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4.2.2 CDM Hierarchical Models

As mentioned above, current theoretical models of galaxy formation and evolution are based on historical papers, in particular those by Press and Schechter (1974) and by White and Rees (1978). Other pioneering papers (e.g. Gunn, J.E. and Gott, J.R., 1972; Gunn, 1977, and references therein) have also contributed to the presently accepted scenario, which has had a considerable success in explaining a large variety of galaxy and clustering properties.

Previous studies led by Zeldovich (e.g. Zeldovich, 1970; Sunyaev and Zeldovich, 1972) considered that small mass objects formed from nonlinear processes in clusters with a larger hot dark matter mass. Press and Schechter analyzed the opposite point of view, according to which larger mass objects form from the non-linear interaction of smaller masses, with these being formed before. Some of these ideas were suggested by Peebles (1965). Press and Schechter (1974) did not mention dark matter, but a "gas" of self-gravitating mass.

Starting from an initial spectrum of perturbations shortly after Recombination, baryonic aggregates with a small mass condensed, merged to form larger condensations, which in turn merged and so on. In this way, the condensation proceeded to larger and larger scales, at later and later times. They proposed that this merging series very weakly depended on the spectrum of seed masses initially assumed. "When the condensation has proceeded to scales much larger than the seed scale, the gas should have essentially no memory of its initial scale and the condensation process should approach a self-similar solution".

One of the most decisive papers in the modern history of Astronomy was written by White and Rees (1978), which may be considered the progenitor of nearly all current theoretical models of galaxy formation. This model adopted the hierarchical clustering scenario proposed by Press and Schechter (1974) but introduced two new basic ingredients: dark matter and the cooling of the baryon system to produce the visible component of galaxies.

First, these authors proposed $ \Omega$ $ \sim$ 0.2, which is certainly close to present-day estimates. They considered that the baryon to dark matter fraction in the Universe should not very much differ from that in a rich cluster, like Coma, from where they adopted M/L = 400. This is in agreement with modern estimates of 150h$ \le$M/LB$ \le$500h (Bahcall, Lubin and Dorman, 1995). As LB, the blue radiation energy density is of the order of 2 × 108hL$\scriptstyle \odot$Mpc-3 (see for instance, Zucca et al., 1997, for a current value), $ \Omega$ $ \sim$ 0.2 is then deduced.

From this, they proposed that approximately 80% of this matter was dark matter and of the remainding 20%, half was still uncondensed baryons and the other half constituted the luminous component.

In this scenario, small halos formed first through a merging process; the first generation of halos produced a new generation and so on. New generations in the hierarchy are therefore born later and are more massive. The process is interrupted by the finite time of the Universe, and therefore no clustering is to be expected at a large enough scale. The smaller scale virialized systems merged into an amorphous whole, mainly constituted of dark matter but also of gas, as a minor component. When the gas cooled it fell into the centre of the DM halo and there became sufficiently concentrated to produce stellar collapses, which rendered it visible.

"When a halo is disrupted in a larger system the luminous galaxy in its core can preserve its identity because dissipation has made it more concentrated than the surrounding dark material" wrote White and Rees. Therefore small galaxies could be reminiscent of the first generation halos. As they formed earlier, dwarf galaxies could have a small mass and a higher density. When these small halos with a luminous core merged to produce a larger halo with a larger luminous core, the small baryonic concentration would not be destroyed and should be identifiable as orbiting the large galaxy. The familiar observation of a large galaxy, such as ours, surrounded by many dwarf galaxies would then be explained in a very natural way.

Note that this elegant idea could be in conflict with current interpretations of the observations, which seem to indicate that dwarf galaxies have their own halo and they are not so "dwarf" as they may possess specially massive dark halos. We will return to this point when dealing with the magnetic hypothesis.

In more detail, the fate of the gas would depend on other factors. When two or more smaller halos merge, there is an intense heating, produced by shocks during the violent relaxation that accompanies the formation of the halo. The gas could be heated until it reaches a pressure-supported state. At a temperature of about 104 K it would be ionized and able to cool radiatively, via bremsstrahlung, recombination, and so on. The cooling process would settle the concentrated gas into the centre and produce stars, which become a visible component. The pressure-supported gas contraction would be quasi-static. But this slow concentration could be abruptly truncated by a new merging. Therefore, a visible baryonic component would be formed only when the radiative cooling time is less than the typical dynamic or merging time.

Therefore "the luminous material that condensed in their centers may nevertheless have survived to the present day in identifiable stellar systems" (White and Rees, 1978). For instance, this would be not only the case of satellite dwarf galaxies but also of large galaxies within a rich cluster like Coma. Such large clusters would possess a very large common halo, rather than small individual halos. By merging, because of the violent relaxation, halos virialize very fast and lose any internal structure other than the baryonic cores.

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