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.