Annu. Rev. Astron. Astrophys. 2009. 47: 371-425
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5. CHEMICAL EVOLUTION MODELS

The detailed evolutionary histories of dwarf galaxies have intrigued astronomers for decades. One of the main reasons of interest is that they are often extremely low metallicity systems, and thus assumed to be highly unevolved. Their low abundances of metals and helium, derived from HII region spectra, allow the determination of the primordial helium abundance with a minimum of extrapolation (e.g., Peimbert & Torres-Peimbert 1974, Izotov & Thuan 1998, Olive, Steigman & Skillman 1997, Izotov, Thuan & Stasinska 2007) and thus provide insights into Big Bang Nucleosynthesis.

Most recently dwarf galaxies have been of interest due to their cosmological importance as potential building blocks of larger systems. Nearby dwarf galaxies are the closest we can get to the detailed study of a primordial system. They typically have relatively simple structures and often very low metallicities. We assume that because small systems are believed to be the first to collapse in the early universe it was galaxies like these that were the first to form and are thus potential hosts of the first stars. Their widespread distribution throughout the early Universe also makes them suitable candidates to be able to re-ionise the Universe uniformly and rapidly (e.g., Choudhury, Ferrara & Gallerani 2008, Stark et al. 2007). Recently there have been large samples of stellar abundances of individual stars obtained in nearby dwarf galaxies (e.g., Hill et al. 2009, in prep., Letarte 2007, Monaco et al. 2007). These will provide a wealth of information on chemical evolution through time, and determine the accurate evolutionary path of these small systems and their contribution to Universal processes such as the build up of metals in the Universe.

Beatrice Tinsley, beginning in the mid 1960s pioneered the field of galactic chemical evolution modelling. The cornerstones were laid by E. Salpeter in 1955 with his paper on the IMF and in 1959 with his first determination of the effects of stellar evolution on the metallicity evolution of stellar populations. This work was extended by M. Schmidt in 1959 and 1963 to determine universal predictions for the SFR in a galaxy. Tinsley however provided the first full description of the theoretical modelling of galactic chemical evolution and of its relevance to many astrophysical topics. In 1968 she was already studying the evolutionary properties of galaxies of different morphological types (Tinsley 1968), and with subsequent seminal papers (Audouze & Tinsley 1976, Tinsley 1980) she set the stage for all future studies of galactic chemical evolution. Since the late seventies (e.g., Lequeux et al. 1979) a wealth of chemical evolution models have been computed for dwarf galaxies in general and for late-type dwarfs in particular (see e.g., Matteucci & Chiosi 1983, Pilyugin 1993, Marconi, Matteucci & Tosi 1994, Carigi et al. 1995, Tosi 1998) and references therein).

The predictions of early models of the chemical evolution of dwarf galaxies were far from unique (as reviewed e.g., by Tosi 1998), because few observational constraints were available: the ISM chemical abundances (helium, nitrogen and oxygen as derived from the emission lines of HII regions), and the gas and total mass (mainly from 21 cm radio observations). These data define present-day galaxy properties, and do not constrain the early epochs. This allows for little discrimination between different models which may have very different paths to the same end point. Star formation laws, IMF and gas flows could be treated as free parameters and with their uncertainties it was inconceivable to model the evolution of individual galaxies, unless unusually rich in observational data. In practice, until recently, only the Magellanic Clouds were modelled individually (e.g., Gilmore & Wyse 1991, Pagel & Tautvaisiene 1998), even though many constraints were still missing (e.g., accurate field star metallicity distribution, detailed abundances in older populations, etc.). It is fair to ask how good the predictions of some of these models were because 30 years later we are still arguing whether or not dIs and BCDs differ only in the recent SFH, and if BCDs are actually ancient systems with a recent burst, as predicted by Lequeux et al. (1979), or something entirely different.

Detailed chemical evolution models of individual dwarf galaxies have recently become possible as more accurate SFHs become available combined with large samples of stellar abundances for individual stars over a range of ages. This provides an accurate age-metallicity relation which is a key constraint for chemical evolution models.

