A Comparison of Simple Mass Estimators for Galaxy Clusters

Abstract

High-resolution N-body simulations are used to investigate systematic trends in the mass profiles and total masses of clusters as derived from 3 simple estimators: (1) the weak gravitational lensing shear field under the assumption of an isothermal cluster potential, (2) the dynamical mass obtained from the measured velocity dispersion under the assumption of an isothermal cluster potential, and (3) the classical virial estimator. The clusters consist of order 2.5e+05 particles of mass $m_p \simeq 10^{10} \Msun$, have triaxial mass distributions, and significant substructure exists within their virial radii. Not surprisingly, the level of agreement between the mass profiles obtained from the various estimators and the actual mass profiles is found to be scale-dependent. The virial estimator yields a good measurement of the total cluster mass, though it is systematically underestimated by of order 10%. This result suggests that, at least in the limit of ideal data, the virial estimator is quite robust to deviations from pure spherical symmetry and the presence of substructure. The dynamical mass estimate based upon a measurement of the cluster velocity dispersion and an assumption of an isothermal potential yields a poor measurement of the total mass. The weak lensing estimate yields a very good measurement of the total mass, provided the mean shear used to determine the equivalent cluster velocity dispersion is computed from an average of the lensing signal over the entire cluster (i.e. the mean shear is computed interior to the virial radius). [abridged]Comment: Accepted for publication in The Astrophysical Journal. Complete paper, including 3 large colour figures can also be obtained from http://bu-ast.bu.edu/~brainerd/preprints

Weak Gravitational Lensing by a Sample of X‐Ray–luminous Clusters of Galaxies. II. Comparison with Virial Masses

“…In their study, Brainerd et al (1999) did not consider the possible effect of structures outside their clusters on the lensing mass estimates. Galaxy clusters are believed to be connected by large filaments of dark matter, diffuse gas, and galaxies, and mass within such filaments will contribute significantly to the lensing mass when seen in projection along the line of sight to a cluster, even if it is physically separated from the cluster by several Mpc (Metzler, White, & Loken 2001).…”

“…If there is significant substructure in the central regions of the clusters, or if the density profiles of the clusters are significantly shallower than an SIS-type model at small radii, the shear measurements are likely to underestimate the true cluster mass. Brainerd et al (1999) have used ray-tracing through high-resolution N-body simulations of massive (M V $ 10 15 h À1 M ) clusters to show that the average tangential shear, when measured within an annulus with an outer radius R MAX significantly smaller than the virial radius (and assuming an SIS-type mass profile), will tend to underestimate the true cluster mass. For R MAX ' R V , they find that the SIS-model fit yields quite accurate mass values (typically 5%-10% underestimates; see their Fig.…”

A Plasma Instability Theory of Gamma‐Ray Burst Emission

“…A plasma instability theory for the prompt emission of gamma-ray bursts is presented. [5] In this theory, a relativistic shell with Γ ≫ 1 passes through the interstellar medium. Two plasma instabilities, the filamentation instability and the two-stream instability, generate a magnetic field and heat the electrons to relativistic energies.…”

Weak Lensing

“…Lensing stands out from X-ray and dynamical methods in being a projected statistic, so it is worth asking whether this introduces any bias. It appears that anisotropy in simulated clusters has little systematic effect [21], and so do uncorrelated structures along the line of sight [56]; both effects are around the 5% level. However, in reality there are also correlated structures along the line of sight, and these can bias masses upwards by tens of percent [26,90].…”