# Sunyaev--Zel'dovich profile fitting with joint AMI-Planck analysis

## TL;DR

This paper introduces a Bayesian joint analysis method for Sunyaev-Zel'dovich data from AMI and Planck, improving cluster parameter constraints and resolving discrepancies in measurements.

## Contribution

A novel Bayesian approach for joint SZ data analysis from interferometers and satellites, enabling unbiased cluster parameter estimation and profile shape constraints.

## Key findings

- Joint dataset yields precise cluster parameters when pressure profile is known.
- Allowing profile shape variation removes bias and constrains shape parameters.
- Method resolves discrepancies in Planck and AMI measurements for a real cluster.

## Abstract

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.