Galaxy clusters and microwave background anisotropy

Abstract

Previous estimates of the microwave background anisotropies produced by freely falling spherical clusters are discussed. These estimates are based on the Swiss-Cheese and Tolman-Bondi models. It is proved that these models give only upper limits to the anisotropies produced by the observed galaxy clusters. By using spherically symmetric codes including pressureless matter and a hot baryonic gas, new upper limits are obtained. The contributions of the hot gas and the pressureless component to the total anisotropy are compared. The effects produced by the pressure are proved to be negligible; hence, estimations of the cluster anisotropies based on N-body simulations are hereafter justified. After the phenomenon of violent relaxation, any realistic rich cluster can only produce small anisotropies with amplitudes of order 10 −7 . During the rapid process of violent relaxation, the anisotropies produced by nonlinear clusters are expected to range in the interval (10 −6 , 10 −5 ). The angular scales of these anisotropies are discussed.

Microwave background anisotropies and non-linear structures — II. Numerical computations

“…We note that (3) and (4) are valid for Ω( t i )≈1, which will always be true if t i is soon after inflation. An important respect in which our approach differs from that of Panek (1992) or Quilis et al (1995) is that the density enhancement resulting from the initial velocity perturbation is automatically compensated within a finite region by a slightly underdense region surrounding it. Thus the external Universe never feels a gravitational influence from the perturbed region.…”

“…The only guide to fixing the initial parameters a , R i and m is the final properties of the cluster, as observed today. In this section we model a very rich Abell cluster, in order to compare our results with those obtained by Panek (1992) and Quilis et al (1995). As our standard configuration, we consider a cluster at a redshift z =0.09, with a core radius R c =0.23 h 0 −1 Mpc (where R c is defined as the radius at which the cluster density falls to one‐half its maximum value).…”

“…For typical clusters, however, the assumption is perhaps questionable, since 10‐‐30 percent of the mass of the cluster may comprise a hot baryon component, with a non‐negligible pressure, that is gravitationally coupled to the dark matter. Nevertheless, calculations by Quilis, Ibáñez & Sáez (1995), that include a hot gas component, show that the effects of pressure are in fact negligible, and that the collapse of the cluster is well approximated by assuming a pressureless fluid. However, the combined use of spherical symmetry and pressureless assumptions lead inevitably to the unrealiztic situation where the cluster collapses to form a singularity.…”

A study of the galaxy redshift distribution towards the cosmic microwave background cold spot in the Corona Borealis supercluster

“…They modelled primordial density perturbations of a pressureless field, whose evolution is governed by exact general relativistic solutions of the Einstein equations. For a nearby cluster at z = 0.09, they predicted a RS effect with a minimum decrement of ≈−25μK, extending up to ≈4°, in agreement with Quilis et al (1995). They also note that the spherical free‐fall collapse model they used may not be reliable in the case of such low‐redshift clusters which may be virialized.…”

“…Quilis, Ibáñez & Sáez (1995) used the TB formalism to estimate the RS effect towards galaxy clusters. For a nearby typical cluster at z ≈ 0.02, they estimated a RS decrement of ≈−30μK, with an angular size of ∼6°.…”