Studying the leptonic structure of galaxy cluster atmospheres from the spectral properties of the SZ effect

¹ ASI Science Data Center, ASDC c/o ESRIN, via G. Galilei, 00044 Frascati, Italy
² ASI, Viale Liegi 26, Roma, Italy
³ INAF – Osservatorio Astronomico di Roma, via Frascati 33, 00040 Monteporzio, Italy e-mail: cola@mporzio.astro.it
⁴ Moscow Institute of Physics and Technology, Institutskii lane, 141700 Moscow Region, Dolgoprudnii, Russia
⁵ Institut d'Astrophysique de Paris, CNRS, UMR 7095, Université Pierre et Marie Curie, 98bis Bd Arago, 75014 Paris, France
⁶ Lebedev Physical Institute, 117924 Moscow, Russia

Received: 2 May 2008
Accepted: 21 October 2008

Abstract

We study the energetics of galaxy-cluster atmospheres by analyzing the SZ effect spectra around the crossover frequency. We calculate analytically the expressions of both the crossover frequency and the spectral slope of the SZE around the crossover frequency in various cases: a thermal electron population; a power-law, non-thermal, electron population; and a population of electrons experiencing a stochastic acceleration. We find that the value of the crossover frequency X₀ of the SZE depends significantly on the cluster peculiar velocity V_r which determines the amplitude of the kinematic SZE), while the value of the slope of the SZE does not depend on the kinematic SZE spectrum in the optimal frequency range around the crossover frequency of the thermal SZE, i.e. in the frequency range . Therefore, while the amplitude of the SZ_kin  produces a systematic bias in the position of the crossover frequency X₀, it does not affect significantly the spectral slope of the SZE. We therefore propose using measurements of the spectral slope of the SZE to obtain unbiased information about the specific properties of various electron distributions in galaxy clusters as well as in other cosmic structures in which a SZE can be produced.