1. Off-Axis Telescopes for Dark Energy Investigations SPIE 7731-52, 30 June 2010 M.Lampton (UC Berkeley) M. Sholl (UC Berkeley) M. Levi (LBNL Berkeley)

2. Dark energy Our observed universe: expanding, accelerating, lumpy – Hubble: and many many others: expanding! H(0) – COBE, WMAP: warm, isotropic, shows primordial structure – Perlmutter et al; Riess et al.: SNe, standard candles: accelerating! H(z) – Eisenstein et al; Cole et al.; structure; standard rulers: BAO => H(z) Explanations – Einstein (1917) General Relativity: geometry; many tests tried and passed – Many alternative theories are out there If GR is correct… Ω m + Ω k + Ω Λ = 1 – Empirically today… 0.27 + 0 + 0.73 ≈ 1 …But there are puzzling aspects of this! – What is Λ? Physics offers no answer. – Why is Ω m ~ Ω Λ today, i.e. why now? 2Lampton Sholl & Levi 2010 Physical baryon density Ω b Physical CDM density Ω c Physical DE density Ω Λ Scalar curvature Δ 2 R Spectral index n s Reionization optical depth τ SIX PARAMETER FLAT ΛCDM

3. DETF Recommendations http://www.NSF.gov/mps/ast/detf.jsp (2006) http://www.NSF.gov/mps/ast/detf.jsp Recommended that multiple techniques be pursued Baryon Acoustic Oscillations: less affected by astrophysical uncertainties than other methods, but presently less proven Supernovae: presently is most powerful & best proven; but systematics will depend on astronomical flux calibration Weak Lensing: emerging technique; may become the most powerful technique in constraining dark energy. Clusters: good statistical potential; but presently has largest systematic errors. Lampton Sholl & Levi 20103 “… For these reasons, the nature of dark energy ranks among the very most compelling of all outstanding problems in physical science. These circumstances demand an ambitious observational program to determine the dark energy properties as well as possible.”

4. JDEM Interim Science Working Group http://jdem.lbl.gov (2010)http://jdem.lbl.gov Science ObjectiveDesign ADesign B Supernova Redshift Survey 1500 supernovae Redshifts 0.2<z<1.5 Tiered survey areas for discovery Same as Design A BAO Galaxy Survey Halpha flux 2e-16 erg/cm2sec Spectroscopic redshifts 1.3<z<2.0 RMS z < 0.001·(1+z) 16000 square degrees in 1.5 years Same as Design A Weak Lensing Surveynone 10000 square degrees 30 galaxies per square arcmin Redshifts from Photo-Z 1e5 spectro calibration galaxies Lampton Sholl & Levi 20104

5. JDEM Interim Science Working Group http://jdem.lbl.gov (2010)http://jdem.lbl.gov Lampton Sholl & Levi 20105 ElementDesign ADesign B Telescope1.1m unobscured aperture TMASimilar to A Wide field imager For BAO centroids For SN discovery searches In Design B, for cosmic shear 0.5 square degree FoV Two bands: 0.7-1um, 1-1.5um 32 Mpixels, each 0.45arcsec HgCdTe 2Kx2K Similar to A More & finer pixels HgCdTe and/or Si CCD Slitless prism spectrometer For BAO galaxy redshifts 0.5 square degree FoV One waveband 1.5 – 2.0 um 32 Mpixels, each 0.45arcsec Similar to A Supernova Slit orIFU spectrometer Light curves, spectra, host redshifts Narrow field (a few arcseconds) One waveband 0.4 – 2.0um Similar to A

6. Baryon Acoustic Oscillations: what are they? The very early universe had broadband small amplitude thermoacoustic waves At decoupling (z=1100, t=0.4My) this wave structure froze out and is still visible today in CMB Subsequently in the expanding universe these waves grew in amplitude due to gravity Matter waves are visible today in 3-D galaxy correlations, e.g. the 2dF Galaxy Redshift Survey BAO can be used to test theories about the growth of structure in the universe Lampton Sholl & Levi 20106 Komatsu et al arXiv 1001.4538

