Off-Axis Telescopes for Dark Energy Investigations
SPIE 7731-52, 30 June 2010M.Lampton (UC Berkeley)
M. Sholl (UC Berkeley)M. Levi (LBNL Berkeley)
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… Ωm + Ωk + ΩΛ = 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 Ωm ~ ΩΛ today, i.e. why now?
2Lampton Sholl & Levi 2010
Physical baryon density Ωb Physical CDM density Ωc Physical DE density ΩΛ
Scalar curvature Δ2R
Spectral index ns
Reionization optical depth τ
SIX PARAMETER FLAT ΛCDM
DETF Recommendations http://www.NSF.gov/mps/ast/detf.jsp (2006)
• 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 2010 3
“… 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.”
JDEMInterim Science Working Group http://jdem.lbl.gov (2010)
Science Objective Design A Design B
Supernova Redshift Survey
1500 supernovaeRedshifts 0.2<z<1.5
Tiered survey areas for discoverySame as Design A
BAO Galaxy SurveyHalpha flux 2e-16 erg/cm2sec
Spectroscopic redshifts 1.3<z<2.0RMS z < 0.001·(1+z)
16000 square degrees in 1.5 years
Same as Design A
Weak Lensing Survey none10000 square degrees
30 galaxies per square arcminRedshifts from Photo-Z
1e5 spectro calibration galaxies
Lampton Sholl & Levi 2010 4
JDEMInterim Science Working Group http://jdem.lbl.gov (2010)
Lampton Sholl & Levi 2010 5
Element Design A Design BTelescope 1.1m unobscured aperture TMA Similar to A
Wide field imager For BAO centroids
For SN discovery searches In Design B, for cosmic shear
0.5 square degree FoVTwo bands: 0.7-1um, 1-1.5um32 Mpixels, each 0.45arcsec
HgCdTe 2Kx2K
Similar to ASimilar to A
More & finer pixelsHgCdTe and/or Si CCD
Slitless prism spectrometer For BAO galaxy redshifts
0.5 square degree FoVOne waveband 1.5 – 2.0 um32 Mpixels, each 0.45arcsec
Similar to ASimilar to ASimilar to A
Supernova Slit orIFU spectrometer Light curves, spectra, host redshifts
Narrow field (a few arcseconds)One waveband 0.4 – 2.0um
Similar to ASimilar to A
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 2010 6
Komatsu et al arXiv 1001.4538
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 σz = 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 2010 7
http://jdem.lbl.gov/ “Rolling Disperser”
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…• 12C→24Mg →56Ni →56Co →56Fe + 0.12% Mc2
– 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.
8Lampton Sholl & Levi 2010
Kowalski et al arXiv 0804.4142 (2008)
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 2010 9
explosion
Peak spectrum
Reference spectrum
Figure courtesy A.G.Kim 2010
Off-peak spectra
• 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.
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 2010 11
http://www.cita.utoronto.ca/~hoekstra/lensing.html
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 2010 12
Jouvel et al., “Designing Future Dark Energy Missions” A&A 504, 359 (2009)
Rhalf, arcseconds
Supernovae, BAO, and CMB constrain the equation of state of the Universe
current (2010) data constraints
Lampton Sholl & Levi 2010 13
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.
Survey Rate for simplest caseContinuum target, Diffuse background
Lampton Sholl & Levi 2010 14
2half
2
2min
R π
AEFFoV
BSNR
ΔλN0.25 RateSurvey
Nmin = minimum needed continuum photon fluxSNR = required signal to noise ratioB = diffuse sky continuum levelFoV = imager survey area on skyA = telescope light gathering areaE = system throughput efficiencyF = fraction of time allocated Δλ = wavelength bandpassRhalf = 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
JSIM http://jdem.lbl.gov/ “Exposure Time Calculator”
• 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
JSIM Internal Databases & Models http://jdem.lbl.gov/ “Exposure Time Calculator”
• 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
JSIM Primary Mission Input Parameters http://jdem.lbl.gov/ “Exposure Time Calculator”
17Lampton Sholl & Levi 2010
JSIM Summary Output Results http://jdem.lbl.gov/ “Exposure Time Calculator”
• 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
Obscured vs Unobscured Focal TMAsThese historical examples are both focal but afocal configurations are equally good
Lampton Sholl & Levi 2010 19
Obscured, here with 1.2m aperturef/11; 13mEFL 18um = 0.285”FoV = 0.73x1.46deg =166 x 330mmEasy fit to 4x8 sensors.< 3umRMS theoretical PSFReal Cassegrain image: control stray lightReal exit pupil: control of stray heatBest 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 aperturef/11, 13mEFL, 18um=0.285”FOV = 0.73 x1.46deg = 166x330mmEasy fit to 4x8 sensors.< 3umRMS theoretical PSFReal Cassegrain image: control stray lightReal exit pupil: control of stray heatEasy heat path to cold side of payload for entire SM-TM-FP assembly; can accommodate several focal planes.
