Wide-field Survey PanoramicPer Scan Co-added Scans (AB mag)

1 4400 1000 26.4 29.0 26.8 25.22 5060 1150 26.3 28.9 26.7 25.33 5819 1322 26.3 28.9 26.6 25.34 6691 1520 26.2 28.8 26.6 25.35 7695 1749 26.3 28.9 26.6 25.36 8849 2011 26.2 28.8 26.5 25.37 10177 2313 26.2 28.8 26.5 25.38 11704 2660 26.2 28.8 26.5 25.39 13459 3059 26.1 28.7 26.5 25.3

aRandom cosmic-ray hits make theS/N for a given position probabilistic; see text. Thechoice of filter set is currently subject to optimization studies; the filters and depths presentedhere are meant to be illustrative.

man break. For SNAP, the Lyman break entersthe optical imager around redshift 3. In princi-ple it can be followed using SNAP data beyondredshift 10, allowing identification of extremelyhigh-redshift galaxies. The magnitude depthalso allows discovery of low-surface-brightnessand very high-redshift galaxies. High-resolutionimages will provide a view of the internal struc-ture of galaxies and their interactions with eachother. This data set, which will include morpho-logical information for every object, will pro-vide a unique opportunity to study the evolu-tion of galaxies. The flood of galaxy evolutionpapers based on the Hubble Deep Fields pointsthe way to what will be possible with the SNAPimaging data set.

• Galaxy structure formation — The wide-fieldsurveys from SNAP offer an excellent oppor-tunity to study galaxy clustering and its evolu-tion at high redshifts (≈ 0.3 – 3). This is aregime which is both especially interesting andrather poorly understood. There are some mea-surements of galaxy clustering at high redshift(Steidel et al. 1996), but these are severely lim-ited by sample variance (Somerville et al. 2004).SNAP, increasing the size of high redshift sur-veys by several orders of magnitude, will be sub-

stantially less sensitive to cosmic variance. Pho-tometric redshifts greatly enhance this work, al-lowing detailed study of the evolution of galaxyclustering.

• Galaxy clusters — Galaxy clusters, the mostmassive bound objects in the Universe, pro-vide important probes of our understanding ofstructure formation (Evrard 1989). Constrain-ing their formation and evolution is an impor-tant observational goal for the coming decade.Recent advances have overcome earlier limita-tions of optically selected cluster samples, es-sentially by using photometric redshift informa-tion to eliminate projection effects (Gladders &Yee 2000; Bahcall et al. 2003). Hubble VolumeΛCDM simulations (Evrard et al. 2002) predictthat the SNAP surveys will provide detailed in-formation on tens of thousands of galaxy clus-ters with masses above5× 1013 M⊙. With NIRsensitivity, SNAP will allow sensitive detectionof galaxy clusters all the way back to their earli-est appearance aroundz = 2. The overall num-ber of galaxy clusters is exponentially sensitiveto the amplitude of initial density fluctuations.

• Quasars — Quasars are identified in multi-colorimaging surveys by their non-stellar colors. This

34

method has been shown by the Sloan DigitalSky Survey to be extremely effective at identi-fying quasars to redshift 6 and beyond. SDSSquasar discovery is limited to redshift 6.4 bythe CCD sensitivity cutoff at 1.0µm (Penter-icci et al. 2002). The most distant SDSS quasar,at redshift 6.42 (Fan et al. 2003), has az-bandmagnitude of 20. By probing to wavelengths1.7 times greater, and to depths 9 magnitudesfainter, SNAP will be able to detect quasars toredshift 10, and to probe the quasar luminosityfunction to 100 times fainter than the brightestquasars. SNAP’s ability to identify diffuse ob-jects associated with quasars may present inter-esting opportunities for the study of galaxy for-mation.

• Gamma-ray burst afterglows — Current evi-dence suggests that gamma-ray bursts are asso-ciated with the collapse of massive stars whichlive short lives and die where they are born.As a result, GRB’s may trace the cosmic starformation rate. If so, there should be GRB’sessentially coincident with the epoch of forma-tion of the first stars. The most distant GRBknown occurred at redshift of 4.5 (Andersenet al. 2000). SNAP will be able to identify GRBafterglows, and the orphan afterglows predictedby some models of beaming in GRB’s toz = 10.Such orphan afterglows may even be detected asbackgrounds to the SNe search.