7. BAO: Requirements & Implementation Require: redshift range 1.3<z<2.0 Survey 16000 sq degrees of sky Identify emission line galaxies by the Hα line feature, and/or other lines Sample faint enough to reach ~2E-16 erg/cm2sec line flux Yields about 1 galaxy /sq arcmin Yields about 50 million galaxies Required accuracy σ z = 0.001/(1+z) Plan: slitless spectrometer with a wide FoV ~ 0.5 square degree Span wavelengths 1.5µm<λ< 2.0µm Exposure time ~ 1ksec/field 32000 spectro fields + cal fields Lampton Sholl & Levi 20107 http://jdem.lbl.gov/http://jdem.lbl.gov/ “Rolling Disperser”

8. Type Ia Supernovae: What are they? “SD” model: Whelan & Iben (1973) Carbon or oxygen white dwarf star; no H or He Accrete matter to 1.38 Msun = – Radius begins shrinking rapidly – Gravitational energy = -1E44 joule It will heat and collapse. Fusion ensues… 12 C→ 24 Mg → 56 Ni → 56 Co → 56 Fe + 0.12% Mc 2 – If 67% efficient: 2E44 joule Annihilates the WD star! Roughly 1E44 joules remain for KE & light Good uniformity: calibrated standard candles Measure each peak brightness and redshift Fit a SN population to a distance modulus curve Each DE model predicts a distance modulus curve So… compare these to constrain models. 8 Lampton Sholl & Levi 2010 Kowalski et al arXiv 0804.4142 (2008)

9. Supernova Program Requirements Quantity of Supernovae for statistics – Span the redshift range 0.2<z<1.5 – Discover and analyze about 100 SNe per redshift bin Δz=0.1 – Use ~ four day cadence revisiting discovery fields, two wavebands Diagnostic spectra throughout light curve for systematics – “Onion peeling” to detect unusual changes in colors for subclassification – Approx 12 lightcurve spectra on a four day cadence in SN restframe – Near peak, one deep accurate spectrum with R1pixel = 100, SNR/pix = 17 @ Si II – Accuracy: error of a few percent per supernova is OK….. – But relative systematic flux error over redshift should be less than 1% – One or more reference spectra post-supernova for subtraction Lampton Sholl & Levi 20109 explosion Peak spectrum Reference spectrum Figure courtesy A.G.Kim 2010 Off-peak spectra

10. Discovery Phase: repeatedly visit tiered survey fields with a two-filter imager – Nearby SNe: short exposures, broad field ~ 10 sqdeg, large A∙  – Distant SNe: long exposures, smaller field ~ 1.6 sqdeg, small A∙  – Efficient! <10% of SN program time – Can reject some Type II supernovae Spectroscopy Phase: revisit with dedicated spectrometer, R>100 – Early rejection of Type II SNe from first few spectra: presence of hydrogen – Subclassification of Type Ia’s using synthetic photometry lightcurve – Detailed subclassification near peak – Also gives host galaxy redshift Supernova Program Implementation 10Lampton Sholl & Levi 2010 Top curve: deep spectrum SNR taken near peak light, z=1.2 Lower curves: short exposure SNRs before and after peak; sufficient SNR for broad “UBVRI” colors, and no K- correction required for fixed filter edges & responses. Figure courtesy A.G.Kim 2010.

11. Weak Lensing: what is it? Dark matter is invisible yet is by far the largest source of gravitation in the universe Dark matter can be mapped by its deflection of light from background galaxies Strong lensing is already a well established tool for mapping individual massive clusters (A2218) Weak lensing is a statistical buildup of ellipticity (shear) as light paths traverse volumes of space containing irregularly distributed matter The measurement of shear of 1E9 galaxies, with a wide range of redshifts, could yield a useful measure of the growth in structure over cosmic time. Lampton Sholl & Levi 201011 http://www.cita.utoronto.ca/~hoekstra/lensing.html

