Sunyaev-Zel'dovich observations of galaxy clusters out to the virial
  radius with the Arcminute Microkelvin Imager
  We present observations using the Small Array of the Arcminute Microkelvin
Imager (AMI; 14-18 GHz) of four Abell and three MACS clusters spanning
0.171-0.686 in redshift. We detect Sunyaev-Zel'dovich (SZ) signals in five of
these without any attempt at source subtraction, although strong source
contamination is present. With radio-source measurements from high-resolution
observations, and under the assumptions of spherical $\beta$-model,
isothermality and hydrostatic equilibrium, a Bayesian analysis of the data in
the visibility plane detects extended SZ decrements in all seven clusters over
and above receiver noise, radio sources and primary CMB imprints. Bayesian
evidence ratios range from 10^{11}:1 to 10^{43}:1 for six of the clusters and
3000:1 for one with substantially less data than the others. We present
posterior probability distributions for, e.g., total mass and gas fraction
averaged over radii internal to which the mean overdensity is 1000, 500 and
200, r_200 being the virial radius. Reaching r_200 involves some extrapolation
for the nearer clusters but not for the more-distant ones. We find that our
estimates of gas fraction are low (compared with most in the literature) and
decrease with increasing radius. These results appear to be consistent with the
notion that gas temperature in fact falls with distance (away from near the
cluster centre) out to the virial radius.