• Reionization history — The Universe becameneutral at the time of recombination, aroundz = 1000, and the thermal radiation from thatepoch travels to us undisturbed as the cosmicmicrowave background radiation. The lack ofa Gunn-Peterson effect in the spectra of mostquasars demonstrates that the Universe wasreionized at some time betweenz = 1000 andz = 6. The source of the ionizing radiation is thesubject of substantial speculation. The recentdiscovery of an apparent Gunn-Peterson troughin the spectra of severalz > 6 SDSS quasarsmay provide the first glimpse of the epoch ofreionization (White et al. 2003). By identify-ing many quasars and galaxies toz = 10, SNAPwill set the stage for mapping the epoch of reion-ization in unprecedented detail. In combinationwith ground based and JWST spectroscopy, itwill enable measurements of the proximity ef-

fect and studies of the spatial structure of reion-ization.

• Transients/Variables — The discovery and ob-servation of SNe Ia are the primary goals ofSNAP, but transient “backgrounds” are interest-ing in their own right: quasars, active-galactic-nuclei, gamma-ray-burst optical counterparts,supernovae of other types, variable stars, andeclipsing binaries. Of particular interest to cos-mology are time-delay measurements of thelarge expected number of strongly lensed vari-ables (Blandford & Koopmans 2001). Gravita-tional microlensing studies of stars and quasarsas probes of compact dark matter are also possi-ble.

• Stars — Faint limiting magnitudes and excel-lent star-galaxy separation will yield faint dwarfand halo stars. Proper motion can be detectedwith high-resolution and a long time reference.SNAP’s accurate colors will yield excellent pho-tometric parallaxes to all stars in the field. Thegeometry and substructure of the Galactic haloand disk in the direction of the SNAP fields canbe mapped. Of particular interest would be acensus of low-mass L and T stars and browndwarfs throughout the Milky Way disk (Leggettet al. 2000).

• Solar-system objects — The peculiar motionand parallax in the time-series data will facilitatethe identification of local objects such as aster-oids and Kuiper-belt objects. SNAP time seriesdata will provide an excellent probe of faint, redobjects in the Kuiper belt and beyond. A 2-3month dedicated ecliptic survey with the SNAPsurvey would detect 10–50,000 Kuiper belt ob-jects down to the size of the Comet Halley’s nu-cleus.

• Weak gravitational lensing — The importanceof weak gravitational lensing for dark energy isdescribed in§3. Weak gravitational lensing isalso a powerful tool in mapping the distributionof mass in the Universe. Maps reconstructedfrom the observed shear field are sensitive toany mass along a given line of sight, regard-less of its nature or state allowing dark mattermapping and the unbiased detection of galaxyclusters and their mass. The high surface den-sity of resolved background galaxies enables the

35

construction of both two- and three-dimensionalmaps of the foreground dark matter distribution.In addition to providing further constraints uponcosmological parameters, these maps trace thegrowth of structure in the Universe and can beuse to study the bias between mass and lightthrough comparison with the galaxy distribu-tion.

In recent years many groups have measured theshape distortions of field galaxies due to weaklensing and used these shear measurements toset constraints on cosmological parameters. Ina number of weak-lensing surveys using groundand space-based data the second moment of theshear field has provided a constraint on the mat-ter power spectrum, in particular on the quantityΩMσ0.5

8 , that is comparable to the constraints setby more traditional methods such as the abun-dance of X-ray clusters. Current weak-lensingsurveys seeking to measure higher order mo-ments of the shear field and the magnificationof background galaxies promise to provide anindependent measure ofΩM , thus breaking thedegeneracy betweenΩM and σ8, whereσ8 isthe amplitude of mass fluctuations on the scale8h−1 Mpc.

Precise photometric redshifts enable the makingof 2-dimensional mass maps in multiple redshiftslices, and even 3-dimensional mass reconstruc-tions. This redshift tomography is much lesseffective from the ground because of the lowersurface density of resolved galaxies, and can-not be extended as far. Space-based imagingis needed to resolve sufficiently many sourcegalaxies atz > 1 and follow the growth ofstructure at those redshifts. Furthermore, high-resolution images coupled with photometric red-shifts permit the use of a recently formulatedapproach to 3-D mapping (Taylor 2001) whichrecreates the full 3-D mass distribution by si-multaneously considering both the shear estima-tor and the photometric redshift of a galaxy. Ap-plied to the SNAP deep survey, this techniquewill detect mass overdensities with a1σ sen-sitivity of 1013M⊙ (1/5 the mass of the Virgocluster) atz = 0.25.