12. WL: Requirements & Implementation Requires a dense survey: 30 galaxies per square arcminute Translates to ABmag ~ 25 Requires a wide survey: > 10000 square degrees Requires good PSF: e.g. 0.2 arcsec pixels Requires Photo-Z grade redshifts That in turn means an associated redshift calibration program Plan: Wide Field Imager, ~ 0.5 sqdeg Texposure ~ few kiloseconds 20000 frames, with 4x dithering Use stars in each frame for instrumental PSF map and shear calibration Lampton Sholl & Levi 201012 Jouvel et al., “Designing Future Dark Energy Missions” A&A 504, 359 (2009) Rhalf, arcseconds

13. Supernovae, BAO, and CMB constrain the equation of state of the Universe current (2010) data constraints Lampton Sholl & Levi 201013 Equation of state w = p/ρ For a cold gas or nonrelativistic fluid, w = 0 For a DE dominated Λ universe, w = -1 Then … w is a key diagnostic of the universe and the prevalence of dark energy, including its evolution over cosmic time.

14. Survey Rate for simplest case Continuum target, Diffuse background Lampton Sholl & Levi 201014 Nmin = minimum needed continuum photon flux SNR = required signal to noise ratio B = diffuse sky continuum level FoV = imager survey area on sky A = telescope light gathering area E = system throughput efficiency F = fraction of time allocated Δλ = wavelength bandpass Rhalf = half light radius of target image To maximize survey rate: maximize that last group of factors, and of course minimize the half light radius of the faintest images. This talk

15. JSIM http://jdem.lbl.gov/ “Exposure Time Calculator” http://jdem.lbl.gov/ Public web-based tool created by M.Levi with Project Office inputs Inputs are high-level mission parameters – Telescope Aperture, central obstruction size, WFE… – Field of view on sky, pixel scale, focal length, number of sensor chips – Detector Technology: pixel size, pixels per chip, waveband, QE curve – Fraction of time allocated to BAO, SNe, WL, calibration, downlink, … – Mission duration Also low-level inputs for sensors, filter bandwidths, etc Outputs are available at “high level” i.e. productivity yield measures per year of operations for a given objective and figures-of-merit scaled from comparisons with DETF estimates Also “low level” outputs, decomposing yield into redshift bins, for estimating individual cosmological parameter constraints 15Lampton Sholl & Levi 2010

16. JSIM Internal Databases & Models http://jdem.lbl.gov/ “Exposure Time Calculator” http://jdem.lbl.gov/ BAO emission line galaxy Hα flux, size, and redshift distribution – Ilbert et al 2005 WL galaxy magnitude, size, and redshift distribution – Leauthaud et al 2008 zCOSMOS; Jouvel et al 2009 Supernova occurrence rate vs redshift – Lesser of published curves by Sullivan et al 2006 and Dahlen et al 2008 Zodiacal light vs wavelength and ecliptic latitude – Leinert et al 1998; Aldering 2001 Optical point spread function – MTF contributions from pupil diffraction and WFE via Fischer’s Hopkins Ratio – Gaussian two dimensional random attitude control errors – Sensor pixel size; interpixel diffusion Sensor contributions (dark current, read noise, QE) Signal-to-noise ratio estimation – Optimal extraction, convolving galaxy exponential with system PSF 16Lampton Sholl & Levi 2010

17. JSIM Primary Mission Input Parameters http://jdem.lbl.gov/ “Exposure Time Calculator” http://jdem.lbl.gov/ 17Lampton Sholl & Levi 2010

18. JSIM Summary Output Results http://jdem.lbl.gov/ “Exposure Time Calculator” http://jdem.lbl.gov/ Gives both broad & detailed predictions of a JDEM design Confirms the notion that shrinking Rhalf boosts performance Roughly, 1.1m unobscured aperture ≈ 1.4m 50% obscured 18Lampton Sholl & Levi 2010

