The non-thermal Sunyaev–Zel'dovich effect in clusters of galaxies

Abstract

Abstract. In this paper we provide a general derivation of the non-thermal Sunyaev-Zel'dovich (SZ) effect in galaxy clusters which is exact in the Thomson limit to any approximation order in the optical depth τ. The general approach we use also allows us to obtain an exact derivation of the thermal SZ effect in a self-consistent framework. Such a general derivation is obtained using the full relativistic formalism and overcoming the limitations of the Kompaneets and of the single scattering approximations. We compare our exact results with those obtained at different approximation orders in τ and we give estimates of the precision fit. We verified that the third order approximation yields a quite good description of the spectral distortion induced by the Comptonization of CMB photons in the cluster atmosphere. In our general derivation, we show that the spectral shape of the thermal and non-thermal SZ effect depends not only on the frequency but also on the cluster parameters, like the electron pressure and optical depth and from the energy spectrum of the electron population. We also show that the spatial distribution of the thermal and non-thermal SZ effect in clusters depends on a combination of the cluster parameters and on the spectral features of the effect. To have a consistent description of the SZ effect in clusters containing non-thermal phenomena, we also evaluate in a consistent way -for the first time -the total SZ effect produced by a combination of thermal and nonthermal electron population residing in the same environment, like is the case in radio-halo clusters. In this context, we show that the location of the zero of the total SZ effect increases non-linearly with increasing values of the pressure ratio between the non-thermal and thermal electron populations and its determination provides a unique way to determine the pressure of the relativistic particles residing in the cluster atmosphere. We discuss in detail both the spectral and the spatial features of the total (thermal plus non-thermal) SZ effect and we provide specific predictions for a well studied radio-halo cluster like A2163. Our general derivation allows also to discuss the overall SZ effect produced by a combination of different thermal populations residing in the cluster atmosphere. Such a general derivation of the SZ effect allows to consider also the CMB Comptonization induced by several electron populations. In this context, we discuss how the combined observations of the thermal and non-thermal SZ effect and of the other non-thermal emission features occurring in clusters (radio-halo, hard X-ray and EUV excesses) provide relevant constraints of the spectrum of the relativistic electron population and, in turn, on the presence and on the origin of non-thermal phenomena in galaxy clusters. We finally discuss how SZ experiments with high sensitivity and narrow-band spectral coverage, beyond the coming PLANCK satellite, can definitely probe the presence of a non-thermal SZ effect in galaxy clusters and disentangle this source o...

Untangling the atmosphere of the Bullet cluster with Sunyaev-Zel’dovich effect observations

“…We verified that, for a plasma with kT = 13.9 keV and τ = 1.3 × 10 −2 , the second-order corrections in τ to the spectral shape (see Colafrancesco et al 2003, for technical details) do not produce appreciable variations with respect to the firstorder calculation of the SZE spectrum. This means that the leptonic atmosphere of the Bullet cluster is still in the optically thin regime, for which CMB photons do not suffer, on average, more than one scattering off the electron population.…”

“…where f e (p) is the normalized electron momentum distribution function, is the average energy of the electron plasma (see Colafrancesco et al 2003). The optical depth of the electron population along the line of sight is…”

“…The previous description is general enough to be applied to both thermal and nonthermal plasma, as well as to a combination of the two (see Colafrancesco et al 2003, for details).…”

“…In this context, precise observations of the Sunyaev Zel'dovich effect (hereafter SZE) at mm wavelengths are crucial for unveiling the detailed structure of cluster atmospheres, their temperature distribution, and the possible presence of suprathermal and/or nonthermal plasma because the high-frequency part (i.e. at ν ∼ > 350 GHz) of the SZE spectrum is more sensitive to the relativistic effects of the momentum distribution of the electrons plasma (see, Colafrancesco & Marchegiani 2007; see also Birkinshaw 1999;Colafrancesco et al 2003;Colafrancesco 2007, for reviews and references). This is even more so for galaxy clusters with a complex plasma distribution as found, e.g., for powerful merging clusters, like the exemplary case offered by the Bullet cluster (1ES0657-56).…”

Can electron distribution functions be derived through the Sunyaev-Zel’dovich effect?

“…Relativistic corrections for the SZ effect allow us to measure the temperature of intracluster plasma (see, e.g., Pointecouteau et al 1998;Hansen et al 2002) and have been studied both analytically (Colafrancesco et al 2003;Colafrancesco & Marchegiani 2010) and by means of numerical simulations (Prokhorov et al 2010a). …”