• Strong gravitational lensing — The high spa-tial resolution of SNAP NIR observations willenable the discovery of a large number of new

strong lenses (Kuhlen et al. 2004). The statis-tics from such a large, uniformly selected sam-ple would be ideal to impose constraints on thedensity profiles of galaxies and clusters, as wellas to constrain cosmological parameters beyondthose of dark energy. The NIR observations,which are much less sensitive to dust extinctionwithin the lens galaxy, are especially importantin regard to strong lensing observations. Goobaret al. (2002b) find that assuming a flat universe,the statistical uncertainty on the mass density isσstat

ΩM

<∼

0.05, although uncertainty of the lensmodeling are likely to dominate.

The SDSS demonstrates clearly the way in whicha wide-field survey can produce scientific yield wellbeyond its primary design goals. Individual objectsfound on SDSS images are routinely observed spec-troscopically at the largest telescopes in the world, ful-filling the historical trend of wide-field small-aperturetelescope imaging feeding targets for large-aperturetelescope spectroscopy. The SNAP surveys will pro-vide a similar opportunity in working with JWST andthe next generation of ground-based extremely largetelescopes.

9. Conclusion

The discoveries of recent years make this a fasci-nating new era of empirical cosmology, in which weare developing new technologies and instrumentationcapable of addressing fundamental questions. The ex-traordinary challenge of the precision and accuracynecessary to explore the properties of dark energy re-quires a new stringent data set in order to improve sta-tistical uncertainties and control systematic uncertain-ties; large numbers of supernovae over an extendedredshift range with light curves and spectra measuredto high signal-to-noise and deep, wide fields full ofweak-lensed galaxies with high-resolution PSFs withunprecedented stability.

Based on these data requirements, we have devel-oped a reference mission called the Supernova / Ac-celeration Probe, consisting of a detailed observingprogram carried out with an optimized wide-field tele-scope and attendant imaging and spectrograph instru-ments. The optical, mechanical, and thermal studiesand analyses conducted to date indicate that the ref-erence model is manufacturable and testable usingproven techniques. The imager will provide PSF-controlled wide-field images of galaxies with effi-

36

cient multiplexed supernova discovery and light-curvebuilding while the spectrograph satisfies the perfor-mance requirements for measuring key spectral fea-tures of the faintest supernovae.

The reference model presented in this paper ad-dresses the many requirements necessary for a high-precision supernova experiment, a PSF-controlledweak-lensing experiment, and makes possible a rangeof further complementary dark-energy studies. Weuse numerical simulations and trade studies to refinethe mission concept and quantify the expected scienceyield of SNAP. This paper will be followed up withfurther results of these studies and the progress in theoptimization of SNAP.

Although SNAP is designed as a self-contained ex-periment, its surveys can be used in conjunction withcomplementary ground-based and JWST-based studiesthat can further strengthen the reference SNAP mis-sion.

SNAP presents a unique opportunity to probe thedark energy and advance our understanding of the Uni-verse. Moreover, the principal survey missions ofSNAP will produce a cornucopia of observations capa-ble of revolutionizing other areas of astrophysics andcosmology. After completion of these primary mis-sions, a guest survey program is envisioned filling theremaining satellite lifetime to allow the full potentialof SNAP to be realized.

Acknowledgments

We thank Masahiro Takada for making detailed re-sults of his work available. This work was supportedby the Director, Office of Science, of the U.S. De-partment of Energy under Contract No. DE-AC03-76SF00098.

