How well can we determine cluster mass profiles from weak lensing?

Weak gravitational lensing provides a direct way to study the mass distribution of clusters of galaxies at large radii. Unfortunately, large scale structure along the line of sight also contributes to the lensing signal, and consequently affects the measurements. We quantify the effect of distant uncorrelated large scale structure on the inferred mass profile of clusters as measured from weak lensing. We consider NFW profiles, and find that large scale structure is a major source of uncertainty for most practical situations, when a model, with the mass M_200 and the concentration parameter c as free parameters, is fit to the observations. We find that the best constraints are found for clusters at intermediate redshifts (z~0.3). For a cluster at z=0.3, optimal results are obtained when the lensing signal is measured out to 10-15 arcminutes. Measurements at larger radii do not improve the accuracy with which the profile can be determined, contrary to what is expected when the contribution from large scale structure is ignored. The true uncertainties in M_200 and the concentration parameter c are ~2 times larger than when distant large scale structure is not included in the error budget.Comment: submitted to MNRA

Large scale bias and stochasticity of halos and dark matter

On large scales galaxies and their halos are usually assumed to trace the dark matter with a constant bias and dark matter is assumed to trace the linear density field. We test these assumption using several large N-body simulations with 384^3-1024^3 particles and box sizes between 100-1000h/Mpc, which can both resolve the small galactic size halos and sample the large scale fluctuations. We explore the average halo bias relation as a function of halo mass and show that existing fitting formulae overestimate the halo bias by up to 20% in the regime just below the nonlinear mass. We propose a new expression that fits our simulations well. We find that the halo bias is nearly constant, b~0.65-0.7, for masses below one tenth of the nonlinear mass. We explore next the relation between the initial and final dark matter in individual Fourier modes and show that there are significant fluctuations in their ratio, ranging from 10% rms at k~0.03h/Mpc to 50% rms at k~0.1h/Mpc. We argue that these large fluctuations are caused by perturbative effects beyond the linear theory, which are dominated by long wavelength modes with large random fluctuations. Similar or larger fluctuations exist between halos and dark matter and between halos of different mass. While these fluctuations are small compared to the sampling variance, they are significant for attempts to determine the bias by relating directly the maps of galaxies and dark matter or the maps of different galaxy populations, which would otherwise be immune to sampling variance.Comment: 9 pages, 8 figures, matches accepted version in MNRA

Halo stochasticity in global clustering analysis

In the present work we study the statistics of haloes, which in the halo model determines the distribution of galaxies. Haloes are known to be biased tracer of dark matter, and at large scales it is usually assumed there is no intrinsic stochasticity between the two fields. Following the work of Seljak & Warren (2004), we explore how correct this assumption is and, moving a step further, we try to qualify the nature of stochasticity. We use Principal Component Analysis applied to the outputs of a cosmological N-body simulation to: (1) explore the behaviour of stochasticity in the correlation between haloes of different masses; (2) explore the behaviour of stochasticity in the correlation between haloes and dark matter. We show results obtained using a catalogue with 2.1 million haloes, from a PMFAST simulation with box size of 1000h^{-1}Mpc. In the relation between different populations of haloes we find that stochasticity is not-negligible even at large scales. In agreement with the conclusions of Tegmark & Bromley (1999) who studied the correlations of different galaxy populations, we found that the shot-noise subtracted stochasticity is qualitatively different from `enhanced' shot noise and, specifically, it is dominated by a single stochastic eigenvalue. We call this the `minimally stochastic' scenario, as opposed to shot noise which is `maximally stochastic'. In the correlation between haloes and dark matter, we find that stochasticity is minimized, as expected, near the dark matter peak (k ~ 0.02 h Mpc^{-1} for a LambdaCDM cosmology) and, even at large scales, it is of the order of 15 per cent above the shot noise. Moreover, we find that the reconstruction of the dark matter distribution is improved when we use eigenvectors as tracers of the bias. [Abridged]Comment: 9 pages, 12 figures. Submitted to MNRA

Optimal capture of non-Gaussianity in weak lensing surveys: power spectrum, bispectrum and halo counts

We compare the efficiency of weak lensing-selected galaxy clusters counts and of the weak lensing bispectrum at capturing non-Gaussian features in the dark matter distribution. We use the halo model to compute the weak lensing power spectrum, the bispectrum and the expected number of detected clusters, and derive constraints on cosmological parameters for a large, low systematic weak lensing survey, by focusing on the $\Omega_m$-$\sigma_8$ plane and on the dark energy equation of state. We separate the power spectrum into the resolved and the unresolved parts of the data, the resolved part being defined as detected clusters, and the unresolved part as the rest of the field. We consider four kinds of clusters counts, taking into account different amount of information : signal-to-noise ratio peak counts; counts as a function of clusters' mass; counts as a function of clusters' redshift; and counts as a function of clusters' mass and redshift. We show that when combined with the power spectrum, those four kinds of counts provide similar constraints, thus allowing one to perform the most direct counts, signal-to-noise peaks counts, and get percent level constraints on cosmological parameters. We show that the weak lensing bispectrum gives constraints comparable to those given by the power spectrum and captures non-Gaussian features as well as clusters counts, its combination with the power spectrum giving errors on cosmological parameters that are similar to, if not marginally smaller than, those obtained when combining the power spectrum with cluster counts. We finally note that in order to reach its potential, the weak lensing bispectrum must be computed using all triangle configurations, as equilateral triangles alone do not provide useful information.Comment: Matches ApJ-accepted versio

Weak Lensing by Galaxies in Groups and Clusters: I.--Theoretical Expectations

Galaxy-galaxy lensing is rapidly becoming one of the most promising means to accurately measure the average relation between galaxy properties and halo mass. In order to obtain a signal of sufficient signal-to-noise, one needs to stack many lens galaxies according to their property of interest, such as luminosity or stellar mass. Since such a stack consists of both central and satellite galaxies, which contribute very different lensing signals, the resulting shear measurements can be difficult to interpret. In the past, galaxy-galaxy lensing studies have either completely ignored this problem, have applied rough isolation criteria in an attempt to preferentially select `central' galaxies, or have tried to model the contribution of satellites explicitely. However, if one is able to {\it a priori} split the galaxy population in central and satellite galaxies, one can measure their lensing signals separately. This not only allows a much cleaner measurement of the relation between halo mass and their galaxy populations, but also allows a direct measurement of the sub-halo masses around satellite galaxies. In this paper, we use a realistic mock galaxy redshift survey to show that galaxy groups, properly selected from large galaxy surveys, can be used to accurately split the galaxy population in centrals and satellites. Stacking the resulting centrals according to their group mass, estimated from the total group luminosity, allows a remarkably accurate recovery of the masses and density profiles of their host haloes. In addition, stacking the corresponding satellite galaxies according to their projected distance from the group center yields a lensing signal that can be used to accurate measure the masses of both sub-haloes and host haloes. (Abridged)Comment: 16 pages, 10 figures, Accepted for publication in MNRA