P5: February 22, 2008Weak Gravitational Lensing

Bhuvnesh JainUniversity of Pennsylvania

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Outline

• Lensing measurements as probes of distance and growth

• Systematic Errors

Recent advances

What we don’t know (and will need to within 5 years)

• Ground based surveys: Stage III and IV

• Lensing from space

• Discovery potential beyond the dark energy equation of state

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Lensing Basics

• Distances affect W

• Linear growth rate affects (z)

• The observable shear is similar to (but due to tidal fields)

Lensing Statistics

• Shear-shear correlations: C

• Galaxy-shear correlations: Cg

• Cluster statistics

• Higher order shear correlations

These multiple statistics make weak lensing more complex than other probes. But they also provide better statistical power and robustness to systematics.

Consider the lensing convergence

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Beyond the DETF Figure of Merit

• Stage III surveys aim for x3 improvement on w0-wa Figure of Merit; Stage IV surveys aim for x10 or more.

• DE parameter space has more than two parameters that can be well measured Stage IV surveys in fact do much better.

• Modified Gravity: Lensing sensitivity to growth makes it a valuable probe. Gravity can be tested in different ways and on different scales (see discussion at end).

• This changes the metric of survey capability. E.g. nonlinear regime and individual clusters may provide new tests. (Current work is targeting linear growth to get an extended Figure of Merit.)

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Lensing tomography

• Shear of galaxies at z1 and z2 given by integral of growth function & distances over lensing mass distribution.

z1

z2

zl1

lensing mass

zl2

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Shear-shear and galaxy-shear correlations

Cg Mean tangential shear inside apertures. Can be used in the nonlinear regime.

C compared at different z. Angle must be large to stay in quasi-linear or linear regime.

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Shear 3-point correlations:

+

x

•8 components and multiple triangle configurations

•Barely detected currently but will be measured with high S/N in Stage III and IV surveys.

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Lensing Cl’s

Dark energy signature: relative amplitudes of the different spectra. Full power spectra contain other cosmological information.5000 sq. deg. survey with 40 galaxies/sq. arcmin. Takada & Jain 2004

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Lensing Cl’s: Sources of uncertainty

Baryonic physicsNonlinearRegime

Sample Variance Regime

Additive and multiplicative systematic errors enter at different l and z.

ground space

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Statistical errors

• Requiring a systematic error to be, say, half the statistical error leads to a quantitative estimate of tolerable level of systematics for a given survey.

• Stage IV surveys will achieve sub-percent level statistical accuracy on lensing power over a decade in l.

• For l < 1000, even deep ground based surveys are in the sample variance regime.

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The Lensing Pipeline

• 1. Object detection, star-galaxy classification

• 2. PSF (point spread function) measurement from stars

• 3. PSF interpolation onto galaxy positions

• 4. Galaxy shape measurement and PSF deconvolution

• 5. Shear correlation measurement + Redshift binning cosmological parameters

• Systematic errors can enter at all stages of the lensing pipeline. Progress so far:

• 2000: First detection of cosmological lensing signal.

• 2002-2008: significant advances in correction and testing for systematics.

• Currently measure ~0.1% rms shear to ~5% accuracy

• Using galaxy-shear cross-correlation, shear values below 10-4 have been measured!

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Galaxy and star images

Figure from S. Bridle

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Primary Systematic Errors

• PSF correction

• Shear calibration

• Intrinsic alignments

• Theory uncertainty/high l information

• Photo-z calibration

• Level of each of these systematics in current data would exceed statistical errors in Stage III and IV surveys.

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Systematic errors: what we have learned

• Formulation of lensing systematic errors: 1. Additive, 2. Multiplicative, 3. Redshift errors

• PSF correction (1)

PCA interpolation; fit for telescope aberrations

Multiple exposures help PSF correction

Cross-correlating shapes from different exposures get rid of atmosphere

• Shear calibration (2): STeP sims now get sub-percent performance.

• Spectroscopic calibration of photo-z’s (3):

Estimation of needed sample. Shortcuts based on cross-correlations will help.

• Intrinsic alignment errors (1): there are two kinds! Measured from SDSS.

Lensing P5 15Degradation in w: shear and

redshift calibration errors

Self-calibration regime. Note: 1. Degradation higher for survey with lower statistical error. 2. PS+Bispectrum curves too optimistic (Gaussian covariances). 3. Such analysis needed for all key lensing statistics and sources of systematics.

