  Clusters of galaxies have been used extensively to determine cosmological
parameters. A major difficulty in making best use of Sunyaev-Zel'dovich (SZ)
and X-ray observations of clusters for cosmology is that using X-ray
observations it is difficult to measure the temperature distribution and
therefore determine the density distribution in individual clusters of galaxies
out to the virial radius. Observations with the new generation of SZ
instruments are a promising alternative approach. We use clusters of galaxies
drawn from high-resolution adaptive mesh refinement (AMR) cosmological
simulations to study how well we should be able to constrain the large-scale
distribution of the intra-cluster gas (ICG) in individual massive relaxed
clusters using AMiBA in its configuration with 13 1.2-m diameter dishes
(AMiBA13) along with X-ray observations. We show that non-isothermal beta
models provide a good description of the ICG in our simulated relaxed clusters.
We use simulated X-ray observations to estimate the quality of constraints on
the distribution of gas density, and simulated SZ visibilities (AMiBA13
observations) for constraints on the large-scale temperature distribution of
the ICG. We find that AMiBA13 visibilities should constrain the scale radius of
the temperature distribution to about 50% accuracy. We conclude that the
upgraded AMiBA, AMiBA13, should be a powerful instrument to constrain the
large-scale distribution of the ICG.