REFERENCES

Abazajian, K. & Dodelson, S. 2003, Physical ReviewLetters, 91, 41301

Abazajian, K. et al. 2003, AJ, 126, 2081

Aguirre, A. 1999, ApJ, 512, L19

Aguirre, A. & Haiman, Z. 2000, ApJ, 532, 28

Aldering, G., Knop, R., & Nugent, P. 2000, AJ, 119,2110

Aldering, G. et al. 2002, Proc. SPIE, 4836, 61

Allen, S. W., Schmidt, R. W., Fabian, A. C., & Ebel-ing, H. 2003, MNRAS, 342, 287

Amanullah, R., Mortsell, E., & Goobar, A. 2003,A&A, 397, 819

Andersen, M. I. et al. 2000, A&A, 364, L54

Bahcall, N. A., Ostriker, J. P., Perlmutter, S., & Stein-hardt, P. J. 1999, Science, 284, 1481

Bahcall, N. A. et al. 2003, ApJS, 148, 243

Balbi, A. et al. 2000, ApJ, 545, L1

Baron, E., Hauschildt, P. H., Branch, D., Wagner,R. M., Austin, S. J., Filippenko, A. V., & Mathe-son, T. 1993, ApJ, 416, L21

Baron, E. et al. 1995, ApJ, 441, 170

Bebek, C. J. et al. 2002a, Proc. SPIE, 4669, 161

—. 2002b, IEEE Trans. Nucl. Sci., 49, 1221

Bennett, C. L. et al. 2003, ApJS, 148, 1

Bernstein, G. 2002, PASP, 114, 98

Bernstein, G. & Jain, B. 2004, ApJ, 600, 17

Bernstein, G. & Kim, A. 2004, in preparation

Bessell, M. S. 1990, PASP, 102, 1181

Blandford, R. D. & Koopmans, L. V. E. 2001, Bulletinof the American Astronomical Society, 33, 1481

Bohlin, R. C., Dickinson, M. E., & Calzetti, D. 2001,AJ, 122, 2118

Borys, C., Chapman, S. C., Halpern, M., & Scott, D.2002, MNRAS, 330, L63

Bowen, I. S. 1938, ApJ, 88, 113

Branch, D., Perlmutter, S., Baron, E., & Nu-gent, P. 2001, ArXiv Astrophysics e-prints, astro-ph/0109070

Branch, D. & van den Bergh, S. 1993, AJ, 105, 2231

Brax, P. & Martin, J. 2000, Phys. Rev., D61, 103502

Caldwell, R. R., Dave, R., & Steinhardt, P. J. 1998,Phys. Rev. Lett., 80, 1582

Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989,ApJ, 345, 245

37

Carroll, S. M., Duvvuri, V., Trodden, M., & Turner,M. S. 2003, ArXiv Astrophysics e-prints, astro-ph/0306438

Coble, K., Dodelson, S., & Frieman, J. A. 1997,Phys. Rev. D, 55, 1851

Content, R. 1997, Proc. SPIE, 2871, 1295

Cooray, A., Huterer, D., & Baumann, D. 2004,Phys. Rev. D, 69, 027301

Couch, W. J. et al. 1989, in Particle Astrophysics:Forefront Experimental Issues, 192

Dvali, G., Gabadadze, G., & Porrati, M. 2000,Phys. Rev. B, 485, 208

Ealet, A. et al. 2003, Proc. SPIE, 4850

Efstathiou, G. et al. 2002, MNRAS, 330, L29

Evrard, A. E. 1989, ApJ, 341, L71

Evrard, A. E. et al. 2002, ApJ, 573, 7

Fan, X. et al. 2003, AJ, 125, 1649

Ferreira, P. G. & Joyce, M. 1998, Phys. Rev. D, 58,23503

Frieman, J. A., Hill, C. T., Stebbins, A., & Waga, I.1995, Phys. Rev. Lett., 75, 2077

Frieman, J. A., Huterer, D., Linder, E. V., & Turner,M. S. 2003, Phys. Rev. D, 67, 83505

Garnavich, P. M. et al. 1998, ApJ, 509, 74

Gladders, M. D. & Yee, H. K. C. 2000, AJ, 120, 2148

Goldhaber, G. et al. 2001, ApJ, 558, 359

Goobar, A., Bergstrom, L., & Mortsell, E. 2002a,A&A, 384, 1

Goobar, A., Mortsell, E., Amanullah, R., & Nugent, P.2002b, A&A, 393, 25

Goobar, A. & Perlmutter, S. 1995, Ap. J., 450

Groom, D. E. et al. 2000, Nuclear Instruments andMethods in Physics Research A, 442, 216

Haiman, Z., Mohr, J. J., & Holder, G. P. 2001, ApJ,553, 545

Hamuy, M., Phillips, M. M., Suntzeff, N. B., Schom-mer, R. A., Maza, J., & Aviles, R. 1996a, AJ, 112,2391

