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The REGLENS method

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

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The REGLENS method

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

  2. 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

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

  4. Geneology of PSF Correction Schemes

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

  6. Re-gaussianization, cont. • We want I’= Gf = 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’

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

  8. Weighting scheme • Weight by inverse shape + measurement error: wi = 1 SN + e • SN = <e2 - e > 2 2 2 2

  9. 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

  10. 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)

  11. 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

  12. 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)

  13. 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

  14. 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

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