20Lampton Sholl & Levi 2010
PSFs For Unaberrated PupilsScaled to include both obstructed light loss and diffraction
Fresnel-Kirchoff diffraction integral
Unobstructed Obstructed: 50% linear, 25% area
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%
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
EE50 Radius (arcsec) ComparisonHeld 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 2010 23
1.1m obscured
1.3m obscured
1.1m unobscured
1.3m unobscured
Wavelength microns
Some Unobscured Concepts
Lampton Sholl & Levi 2010 24
Mountaintop Solar McMath: Pierce11
NST: Denker et al.12
ATST: Rimmele13
Mountaintop General Astron LAPCAT (proposed): Storey et al14
NPT (proposed): Moretto & Kuhn15
4m DFL (proposed): Moretto & Kuhn16
Spaceborne Remote Sensing MTI: Kay et al.17
TopSat: Price18
QuickBird: Figoski19
EO-1 ALI: Lencione et al20
CartoSat: Subrahmanyam et al21
Spaceborne Stellar GAIA: Perryman22
DIVA (proposed): Graue et al23
Spaceborne Planet Search JPF (proposed): Krist et al24
TPF (proposed): Noecker25
ECLIPSE (proposed): Trauger et al26, Hull et al27
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 2010 25
-500 0 500 1000 15000
0.1
0.2
0.3
0.4
0.5
Radius from optical axis (mm)
Asp
heric
Dep
artu
re (
mm
)
Aspheric Departure of 1.1m f/11 On-axis and Off-axis TMA Primary Mirror
On-axis Telescope
Off-axis Telescope
Many JDEM Trade Studies RemainContent 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 2010 26
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
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 2010 28
Backups
Lampton Sholl & Levi 2010 29
Supernova Redshift RangeFigures 1, 2 from Kent et al. arXiv 0903.2799 (2009)
Lampton Sholl & Levi 2010 30
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
JSIM Secondary Input Fields http://jdem.lbl.gov/ “Exposure Time Calculator”
32Lampton Sholl & Levi 2010
JSIM Secondary Results: WL and BAO http://jdem.lbl.gov/ “Exposure Time Calculator”
33Lampton Sholl & Levi 2010
JSIM Secondary Results: SN Spectroscopy http://jdem.lbl.gov/ “Exposure Time Calculator”
34Lampton Sholl & Levi 2010
• Aperture size (1.1m unobscured, 1.3m obscured)• Jitter: 0.025 arcsec, rms/axis• Detector diffusion = 1.9m NIR, 3.8m CCD• WFE for imaging: 70 nm• 4 Dithers• NIR: 1.7um and Tsca=130K, Idark=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
• Require photometric measurement of 5% in NIR band.– Eg. filter 1040nm-1410nm (30%)– S/N=20
• Require ellipticity measurement e<0.2.
– if r1/2 > 1.5*ee50, then S/N>14.4 to achieve requirement– if r1/2 > 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
• At 24.0th mag: >19 resolved gal/sq.amin (@ =0.8m)• At 24.5th mag: >28 resolved gal/sq.amin• At 25.0th mag: >40 resolved gal/sq.amin
Limiting Magnitude
Euclid
37Lampton Sholl & Levi 2010
Weak Lensing Assumptions
Parameter
Central Wavelength 800nm/1100nm
Bandpass 30% (eg 935-1265nm)
SNR Photo-z ≥ 20
Ellipticity Error e ≤ 0.2
Size Cut (*ee50) ≥ 1.25
Magnitude ≥ 24.5
38Lampton Sholl & Levi 2010
1.1m Obstructed=1.7m: 0.402”
39Lampton Sholl & Levi 2010