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Learn the innovative REGLENS method for accurate galaxy shear measurement in SDSS data, including adaptive PSF corrections and precise shear computation. Developed by Rachel Mandelbaum in collaboration with Christopher Hirata and Uros Seljak.
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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:
Re-Gaussianization, cont. • PSF g, best-fit Gaussian G (Mg), residual : g = G + • Measured image I (MI): I = Gf + f, or I’= Gf = I-f
Re-gaussianization, cont. • We want I’= Gf = I-f • || << |G| compute f using f=elliptical Gaussian obtained via Mf = MI - Mg • Construct I’ = galaxy image convolved with Gaussian PSF (at image level), compute moments MI’
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: wi = 1 SN + e • SN = <e2 - e > 2 2 2 2
Shear computation • Weighted summation over individual galaxy ellipticities performed via = ∑ wi ei 2 Ssh∑ wi • Shear responsivity Ssh computed using results from BJ02, Ssh ~ 1-erms 2
Object selection • Require R2 > 1/3 • Require r < 21.8 (SDSS) or S/N on shear measurement > 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 Huff @ 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