Warming rays in cluster cool cores

We present a model of cosmic ray heating of clusters' cores that reproduces the observed temperature distribution in clusters by using an energy balance condition in which the emitted X-ray energy is supplied by the hadronic cosmic rays, which act as warming rays (WRs). The temperature profile of the IC gas is correlated with the WR pressure distribution and, consequently, with the non-thermal emission (radio, hard X-ray and gamma-ray) induced by the interaction of the WRs with the IC gas and magnetic field. The temperature distribution of the IC gas in both cool-core and non cool-core clusters is successfully predicted from the measured IC gas density distribution. Under this contraint, the WR model is also able to reproduce the thermal and non-thermal pressure distribution in clusters, as well as their radial entropy distribution. The WR model provides other observable features: a correlation of the pressure ratio (WRs to thermal IC gas) with the inner cluster temperature T_{inner}, a correlation of the gamma-ray luminosity with T_{inner}, a substantial number of cool-core clusters observable with the GLAST-LAT experiment, a surface brightness of radio halos in cool-core clusters that recovers the observed one, a hard X-ray emission from cool-core clusters that is systematically lower than the observed limits and yet observable with the next generation HXR experiments like Simbol-X. The specific theoretical properties and the multi-frequency distribution of the e.m. signals predicted in the WR model render it quite different from the other models proposed for the heating of clusters' cool-cores. Such differences make it possible to prove or disprove our model as an explanation of the cooling-flow problems on the basis of multi-frequency observations of galaxy clusters.Comment: 19 pages, 17 figures, A&A in pres

Spatial features of non-thermal SZ effect in galaxy clusters

We investigate the spatial behaviour of the total comptonization parameter $y_{tot}$ evaluated for a galaxy cluster containing two population of electrons: the thermal population, with energy around some KeV and whose trace is evident in the X-ray emission of the ICM (Intra-Cluster Medium), and the relativistic population, which give rise to the radio halo emission found in several clusters of galaxies. We present the first results obtained from our analysis showing that there are remarkable features in such spatial trend, which might throw a new light in understanding the cluster internal processes.Comment: 4 pages, 1 figure, to appear in the proceedings of the 2k1bc workshop ""Experimental comsology @ millimetre wavelengths", july 9-12 2001, Breuil-Cervinia, Ital

A multi-frequency study of the SZE in giant radio galaxies

Radio-galaxy (RG) lobes contain relativistic electrons embedded in a tangled magnetic field that produce, in addition to low-frequency synchrotron radio emission, inverse-Compton scattering (ICS) of the cosmic microwave background (CMB) photons. This produces a relativistic, non-thermal Sunyaev-Zel'dovich effect (SZE). We study the spectral and spatial properties of the non-thermal SZE in a sample of radio galaxies and make predictions for their detectability in both the negative and the positive part of the SZE, with space experiments like Planck, OLIMPO, and Herschel-SPIRE. These cover a wide range of frequencies, from radio to sub-mm. We model the SZE in a general formalism that is equivalent to the relativistic covariant one and describe the electron population contained in the lobes of the radio galaxies with parameters derived from their radio observations, namely, flux, spectral index, and spatial extension. We further constrain the electron spectrum and the magnetic field of the RG lobes using X-ray, gamma-ray, and microwave archival observations. We determine the main spectral features of the SZE in RG lobes, namely, the minimum, the crossover, and the maximum of the SZE. We show that these typical spectral features fall in the frequency ranges probed by the available space experiments. We provide the most reliable predictions for the amplitude and spectral shape of the SZE in a sample of selected RGs with extended lobes. In three of these objects, we also derive an estimate of the magnetic field in the lobe at the muG level by combining radio (synchrotron) observations and X-ray (ICS) observations. These data, together with the WMAP upper limits, set constraints on the minimum momentum of the electrons residing in the RG lobes and allow realistic predictions for the visibility of their SZE to be derived with Planck, OLIMPO, and Herschel-SPIRE. [abridged]Comment: 26 pages, 21 figures; Astronomy and Astrophysics, in pres

Polarization of the Sunyaev-Zel'dovich effect: relativistic imprint of thermal and non-thermal plasma

