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...

We have deduced the cosmic microwave background (CMB) temperature in the Coma cluster (A1656, $z=0.0231$), and in A2163 ($z=0.203$) from spectral measurements of the Sunyaev-Zel'dovich (SZ) effect over four passbands at radio and microwave frequencies. The resulting temperatures at these redshifts are $T_{Coma} = 2.789^{+0.080}_{-0.065}$ K and $T_{A2163} = 3.377^{+0.101}_{-0.102}$ K, respectively. These values confirm the expected relation $T(z)=T_{0}(1+z)$, where $T_{0}= 2.725 \pm 0.002$ K is the value measured by the COBE/FIRAS experiment. Alternative scaling relations that are conjectured in non-standard cosmologies can be constrained by the data; for example, if $T(z) = T_{0}(1+z)^{1-a}$ or $T(z)=T_{0}[1+(1+d)z]$, then $a=-0.16^{+0.34}_{-0.32}$ and $d = 0.17 \pm 0.36$ (at 95% confidence). We briefly discuss future prospects for more precise SZ measurements of $T(z)$ at higher redshifts.Comment: 13 pages, 1 figure, ApJL accepted for publicatio

ABSTRACT170 ‫ע‬ 35 t p (4.1 ‫ע‬ 0.9) # 10 errors) with both the value from a previous low-frequency SZ measurement and the value predicted from the Xray-deduced gas parameters.

We analyse the Las Campanas Redshift Survey using the integrated conditional density (or density of neighbors) in volume-limited subsamples up to unprecedented scales (200 Mpc/h) in order to determine without ambiguity the behavior of the density field. We find that the survey is well described by a fractal up to 20-30 Mpc/h, but flattens toward homogeneity at larger scales. Although the data are still insufficient to establish with high significance the expected homogeneous behavior, and therefore to rule out a fractal trend to larger scales, a fit with a CDM-like spectrum with high normalization well represents the data.Subject headings: galaxies: clusters: general -large-scale structure of universe Following seminal work of Pietronero and coworkers, (see e.g. Pietronero et al. 1996), the possibility of a large-scale fractal distribution of the galaxies has been investigated by various authors. In the current literature, however, there are several conflicting estimates of the largest scale at which the galaxy distribution can be approximated by a fractal, ranging from a few Megaparsecs (e.g. Peebles 1993), to 20 Mpc/h (Davis 1996), to 40 Mpc/h (Cappi et al. 1998), up to more than 100 Mpc/h (e.g. Pietronero et al. 1996). A fractal distribution with dimension D is characterized by the property that the correlation function g(r) = 1 + ξ(r)(1) decreases as a power law, ∼ r 3−D . Consequently, the average density ρ c of galaxies at distance r from another galaxy , or conditional density, also decreases as ∼ r 3−D since, by the definition of correlation function, ρ c = ρ 0 [1 + ξ(r)], where ρ 0 is the cosmic average density.Naturally, one can infer the scale at which fractality gives way to homogeneity from several other observations, like the cosmic backgrounds, although the conclusions are bound to be model dependent. The availability in recent years of deep redshift surveys allows finally to study the matter distribution directly from its primary tracers, the galaxies. The deepest galaxy redshift survey so far published is the Las Campanas Redshift Survey (LCRS), Schectman et al. (1996). LCRS contains 23,697 galaxies with an average redshift z = 0.1 , distributed over six 1.5 0 ×80 0 slices. In this paper we determine the behavior of g(r), the volume integral of g(r), and of the

The Sunyaev-Zeldovich (SZ) effect was previously measured in the Coma cluster by the Owens Valley Radio Observatory and Millimeter and IR Testa Grigia Observatory experiments and recently also with the Wilkinson Microwave Anisotropy Probe satellite. We assess the consistency of these results and their implications on the feasibility of high-frequency SZ work with ground-based telescopes. The unique data set from the combined measurements at six frequency bands is jointly analyzed, resulting in a best-fit value for the Thomson optical depth at the cluster center, τ 0 = (5.35 ± 0.67) × 10 −3 . The combined X-ray and SZ determined properties of the gas are used to determine the Hubble constant. For isothermal gas with a β density profile we derive H 0 = 84 ± 26 km/(s · Mpc); the (1σ) error includes only observational SZ and X-ray uncertainties.