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

1. Introduction

Most theories of hierarchical structure formation are based on the study of the evolution of density perturbations under their own gravity. A density fluctuation, which represents an over- (or under-) density with respect to the mean matter distribution, contains both baryonic and dark matter (DM). The baryonic component sinks into the gravitational potential of the DM halo. It collapses and cools, resulting in star formation. In these scenarios, after the gravitational collapse of the DM halo, stars are assumed to be the first objects to form. A structure will thus end up as an emitting object after virialisation has occurred.

An alternative picture involves the formation of a super-massive black hole (BH) that powers the central regions of galaxies (Lynden-Bell 1969). Numerous studies have been performed that relate the quasar luminosity function to galaxy formation scenarios by assuming that the formation of quasars (i.e., BH) in the potential well of the DM halos constitutes one of the phases in the galaxy formation process (Efstathiou & Rees 1988; Haehnelt & Rees 1993; Nusser & Silk 1993; Haiman & Loeb 1997). Recent observations even suggest that a super-massive BH may be present in the centres of all galaxies with spheroidal components (Kormendy & Richstone 1995).

Several authors have looked at several consequences of the presence of massive BHs on galaxy formation and evolution (Haiman & Loeb 1997; Natarajan et al. 1998; Silk & Rees 1998). In this paper, we investigate the cosmological implications of such an alternative scenario for the Cosmic Microwave Background (CMB) anisotropies and spectral distortions. More specifically, we study the effects of the outflows, driven by the BH activity, on the gas within the seeded proto-galaxy. In fact, the outflow expands and shock-heats the ambient medium (proto-galactic gas), and then interacts with the inter-galactic medium (IGM). Three regimes of interest may be considered: 1) the high density region of the proto-galaxy, 2) the low density IGM and 3) the thin compressed layer (four times denser than the IGM) induced by the front shock. The second and third regimes give results very similar to those computed in Aghanim et al. (1996). We thus focus on the first regime, i.e. the localised effects of the BH-driven shock on the gas within the seeded proto-galaxy. This shock-heated gas will Compton scatter the CMB photons and induce spectral distortions and temperature anisotropies through the so-called Sunyaev-Zel'dovich (SZ) effect (Sunyaev & Zel'dovich 1980). The thermal SZ effect depresses the CMB brightness in the Rayleigh-Jeans region and increases it above a frequency of about 219 GHz. Its amplitude represents the integral along the line of sight of the electron pressure. It is proportional to the electron density and is characterised by the Compton parameter y defined by:

where T is the temperature of the gas, R the physical size of the structure, the electron mass, k the Boltzmann constant, c the speed of light and the Thomson cross section. An additional secondary anisotropy arises due to the first-order Doppler effect of the CMB photons when they scatter on a structure moving with respect to the Hubble flow, with radial peculiar velocity . This interaction is called the SZ kinetic effect. It generates an anisotropy, with no specific spectral signature, whose amplitude is given by:

Previous work on galaxy formation has evaluated the global distortion of a population of galaxies in the virialised regime. The global Compton parameter was found to be much smaller than the constraints set by the FIRAS instrument (Far InfraRed Absolute Spectro-photometer) on board COBE (COsmic Background Explorer) (Fixsen et al. 1996) on the global SZ distortion of the universe. By contrast, our model focuses on a regime in which proto-galaxies undergo a BH formation phase that induces larger distortions. The paper is organised as follows: in Sect. 2, we model the shock in an individual structure and give its physical characteristics (size and temperature). In Sect. 3, we compute the predicted number density of primordial galaxies, using the Press & Schechter (1974) mass function. In Sect. 4, we generalise the description of the shock to the whole population of proto-galaxies and we simulate maps of the induced secondary anisotropies. We estimate this contribution to the CMB anisotropies. We also compare our predicted global y parameter to the COBE-FIRAS value and derive constraints on the model. Conclusions are given in the last section.

© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000
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