Parameterization Effects in the analysis of AMI Sunyaev-Zel'dovich
  Observations
  Most Sunyaev--Zel'dovich (SZ) and X-ray analyses of galaxy clusters try to
constrain the cluster total mass and/or gas mass using parameterised models and
assumptions of spherical symmetry and hydrostatic equilibrium. By numerically
exploring the probability distributions of the cluster parameters given the
simulated interferometric SZ data in the context of Bayesian methods, and
assuming a beta-model for the electron number density we investigate the
capability of this model and analysis to return the simulated cluster input
quantities via three rameterisations. In parameterisation I we assume that the
T is an input parameter. We find that parameterisation I can hardly constrain
the cluster parameters. We then investigate parameterisations II and III in
which fg(r200) replaces temperature as a main variable. In parameterisation II
we relate M_T(r200) and T assuming hydrostatic equilibrium. We find that
parameterisation II can constrain the cluster physical parameters but the
temperature estimate is biased low. In parameterisation III, the virial theorem
replaces the hydrostatic equilibrium assumption. We find that parameterisation
III results in unbiased estimates of the cluster properties. We generate a
second simulated cluster using a generalised NFW (GNFW) pressure profile and
analyse it with an entropy based model to take into account the temperature
gradient in our analysis and improve the cluster gas density distribution. This
model also constrains the cluster physical parameters and the results show a
radial decline in the gas temperature as expected. The mean cluster total mass
estimates are also within 1 sigma from the simulated cluster true values.
However, we find that for at least interferometric SZ analysis in practice at
the present time, there is no differences in the AMI visibilities between the
two models. This may of course change as the instruments improve.
