Off-Axis Telescopes for Dark Energy Investigations SPIE 7731-52, 30 June 2010 M.Lampton (UC...

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.”

http://www.nsf.gov/mps/ast/detf.jsp

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


http://jdem.lbl.gov/

JDEMInterim Science Working Group http://jdem.lbl.gov (2010)


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


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


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.


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


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


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

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


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


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


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



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



JSIM Primary Mission Input Parameters http://jdem.lbl.gov/ “Exposure Time Calculator”



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



Obscured vs Unobscured Focal TMAsThese historical examples are both focal but afocal configurations are equally good


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.


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


Linear obstruction = 0%, 10%, 20%, 30%, 40%, 50%


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.


1.1m obscured

1.3m obscured

1.1m unobscured

1.3m unobscured

Wavelength microns

Some Unobscured Concepts


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”


-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!


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


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


Backups


Supernova Redshift RangeFigures 1, 2 from Kent et al. arXiv 0903.2799 (2009)


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


JSIM Secondary Input Fields http://jdem.lbl.gov/ “Exposure Time Calculator”



JSIM Secondary Results: WL and BAO http://jdem.lbl.gov/ “Exposure Time Calculator”



JSIM Secondary Results: SN Spectroscopy http://jdem.lbl.gov/ “Exposure Time Calculator”



• 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


• 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


• 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


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


1.1m Obstructed=1.7m: 0.402”


Off-Axis Telescopes for Dark Energy Investigations SPIE 7731-52, 30 June 2010 M.Lampton (UC...

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