Mock weak lensing analysis of simulated galaxy clusters: bias and scatter in mass and concentration

(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.Comment: 18 pages, 12 figures. Minor changes to match final published paper. High-resolution figures available at http://www.ast.cam.ac.uk/~ybahe/Lensing.pd

Non-Gaussian Scatter in Cluster Scaling Relations

We investigate the impact of non-Gaussian scatter in the cluster mass-observable scaling relation on the mass and redshift distribution of clusters detected by wide area surveys. We parameterize non-Gaussian scatter by incorporating the third and forth moments (skewness and kurtosis) into the distribution P(Mobs|M). We demonstrate that for low scatter mass proxies the higher order moments do not significantly affect the observed cluster mass and redshift distributions. However, for high scatter mass indicators it is necessary for the survey limiting mass threshold to be less than 10^14 h^-1 Msol to prevent the skewness from having a significant impact on the observed number counts, particularly at high redshift. We also show that an unknown level of non-Gaussianity in the scatter is equivalent to an additional uncertainty on the variance in P(Mobs|M) and thus may limit the constraints that can be placed on the dark energy equation of state parameter w. Furthermore, positive skewness flattens the mass function at the high mass end, and so one must also account for skewness in P(Mobs|M) when using the shape of the mass function to constrain cluster scaling-relations.Comment: 6 Pages, 3 Figures, to be submitted to ApJ Letter

Tyler shape depth

In many problems from multivariate analysis, the parameter of interest is a shape matrix, that is, a normalized version of the corresponding scatter or dispersion matrix. In this paper, we propose a depth concept for shape matrices that involves data points only through their directions from the center of the distribution. We use the terminology Tyler shape depth since the resulting estimator of shape, namely the deepest shape matrix, is the median-based counterpart of the M-estimator of shape of Tyler (1987). Beyond estimation, shape depth, like its Tyler antecedent, also allows hypothesis testing on shape. Its main benefit, however, lies in the ranking of shape matrices it provides, whose practical relevance is illustrated in principal component analysis and in shape-based outlier detection. We study the invariance, quasi-concavity and continuity properties of Tyler shape depth, the topological and boundedness properties of the corresponding depth regions, existence of a deepest shape matrix and prove Fisher consistency in the elliptical case. Finally, we derive a Glivenko-Cantelli-type result and establish almost sure consistency of the deepest shape matrix estimator.Comment: 28 pages, 5 figure

Application of Pade Approximants to Determination of alpha_s(M_Z^2) from Hadronic Event Shape Observables in e+e- Annihilation

We have applied Pade approximants to perturbative QCD calculations of event shape observables in e+e- --> hadrons. We used the exact O(alpha_s^2) prediction and the [0/1] Pade approximant to estimate the O(alpha_s^3) term for 15 observables, and in each case determined alpha_s(M_Z^2) from comparison with hadronic Z^0 decay data from the SLD experiment. We found the scatter among the alpha_s(M_Z^2) values to be significantly reduced compared with the standard O(alpha_s^2) determination, implying that the Pade method provides at least a partial approximation of higher-order perturbative contributions to event shape observables.Comment: 15 pages, 1 EPS figure, Submitted to Physics Letters

A low energy rare event search with the MAJORANA DEMONSTRATOR

Abstract The MAJORANA DEMONSTRATOR is sensitive to rare events near its energy threshold, including bosonic dark matter, solar axions, and lightly ionizing particles. In this analysis, a novel training set of low energy small-angle Compton scatter events is used to determine the efficiency of pulse shape analysis cuts, and we present updated bosonic dark matter and solar axion results from an 11.17 kg-y dataset using a 5 keV analysis threshold

The Fundamental Plane for cluster E and S0 galaxies

We have analyzed the Fundamental Plane (FP) for a sample of 226 E and S0 galaxies in ten clusters of galaxies. For photometry in Gunn r the best fitting plane is log r_e=1.24 log sigma - 0.82 log _e + cst. The scatter is 0.084 in log r_e. The slope of the FP is not significantly different from cluster to cluster. The residuals of the FP correlate weakly with the velocity dispersion and the surface brightness. Thus, to avoid biases of derived distances the galaxies need to be selected in a homogeneous way. The FP has significant intrinsic scatter. No other structural parameters like ellipticity or isophotal shape can reduce the scatter significantly. The Mg_2-sigma relation differs slightly from cluster to cluster. Galaxies in clusters with lower velocity dispersions have systematically lower Mg_2. With the current stellar population models, it is in best agreement with our results regarding the FP if the offsets are mainly caused by differences in metallicity. Most of the distances that we derive from the FP imply small peculiar motions, <1000km/s. The zero point of the FP must therefore be quite stable. The residuals from the Mg_2-sigma relation may be used to flag galaxies with deviant populations, and possibly to correct the distance determinations for the deviations.Comment: 20 pages, gzipped PostScript, 14 figures included. Accepted for publication in MNRA

SZE Observables, Pressure Profiles and Center Offsets in Magneticum Simulation Galaxy Clusters

We present a detailed study of the galaxy cluster thermal \ac{sze} signal $Y$ and pressure profiles using {\it Magneticum} Pathfinder hydrodynamical simulations. With a sample of 50,000 galaxy clusters ($M_{\rm 500c}>1.4\times10^{14} \rm M_{\odot}$) out to $z=2$, we find significant variations in the shape of the pressure profile with mass and redshift and present a new generalized NFW model that follows these trends. We show that the thermal pressure at $R_{\rm 500c}$ accounts for only 80~percent of the pressure required to maintain hydrostatic equilibrium, and therefore even idealized hydrostatic mass estimates would be biased at the 20~percent level. We compare the cluster \ac{sze} signal extracted from a sphere with different virial-like radii, a virial cylinder within a narrow redshift slice and the full light cone, confirming small scatter ($\sigma_{\ln Y}\simeq 0.087$) in the sphere and showing that structure immediately surrounding clusters increases the scatter and strengthens non self-similar redshift evolution in the cylinder. Uncorrelated large scale structure along the line of sight leads to an increase in the \ac{sze} signal and scatter that is more pronounced for low mass clusters, resulting in non self-similar trends in both mass and redshift and a mass dependent scatter that is $\sim0.16$ at low masses. The scatter distribution is consistent with log-normal in all cases. We present a model of the offsets between the center of the gravitational potential and the \ac{sze} center that follows the variations with cluster mass and redshift.Comment: 20 pages, 15 figures, submitted to MNRA