On the ability of spectroscopic SZ effect measurements to determine the
  temperature structure of galaxy clusters
  (abridged) We explore in this paper the ability of spatially resolved
spectroscopic measurements of the SZ effect (SZE) to determine the temperature
profile of galaxy clusters. We derive a general formalism for the thermal SZE
in galaxy clusters with a non-uniform temperature profile that can be applied
to both cool-core clusters and non-cool core cluster with an isothermal or
non-isothermal temperature structure. We derive an inversion technique through
which the electron distribution function can be extracted from spectroscopic
SZE observations over a wide frequency range. We study the fitting procedure to
extract the cluster temperature from a set of simulated spatially resolved
spectroscopic SZE observations in different bands of the spectrum, from 100 to
450 GHz. The results of our analysis for three different cluster prototypes
(A2199 with a low-temperature cool core, Perseus with a relatively
high-temperature cool core, Ophiuchus with an isothermal temperature
distribution) provide both the required precision of the SZE observations and
the optimal frequency bands for a determination of the cluster temperature
similar or better than that obtainable from X-ray observations. The precision
of SZE-derived temperature is also discussed for the outer regions of clusters.
We also study the possibility to extract, from our method, the parameters
characterizing the non-thermal SZE spectrum of the relativistic plasma
contained in the lobes of radio galaxies as well as the spectrum of
relativistic electrons co-spatially distributed with the thermal plasma in
clusters with non-thermal phenomena. We find that the next generation SZE
experiments with spectroscopic capabilities can provide precise temperature
distribution measurements (...)
