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Astron. Astrophys. 357, 1-6 (2000)

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3. Number counts of primordial galaxies

In 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 [FORMULA].

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 [FORMULA] on galaxy scales. We express the amplitude of primordial matter fluctuations in terms of the rms variance in spheres of 8[FORMULA] Mpc, [FORMULA] (as cluster-normalised, e.g. Viana & Liddle (1996)), which corresponds to a bias factor [FORMULA]. For [FORMULA], 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 [FORMULA]. In our picture (no stars are formed yet), the spheroid is gaseous. Its mass is related to the mass of the DM halo via [FORMULA]. The mass and luminosity of the central BH and thus the predicted SZ distortions are therefore inferred from [FORMULA] ([FORMULA], and [FORMULA]; 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 [FORMULA]. In the range of redshifts we have adopted, the structures are in the linear regime, so that [FORMULA], where the redshift dependence of the velocities is given by [FORMULA](Peebles 1980, 1993) as a function of the cosmological parameters. In this equation, [FORMULA] is the present-day rms peculiar velocity. It is related to the mass variance on mass scale M, [FORMULA] (Mathiesen & Evrard 1998), where n is the index of the power spectrum. The rms velocity can thus be computed for each mass scale.

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© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000