On the ability of the spectroscopic Sunyaev-Zeldovich effect measurements to determine the temperature structure of galaxy clusters

Aims. We explore 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 clusters with an isothermal or non-isothermal temperature structure. Methods. We develop an inversion technique by means of 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. Results. We present our analysis results for three different cluster prototypes: A2199 with a low-temperature cool core, Perseus with a relatively high-temperature cool core, and Ophiuchus with an isothermal temperature distribution. These results indicate both the precision of the SZE observations and the optimal frequency bands required to determine the cluster temperature with similar or better accuracy than that obtainable from X-ray observations. The precision of SZE-derived temperature is also discussed for the outer regions of clusters. Using our method, we also study the possibility of extracting 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 cospatially distributed with the thermal plasma in clusters that exhibit non-thermal phenomena. Conclusions. We find that the next generation SZE experiments, which will have both spectroscopic capabilities with moderate resolution of a few to tens GHz and imaging capabilities with spatial resolution of tens of arcsec up to arcmin, can provide precise temperature distribution measurements over a wide range of radial distances for galaxy clusters even out to high redshift.