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.
