The REGLENS method Rachel Mandelbaum STEP Workshop 2007 Collaborators: Christopher Hirata, Uros Seljak

Inputs required for method List of object positions Postage stamps PSF as a function of position For all past science projects, used SDSS Photo pipeline to perform these tasks + get photometry, s/g separation, … Developing independent pipeline

Re-Gaussianization in detail Defining adaptive moments of PSF g using elliptical Gaussians that minimize: Trace = measure of size PSF ellipticity:

Geneology of PSF Correction Schemes

Re-Gaussianization, cont. PSF g, best-fit Gaussian G (M g ), residual  : g = G +  Measured image I (M I ): I = G  f +  f, or I’= G  f = I-  f

Re-gaussianization, cont. We want I’= G  f = I-  f |  | << |G|  compute  f using f=elliptical Gaussian obtained via M f = M I - M g Construct I’ = galaxy image convolved with Gaussian PSF (at image level), compute moments M I’

Re-gaussianization, cont. Use BJ02 (linear) PSF correction on I’: Shear coordinate system to get circular PSF Use Resolution factor is defined using kurtosis

Weighting scheme Weight by inverse shape + measurement error: w i = 1  SN +  e  SN =

Shear computation Weighted summation over individual galaxy ellipticities performed via  = ∑ w i e i 2 S sh ∑ w i Shear responsivity S sh computed using results from BJ02, S sh ~ 1-e rms 2

Object selection Require R 2 > 1/3 Require r 8.5 (STEP) Minimizes PSF dilution Avoids worst-case noise- rectification bias (Hirata, et. al. 2004)

Performance in simulations Noiseless simulations (Hirata & Seljak, 2003): Calibration bias <4% for deVauc, exponential profiles, with varying magnitude as a function of apparent size STEP: Mean calibration bias ~ -2% (averaged over PSF) Trends in calibration bias with apparent size, magnitude: fainter, larger have more negative calibration bias

STEP vs. SDSS Different PSF ellipticity effects in STEP than in SDSS data New, STEP-like (shapelets-based) simulations in SDSS: Consistent PSF ellipticity effects with SDSS data Consistent shear calibration bias as with STEP, including trends with apparent size Account for difference: different PSF? (skewness, substructure)

More method development Applying to co-added SDSS data using method optimized for shear measurement Convolve each image with kernel before addition to get the same, CIRCULAR PSF (sum of two Gaussians) in each image Preliminary results (ongoing with additional collaborators David Schlegel, Eric LBL / Berkeley) indicate systematic shear eliminated to high precision

Summary Method has been used for many science applications in SDSS g-g lensing, intrinsic alignments Further method development ongoing with simulations, coaddition pipeline Redshift distribution constraints completed Approaching few percent precision for g-g lensing and, eventually, cosmic shear on coadds