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Register a new userCosmic variance of weak lensing surveys in the non-Gaussian regime
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Elisabetta Semboloni
Publication date
2006
fields
Physics
and research's language is
English
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The results from weak gravitational lensing analyses are subject to a cosmic variance error term that has previously been estimated assuming Gaussian statistics. In this letter we address the issue of estimating cosmic variance errors for weak lensing surveys in the non-Gaussian regime. Using standard cold dark matter model ray-tracing simulations characterized by Omega_m=0.3, Omega_Lambda=0.7, h=0.7, sigma_8=1.0 for different survey redshifts z_s, we determine the variance of the two-point shear correlation function measured across 64 independent lines of sight. We compare the measured variance to the variance expected from a random Gaussian field and derive a redshift-dependent non-Gaussian calibration relation. We find that the ratio can be as high as ~30 for a survey with source redshift z_s ~ 0.5 and ~10 for z_s ~ 1. The transition scale theta_c above which the ratio is consistent with unity, is found to be theta_c ~ 20 arcmin for z_s ~ 0.5 and theta_c ~ 10 arcmin for z_s ~ 1. We provide fitting formula to our results permitting the estimation of non-Gaussian cosmic variance errors for any weak lensing analysis, and discuss the impact on current and future surveys. A more extensive set of simulations will however be required to investigate the dependence of our results on cosmology, specifically on the amplitude of clustering.
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The weak lensing power spectrum carries cosmological information via its dependence on the growth of structure and on geometric factors. Since much of the cosmological information comes from scales affected by nonlinear clustering, measurements of the lensing power spectrum can be degraded by non-Gaussian covariances. Recently there have been conflicting studies about the level of this degradation. We use the halo model to estimate it and include new contributions related to the finite size of lensing surveys, following Rimes and Hamiltons study of 3D simulations. We find that non-Gaussian correlations between different multipoles can degrade the cumulative signal-to-noise for the power spectrum amplitude by up to a factor of 2 (or 5 for a worst-case model that exceeds current N-body simulation predictions). However, using an eight-parameter Fisher analysis we find that the marginalized errors on individual parameters are degraded by less than 10% (or 20% for the worst-case model). The smaller degradation in parameter accuracy is primarily because: individual parameters in a high-dimensional parameter space are degraded much less than the volume of the full Fisher ellipsoid; lensing involves projections along the line of sight, which reduce the non-Gaussian effect; some of the cosmological information comes from geometric factors which are not degraded at all. We contrast our findings with those of Lee & Pen (2008) who suggested a much larger degradation in information content. Finally, our results give a useful guide for exploring survey design by giving the cosmological information returns for varying survey area, depth and the level of some systematic errors.
Intrinsic variations of the projected density profiles of clusters of galaxies at fixed mass are a source of uncertainty for cluster weak lensing. We present a semi-analytical model to account for this effect, based on a combination of variations in halo concentration, ellipticity and orientation, and the presence of correlated haloes. We calibrate the parameters of our model at the 10 per cent level to match the empirical cosmic variance of cluster profiles at M_200m=10^14...10^15 h^-1 M_sol, z=0.25...0.5 in a cosmological simulation. We show that weak lensing measurements of clusters significantly underestimate mass uncertainties if intrinsic profile variations are ignored, and that our model can be used to provide correct mass likelihoods. Effects on the achievable accuracy of weak lensing cluster mass measurements are particularly strong for the most massive clusters and deep observations (with ~20 per cent uncertainty from cosmic variance alone at M_200m=10^15 h^-1 M_sol and z=0.25), but significant also under typical ground-based conditions. We show that neglecting intrinsic profile variations leads to biases in the mass-observable relation constrained with weak lensing, both for intrinsic scatter and overall scale (the latter at the 15 per cent level). These biases are in excess of the statistical errors of upcoming surveys and can be avoided if the cosmic variance of cluster profiles is accounted for.
We present an efficient and robust approach for extracting clusters of galaxies from weak lensing survey data and measuring their properties. We use simple, physically-motivated cluster models appropriate for such sparse, noisy data, and incorporate our knowledge of the cluster mass function to optimise the detection of low-mass objects. Despite the methods non-linear nature, we are able to search at a rate of approximately half a square degree per hour on a single processor, making this technique a viable candidate for future wide-field surveys. We quantify, for two simulated data-sets, the accuracy of recovered cluster parameters, and discuss the completeness and purity of our shear-selected cluster catalogues.
We present an exploration of weak lensing by large-scale structure in the linear regime, using the third-year (T0003) CFHTLS Wide data release. Our results place tight constraints on the scaling of the amplitude of the matter power spectrum sigma_8 with the matter density Omega_m. Spanning 57 square degrees to i_AB = 24.5 over three independent fields, the unprecedented contiguous area of this survey permits high signal-to-noise measurements of two-point shear statistics from 1 arcmin to 4 degrees. Understanding systematic errors in our analysis is vital in interpreting the results. We therefore demonstrate the percent-level accuracy of our method using STEP simulations, an E/B-mode decomposition of the data, and the star-galaxy cross correlation function. We also present a thorough analysis of the galaxy redshift distribution using redshift data from the CFHTLS T0003 Deep fields that probe the same spatial regions as the Wide fields. We find sigma_8(Omega_m/0.25)^0.64 = 0.785+-0.043 using the aperture-mass statistic for the full range of angular scales for an assumed flat cosmology, in excellent agreement with WMAP3 constraints. The largest physical scale probed by our analysis is 85 Mpc, assuming a mean redshift of lenses of 0.5 and a LCDM cosmology. This allows for the first time to constrain cosmology using only cosmic shear measurements in the linear regime. Using only angular scales theta> 85 arcmin, we find sigma_8(Omega_m/0.25)_lin^0.53 = 0.837+-0.084, which agree with the results from our full analysis. Combining our results with data from WMAP3, we find Omega_m=0.248+-0.019 and sigma_8 = 0.771+-0.029.
Galaxy surveys that map multiple species of tracers of large-scale structure can improve the constraints on some cosmological parameters far beyond the limits imposed by a simplistic interpretation of cosmic variance. This enhancement derives from comparing the relative clustering between different tracers of large-scale structure. We present a simple but fully generic expression for the Fisher information matrix of surveys with any (discrete) number of tracers, and show that the enhancement of the constraints on bias-sensitive parameters are a straightforward consequence of this multi-tracer Fisher matrix. In fact, the relative clustering amplitudes between tracers are eigenvectors of this multi-tracer Fisher matrix. The diagonalized multi-tracer Fisher matrix clearly shows that while the effective volume is bounded by the physical volume of the survey, the relational information between species is unbounded. As an application, we study the expected enhancements in the constraints of realistic surveys that aim at mapping several different types of tracers of large-scale structure. The gain obtained by combining multiple tracers is highest at low redshifts, and in one particular scenario we analyzed, the enhancement can be as large as a factor of ~3 for the accuracy in the determination of the redshift distortion parameter, and a factor ~5 for the local non-Gaussianity parameter. Radial and angular distance determinations from the baryonic features in the power spectrum may also benefit from the multi-tracer approach.
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