Sunyaev-Zel'dovich observation of the Bullet-like cluster Abell 2146 with the Arcminute Microkelvin Imager

We present 13.9-18.2 GHz observations of the Sunyaev-Zel'dovich (SZ) effect towards Abell 2146 using the Arcminute Microkelvin Imager (AMI). The cluster is detected with a peak signal-to-noise ratio of 13s in the radio source subtracted map from 9 h of data. Comparison of the SZ image with the X-ray image from Russell et al. suggests that both have extended regions which lie approximately perpendicular to one another, with their emission peaks significantly displaced. These features indicate non-uniformities in the distributions of the gas temperature and pressure, and suggest complex dynamics indicative of a cluster merger. We use a fast, Bayesian cluster analysis to explore the high-dimensional parameter space of the cluster-plus-sources model to obtain robust cluster parameter estimates in the presence of radio point sources, receiver noise and primordial cosmic microwave background (CMB) anisotropy; despite the substantial radio emission from the direction of Abell 2146, the probability of SZ + CMB primordial structure + radio sources + receiver noise to CMB + radio sources + receiver noise is 3 x 10(6) : 1. We compare the results from three different cluster models. Our preferred model exploits the observation that the gas fractions do not appear to vary greatly between clusters. Given the relative masses of the two merging systems in Abell 2146, the mean gas temperature can be deduced from the virial theorem (assuming all of the kinetic energy is in the form of internal gas energy) without being affected significantly by the merger event, provided the primary cluster was virialized before the merger. In this model we fit a simple spherical isothermal beta-model to our data, despite the inadequacy of this model for a merging system like Abell 2146, and assume the cluster follows the mass-temperature relation of a virialized, singular, isothermal sphere. We note that this model avoids inferring large-scale cluster parameters internal to r(200) under the widely used assumption of hydrostatic equilibrium. We find that at r(200) the average total mass M-T = (4.1 +/- 0.5) x 10(14) h(-1) M-circle dot and the mean gas temperature T = 4.5 +/- 0.5 keV.