PSF Anisotropy and Cosmology with Current Lensing Data

1
PSF Anisotropy and Cosmology with Current Lensing
Data

• Bhuvnesh Jain
• University of Pennsylvania
• Growth function and geometry with weak lensing
• PSF anisotropy correction reducing systematic
  errors using principal component analysis (Jarvis
  Jain 04, astro-ph/0412234)
• What does current lensing data tell us about
  dark dark energy? (Jarvis, Jain, Bernstein 05, in
  preparation)

2
Weak lensing shear and mass
3
Shear tomography, cross-correlations can we
separate geometry from clustering?
Mean tangential shear inside aperture compared
for source galaxies at different z.
measured at different z.
4
Cross-correlation cosmography
What good are the foreground galaxies?
Cross-correlations give a pure geometric
measure.
zlens
z1
z2

• JainTaylor 03s error analysis I SCREWED UP
• Pure geometric measurement from weak lensing is
  much weaker.
• Conservative approach Use all 2-point
  correlations to improve on shear-shear
  correlations factor of 2 improvement in dark
  energy parameters (Hu Jain 04)

5
Systematic Errors in Weak Lensing PSF Anisotropy

• PSF anisotropy is currently the primary
  systematic errors in weak lensing data.
• Galaxy shapes are convolved by the PSF, so PSF
  anisotropy must be removed to get accurate galaxy
  shapes.
• There are good methods for deconvolving the PSF
• So whats the problem? Interpolating the PSF
  from where it is measured (stars) to where we
  need it (galaxies).
• A fundamental limitations in scaling lensing
  accuracy to ambitious future surveys?

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Anisotropic PSF Interpolation

• Why is interpolation hard?
• Magnitude/direction of the effect vary by order
  unity across an image
• Only 100 stars per degree-sized image 100,000
  galaxies
• Some stars are actually galaxies, so need to
  do outlier rejection
• Maximum of about 4th order polynomial per image.
• Principal Component Analysis allows us to use
  stars from different exposures improved
  interpolation.
• Higher order (10th order for CTIO survey)
  polynomial smaller scales become accessible
• Residuals are almost uncorrelated lower
  systematics on all scales
• Near optimal technique for controlling
  systematics in very large surveys
• (see also the approaches of
  Hoekstra04, van Waerbeke, Hoekstra, Mellier04)

7
CTIO Weak Lensing Survey

• 12 widely separated fields
• Each field is 2.5º x 2.5º
• Total area 75 square degrees
• Total usable galaxies 1.8 million
• Magnitude range 19 lt m lt 23 (R band)
• Galaxy redshift distribution peak at z 0.5
• Most Sensitive to Dark Matter at z 0.2-0.3
• Jarvis, Bernstein et al 03

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Anisotropic PSF
Focus too low
Focus (roughly) correct
Focus too high

• Whisker plots for three BTC camera exposures
  10 ellipticity
• Left and right are most extreme variations,
  middle is more typical.
• Is there a correlated variation in the different
  exposures? Yes!

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PCA Fitting for PSF

• PSF patterns dominated by 1-parameterfocus.
  This is the first principal component.
• Using Principal Component Analysis, we can
  estimate a focus number for each exposure, fi.
• Then rather than fitting the star shapes in each
  exposure separately, we use all the stars in all
  the images, along with the focus values, fi.
• In general, we allow for several Principal
  Components, fi,k .
• Big computational fitting problem fit for 2000
  polynomial coefficients (30 principal components,
  10th order polynomials in x,y) using 100,000
  stars.
• These need not correspond to any physical
  variable. As long as theres a correlation
  between exposures, PCA is a nearly optimal way of
  using the information to correct for PSF
  anisotropy.

10
After Processing
Focus (roughly) correct
Focus too high
Focus too low

• Remaining ellipticities are essentially
  uncorrelated.
• Measurement error is the cause of the residual
  shapes.
• 1st improvement higher order polynomial means
  PSF accurate to below 1 arcmin.
• 2nd Much lower correlated residuals on all
  scales!

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Test of PSF correction stellar ellipticity
correlation ?

• Corrected star ellipticity correlation is
  10-100 smaller than lensing signal. (Mosaic
  Camera BTC camera worse below 2 )

12
E/B mode decomposition
Gravitational lensing due to scalar potential
field no B-mode
13
B-mode test

• Log plot

B-mode consistent with zero over all angular
scales Jarvis Jain 2004
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Lensing 2-point correlations

• Shear signal 0.1-1, measured over two decades
  in angular scale. Covariances estimated from
  data.

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Sensitivity to dark energy

• Lensing fields depend on
• Distances affect W , since
• Growth rate affects ?
• Both are given by integrals of expansion rate
• Lensing tomography probes dark energy equation of
  state. Empirical approach
• ?de ?de/?critical dark energy density
• P w(a) ?de equation of state
• w(a) w0 wa(1-a)
• a 1/(1z) - expansion scale factor
• w0 is constant term, wa the time evolution term

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Dark Energy from Lensing

• CMB measures power spectrum at z1000
• Lensing correlations at z0.3 depends on growth
  factor
• Growth factor and distances depend on dark energy
• ?8 in terms of CMB-motivated parameters

G0 has dark energy information, so ?8 measures
d.e. Hu Jain 2004
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?8-?m Constraints
Green CMB (WMAPext), Red SN (Riess et al
2004), Blue Lensing. Priors No curvature,
neutrino mass, running. Thats it! w is
marginalized over, but assumed constant.
(Jarvis, Jain, Bernstein 05)
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?de-w Constraints
Green CMB, Red SN, Blue Lensing
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Dark Energy CMBSNSDSS

• Tegmark et al 2004 95 C.L.
• See also Seljak et al Riess et al Huterer
  Cooray Lewis, Weller..

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Cosmology Constraints

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Fully marginalized parameter estimates.
WLCMBSN Errors Green statistical, Red
systematic. (Jarvis, Jain Bernstein 05)
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Dark energy time evolution

• w(a)w0 wa (1-a).
• Full marginalization is important.

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Systematic Uncertainties

• Shape measurements small residual error!
  B-mode add or subtract? We use E /- B
• Source redshift distribution
• Overall calibration of shear (5)
• Non-linear prediction
• Sum of Systematic errors lt Statistical errors
• (well below half for dark energy parameters)

23
Planning a lensing survey? The 3 stages of
self-doubt

• 1. Instrumental effects are they much lower for
  my new telescope?
• 2. Correct from the data Given some level errors
  due to instrument and atmosphere, how well can I
  correct them using stellar PSFs?
• 3. Self-calibration regime Given the remaining
  errors, how much does it degrade cosmo errors? If
  you combine power spectrum, bispectrum, does the
  degradation plateau?
• Any planned survey needs to answer these
  question. Its hard, but,
• the right answer (could) get a 100 million
  dollars.
• A brief history lensing in blank fields is a
  21st century baby.
• Since then, advances in shape measurement and PSF
  interpolation ? correction from data is
  promising.
• Reduction in systematics could keep pace with
  statistical errors.

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Conclusions

• PCA technique is effective at removing
  systematic shape errors due to PSF.
• Even better for future surveys with more images
  correction improves with Nexp
• In WL, shear calibration is most significant
  remaining systematic (assuming photo-zs give
  dn/dz)
• Lensing data is complementary with CMB, SNe data
  for constraining dark energy, cosmology.