## 3. Number counts of primordial galaxiesIn order to quantify the global effect of the formation of primordial galaxies on the CMB, we apply our formalism to a synthetic population of galaxies with masses . We first assume that the galaxy number density traces, within a linear bias, the abundance of collapsed DM halos, as predicted by the Press-Schechter (PS) mass function (Press & Schechter 1974). We use an initial power-law spectrum with an effective spectral index on galaxy scales. We express the amplitude of primordial matter fluctuations in terms of the rms variance in spheres of 8 Mpc, (as cluster-normalised, e.g. Viana & Liddle (1996)), which corresponds to a bias factor . For , the set of parameters corresponds to the "standard" biased cold DM model, which does fit neither small- and large-scale velocities (Vittorio et al. 1986) nor COBE normalisation. However, we take it as a study case for the computations, our second model is the low density cosmological model with . In our picture (no stars are formed yet), the spheroid is gaseous. Its mass is related to the mass of the DM halo via . The mass and luminosity of the central BH and thus the predicted SZ distortions are therefore inferred from (, and ; cf Sect. 2). To compute the kinetic SZ term of a population of proto-galaxies,
we need an estimate of their peculiar velocities with respect to the
reference frame. As suggested by numerical simulations (Bahcall et al.
1994; Moscardini et al. 1996), we assume that velocities follow a
Gaussian distribution. The peculiar velocity of each proto-galaxy is
drawn from a Gaussian which is completely defined by its rms value
. In the range of redshifts we have
adopted, the structures are in the linear regime, so that
, where the redshift dependence of
the velocities is given by (Peebles
1980, 1993) as a function of the cosmological parameters. In this
equation, is the present-day rms
peculiar velocity. It is related to the mass variance on mass scale
© European Southern Observatory (ESO) 2000 Online publication: May 3, 2000 |