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Register a new userMock weak lensing analysis of simulated galaxy clusters: bias and scatter in mass and concentration
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Yannick M. Bahe
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(Abridged) We quantify the bias and scatter in galaxy cluster masses and concentrations derived from an idealised mock weak gravitational lensing (WL) survey, and their effect on the cluster mass-concentration relation. For this, we simulate WL distortions on a population of background galaxies due to a large (~3000) sample of galaxy cluster haloes extracted from the Millennium Simulation at z~0.2. This study takes into account the influence of shape noise, cluster substructure and asphericity as well as correlated large-scale structure, but not uncorrelated large-scale structure along the line of sight and observational effects. We find a small, but non-negligble, negative median bias in both mass and concentration at a level of ~5%, the exact value depending both on cluster mass and radial survey range. Both the mass and concentration derived from WL show considerable scatter about their true values. This scatter has, even for the highest mass clusters of M200 > 10^14.8 M_sun, a level of ~30% and ~20% for concentration and mass respectively and increases strongly with decreasing cluster mass. For a typical survey analysing 30 galaxies per arcmin^2 over a radial range from 30 to 15 from the cluster centre, the derived M200-c relation has a slope and normalisation too low compared to the underlying true (3D) relation by ~40% and ~15% respectively. The scatter and bias in mass are shown to reflect a departure at large radii of the true WL shear/matter distribution of the simulated clusters from the NFW profile adopted in modelling the mock observations. Orientation of the triaxial cluster haloes dominates the concentration scatter (except at low masses, where galaxy shape noise becomes dominant), while the bias in c is mostly due to substructure within the virial radius.
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We study a sample of ~10^4 galaxy clusters in the redshift range 0.2<z<0.8 with masses M_200 > 5x10^13 h_70^-1 M_sun, discovered in the second Red-sequence Cluster Survey (RCS2). The depth and excellent image quality of the RCS2 enable us to detect the cluster-mass cross-correlation up to z~0.7. To obtain cluster masses, concentrations and halo biases, we fit a cluster halo model simultaneously to the lensing signal and to the projected density profile of red-sequence cluster members, as the latter provides tight constraints on the cluster miscentring distribution. We parametrise the mass-richness relation as M_200 = A x (N_200/20)^alpha, and find A = (15.0 +- 0.8) x 10^13 h_70^-1 M_sun and alpha = 0.73 +- 0.07 at low redshift (0.2<z<0.35). At intermediate redshift (0.35<z<0.55), we find a higher normalisation, which points at a fractional increase of the richness towards lower redshift caused by the build-up of the red-sequence. The miscentring distribution is well constrained. Only ~30% of our BCGs coincide with the peak of the dark matter distribution. The distribution of the remaining BCGs are modelled with a 2D-Gaussian, whose width increases from 0.2 to 0.4 h_70^-1 Mpc towards higher masses; the ratio of width and r_200 is constant with mass and has an average value of 0.44 +- 0.01. The mass-concentration and mass-bias relation agree fairly well with literature results at low redshift, but have a higher normalisation at higher redshifts, which may be due to selection and projection effects. The concentration of the satellite distribution decreases with mass and is correlated with the concentration of the halo.
This article is the second in a series in which we perform an extensive comparison of various galaxy-based cluster mass estimation techniques that utilise the positions, velocities and colours of galaxies. Our aim is to quantify the scatter, systematic bias and completeness of cluster masses derived from a diverse set of 25 galaxy-based methods using two contrasting mock galaxy catalogues based on a sophisticated halo occupation model and a semi-analytic model. Analysing 968 clusters, we find a wide range in the RMS errors in log M200c delivered by the different methods (0.18 to 1.08 dex, i.e., a factor of ~1.5 to 12), with abundance matching and richness methods providing the best results, irrespective of the input model assumptions. In addition, certain methods produce a significant number of catastrophic cases where the mass is under- or over-estimated by a factor greater than 10. Given the steeply falling high-mass end of the cluster mass function, we recommend that richness or abundance matching-based methods are used in conjunction with these methods as a sanity check for studies selecting high mass clusters. We see a stronger correlation of the recovered to input number of galaxies for both catalogues in comparison with the group/cluster mass, however, this does not guarantee that the correct member galaxies are being selected. We do not observe significantly higher scatter for either mock galaxy catalogues. Our results have implications for cosmological analyses that utilise the masses, richnesses, or abundances of clusters, which have different uncertainties when different methods are used.
