A model aimed to study the physics and evolution of disk galaxies should include a self-consistent and local description of dark matter processes, and gas dissipation, infall, SF, stellar evolution, and feedback. Under the assumptions of (i) dominance of accretion rather than mergers, and (ii) detailed angular momentum conservation during gas infall, several authors have been able to reproduce the main properties and correlations of disk galaxies in the hierarchical CDM scenario. The former assumption is motivated by the fact that disks are dynamically fragile objects and collisions with other galaxies heat and thicken the stellar disk beyond the level observed at present (Tóth & Ostriker 1992). The latter assumption is argueable, and is currently among the key questions of disk formation models (see e.g., van den Bosch et al. 2002). Following, we discuss the main predictions of models of disk formation inside CDM halos. A seminal paper on this subject was that of Fall & Efstathiou (1980).
4.1. Disk models at z = 0
The stellar surface density profile is roughly exponential, but with an excess at the inner and outer regions (Dalcanton et al. 1997; Firmani & Avila-Reese 2000; Bullock et al. 2001a; van den Bosch 2002). The inner cusp may be crucial for the secular bulge formation. The surface density of the disks depends mainly on the spin parameter : the angular momentum drives the sequence from high surface brightness (HSB) to low surface brightness (LSB) galaxies. The surface density also depends on fgal. Mainly due to the inside-out formation, the disks have negative color index and metallicity gradients in agreement with observations (Avila Reese & Firmani 2000; Boissier & Prantzos 1999, 2001).
The rotation curves are roughly flat. The shape of rotation curves depends on the disk surface density (Mo, Mao & White 1998; Firmani & Avila-Reese 2000). LSB galaxy models are dominated by the dark halo and even for the extreme HSB models, the CDM halo is competitive with the disk at the maximum rotation velocity. For the inner region of normal HSB galaxy rotation curves to be dominated by disk (maximum disk case), a soft core in the CDM halo is necessary (Avila-Reese et al. 2002; see also Salucci & Burkert 2000; Salucci 2001).
The slope of the infrared Tully-Fisher relation (TFR) is interpreted as a consequence of the mass-velocity relation of the CDM halos, determined in turn by the power spectrum of fluctuations (e.g., Mo et al. 1998; Avila-Reese et al. 1998, 1999; Steinmetz & Navarro 1999; Firmani & Avila-Reese 2000; Buchalter et al. 2001). The slope of the halo mass-velocity relation derived from theory is 3.2 - 3.4, which agrees with the TFR slope in the infrared bands found by most observers (e.g., Gavazzi 1993; Giovanelli et al. 1997; Tully et al. 1998; Tully & Pierce 2000). After the formation of the disk and the stars within it, the zero point of the model TFR is slightly fainter than observations for the concordance CDM cosmology (see Fig. 2), and is far too faint for the SCDM one. The introduction of soft halo cores improves the comparison with observations (Firmani & Avila-Reese 2000; Mo & Mao 2001). The N-body+hydrodynamical simulations predict a too faint zero point even for the CDM model (e.g., Steinmetz & Navarro 2000), but this is mainly because the disks in these simulations are formed highly concentrated (angular momentum catastrophe), implying very peaked rotation curves.
Figure 2. Tully-Fisher relation in the band K as inferred by Tully et al. (1998). Solid line is the linear regression to the data. Dashed line is the TFR from models of galaxy evolution in the CDM cosmogony (Firmani & Avila-Reese 2000); detailed angular momentum conservation was assumed. Dotted lines correspond to the model scatter (±1 - dispersion). The dot-dashed lines is the TFR for the same models, but introducing a soft core in the halos to be in accord with the rotation curve inner shapes of LSB and dwarf galaxies. The agreement with observations is excellent. The TFR is an imprint of the density fluctuation power spectum.
Variations in fgal and do not affect significantly the TFR. For a larger fgal, the luminosity will be higher, but Vmax also results larger. A smaller implies a more dominant disk component and therefore a larger Vmax for a given mass; however, the SF efficiency is higher in such a way that the stellar mass (luminosity) for a fixed baryonic mass will be also larger (Firmani & Avila-Reese 2000). This is the way we interpret why the TFRs of LSB and HSB galaxies are similar and why the residuals of the TFR do not correlate with the residuals of the magnitude-radius relation (Courteau & Rix 1999). We also find that the main source of intrinsic scatter in the TFR derives from the scatter in the halo concentrations due to the stochastic nature of the MAHs (Eiseinstein & Loeb 1996); the average scatter we measure is ~ 0.3 mag, close to the observational estimates.
If bulges are modeled as the gravitationally unstable stellar disk region (secular scenario), then higher surface brightness galaxies have larger bulge-to-disk ratios (van den Bosch 1998; Avila-Reese & Firmani 2000). The models reproduce the main correlations along the disk HS: the higher the SB and the redder the disk, the larger the bulge-to-disk ratio and the lower the disk gas fraction. Bulges formed secularly seem to be in agreement with observations, at least for late-type galaxies (see for a review Wyse et al. 1997).
Models can be tested even in the solar neighborhood. For a MW fiducial model (based on the statistically most probable cosmological MAH), the predicted evolution of the SF rate in the solar neighborhood agrees within the uncertainty with the evolution derived from the HR diagram provided by the Hipparco satellite (Hernández, Avila-Reese & Firmani 2001). On the other hand, chemical and photometric models, starting from the observed distributions in the MW, infer infall, structural and SF conditions similar to those expected from the hierarchical scenario (e.g., Boissier & Prantzos 1999; Prantzos, this volume). However, the inner dynamics again reveals a conflict: the CDM halo concentrates too much mass in the central regions in such a way that the shapes of the model and observed MW rotation curves do not agree. A soft core of size as inferred from observations of LSB and dwarf galaxies, eliminates the discrepancy.