[Abridged] Inverse Compton scattering of CMB fluctuations off cosmic electron plasma generates a polarization of the associated Sunyaev-Zel'dovich (SZ) effect. This signal has been studied so far mostly in the non-relativistic regime and for a thermal electron population and, as such, has limited astrophysical applications. Partial attempts to extend this calculation for a thermal electron plasma in the relativistic regime have been done but cannot be applied to a general relativistic electron distribution. Here we derive a general form of the SZ effect polarization valid in the full relativistic approach for both thermal and non-thermal electron plasmas, as well as for a generic combination of various electron population co-spatially distributed in the environments of galaxy clusters or radiogalaxy lobes. We derive the spectral shape of the Stokes parameters induced by the IC scattering of every CMB multipole, focusing on the CMB quadrupole and octupole that provide the largest detectable signals in galaxy clusters. We found that the CMB quadrupole induced Stoke parameter Q is always positive with a maximum amplitude at 216 GHz which increases slightly with increasing cluster temperature. The CMB octupole induced Q spectrum shows, instead, a cross-over frequency which depends on the cluster electron temperature, or on the minimum momentum p_1 as well as on the power-law spectral index of a non-thermal electron population. We discuss some possibilities to disentangle the quadrupole-induced Q spectrum from the octupole-induced one which allow to measure these quantities through the SZ effect polarization. We finally apply our model to the realistic case of the Bullet cluster and derive the visibility windows of the total, quandrupole-induced and octupole-induced Stoke parameter Q in the frequency ranges accessible to SKA, ALMA, MILLIMETRON and CORE++ experiments.Comment: 31 pages, 11 figures, submitted to JCA

Multi-frequency constraints on the non-thermal pressure in galaxy clusters

The origin of radio halos in galaxy clusters is still unknown and is the subject of a vibrant debate both from the observational and theoretical point of view. In particular the amount and the nature of non-thermal plasma and of the magnetic field energy density in clusters hosting radio halos is still unclear. The aim of this paper is to derive an estimate of the pressure ratio X between the non-thermal and thermal plasma in radio halo clusters that have combined radio, X-ray and SZ effect observations. From the simultaneous P_{1.4}-L_X and P_{1.4}-Y_{SZ} correlations for a sample of clusters observed with Planck, we derive a correlation between Y_{SZ} and L_X that we use to derive a value for X. This is possible since the Compton parameter Y_{SZ} is proportional to the total plasma pressure in the cluster (that we characterize as the sum of the thermal and non-thermal pressure) while the X-ray luminosity L_X is proportional only to the thermal pressure of the intracluster plasma. Our results indicate that the average (best fit) value of the pressure ratio in a self-similar cluster formation model is X =0.55 \pm 0.05 in the case of an isothermal beta-model with beta=2/3 and a core radius r_c = 0.3 R_{500} holding on average for the cluster sample. We also show that the theoretical prediction for the Y_{SZ}-L_X correlation in this model has a slope that is steeper than the best fit value for the available data. The agreement with the data can be recovered if the pressure ratio X decreases with increasing X-ray luminosity as L_X^{-0.96}. We conclude that the available data on radio halo clusters indicate a substantial amount of non-thermal pressure in cluster atmospheres whose value must decrease with increasing X-ray luminosity, or increasing cluster mass (temperature). (abridged)Comment: A&A, in press; 10 pages; 10 figure

Effect of the non-thermal Sunyaev–Zel’dovich effect on the temperature determination of galaxy clusters

A recent stacking analysis of Planck HFI data of galaxy clusters led to the derivation of the cluster temperatures using the relativistic corrections to the Sunyaev-Zel'dovich effect (SZE). However, the temperatures of high-temperature clusters, as derived from this analysis, were basically higher than the temperatures derived from X-ray measurements, at a moderate statistical significance of 1.5 sigma. This discrepancy has been attributed by Hurier to calibration issues. In this paper, we discuss an alternative explanation for this discrepancy in terms of a non-thermal SZE astrophysical component. We find that this explanation can work if non-thermal electrons in galaxy clusters have a low minimum momentum (p(1) similar to 0.5-1), and if their pressure is of the order of 20-30 per cent of the thermal gas pressure. Both these conditions are hard to obtain if the non-thermal electrons are mixed with the hot gas in the intracluster medium, but can be possibly obtained if the non-thermal electrons are mainly confined in bubbles with a high amount of non-thermal plasma and a low amount of thermal plasma, or are in giant radio lobes/relics in the outskirts of the clusters. To derive more precise results on the properties of the non-thermal electrons in clusters, and in view of more solid detections of a discrepancy between X-ray- and SZE-derived cluster temperatures that cannot be explained in other ways, it would be necessary to reproduce the full analysis done by Hurier by systematically adding the non-thermal component of the SZE.EM201