Cosmological inference from cluster number counts is systematically limited by the accuracy of the mass calibration, i.e. the empirical determination of the mapping between cluster selection observables and halo mass. In this work we demonstrate a method to quantitatively determine the bias and uncertainties in weak-lensing mass calibration. To this end, we extract a library of projected matter density profiles from hydrodynamical simulations. Accounting for shear bias and noise, photometric redshift uncertainties, mis-centering, cluster member contamination, cluster morphological diversity, and line-of-sight projections, we produce a library of shear profiles. Fitting a one-parameter model to these profiles, we extract the so-called emph{weak lensing mass} $M_text{WL}$. Relating the weak-lensing mass to the halo mass from gravity-only simulations with the same initial conditions as the hydrodynamical simulations allows us to estimate the impact of hydrodynamical effects on cluster number counts experiments. Creating new shear libraries for $sim$1000 different realizations of the systematics, provides a distribution of the parameters of the weak-lensing to halo mass relation, reflecting their systematic uncertainty. This result can be used as a prior for cosmological inference. We also discuss the impact of the inner fitting radius on the accuracy, and determine the outer fitting radius necessary to exclude the signal from neighboring structures. Our method is currently being applied to different Stage~III lensing surveys, and can easily be extended to Stage~IV lensing surveys.
The statistics of peaks in weak lensing convergence maps is a promising tool to investigate both the properties of dark matter haloes and constrain the cosmological parameters. We study how the number of detectable peaks and its scaling with redshift depend upon the cluster dark matter halo profiles and use peak statistics to constrain the parameters of the mass - concentration (MC) relation. We investigate which constraints the Euclid mission can set on the MC coefficients also taking into account degeneracies with the cosmological parameters. To this end, we first estimate the number of peaks and its redshift distribution for different MC relations. We find that the steeper the mass dependence and the larger the normalisation, the higher is the number of detectable clusters, with the total number of peaks changing up to $40%$ depending on the MC relation. We then perform a Fisher matrix forecast of the errors on the MC relation parameters as well as cosmological parameters. We find that peak number counts detected by Euclid can determine the normalization $A_v$, the mass $B_v$ and redshift $C_v$ slopes and intrinsic scatter $sigma_v$ of the MC relation to an unprecedented accuracy being $sigma(A_v)/A_v = 1%$, $sigma(B_v)/B_v = 4%$, $sigma(C_v)/C_v = 9%$, $sigma(sigma_v)/sigma_v = 1%$ if all cosmological parameters are assumed to be known. Should we relax this severe assumption, constraints are degraded, but remarkably good results can be restored setting only some of the parameters or combining peak counts with Planck data. This precision can give insight on competing scenarios of structure formation and evolution and on the role of baryons in cluster assembling. Alternatively, for a fixed MC relation, future peaks counts can perform as well as current BAO and SNeIa when combined with Planck.
We present a joint shear-and-magnification weak-lensing analysis of a sample of 16 X-ray-regular and 4 high-magnification galaxy clusters at 0.19<z<0.69 selected from the Cluster Lensing And Supernova survey with Hubble (CLASH). Our analysis uses wide-field multi-color imaging, taken primarily with Suprime-Cam on the Subaru Telescope. From a stacked shear-only analysis of the X-ray-selected subsample, we detect the ensemble-averaged lensing signal with a total signal-to-noise ratio of ~25 in the radial range of 200 to 3500kpc/h. The stacked tangential-shear signal is well described by a family of standard density profiles predicted for dark-matter-dominated halos in gravitational equilibrium, namely the Navarro-Frenk-White (NFW), truncated variants of NFW, and Einasto models. For the NFW model, we measure a mean concentration of $c_{200c}=4.01^{+0.35}_{-0.32}$ at $M_{200c}=1.34^{+0.10}_{-0.09} 10^{15}M_{odot}$. We show this is in excellent agreement with Lambda cold-dark-matter (LCDM) predictions when the CLASH X-ray selection function and projection effects are taken into account. The best-fit Einasto shape parameter is $alpha_E=0.191^{+0.071}_{-0.068}$, which is consistent with the NFW-equivalent Einasto parameter of $sim 0.18$. We reconstruct projected mass density profiles of all CLASH clusters from a joint likelihood analysis of shear-and-magnification data, and measure cluster masses at several characteristic radii. We also derive an ensemble-averaged total projected mass profile of the X-ray-selected subsample by stacking their individual mass profiles. The stacked total mass profile, constrained by the shear+magnification data, is shown to be consistent with our shear-based halo-model predictions including the effects of surrounding large-scale structure as a two-halo term, establishing further consistency in the context of the LCDM model.
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