19. Obscured vs Unobscured Focal TMAs These historical examples are both focal but afocal configurations are equally good Lampton Sholl & Levi 201019 Obscured, here with 1.2m aperture f/11; 13mEFL 18um = 0.285” FoV = 0.73x1.46deg =166 x 330mm Easy fit to 4x8 sensors. < 3umRMS theoretical PSF Real Cassegrain image: control stray light Real exit pupil: control of stray heat Best with auxiliary optics behind PM; Easy heat path for one focal plane. Korsch,D., A.O. 16 #8, 2074 (1977) Cook,L.G., Proc.SPIE v.183 (1979) Unobscured, also with 1.2m aperture f/11, 13mEFL, 18um=0.285” FOV = 0.73 x1.46deg = 166x330mm Easy fit to 4x8 sensors. < 3umRMS theoretical PSF Real Cassegrain image: control stray light Real exit pupil: control of stray heat Easy heat path to cold side of payload for entire SM-TM-FP assembly; can accommodate several focal planes.

20. 20Lampton Sholl & Levi 2010 PSFs For Unaberrated Pupils Scaled to include both obstructed light loss and diffraction Fresnel-Kirchoff diffraction integral UnobstructedObstructed: 50% linear, 25% area

21. Encircled Energy as a Fraction of the Total Transmitted Light with no aberrations Fresnel-Kirchoff diffraction integral: Schroeder 10.2 21Lampton Sholl & Levi 2010 Linear obstruction = 0%, 10%, 20%, 30%, 40%, 50%

22. 22Lampton Sholl & Levi 2010 Eliminating the SM support spider legs For a Galactic Midlatitude distribution of stars, diffraction rings and spikes bring the focal plane irradiance to twice or more times Zodi over 3% of random locations. Elimination: slightly improved survey efficiency; eases background subtraction. HST file image courtesy STScI

23. EE50 Radius (arcsec) Comparison Held constant: f/11, WFE=0.1µm rms, pixel =18µm, blur= 1µm, ACS blur=0.02 arcsec. Results show little difference in the visible since we are not diffraction limited there However longward of one micron, diffraction dominates the PSF, and the unobscured looks attractive. Lampton Sholl & Levi 201023 1.1m obscured 1.3m obscured 1.1m unobscured 1.3m unobscured Wavelength microns

24. Some Unobscured Concepts Lampton Sholl & Levi 201024 MountaintopSolarMcMath: Pierce 11 NST: Denker et al. 12 ATST: Rimmele 13 MountaintopGeneral AstronLAPCAT (proposed): Storey et al 14 NPT (proposed): Moretto & Kuhn 15 4m DFL (proposed): Moretto & Kuhn 16 SpaceborneRemote SensingMTI: Kay et al. 17 TopSat: Price 18 QuickBird: Figoski 19 EO-1 ALI: Lencione et al 20 CartoSat: Subrahmanyam et al 21 SpaceborneStellarGAIA: Perryman 22 DIVA (proposed): Graue et al 23 SpacebornePlanet SearchJPF (proposed): Krist et al 24 TPF (proposed): Noecker 25 ECLIPSE (proposed): Trauger et al 26, Hull et al 27

25. Manufacturing & Testing Challenges? Off-axis: more material removal and greater aspheric departure Off-axis: non axisymmetric test setups need more time & care Vendors caution us that going off-axis is do-able but not “free” Lampton Sholl & Levi 201025

26. Many JDEM Trade Studies Remain Content et al.; Sholl et al.; Lieber et al.; Noecker; Edelstein et al.; Besuner et al.; Reil et al. Focal vs Afocal rear-end architecture Imager requirements and design – Field of view; plate scale; pixel size; waveband(s)… – How to calibrate it: flats, darks, wavelength, linearity… Wide field spectrometer requirements – Field of view; plate scale; pixel size; waveband… – Resolving power; issue of redshift accuracy. – How to calibrate it: flats, darks, wavelength, linearity… Supernova spectrometer requirements – Single slit vs integral field slicer architecture – Field of view; plate scale; pixel size; waveband – How to calibrate it: flats, darks, wavelength, linearity… The overall mission design: how to best integrate objectives And then… of course … there’s all the engineering! Lampton Sholl & Levi 201026