Huterer et al 2006

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Systematic errors: understanding galaxies

• Three reasons we need to learn about galaxies

How best to calibrate photo-z’s? Which are the (impossibly) difficult populations?

Intrinsic alignment errors: how does the signal grow with redshift? Which galaxies are immune?

How best to use cross-correlations, including tests of general relativity?

• We will need to understand the relevant properties of galaxies as a function of type up to z~1 and beyond.

• Important simplification: lensing does not require fair sampling of galaxies. We have the liberty to discard 10s of percent of galaxies of certain type or redshift.

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Systematic Errors: Outlook for Stage IV (ground)

•Sources of systematic errors Improvement Factor Comments

Observed PSF anisotropy - Depends on telescope

Interpolation of PSF >10 Analytical scaling OK. Tests needed.

Dilution/Shear calibration ~10* In progress w/ simulations. Algorithm driven. Self-calibrates.

Source redshift distribution >10 Extra Data. Need ~ 105 spectra.Cross-correlation shortcuts?

Power spectrum prediction 4 In progress. Gas physics?

Intrinsic shape correlations ? Measured from SDSS. Need more data and modeling. Self-calibrates.

Note: For systematics like PSF correction, current datasize (~2 million galaxies) is what limits tests of systematic correction schemes.

Lensing P5 18Systematic errors: a 5 year wish-list

• What is the accuracy of photo-z’s as a function of redshift and galaxy type? (Depends on photo-z calibration and PSF. )

• What is the correct model for intrinsic alignments? Are most galaxy types immune? What is the overall degradation if fit from data?

• How well does self-calibration work from real data (e.g. with photo-z outliers)? Especially relevant for shear calibration, intrinsic alignments.

• Theory uncertainty at high l: how well can we model/measure gas physics? Are current forecasts too optimistic/pessimistic?

• What is the highest redshift bin with useful lensing information from the ground? What subset of galaxies are useful beyond the limit inferred from median seeing and median galaxy size?

• How much will cross-correlation and other shortcuts reduce the needed redshift calibration sample?

• Galaxy bias: how well is it measurable, and what is the level of nonlinear and stochastic bias at large scales?

Worry

/ Hop

e

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Systematic errors: show stoppers?

• Lensing power spectra and cross-spectra have a large amount of partially redundant information.

• Multiple statistics, gravitational origin of the signal, and redshift tomography data provides many cross-checks. There isn’t a single exceptional property, as in SNIa or even galaxy clusters, that could let us down!

• Lensing shape measurements are very challenging. But given (i) PSF correction from stars, which scales with survey size, and, (ii) the recent progress in algorithm/software development, there do not seem to be show stoppers for Stage III or IV surveys.

• The accuracy of redshift calibration is critical in suppressing a direct bias in dark energy parameters and in controlling intrinsic alignment. If inadequate, it would make certain galaxy types and redshift ranges inaccessible from the ground loss of depth and effective number density.

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Ground surveys: Stage III Stage IV

• Stage III suveys: DES, Subaru (also PS1 and KiDS). More than an order of magnitude increase over current datasize.

• Stage IV (LSST) survey size increase: factor of 4-10 in area; up to 3 in number density due to depth; and additional filter(s).

• Telescope capability: Stage III surveys have different strengths and strategies. Stage IV must learn lessons from all of them.

• Currently vigorous activity in algorithm development and code testing. The progress in software developed and in systematic error analysis will be invaluable to Stage IV survey.

• The importance of this staged progress in ground based lensing cannot be over-emphasized. Stage III experiences could lead to changes in Stage IV survey strategy and many other elements.

• Analysis methods and software testing need continued support all the way to Stage IV !

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Space: advantages in shape measurement

• For shape measurements the most important factor in favor of space is PSF size:

Residual systematics scale with PSF size for all galaxies

Galaxies smaller than PSF provide very little information. E.g. effective number density for SNAP lensing survey is ~3x bigger.

• PSF anisotropy and stability: a space mission that performs to specs will require only modest PSF correction on galaxy shapes.

• We can be confident that lensing measurements from a well designed space telescope will meet

Stage IV targets.

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Space: systematics beyond shapes

• Photo-z calibration errors

NIR imaging and better photometric calibration will produce improved photo-z’s to begin with. But how high in redshift is calibration feasible?

• Intrinsic alignments

• Theory uncertainty at high l

• The high-z and high l regime requires significant progress in the next ~5 years.

