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Cosmological simulations including gas show that at z = 0 only 30 - 40% of the universal baryon matter is within collapsed halos; the rest is in the form of warm-hot IGM in the filaments and voids (Davé et al. 2001). Recent observations tend to confirm this prediction (e.g., Manucci, this volume). Not all the gas trapped within the galactic halos ends up in the central galaxy: for large halos (M gtapprox 1012 Modot) the cooling time may be longer than the Hubble time, while for small halos (M ltapprox 1010 Modot) a large fraction of gas may be expelled due to feedback. Owing to the combination of cooling and feedback, galaxies incorporate on average only half of the baryons originally trapped within halos (van den Bosch 2002). Therefore, for a universal fraction Omegabar / OmegaCDM approx 0.15, the actual fraction of matter trapped in galaxies, fgal, is only approx 0.15 × 0.4 × 0.5 = 0.03.

The physics of baryons within the collapsing and merging dark matter halos is a highly complex process. In some cases, instead of radiative cooling, turbulent dissipation in a multi-phase regime (unexplored in detail yet) dominates. The process is further complicated by the gravitational fragmentation and consequent transformation of gas into stars. The energy and momentum input on gas from stars introduces a feedback. The feedback establishes a control and self-regulates the SF. The self-regulation may be either (a) at the level of the disk ISM, where, according to the nature of the feedback, a variety of regimes appear, ranging from stationary SF to bursting SF (e.g., Firmani & Tutukov 1994), or (b) at the level of the whole intrahalo medium, giving rise to a huge hot gas halo around the luminous galaxy (e.g., White & Frenk 1991; Benson et al. 2000). Models of galaxy evolution in the cosmological context used either case (a) for disks (Firmani et al. 1996, Firmani & Avila-Reese 2000; Avila-Reese & Firmani 2000; van den Bosch 2000) or case (b) (e.g., Kauffmann et al. 1993, 1999; Cole et al. 1994, 2000; Baugh et al. 1996).

Since dark halos have some angular momentum, during the smooth mass accretion phase, the dissipating gas falls until it reaches centrifugal equilibrium: disks are a generic prediction of the hierarchical scenario (Kauffmann et al. 1993). As the disk ISM is dense, highly dissipative and with shielding magnetic fields, the energy injection on gas is confined to a few disk scale heights (Avila-Reese & Vázquez-Semadeni 2001, and references therein). The lack of bright X-ray halos around spirals (Benson et al. 2000) reinforces the idea that case (a) rather than case (b) applies for disk galaxies. On the other hand, case (b) probably is working in spheroids where the low internal gas density makes dissipation inefficient. It seems also that cooling is more efficient than that calculated by simple approaches in the semi-analytic models (Toft et al. 2002). When the halo angular momentum is sufficiently low or the gas angular momentum loss is efficient, then highly concentrated disks may form. These disks are gravitationaly unstable and a spheroid may be produced by a secular process, which involves the formation and dissolution of a bar (Combes et al 1990; Norman et al. 1996; Merrifield & Kuijken 1999; Valenzuela & Klypin 2003).

As mentioned in Section 2, dark halos grow by a variety of merging regimes. Major mergers induce collisions between the central luminous galaxies. In this case, SF follows a bursting regime (Firmani & Tutukov 1994), feedback is very efficient, and the morphological Hubble type is strongly affected. Collisions between galaxies are indeed able to produce dynamically hot spheroids (Toomre & Toomre 1972; Schweizer 1982; Barnes 1988; Hernquist 1990, 1992). If the colliding galaxies are gas rich disks, then gas dissipation makes it possible to concentrate the spheroid up to the observed densities (Mihos and Hernquist 1994, 1996; see also Hibbard and Yun 1999). Collisions between galaxies and secular formation from bar dissolution represent two competitive processes for the formation of spheroids.

Using the semi-analytical models, several authors extended the hierarchical merging of CDM halos to a merging picture of luminous disk/bulge/elliptical galaxy formation (e.g., Baugh et al. 1996; Cole et al. 2000). According to this picture, the driver of galaxy evolution, as far as concerns the HS, is the dark halo merging. Cosmological simulations indeed show the possibility of rapid galaxy morphological transformations due to intermittent changes of quiescent phases of disk accretion with violent phases of spheroid formation by major mergers (e.g., Steinmetz & Navarro 2002). However, cosmological simulations also show that most galaxies are formed actually by smooth accretion rather than mergers (Murali et al. 2000). This is in agreement with the predominance in number of disk galaxies in the local universe.

All these physical ingredients are involved in galaxy evolution, and are crucial to the understanding of the origin of the HS. It is now natural to concentrate our attention on the physics of disks and spheroids.

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