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

Abstract

Aims. Measurements of the Sunyaev-Zel'dovich (hereafter SZ) effect distortion of the cosmic microwave background provide methods to derive the gas pressure and temperature of galaxy clusters. Here we study the ability of SZ effect observations to derive the electron distribution function (DF) in massive galaxy clusters. Methods. Our calculations of the SZ effect include relativistic corrections considered within the framework of the Wright formalism and use a decomposition technique of electron DFs into Fourier series. Using multi-frequency measurements of the SZ effect, we find the solution of a linear system of equations that is used to derive the Fourier coefficients; we further analyze different frequency samples to decrease uncertainties in Fourier coefficient estimations. Results. We propose a method to derive DFs of electrons using SZ multi-frequency observations of massive galaxy clusters. We found that the best frequency sample to derive an electron DF includes high frequencies ν = 375, 600, 700, 857 GHz. We show that it is possible to distinguish a Juttner DF from a Maxwell-Bolzman DF as well as from a Juttner DF with the second electron population by means of SZ observations for the best frequency sample if the precision of SZ intensity measurements is less than 0.1%. We demonstrate by means of 3D hydrodynamic numerical simulations of a hot merging galaxy cluster that the morphologies of SZ intensity maps are different for frequencies ν = 375, 600, 700, 857 GHz. We stress that measurements of SZ intensities at these frequencies are a promising tool for studying electron distribution functions in galaxy clusters.

PRISM (Polarized Radiation Imaging and Spectroscopy Mission): an extended white paper

“…These could signal the presence of highly energetic particles, dark matter annihilation products, AGN outflows, intracluster cavities and shocks [46][47][48][50][51][52]. We may even study the temperature structure of the most massive systems [49,60] and derive the electron distribution function [179].…”

Multi-Frequency Study of the SZ Effect in Cosmic Structures

“…As an example, the additional data points on the SZE spectrum of the Bullet cluster observed with Herschel-Spire [60] allowed to establish a number of properties for the thermal and non-thermal plasma superposition in the atmosphere of this strong merging cluster (see, e.g. [18,48,49]. A consequence of such superposition is that cluster temperature distribution has a high value of of the temperature standard deviation σ T , as in the case of the Bullet cluster where it is found σ T = 10.6 ± 3.8 keV [50].…”

“…SZE observations over a wide frequency range, and especially with high sensitivity in the high-ν range, can also add relevant information on the electron distribution function (DF) in the ICM, a subject that -even though relevant for a proper analysis of the SZE -has not been addressed in details so far. The relativistic kinetic theory, on which the DF derivation is based, is still a subject of numerous debates (see discussion in [48]). SZE observations can separate the SZE spectrum caused by a departure from the diffusive approximation based on the Kompaneets approach [31] from those which are due to using a relativistic correct DF instead of a Maxwell-Boltzman DF (see Fig.3) and therefore set constraints to the actual electron DF [48].…”

“…The relativistic kinetic theory, on which the DF derivation is based, is still a subject of numerous debates (see discussion in [48]). SZE observations can separate the SZE spectrum caused by a departure from the diffusive approximation based on the Kompaneets approach [31] from those which are due to using a relativistic correct DF instead of a Maxwell-Boltzman DF (see Fig.3) and therefore set constraints to the actual electron DF [48]. This analysis is best fulfilled in hot massive clusters because the SZE intensity change due to using a relativistic correct DF instead of a Maxwell-Boltzman DF are much larger in hot clusters due to the fact that relativistic SZE corrections scale as ∝ T 5/2 .…”

“…This analysis is best fulfilled in hot massive clusters because the SZE intensity change due to using a relativistic correct DF instead of a Maxwell-Boltzman DF are much larger in hot clusters due to the fact that relativistic SZE corrections scale as ∝ T 5/2 . A method used to derive the DF of electrons using SZE multi-frequency observations of massive hot clusters [48] makes use of Fourier analysis representation of the approximate electron DF whose parameters are best fitted using observations in the (optimal) frequency channels at 375, 600, 700, 857 GHz. Figure 2: The SZE spectrum at the Bullet cluster center modeled with a thermal plus nonthermal plasma: thermal plasma with kT = 13.9 keV and τ = 1.1 × 10 −2 (dot-dashed); nonthermal plasma with p 1 = 1, s = 2.7 and τ = 2.3 × 10 −4 (dotted); total SZE produced by the sum of the two plasmas (solid).…”