postscript
2 Observations of the ...
Abstract...
4 Errors In Determination ...
The temperature decrement of the CMB due to the S--Z effect in the low-frequency limit is given by
and so is proportional to the line integral of pressure along the line of sight
through the cluster. The electrons in the hot cluster atmosphere also emit
thermal bremsstrahlung radiation, which will have a broad-band X-ray luminosity
The cluster temperature can be determined from the X-ray spectrum. If S--Z and
X-ray data are combined, then it is possible to solve for both the electron
density and the physical size of the emitting gas cloud. By measuring its
angular extent, and by assuming that the line of sight depth through the
cluster is equal to the width in the plane of the sky, it is possible to
directly calculate the distance to the cluster and hence estimate
(Silk & White (1978), Birkinshaw (1979), Cavaliere et al. (1979)). In the simplified case of a uniform, isothermal
cube of gas, subtending an angle 
, which has an X-ray surface
brightness 
, and assuming that 
then (Jones (1995)):
where 
is an emissivity constant which depends on the gas temperature, the
energy response of the X-ray telescope (corrected for the redshift of the
cluster) and the absorbing column to the cluster. In practise, when combining
X-ray and S--Z data we assume that the cluster atmosphere is in hydrostatic
equilibrium and can be described by an isothermal King model (Cavaliere & Fusco-Femiano (1976)),
