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In the previous sections we have pointed out several processes which intervene in the evolution of luminous galaxies. Summarizing, the first step in galaxy formation is the assembling of the dark matter halos, which may happen either quiescently or violently, depending mostly on the environment. In the former case, the gas trapped inside the halos dissipates (radiatively and turbulently), infalls to the center and forms an inside-out disk in centrifugal equilibrium with a surface density that depends mainly on the halo spin parameter. SF in disks is expected to be stationary and self-regulated by feedback and turbulent dissipation. In this case, the main drivers of the SF history are the gas infall and the angular momentum. Both of them are tightly related to the cosmological conditions. Some disks may suffer further morphological evolution due to internal gravitational instabilities (spiral arms, bars and bulges).

However, the strongest changes are expected when violent major mergers occur: the stellar disk is heated and gas angular momentum is transferred, leading to the formation of spheroids and SF bursts. In this phase ULIGs and AGNs can appear. The products of galaxy collisions depend on the gas fraction, the stellar disk-to-bulge ratio and the dynamics of the encounter (Barnes & Hernquist 1991, 1996; Mihos & Hernquist 1994, 1996; Barnes 2002). Numerical simulations show that a wide range of final products can be obtained, depending on these parameters. Nevertheless, the stellar component is almost always heated and thickened, acquiring the structure of a spheroid. The gas that suffers strong shocks transfers its angular momentum, and may originate a bulge. The gas that has not been involved in strong shocks retains a large amount of angular momentum and can feed an extended disk. Accretion from the environment supplies the spheroid/disk system with further angular-momentum-rich gas. The ultimate fate of gas is to be converted into stars. When the gas surface density is sufficiently high, the disk stellar population is practically coeval to the bulge, but as the gas surface density is lower, the slower is the SF rate.

In the hierarchical framework, the major merging rate is easily estimated by the extended Press-Schechter formalism or by N-body simulations (e.g., Gottloeber et al. 2001) and, for a given mass, is increasing with z. Multiplying the merging rate by the halo mass function at different z's, one obtains that the merging rate density (per unit of volume) for halos with masses smaller than 1013 Modot has its maximum at z > 1; for halos in clusters, the maximum is shifted to earlier epochs. Therefore, most of spheroids, upon the understanding that they arise from major mergers, are born at high redshifts, when galaxies are still gas rich. The smaller fraction of major mergers at late epochs occurs mainly between gas-poor galaxies with an important spheroidal component. Around the spheroid a disk grows by gas accretion according to the conditions of the environment and by the energy feedback of the spheroid, the bulge-to-disk mass ratio being an indicator of the Hubble type. When the spheroid is more massive than the disk, we have an elliptical or S0 galaxy. The lack of a massive disk in these cases may be due to the facts that (i) the merger has occurred recently, (ii) the gas accretion has been inhibited, or (iii) the environment is poor in gas. The existence of field elliptical galaxies with an old stellar population may be indicative of conditions that inhibit the formation and growth of a disk.

Using semi-analytic modelation and taking into account many of the physical processes mentioned above, Cole et al. (2000) have made predictions about the morphology mixing of galaxies and the dependence on the environment. Their models reproduce the relative number of E+S0 galaxies. However, concerning the age of spheroids, the situation is not so clear. Their predicted colour-magnitude relation for ellipticals in clusters is significantly flatter than that observed at bright magnitudes. Benson et al. (2002) have compared the same models with samples of field spheroidal galaxies with redshifts up to two. Models reveal some difficulty predicting the observed red population of E+S0 galaxies, while on the blue side the agreement is satisfactory. Colours reflect only approximately the ages of old spheroids. The ages of elliptical galaxies derived by different observational methods, such as those mentioned in section 5.1, are difficult to reconcile with the model predictions. Again, the situation could be alleviated if gas accretion and disk growth around spheroids would be inhibited (item (ii) above), in this way allowing some of the spheroids to evolve with a negligible SF activity. A careful comparison between models and observations of the relation between the intrinsic colours of the disk and the Hubble type should be of some relevance. In fact, a growing disk around a spheroid would evolve inside-out from blue to red while the bulge-to-disk ratio decreases; however, this situation depends on the physical conditions created by the collision as well by gas accretion and the intense feedback.

Back to galaxy collisions, it should be noted that its stochastic nature (as well as the extended redshift range of spheroid formation) contribute to the scatter of the FJR and KR, and possibly of the FP. While the scatter of TFR is a faithful product of the stochastical properties of the primordial density fluctuations (Section 4.1), the scatters of the spheroid scaling relations (FJR, KR, FP) are further increased by the astrophysical processes in which they have been involved (collisions, feedback).

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