Hamuy, M., Trager, S. C., Pinto, P. A., Phillips, M. M.,Schommer, R. A., Ivanov, V., & Suntzeff, N. B.2000, AJ, 120, 1479

Hamuy, M. et al. 1996b, AJ, 112, 2408

Hatano, K., Branch, D., & Deaton, J. 1998, ApJ, 502,177

Hatano, K., Branch, D., Lentz, E. J., Baron, E., Filip-penko, A. V., & Garnavich, P. M. 2000, ApJ, 543,L49

Hawkins, E. et al. 2003, MNRAS, 346, 78

Hayes, D. S. 1985, in IAU Symp. 111: Calibrationof Fundamental Stellar Quantities, ed. D. S. Hayes,L. E. Pasinetti, & A. G. D. Philip, 225–249

Hayes, D. S. & Latham, D. W. 1975, ApJ, 197, 593

Hoflich, P., Gerardy, C., Linder, E., & Marion, H.2003, in Stellar candles for the extragalactic dis-tance scale, ed. D. Alloin & W. Gieren, Lecturenotes in physics,0075-8450 ;635 (Springer)

Hoflich, P., Wheeler, J. C., & Thielemann, F. K. 1998,ApJ, 495, 617

Holland, S. E., Groom, D. E., Palaio, N. P., & Stover,R. J.and Wei, M. 2003, IEEE Trans. Elec. Dev.,50(1), 225

Holz, D. E. 2001, ApJ, 556, L71

Holz, D. E. & Wald, R. M. 1998, PRD, 58, 063501

Hu, W. 1999, ApJ, 522, L21

Huterer, D. 2002, Phys. Rev. D, 65, 63001

Huterer, D. & Cooray, A. 2004, ArXiv Astrophysicse-prints, astro-ph/0404062

Huterer, D., Kim, A., Krauss, L. M., & Broder-ick, T. 2004, ArXiv Astrophysics e-prints,astro-ph/0402002

Huterer, D. & Starkman, G. 2003, Phys. Rev. Lett., 90,031301

Huterer, D. & Turner, M. S. 2001, Phys. Rev. D, 64,123527

38

Jain, B. & Taylor, A. 2003, Physical Review Letters,91, 141302

Kaiser, N. 1998, ApJ, 498, 26

Kim, A., Goobar, A., & Perlmutter, S. 1996, PASP,108, 190

Kim, A. G., Linder, E. V., Miquel, R., & Mostek, N.2004, MNRAS, 347, 909

Kirshner, R. P. & Kwan, J. 1974, ApJ, 193, 27

Knop, R. A. et al. 2003, ApJ, 598, 102

Korsch, D. 1977, ApOpt, 16, 2074

Kuhlen, M., Keeton, C. R., & Madau, P. 2004, ApJ,601, 104

Kujat, J., Linn, A. M., Scherrer, R. J., & Weinberg,D. H. 2002, ApJ, 572, 1

Lampton, M. L. et al. 2002a, Proc. SPIE, 4854, 632

—. 2002b, Proc. SPIE, 4849, 215

—. 2003, Proc. SPIE, 5166

Lange, A. E. et al. 2001a, Phys. Rev. D, 63, 42001

—. 2001b, Phys. Rev. D, 63, 42001

Leggett, S. K. et al. 2000, ApJ, 536, L35

Lentz, E. J., Baron, E., Branch, D., Hauschildt, P. H.,& Nugent, P. E. 2000, ApJ, 530, 966

Leonard, D. C., Kanbur, S. M., Ngeow, C. C., & Tan-vir, N. R. 2003, ApJ, 594, 247

Linder, E. V. 2003a, Phys. Rev. Lett., 90, 91301

—. 2003b, ArXiv Astrophysics e-prints, astro-ph/0311403

—. 2004, ArXiv Astrophysics e-prints, astro-ph/0402503

Linder, E. V. & Huterer, D. 2003, Phys. Rev. D, 67,81303

Mortsell, E. & Goobar, A. 2003, Journal of Cosmol-ogy and Astro-Particle Physics, 9, 9

Mortsell, E., Goobar, A., & Bergstrom, L. 2001, ApJ,559, 53

Madau, P., della Valle, M., & Panagia, N. 1998, MN-RAS, 297, L17

Massey, R. et al. 2004, AJ, accepted

Matsubara, T. & Szalay, A. S. 2003, Phys. Rev. Lett.,90, 021302

Norgaard-Nielsen, H. U., Hansen, L., Jorgensen, H. E.,Aragon Salamanca, A., & Ellis, R. S. 1989, Nature,339, 523