27. Obscured Unobscured Traditional in space astronomy Axisymmetric PM has lower manufacture & test cost for given aperture because total departure from sphere is less If Wide field: SM baffle is large then there is appreciable light loss from SM blockage of the pupil Diffraction by SM: a concern Scattering by SM support spiderlegs: a minor annoyance, even for WL Spider leg flex can contribute to resonances that influence PSF Unobscured space telescopes are employed for terrestrial remote sensing (DoE M.T.I.) with severe requirements on stray light Superior MTF, PSF, and EE nearly equal to ideal Airy pattern Industry lacks experience in sizes above 0.6m => higher risk and potentially higher fab cost Potentially reduced stray light, stray heat => tiny risk reduction and possibly more thorough testing Potentially a stiffer, stronger structure: no spider legs Decision: to be based on benefits, cost, and risk assessment 27Lampton Sholl & Levi 2010

28. Conclusions At λ>1µm, pupil obstruction is a concern – Diffraction dominates the PSF and EE – PSF and EE influence science return – S/N ratio is major driver on Texp, aperture, FoV. – BAO team seeks a high survey rate in the NIR – WL team seeks a high survey rate and a high density of resolved galaxies, which is very sensitive to PSF growth – SN team seeks high S/N spectroscopy at highest redshifts Unobstructed pupil can help achieve all these results Lampton Sholl & Levi 201028

29. Backups Lampton Sholl & Levi 201029

30. Supernova Redshift Range Figures 1, 2 from Kent et al. arXiv 0903.2799 (2009) Lampton Sholl & Levi 201030

31. Jouvel et al “Designing Future Dark Energy Missions” A&A 504, 359 (2009) HST ACS PSF 0.07 arcsec from Koekemoer et al ApJS 172 196 (2007) half light radius 31Lampton Sholl & Levi 2010

32. JSIM Secondary Input Fields http://jdem.lbl.gov/ “Exposure Time Calculator” http://jdem.lbl.gov/ 32Lampton Sholl & Levi 2010

33. JSIM Secondary Results: WL and BAO http://jdem.lbl.gov/ “Exposure Time Calculator” http://jdem.lbl.gov/ 33Lampton Sholl & Levi 2010

34. JSIM Secondary Results: SN Spectroscopy http://jdem.lbl.gov/ “Exposure Time Calculator” http://jdem.lbl.gov/ 34Lampton Sholl & Levi 2010

35. Aperture size (1.1m unobscured, 1.3m obscured) Jitter: 0.025 arcsec, rms/axis Detector diffusion = 1.9  m NIR, 3.8  m CCD WFE for imaging: 70 nm 4 Dithers NIR: 1.7um and T sca =130K, I dark =0.01 e-/pix-s NIR: Read Noise per Exposure: 7e- (conservative) Assumed 40s repointing time per exposure. Assumed 22 hours/day for science. WL-Specific Assumptions 35Lampton Sholl & Levi 2010

36. Require photometric measurement of 5% in NIR band. – Eg. filter 1040nm-1410nm (30%) – S/N=20 Require ellipticity measurement  e <0.2. – if r 1/2 > 1.5*ee50, then S/N>14.4 to achieve requirement – if r 1/2 > 1.25*ee50, then S/N>16 – ee50 is the 50% encircled energy radius – The latter specification has 20% better FoM, but the former size cut has COSMOS heritage. Weak Lensing Assumptions 36Lampton Sholl & Levi 2010

37. At 24.0 th mag: >19 resolved gal/sq.amin (@ =0.8  m) At 24.5 th mag: >28 resolved gal/sq.amin At 25.0 th mag: >40 resolved gal/sq.amin Limiting Magnitude Euclid 37Lampton Sholl & Levi 2010

38. Weak Lensing Assumptions Parameter Central Wavelength800nm/1100nm Bandpass30% (eg 935-1265nm) SNR Photo-z≥ 20 Ellipticity Error  e ≤ 0.2 Size Cut (*ee50)≥ 1.25 Magnitude≥ 24.5 38Lampton Sholl & Levi 2010

39. 1.1m Obstructed =1.7  m: 0.402” 39Lampton Sholl & Levi 2010