|Annu. Rev. Astron. Astrophys. 2005. 43:
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In the "global" approximation, one averages all quantities over large comoving volumes and then solves the chemical evolution equations to deduce metal production rates from the comoving SFR, * (z), which is computed by tracking changes in the neutral-gas density, g(z) (Edmunds & Phillipps 1997; Lanzetta, Wolfe & Turnshek 1995; Malaney & Chaboyer 1996; Pei & Fall 1995). However, the factor-of-two decreases between between z 4 and z = 2 suggests that damped Ly systems are replenished by a net inflow of neutral gas (see Section 8.3).
Pei & Fall (1995) considered models with inflow and outflow and searched for self-consistent evolution of the neutral gas, metallicity, and dust. These authors calculated the effects of obscuration on quantities deduced directly from the data, such as N(H I), and found that significant obscuration was necessary to explain the observations. Pei & Fall (1995) fitted the available data with analytic functions for g (z) that increased with z at z < 2 (Lanzetta, Wolfe & Turnshek 1995) and assumed that the net accretion rate, a(z), was proportional to * (z). When more accurate measurements of * (z) (Steidel et al. 1999) and the cosmic background radiation intensity (Hauser & Dwek 2001) became available, Pei, Fall & Hauser (1999) also included the production of background radiation by stars in damped Ly systems (see Fall, Charlot & Pei 1996). With these additional constraints, Pei, Fall & Hauser (1999) worked directly from the measurements of g (z) and eliminated the assumption that a(z) was proportional to * (z). The newer models reproduced the more accurate metallicity measurements not available earlier, and were consistent with measurements of the background radiation intensities and * (z). However, as we discuss in Section 10, these models appear to cause more obscuration than the current observational data imply. Furthermore, the values of * (z) at z < 2 were inferred from changes in g (z) that now appear to be spurious (Rao, Turnshek & Nestor 2004; private communication).
In the "local" approximation, one computes the chemical evolution of isolated galaxies outside a cosmological setting. A star-formation history is imposed from the outset and one solves for the chemical response of stars and gas. Adopting the slow star-formation history for spiral galaxies suggested by Matteucci, Molaro & Vladilo (1997), Lindner, Fritze-v. Alvensleben & Fricke (1999) reproduced the slow evolution of [Zn/H] with z observed in damped Ly systems. However, these authors adopted a "closed box" model and neglected spatial gradients in all physical parameters. Calura, Matteucci & Vladilo (2003) removed these restrictions and also reproduced the slow increase of [Zn/H] with decreasing redshift using star-formation histories predicted for large galactic radii in spirals or for episodic bursts in dwarf irregulars. Furthermore, they used the same models to reproduce the [Si/Fe] versus [Fe/H] relation after correcting for depletion. Dessauges-Zavadsky et al. (2004) used these models to explain the chemical evolution of three damped Ly systems for which abundances of a large number of elements had been obtained. Interestingly, the predicted SFRs per unit area agree with those inferred from the C II* technique. Whereas Wolfe, Gawiser & Prochaska (2003) found that integrating such SFRs between z = 5 and 3 resulted in the overproduction of metals, Dessauges-Zavadsky et al. (2004) found that the cumulative metals produced did not exceed those observed owing to the short timescales for metal production required to explain relative abundance ratios such as [Si/Fe]. However, in some cases the short timescales conflict with the conservative lower limit of 0.25 Gyr on age set by the measurement of [N / ] near the -0.7 plateau (see Section 3.2.2). Other potential problems with these models stem from the depletion corrections applied to the [Si/Fe] ratio, which may be too large (see Section 10).
The most promising approach to chemical evolution is the direct one, which uses cosmological hydrodynamical simulations [see Somerville, Primack & Faber (2001) and Mathlin et al. (2001) for semianalytic and analytic variants of this method]. The simulations unite the "local" and "global" approximations with a self-consistent evolution of stars, gas, metals, and dust within a CDM cosmology. While the microphysics behind star formation and metal production cannot be included in these simulations, recipes calibrated to local observations are used to track stars and metals along with dark matter particles governed by gravity and gas particles governed by gravity and hydrodynamics. As a result, processes such as accretion of neutral gas from the IGM are described physically, and star formation is treated self-consistently rather than being imposed ad hoc. Moreover, merging between dark-matter halos is included for the first time.
Cen & Ostriker (1999) were the first to describe the chemical evolution of damped Ly systems with numerical simulations. Using a low-resolution Eulerian scheme, these authors were unable to resolve the dark-matter halos giving rise to damped Ly absorption. Nevertheless, they pointed out that metallicity is a more sensitive function of overdensity, , than of age: metal-poor objects such as the Ly-forest clouds formed in low-density environments ( 1), while more metal-rich objects such as damped Ly systems and Lyman Break Galaxies formed in regions of higher overdensity ( > 10). Using a more accurate version of this numerical code, Cen et al. (2003) predicted the cosmic metallicity at z ~ 3 to be between 0.3 and 0.5 dex higher than the observed value. They solved this "missing metals problem" (see Section 8.3) by using obscuration corrections that may be larger than allowed by the results of Murphy & Liske (2004). They also predicted that, independent of metallicity, the ages of typical damped Ly systems in the redshift interval z = [2, 4] would be 0.8-2 Gyr, which are consistent with the presence of the upper [N / ] plateau. Another prediction of interest is that the median stellar mass M* ~ 109 M, which is a factor of 10 lower than that of Lyman Break Galaxies, indicating they are different populations.
The present state of the art in cosmological hydrodynamic simulations of damped Ly systems is represented by the recent results of Nagamine, Springel & Hernquist (2004b) who used the SPH code described in Section 2.5.2 (see also Cora et al. 2003). These authors found SFRs per unit area that agree with the predictions of the C II* technique for damped Ly systems (Wolfe, Prochaska & Gawiser 2003). They also predicted an overproduction of metals by z 2.5, but in this case by a factor of 10 compared to the observed metal abundances. The difference with Cen et al. (2003) is likely related to the lower spatial resolution of the latter simulation (about 30 h-1 kpc comoving), which causes the high metallicities of compact regions to be diluted by the low metallicities of diffuse regions. One of the interesting predictions of the Nagamine, Springel & Hernquist (2004b) simulations is that all regions in which N(H I) 2 × 1020 cm-2 exhibit star formation. Confirmation of this prediction would favor the uniform disk model over the bulge model of star formation discussed by Wolfe, Gawiser & Prochaska (2003). As a result, it is important to decide whether this finding is an artifact of the star-formation algorithm employed by Nagamine, Springel & Hernquist (2004b), especially since there are regions in nearby galaxies in which N(H I) 2 × 1020 cm-2, but only low star formation rates (~ 10-5 M year-2kpc-2) are observed (Ferguson et al. 1998).