Nugent, P., Kim, A., & Perlmutter, S. 2002, PASP,114, 803

Nugent, P., Phillips, M., Baron, E., Branch, D., &Hauschildt, P. 1995, ApJ, 455, L147

Pain, R. et al. 2002, ApJ, 577, 120

Pentericci, L. et al. 2002, AJ, 123, 2151

Percival, W. J. et al. 2002, MNRAS, 337, 1068

Perlmutter, S. 1999, FNAL Inner Space/Outer Space IISymposium

Perlmutter, S. & Schmidt, B. P. 2003, ArXiv Astro-physics e-prints, astro-ph/0303428

Perlmutter, S., Turner, M. S., & White, M. 1999a,Phys. Rev. Lett., 83, 670

Perlmutter, S. et al. 1995, ApJ, 440, L41

—. 1997, ApJ, 483

—. 1998, Nature, 391

—. 1999b, ApJ, 517, 565

Phillips, M. M. 1993, ApJ, 413, L105

Phillips, M. M., Lira, P., Suntzeff, N. B., Schommer,R. A., Hamuy, M., & Maza, J. 1999, AJ, 118, 1766

Prieto, E. et al. 2002, Proc. SPIE, 4850

Ratra, B. & Peebles, P. J. E. 1988, Phys. Rev. D, 37,3406

Refregier, A. 2003, ARA&A, 41, 645

Refregier, A. et al. 2004, AJ, accepted

Rhodes, J., Refregier, A., & Groth, E. J. 2000, ApJ,536, 79

Rhodes, J. et al. 2004, Astroparticle Physics, 20, 377

39

Riess, A. G., Press, W. H., & Kirshner, R. P. 1996,ApJ, 473, 88

Riess, A. G. et al. 1998, AJ, 116, 1009

—. 1999, AJ, 117, 707

—. 2004, ApJ, 600, L163

Schlegel, D. J., Finkbeiner, D. P., & Davis, M. 1998,ApJ, 500, 525

Schmidt, B. P. et al. 1998, ApJ, 507, 46

Scott, S. E. et al. 2002, MNRAS, 331, 817

Seo, H. & Eisenstein, D. J. 2003, ApJ, 598, 720

Somerville, R. S., Lee, K., Ferguson, H. C., Gardner,J. P., Moustakas, L. A., & Giavalisco, M. 2004,ApJ, 600, L171

Spergel, D. N. et al. 2003, ApJS, 148, 175

Steidel, C. C., Giavalisco, M., Pettini, M., Dickinson,M., & Adelberger, K. L. 1996, ApJ, 462, L17

Stover, R. J. et al. 2000, in Optical Detectors for As-tronomy II: State-of-the-Art at the Turn of the Mil-lenium, 239

Sullivan, M. et al. 2003, MNRAS, 340, 1057

Takada, M. & Jain, B. 2003, MNRAS, 344, 857

Taylor, A. N. 2001, ArXiv Astrophysics e-prints, asto-ph/0111605

Tegmark, M. 2002, Phys. Rev. D, 66, 103507

Tonry, J. L. et al. 2003, ApJ, 594, 1

Turner, M. S. & White, M. 1997, Phys. Rev. D, 56,4439

Vilenkin, A. 1984, Phys. Rev. Lett., 53, 1016

Vilenkin, A. & Shellard, E. 1994, Cosmic Strings andother Topological Defects (Cambridge, U.K.: Cam-bridge University Press)

Walder, J.-P., Chao, G., Genat, J., Karcher, A., Steck-ert, J., & von der Lippe, H. 2003, IEEE Trans. Nucl.Sci., In press

Weller, J. & Albrecht, A. 2001, Phys. Rev. Lett., 86,1939

—. 2002, Phys. Rev. D, 65, 3512

White, R. L., Becker, R. H., Fan, X., & Strauss, M. A.2003, AJ, 126, 1

Williams, R. E. et al. 1996, AJ, 112, 1335

—. 2000, AJ, 120, 2735

York, D. G. et al. 2000, AJ, 120, 1579

This 2-column preprint was prepared with the AAS LATEX macrosv5.2.

40