Seeing in the dark -- II. Cosmic shear in the Sloan Digital Sky Survey

TL;DR

This study measures cosmic shear using coadded SDSS Stripe 82 imaging to probe the late-time matter power spectrum. It constructs a statistical framework that jointly models gravitational shear, PSF-induced systematics, and intrinsic alignments, and validates the measurement with extensive null tests and E/B-mode decomposition. Using a hybrid prediction approach that combines Halofit with the Coyote Emulator, the authors extract cosmological constraints that modestly augment WMAP7, notably tightening the allowed region in the $\Omega_m h^2$–$\sigma_8$ plane. The work also provides practical insights into handling multi-epoch data systematics, redshift distribution uncertainties, and masking biases, offering guidance for next-generation weak-lensing surveys.

Abstract

Statistical weak lensing by large-scale structure -- cosmic shear -- is a promising cosmological tool, which has motivated the design of several large upcoming surveys. Here, we present a measurement of cosmic shear using coadded Sloan Digital Sky Survey (SDSS) imaging in 168 square degrees of the equatorial region, with r<23.5 and i<22.5, a source number density of 2.2 galaxies per square arcminute and median redshift of 0.52. These coadds were generated using a new method described in the companion Paper I that was intended to minimise systematic errors in the lensing measurement due to coherent PSF anisotropies that are otherwise prevalent in the SDSS imaging data. We present measurements of cosmic shear out to angular separations of 2 degrees, along with systematics tests that (combined with those from Paper I on the catalogue generation) demonstrate that our results are dominated by statistical rather than systematic errors. Assuming a cosmological model corresponding to WMAP7 and allowing only the amplitude of matter fluctuations to vary, we find a best-fit value of sigma_8=0.636 +0.109 -0.154 (1-sigma); without systematic errors this would be sigma_8=0.636 +0.099 -0.137 (1-sigma). Assuming a flat LCDM model, the combined constraints with WMAP7 are sigma_8=0.784 +0.028 -0.026 (1-sigma), +0.055 -0.054 (2-sigma) and Omega_m h^2=0.1303 +0.0047 -0.0048 (1-sigma)+0.009 -0.009 (2-sigma); the 2-sigma error ranges are respectively 14 and 17 per cent smaller than WMAP7 alone. Aside from the intrinsic value of such cosmological constraints from the growth of structure, we identify some important lessons for upcoming surveys that may face similar issues when combining multi-epoch data to measure cosmic shear.

Figures (21)

• Figure 1: The response of the mean ellipticities $\langle e_1\rangle$ and $\langle e_2\rangle$ to applied shear, as determined in the shera-based simulations. Poisson error bars are shown. The additive offset to the response curve is not shown in the fit; these simulations do not accurately measure an additive shear bias.
• Figure 2: The redshift distribution inferred from matching the colours of the spectroscopic calibration sample to those of the lensing catalogue (solid black line, Sec. \ref{['sss:zdist']}) shown alongside the noisier redshift distribution inferred from the shear calibration simulations (dashed red line, Sec. \ref{['subsubsec:othertests']}). The best-fit distribution for the single-epoch SDSS lensing catalogue from 2011arXiv1107.1395N is shown for reference as the blue dot-dashed line.
• Figure 3: The mean ellipticity $\langle e_1\rangle$ as a function of declination in the $r$ and $i$ bands. This signal was removed from the galaxy catalogue prior to computing the final correlation function. The $r$ band data between declination $-0.8^\circ$ and $-0.4^\circ$ were rejected due to the known problems with camcol 2. The error bars are Poisson errors only.
• Figure 4: The loss of actual power due to $e_1$ projection. Using 36 realizations from the Monte Carlo simulation, we find the difference in post-projection ellipticity correlation function $\xi(\theta)$ and original $\xi(\theta)$. These are shown as the solid points ($\xi_{++}$) and dashed points ($\xi_{\times\times}$) in the figure, re-binned to 10 bins in angular separation $\theta$. The dashed lines at top and bottom are the $\pm 1\sigma$ statistical error bars of our measurement. The reduction of actual power is detectable by combining many simulations, but is very small compared to the error bars on the measurement.
• Figure 5: The star-galaxy ellipticity correlation functions. Shown are the $rr$, $ri$ (i.e. star $r$$\times$ galaxy $i$), $ir$, and $ii$ correlation functions, reduced to 10 bins. The solid points, which are offset to slightly lower $\theta$-values for clarity, are the $++$ correlation functions, and the dashed points are the $\times\times$ functions. All error bars are Poisson only.