The SDSS Coadd: Cosmic Shear Measurement

TL;DR

This work reports a robust cosmic shear measurement from the SDSS Stripe 82 coadd (275 deg^2), detecting the E-mode with $>5\sigma$ significance and a B-mode consistent with zero. It employs both real-space (ξ_+ and ξ_E) and Fourier-space (C_l) analyses, using a Quadratic Estimator and a Pseudo Estimator to extract band powers and test for systematics, including careful PSF corrections and photometric redshift handling. The analysis yields a constraint on the combination $Ω_m^{0.7} σ_8 = 0.252^{+0.032}_{-0.052}$, in agreement with WMAP7 and other lensing surveys, and demonstrates consistency between methods and with simulations. The results validate large-area coadded surveys as a powerful avenue for precision cosmology and set a precedent for forthcoming DES/LSST analyses.

Abstract

Stripe 82 in the Sloan Digital Sky Survey was observed multiple times, allowing deeper images to be constructed by coadding the data. Here we analyze the ellipticities of background galaxies in this 275 square degree region, searching for evidence of distortions due to cosmic shear. The E-mode is detected in both real and Fourier space with $>5$-$σ$ significance on degree scales, while the B-mode is consistent with zero as expected. The amplitude of the signal constrains the combination of the matter density $Ω_m$ and fluctuation amplitude $σ_8$ to be $Ω_m^{0.7}σ_8 = 0.252^{+0.032}_{-0.052}$.

Figures (19)

• Figure 1: Photometric redshift distribution for galaxies passing the magnitude, size and ellipticity cuts (grey) and the photometric redshift error cuts $\sigma_{z}<0.20$ (blue) and $\sigma_{z}<0.15$ (red).
• Figure 2: Top panel: The difference between the measured ellipticity component $e_1$ and the PSF model $e_1$, for unsaturated bright stars with $16 < i < 17$, plotted against declination. Note the small overall bias and the trends and discontinuities in these $e_1$ residuals. Bottom panel: Same as the top but after applying the PSF correction procedure described in the text, which removes the bias, as well as reduces the trends and discontinuities in the $e_1$ residuals.
• Figure 3: Map of the galaxy ellipticities, averaged over the $0.1^\circ \times 0.1^\circ$ pixels used in our analysis, for a small region of the Stripe 82 area. The map is shown both before (left) and after (right) PSF correction, showing the effective removal of the PSF-induced ellipticities seen in particular along the top of the map on the left. For reference, a stick of ellipticity $e = 0.1$ is labeled at the top of each panel.
• Figure 4: The distribution (black) of galaxy ellipticities $e_1$ (top) and $e_2$ (bottom), averaged over the $0.1^\circ \times 0.1^\circ$ pixels used in our analysis, for the photo-$z$ error $< 0.15$ sample. The distributions are shown both before (left) and after (right) PSF correction, in order to demonstrate the effectiveness of our procedure in removing the PSF from the galaxy ellipticity measurements. Also shown are best-fit Gaussians (blue), which are good approximations to the PSF-corrected ellipticity distributions. The text in red gives the mean and $\sigma$ of the Gaussian in each panel.
• Figure 5: The window function that weights the power spectrum in Eq. (\ref{['eq:pkappa']}) for background galaxies in the two cuts used in our sample.