Cosmological Constraints From the 100 Square Degree Weak Lensing Survey

TL;DR

This paper demonstrates that combining 100 deg$^2$ of cosmic shear data from four large weak-lensing surveys enables tight joint constraints on $\Omega_m$ and $\sigma_8$ in a flat $\Lambda$CDM framework. It advances the methodology by incorporating non-Gaussian covariance from simulations, calibrating shear measurements with STEP results, and using the largest available deep photometric redshift catalog to model the redshift distribution and its uncertainties via Monte Carlo sampling. The study finds $\sigma_8\left(\frac{\Omega_m}{0.24}\right)^{0.59}=0.84\pm0.05$, with per-survey analyses generally consistent but modest shifts depending on the redshift model; the results are broadly compatible with WMAP3 constraints. The work also emphasizes the critical role of accurately characterizing the source redshift distribution and highlights the need for near-IR data to capture high-$z$ contributions for future precision cosmic shear surveys.

Abstract

We present a cosmic shear analysis of the 100 square degree weak lensing survey, combining data from the CFHTLS-Wide, RCS, VIRMOS-DESCART and GaBoDS surveys. Spanning ~100 square degrees, with a median source redshift z~0.78, this combined survey allows us to place tight joint constraints on the matter density parameter Omega_m, and the amplitude of the matter power spectrum sigma_8, finding sigma_8*(Omega_m/0.24)^0.59 = 0.84+/-0.05. Tables of the measured shear correlation function and the calculated covariance matrix for each survey are included. The accuracy of our results is a marked improvement on previous work owing to three important differences in our analysis; we correctly account for cosmic variance errors by including a non-Gaussian contribution estimated from numerical simulations; we correct the measured shear for a calibration bias as estimated from simulated data; we model the redshift distribution, n(z), of each survey from the largest deep photometric redshift catalogue currently available from the CFHTLS-Deep. This catalogue is randomly sampled to reproduce the magnitude distribution of each survey with the resulting survey dependent n(z) parametrised using two different models. While our results are consistent for the n(z) models tested, we find that our cosmological parameter constraints depend weakly (at the 5% level) on the inclusion or exclusion of galaxies with low confidence photometric redshift estimates (z>1.5). These high redshift galaxies are relatively few in number but contribute a significant weak lensing signal. It will therefore be important for future weak lensing surveys to obtain near-infra-red data to reliably determine the number of high redshift galaxies in cosmic shear analyses.

Figures (6)

• Figure 1: $E$ and $B$ modes of the shear correlation function $\xi$ (filled and open points, respectively) as measured for each survey. Note that the $1\sigma$ errors on the $E$-modes include statistical noise, non-Gaussian sample variance (see §6) and a systematic error given by the magnitude of the $B$-mode. The $1\sigma$ error on the $B$-modes is statistical only. The results are presented on a log-log scale, despite the existence of negative $B$-modes. We have therefore collapsed the infinite space between $10^{-7}$ and zero, and plotted negative values on a separate log scale mirrored on $10^{-7}$. Hence all values on the lower portion of the graph are negative, their absolute value is given by the scaling of the graph. Note that this choice of scaling exaggerates any discrepancies. The solid lines show the best fit $\Lambda$CDM model for $\Omega_m=0.24$, $h=0.72$, $\Gamma = h\Omega_m$, $\sigma_8$ given in Table \ref{['sigma8s']}, and $n(z)$ given in Table \ref{['redshiftfits']}. The latter two being chosen for the case of the high confidence redshift calibration sample, an $n(z)$ modeled by Eq.(\ref{['brainerd']}), and the non-linear power spectrum estimated by 2003MNRAS.341.1311S.
• Figure 2: Normalised redshift distribution for the CFHTLS-Wide survey, given by the histogram, where the error bars include Poisson noise and sample variance of the photometric redshift sample. The dashed curve shows the best fit for Eq.(\ref{['brainerd']}), and the solid curve for Eq.(\ref{['heymans']}). Left: Distribution obtained if all photometric redshifts are used $0.0 \leq z \leq 4.0$, and $\chi^2$ is calculated between $0.0 \leq z \leq 2.5$. Right: Distribution obtained if only the high confidence redshifts are used $0.2 \leq z \leq 1.5$, and $\chi^2$ is calculated on this range. The existence of counts for $z > 1.5$ is a result of drawing the redshifts from their full probability distributions.
• Figure 3: Joint constraints on $\sigma_\mathrm{8}$ and $\Omega_\mathrm{m}$ from the 100 deg$^2$ weak lensing survey assuming a flat $\Lambda$CDM cosmology and adopting the non-linear matter power spectrum of 2003MNRAS.341.1311S. The redshift distribution is estimated from the high confidence photometric redshift catalogue Ilbert..0603217, and modeled with the standard functional form given by Eq.(\ref{['brainerd']}). The contours depict the 0.68, 0.95, and $0.99\%$ confidence levels. The models are marginalised, over $h=0.72\pm0.08$, shear calibration bias (see §4) with uniform priors, and the redshift distribution with Gaussian priors (see §6.1). Similar results are found for all other cases, as listed in Table \ref{['sigma8s']}.
• Figure 4: Joint constraints on $\sigma_\mathrm{8}$ and $\Omega_\mathrm{m}$ for each survey assuming a flat $\Lambda$CDM cosmology and adopting the non-linear matter power spectrum of 2003MNRAS.341.1311S. The redshift distribution is estimated from the high confidence photometric redshift catalogue Ilbert..0603217, and modeled with the standard functional form given by Eq.(\ref{['brainerd']}). The contours depict the 0.68, 0.95, and $0.99\%$ confidence levels. The models are marginalised, over $h=0.72\pm0.08$, shear calibration bias (see §4) with uniform priors, and the redshift distribution with Gaussian priors (see §6.1). Similar results are found for all other cases, as listed in Table \ref{['sigma8s']}.
• Figure 5: Values for $\sigma_\mathrm{8}$ when $\Omega_\mathrm{m}$ is taken to be 0.24, filled circles (solid) give our results with $1\sigma$ error bars, open circles (dashed) show the results from previous analyses (Table \ref{['tab:summary']}). Our results are given for the high confidence photometric redshift catalogue, using the functional form for $n(z)$ given by Eq.(\ref{['brainerd']}), and the 2003MNRAS.341.1311S prescription for the non-linear power spectrum. The literature values use the 1996MNRAS.280L..19P prescription for non-linear power, and are expected to be $\sim3\%$ higher than would be the case for 2003MNRAS.341.1311S. The forward slashed hashed region (enclosed by solid lines) shows the $1\sigma$ range allowed by our combined result, the back slashed hashed region (enclosed by dashed lines) shows the $1\sigma$ range given by the WMAP 3 year results.