Sunyaev--Zel'dovich profile fitting with joint AMI-Planck analysis
  We develop a Bayesian method of analysing Sunyaev-Zel'dovich measurements of
galaxy clusters obtained from the Arcminute Microkelvin Imager (AMI) radio
interferometer system and from the Planck satellite, using a joint likelihood
function for the data from both instruments. Our method is applicable to any
combination of Planck data with interferometric data from one or more arrays.
We apply the analysis to simulated clusters and find that when the cluster
pressure profile is known a-priori, the joint dataset provides precise and
accurate constraints on the cluster parameters, removing the need for external
information to reduce the parameter degeneracy. When the pressure profile
deviates from that assumed for the fit, the constraints become biased. Allowing
the pressure profile shape parameters to vary in the analysis allows an
unbiased recovery of the integrated cluster signal and produces constraints on
some shape parameters, depending on the angular size of the cluster. When
applied to real data from Planck-detected cluster PSZ2 G063.80+11.42, our
method resolves the discrepancy between the AMI and Planck $Y$-estimates and
usefully constrains the gas pressure profile shape parameters at intermediate
and large radii.
