P5:%20February%2022,%202008%20Weak%20Gravitational%20Lensing

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P5 February 22, 2008Weak Gravitational Lensing

• Bhuvnesh Jain
• University of Pennsylvania

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Outline

• Lensing measurements as probes of distance and
  growth
• Systematic Errors
• Recent advances
• What we dont 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
Consider the lensing convergence ?

• 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.

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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
zl1
zl2
z1
lensing mass
z2

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

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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 Cls
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 Cls Sources of uncertainty
Sample Variance Regime
ground
space
Baryonic physics
Nonlinear Regime
Additive and multiplicative systematic errors
enter at different l and z.
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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 lt 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-zs (3)
• Estimation of needed sample. Shortcuts based on
  cross-correlations will help.
• Intrinsic alignment errors (1) there are two
  kinds! Measured from SDSS.

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Degradation in w shear and redshift calibration
errors
Self-calibration regime. Note 1. Degradation
higher for survey with lower statistical error.
2. PSBispectrum 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-zs? 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 z1 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 gt10 Analytical scaling
  OK. Tests needed.
• Dilution/Shear calibration 10 In progress
  w/ simulations. Algorithm driven.
  Self-calibrates.
• Source redshift distribution gt10 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.

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Systematic errors a 5 year wish-list

• What is the accuracy of photo-zs 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 / Hope
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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 isnt 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-zs 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 0.3ltzlt1 and scales 1
  Mpclt?lt200 Mpc.
• Well designed complementary probes, especially
  imagingspectroscopy, 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-zs 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-zs 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 lt 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 l104 for space and l2000
  for ground
• A conservative approach to nonlinear regime
  favors a wide survey over a deep one, down to
  median zlt1. 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 l1000, 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