CFHTLenS tomographic weak lensing cosmological parameter constraints: Mitigating the impact of intrinsic galaxy alignments

TL;DR

This study advances tomographic weak lensing by simultaneously fitting cosmological parameters and a non-linear intrinsic alignment model to CFHTLenS data, mitigating IA contamination. By combining CFHTLenS with WMAP7, BOSS, and a prior on H0, the authors derive precise constraints on σ8, Ω_m, and w, and demonstrate the galaxy-type dependence of intrinsic alignments (strong for early-types, null for late-types). The analysis relies on a covariance matrix built from high-resolution N-body simulations and employs a Population Monte Carlo framework for Bayesian inference. The results reinforce a largely flat Universe with a cosmological constant and highlight the need for improved IA modeling and simulations in future, larger surveys.

Abstract

We present a finely-binned tomographic weak lensing analysis of the Canada-France-Hawaii Telescope Lensing Survey, CFHTLenS, mitigating contamination to the signal from the presence of intrinsic galaxy alignments via the simultaneous fit of a cosmological model and an intrinsic alignment model. CFHTLenS spans 154 square degrees in five optical bands, with accurate shear and photometric redshifts for a galaxy sample with a median redshift of zm =0.70. We estimate the 21 sets of cosmic shear correlation functions associated with six redshift bins, each spanning the angular range of 1.5<theta<35 arcmin. We combine this CFHTLenS data with auxiliary cosmological probes: the cosmic microwave background with data from WMAP7, baryon acoustic oscillations with data from BOSS, and a prior on the Hubble constant from the HST distance ladder. This leads to constraints on the normalisation of the matter power spectrum sigma_8 = 0.799 +/- 0.015 and the matter density parameter Omega_m = 0.271 +/- 0.010 for a flat Lambda CDM cosmology. For a flat wCDM cosmology we constrain the dark energy equation of state parameter w = -1.02 +/- 0.09. We also provide constraints for curved Lambda CDM and wCDM cosmologies. We find the intrinsic alignment contamination to be galaxy-type dependent with a significant intrinsic alignment signal found for early-type galaxies, in contrast to the late-type galaxy sample for which the intrinsic alignment signal is found to be consistent with zero.

Figures (11)

• Figure 1: Tomographic redshift distribution. The upper panel shows the effective weighted number of galaxies as a function of their maximum posterior photometric redshift estimate, separated into six tomographic bins between $0.2<z_{\rm BPZ}<1.3$. The effective weighted number of galaxies in each redshift bin is constant. The lower panel shows the redshift distribution for each selected bin as estimated from the weighted sum of the photometric redshift probability distributions $P(z)$.
• Figure 2: The observed two-point correlation function $\hat{\xi}^{ij}_+(\theta)$. The panels show the different $ij$ redshift bin combinations, ordered with increasing redshift bin $i$ from left to right, and increasing redshift bin $j$ from lower to upper. Refer to table \ref{['tab:zbins']} for the redshift ranges of each tomographic bin. The errors are estimated from an analysis of N-body lensing simulations as discussed in Section \ref{['sec:covest']}. The theoretical curves show our fiducial total GG+GI+II signal as a solid line. When distinguishable from the total, the GG only signal is shown dashed. The magnitude of the GI signal is shown dot-dashed (our fiducial GI model has a negative anti-correlated signal) and the II signal is shown dotted, where the amplitude is more than $10^{-7}$. The results of the broad two-bin tomographic analysis of Benjamin2012 are shown in the lower right corner.
• Figure 3: Compressed CFHTLenS tomographic data where each point represents a different tomographic bin combination $ij$ as indicated by $z_{\rm peak}$, the peak redshift of the lensing efficiency for that bin combination. The best-fitting amplitude $\alpha^{ij}$ of the data relative to a fixed fiducial GG-only cosmology model is shown, multiplied by the fiducial model at $\theta = 1$ arcmin for $\xi_+$ (circles) and $\xi_-$ (crosses, offset along the $z_{\rm peak}$ axis for clarity). The error bars show the $1\sigma$ constraints on the fit. The data can be compared to the fiducial GG-only model, shown dotted. Note that the colour of the points follow the same colour-scheme as Figure \ref{['fig:nofz']}, and indicates the lower redshift bin that is used for each point.
• Figure 4: Flat $\Lambda$CDM parameter constraints (68 per cent confidence) on the amplitude of the matter power spectrum controlled by $\sigma_8$ and the matter density parameter $\Omega_{\rm m}$ from CFHTLenS-only, comparing three cases: 2D weak lensing (blue) and 6-bin tomographic lensing where intrinsic alignments are assumed to be zero (pale blue) and are marginalised over (pink). For reference, the black cross shows the corresponding best-fit values from WMAP7 WMAP7.
• Figure 5: Flat $\Lambda$CDM joint parameter constraints (68 and 95 per cent confidence) on the amplitude of the matter power spectrum controlled by $\sigma_8$ and the matter density parameter $\Omega_{\rm m}$ from CFHTLenS-only (pink), WMAP7-only (blue), BOSS combined with WMAP7 and R11 (green), and CFHTLenS combined with BOSS, WMAP7 and R11 (white).