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New Discovery Modes

• Consider Tests of Modified Gravity and Dark Matter

• High resolution (space) and sky coverage (ground) are complementary. And multi-wavelength imaging and spectroscopy play a role.

• Individual Clusters come in two useful varieties:

Golden lenses (strong and weak lensing): isolated, relaxed, spherical systems

Merging systems with displaced baryons and DM: constrain DM interaction cross-section.

• Bigger sky coverage helps find rare objects; good resolution and redshift info. helps study them in detail.

• Other tests of gravity: robust tests combine lensing or ISW cross-correlations with dynamical measurements. Target 0.3<z<1 and scales 1 Mpc<<200 Mpc.

Well designed complementary probes, especially imaging+spectroscopy, are more important than in a dark energy scenario. E.g. adjust design of BAO surveys?

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Complementarity

• Deep imaging from space of part of a ground survey would facilitate shear calibration and other tests of PSF correction

• Imaging and spectra in NIR would be an enormous asset in calibrating photo-z’s from ground survey

• Tests of gravity benefit from a combination of the depth/resolution of space and sky coverage of ground

• There is ongoing work on the best tests of gravity using dynamics from spectroscopic data plus lensing from imaging surveys.

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Spare Slides

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Typical image

Slide from S. Bridle

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Weak lensing: distance and growth

Illustration of separable D(z) and g(z) constraints at percent level from LSST-scale WL survey (Knox, Song & Tyson).

Power-spectrum tomography only, no systematic errors. Slide from G. Bernstein

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Techniques for PSF correction

• PCA (principal component analysis) uses stars from different exposures and different pointings to improve PSF interpolation. It deals with PSF patterns that are correlated in different exposures.

• Atmospheric PSF patterns are circumvented by measuring shear correlations from cross-correlation of galaxy shapes measured in different exposures. And use of ~100 exposures of per field lowers PSF anisotropy in stacked images.

These two techniques can tackle generic PSF anisotropy patterns.

Requirements: sufficient well measured stars per exposure; few principal components; PSF patterns are smooth and depend linearly on telescope variables; Sufficient exposures per field

Jarvis & Jain 2004, astro-ph/0412234

Jain, Jarvis, Bernstein 2005, astro-ph/0510231

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Space vs. Ground: Metrics

• Survey Speed: see G. Bernstein 2007 talk to BEPAC.

Factor of ~200 in A-Omega of LSST is made up by losses due to sky brightness, duty cycle, resolution, etc. from ground

• Photometric calibration

• Resolution (PSF size)

• PSF Anisotropy

• Systematics: all shape measurement systematics are worse from ground.

• Photo-z’s also have limitations due to absence of NIR. Spectroscopic calibration

• How deep is too deep?! (Early DE? But galaxy population not understood? GI alignments? Spectro calibration?)

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Assorted comments on shape measurement

• Typically use 10-sigma detections for shape measurement

• Size < psf gets significantly down weighted

• 30-40 is the limiting n_eff from ground. Space?? UDF has the answer for ultimate limit (500?). SNAP: 100.

• Shot noise regime is l~104 for space and l~2000 for ground

• A conservative approach to nonlinear regime favors a wide survey over a deep one, down to median z<1. But getting high S/N is helpful for controlling both shape and photo-z systematics

• Multi-filter gain in shape measurement S/N: up to 50%. The sqrt(Nfilter) regime is never valid because galaxies look the same in different filters.

• With Nexp exposures, 1. Will gain more by using the best half or quartile of seeing (though can detect objects using all Nexp). 2. Will split into two (three) sets for 2- (3-) point shear correlations. 3. Some systematics in PSF average down.

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The high-l, high-z regime

• Nonlinear regime will be useful via g-g lensing and cluster counts (regardless of how good simulations or models of the nonlinear power spectrum get).

• Baryonic physics enters at l~1000, but is correctable at the 90% level to higher l. Consistency checks from data by stacking clusters with masses of ~1014 M

• Using the tail of the size distribution, and the best half/quartile of seeing (and an extra 30-40% in Neff from multi-filter data) can get to higher z. How high? Penalty in reduced n_eff due to discarding the small galaxies: how small a fraction of galaxies is worth pursuing?

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Dark Energy Forecasts

• Takada & Jain 2008, in prep.

Power spectrum and Bispectrum with non-Gaussian covariances. Expect that the combination is robust to most

systematics. Takada & Jain 2008