Annu. Rev. Astron. Astrophys. 2005. 43: 727-768 Copyright © 2005 by Annual Reviews. All rights reserved

8. COMPARISON OF MODELS WITH OBSERVATIONS

One of the striking result of the deep surveys concerns the evolution of the infrared and submillimeter galaxy population. The source counts are high when compared to no evolution, or moderate, evolution models ¹ for infrared galaxies. Classical semianalytical models of galaxy formation predicts neither the large numbers of infrared galaxies nor their very strong evolution, revealing a serious gap in our understanding of galaxy formation and evolution. Very recently, several empirical approaches have been proposed to model the high evolution of the infrared output with redshift (e.g., Chary & Elbaz 2001; Franceschini et al. 2001; Rowan-Robinson 2001; Takeuchi et al. 2001; Xu et al. 2001; Lagache et al. 2004) that fit source counts, redshift distributions and CIB intensities and fluctuations, although often not all of them. All these models, however, agree on a general trend - i.e., the luminosity function must change dramatically with redshift, with a rapid evolution of the high-luminosity sources (L > 2 × 10¹¹ L) from z = 0 to z = 1, which then stay rather constant up to redshift 3 or more. The evolution of the infrared luminosity function may be linked to a bimodal star-formation process, one associated with the quiescent and passive phase of the galaxy evolution and one associated with the starburst phase, triggered by merging and interactions. The latter dominates the infrared and submillimeter energy density of the Universe at high z. Consistently, cold dark matter N-body simulations show that halo merger rates increase with redshift as (1 + z)^m with 2.5 m 3.5 (Gottlober et al. 2001). Observations, however, give m values between 0 and 4 (Le Fèvre et al. 2000; Conselice et al. 2003; Bundy et al. 2004; Lin et al. 2004). The spread is due to different selection effects, detection techniques, pair criteria and sample variance. It is therefore not easy to reconcile the different observational results. Moreover, comparisons with models are very difficult because definitions of merger rates may not be consistent. Merger rates can also depend on halo masses. As a consequence, the timescale of the merger phase is difficult to estimate. Peaks of star formation produced by mergers in hydrodynamical models (e.g., Scannapieco & Tissera 2003) has a duration of several hundreds of million years. This is consistent with what is observed. ULIRGs emit more than half of their bolometric luminosity from a starburst of age 10⁷-10⁸ years (Genzel et al. 1998). LIRGs build up their stellar mass in a typical timescale of about 0.1 Gyr (Franceschini et al. 2003). These timescales are also supported by Marcillac et al. (2005) who performed Monte Carlo simulations using synthetic spectra based on the models of Bruzual and Charlot (2003) to derive the past star-formation history of 22 LIRGs. They found that LIRGs experience a major event of star formation in their lifetime that produce about 10% of their stellar mass within 0.1 Gyr. How many such episodes of violent star formation does a typical galaxy experience? Assuming a timescale of 0.1 Gyr, Hammer et al. (2005) estimate the number of episodes per galaxies as about 5 from z = 1 to z = 0.4. These episodic bursts naturally explain the high fraction of LIRGs in the distant Universe.

Models that are more sophisticated than empirical approaches attempt to follow the physics of galaxy formation in greater detail (e.g., Guiderdoni et al. 1998; Hatton et al. 2003; Granato et al. 2004; Silva et al. 2005). In semianalytical models, the collapse of perturbations is described by the classical top-hat model under the assumptions of homogeneity and sphericity. The mass distribution of collapsed halos is computed from the so-called peaks formalism developed by Bardeen et al. (1986). Then dissipative collapse and cooling are introduced, with the usual "overcooling" problem that can partly be solved by introducing stellar feedback. Star-formation processes are deduced from the gas content and the dynamical timescale of the galaxies. Finally spectrophotometric evolution is used to compute the age dependence of the gas content, the spectra of the stellar populations and the mass-to-luminosity ratios. To make specific predictions for the infrared galaxies, these models must include an important additional feature: absorption of the UV/optical radiation and emission by the dust grains. Very often two modes of star formations are considered; a quiescent mode and a burst mode in which the star formation timescales are much shorter. This burst mode is triggered by galaxy mergers and is absolutely required by the infrared to submillimeter observations. There are some indications that to reproduce the submillimeter galaxy counts, a dramatic change of the IMF is required. A top-heavy IMF, in particular, increases the production of dust that is essential for boosting the luminosity of galaxies in the submillimeter. Using an IMF of the form dN / dlnm m^-x with x = 0 for the burst mode, Baugh et al. (2005) were able to reproduce not only the submillimeter observations but also the properties of Lyman-Break galaxies. They predict that the SMGs reside in the more massive halos in place at z = 2 and therefore that they are more strongly clustered than dark matter at this epoch. This is consistent with tentative observational constraints (Blain et al. 2004a). There are several observational "indications" of massive stars (> 100 M) in nearby starburst templates. Wolf-Rayet stars ² have been detected in a large number of galaxies undergoing intense bursts of star formation (e.g., Gonzalez-Delgado et al. 1997; Pindao et al. 2002). However, it remains difficult to measure the IMF at high mass because of aging effects that can mimic real upper-mass IMF cutoff (the highest massive stars have very short lifetimes).

In conclusion, the hierarchical galaxy formation paradigm is very successful in its description of large-scale structure formation and evolution. The next important step will be to test this picture to explain not only the number densities but also the mass assembly and particularly the mass of the SMGs. First mass measurements of SMGs galaxies seem to show that a very flat IMF cannot by itself explain the mass assembly of the baryonic matter at high z (Genzel et al. 2005). Hierarchical clustering underpredicts the high-z volume densities of these massive galaxies. More work needs to be done to test the baryonic mass assembly in the hierarchical paradigm. Both observational and model estimates are still very uncertain, with the former depending on large lifetime corrections and small samples and the latter on ad hoc input recipes for feedback and star formation.

¹ `No-evolution': the co-moving luminosity function remains equal to the local one at all redshifts. Back.

² Wolf-Rayet stars are hot (25,000 to 50,000 K), massive ( 25 M), luminous stars with a high rate of mass loss. The Wolf-Rayet phase appears in an advanced stage of evolution. They are believed to be O stars that have lost their hydrogen envelopes, leading their helium cores exposed. Wolf-Rayet stars are often in a binary system, and are deemed, within a few million years, to explode as type Ib or Ia supernovae. Back.