5.1. Explaining Low Metallicity

One of the major challenges for chemical evolution models of dwarf galaxies has always been to reconcile their low observed metallicity with the fairly high SFR of the most metal-poor systems, many of which are actively star-forming BCDs. Historically, three mechanisms have been envisaged to accomplish this task (Matteucci & Chiosi 1983):

Whether one of these mechanisms is preferable or a combination of any or all of them is required is still matter of debate. When detailed numerical models were computed it was immediately recognized that metal enriched winds are the most straightforward mechanism to recreate the observed properties of dwarf galaxies (Matteucci & Tosi 1985, Pilyugin 1993, Marconi, Matteucci & Tosi 1994, Carigi et al. 1995). The infall of metal-poor gas can in principle explain the evolution of gas-rich dwarfs, but gas accretion is also most likely to trigger more star formation and chemical enrichment. This can quickly lead to more rapid enrichment of small dwarf galaxies. Bottom-heavy IMFs imply abundance ratios for elements produced by stars of different mass which are at odds with the observed values, see section 4.1.1.

5.2. Galactic Winds

It was first proposed by Larson (1974) that gas could be blown out by internal energetic events related to star formation, such as stellar winds and supernovae explosions. These processes can accelerate metal-rich stellar and supernova ejecta beyond the escape velocity of small dwarf galaxies (e.g., Heiles 1990, Tenorio-Tagle 1996, Rieschick & Hensler 2003, Fujita et al. 2004). The theory is periodically further developed (e.g., Dekel & Silk 1986, D'Ercole & Brighenti 1999, Mac Low & Ferrara 1999, Ferrara & Tolstoy 2000, Legrand et al. 2001, Tassis et al. 2003, Marcolini et al. 2006, Salvadori, Ferrara & Schneider 2008), and naturally explains the well established correlation between luminosity and metallicity (e.g., Skillman, Kennicutt & Hodge 1989, Gallazzi et al. 2005), as smaller galaxies are less able to retain their heavy elements. It can also explain the structural similarities observed by Kormendy (1985), and it has even been suggested that many dwarf galaxies have lost most of the gas mass they originally possessed and hence follow the structural relations regardless of the current gas mass fraction (Dekel & Silk 1986, Skillman & Bender 1995). However this theory cannot explain why some galaxies loose all their gas very early and some relatively recently. There has been no global parameter, such as mass, found to explain this. Hence the influence of tidal effects is considered to play an important, but hard to verify, role (e.g., Lin & Faber 1983). It may also be related to the varying initial conditions under which different galaxies may have formed, or perhaps also the density of the DM halo in which they reside.

Galactic winds have been predicted by hydrodynamical simulations (D'Ercole & Brighenti 1999, Mac Low & Ferrara 1999) to be able to remove a large fraction of the elements synthesized by SNII as well as a fraction of the galaxy ISM. Thus galactic winds can be quite effective and lead to a significant reduction of the ISM enrichment. The strength of this effect depends both upon the galaxy mass, or the depth of the potential well, and on the intensity of the star formation, and thus the number of SN explosions that can be expected. This is precisely what is needed by chemical evolution models to reproduce the observed properties of dwarfs. Moreover, there is increasing observational evidence for starburst driven metal-enriched outflows (e.g., Meurer et al. 1992, Heckman et al. 2001, Martin, Kobulnicky & Heckman 2002, Veilleux, Cecil & Bland-Hawthorn 2005, Westmoquette, Smith & Gallagher 2008). Whether early-type dwarfs are connected to late-type dwarfs, as the extreme consequence of tremendous winds from originally gas-rich dwarfs or the consequence of gas stripping or ram pressure in harsh environments is difficult to say. The evidence that gas-poor dwarfs are preferentially located in denser environments than gas-rich ones (Binggeli, Tarenghi & Sandage 1990) seems however to favour the stripping scenario.

5.3. Modelling Individual systems

Two kinds of models for individual galaxies are commonly used: standard chemical evolution models and chemo-dynamical models. The standard models follow the evolution of individual elements, taking into account global parameters such as mass of the system, gas flows and IMF, and stellar parameters such as their chemical yields and lifetimes, but make very simplistic assumptions (if any) on stellar and gas dynamics (see Tinsley 1980 for a comprehensive and still relevant review). The chemo-dynamical models deal with the dynamical processes in great detail. Standard models are quite successful in predicting large-scale, long-term phenomena, but their simplistic treatment of stellar and supernovae feedback and of gas motions, is an obvious drawback. Chemo-dynamical models are more able to account for small-scale, short-term phenomena, but the timescales required to run hydrodynamic codes and the errors that start to creep in have made them less successful to follow galactic scale evolution over more than a Gyr. The challenge in the next few years is to improve both types of approaches and get a more realistic insight into how stars and gas evolve, chemically and dynamically, in their host galaxies.

5.3.1 STANDARD MODELS    A number of standard models have been computed for nearby dSphs adopting the individual SFHs derived from deep HST photometry and comparing the model predictions with the stellar chemical abundances inferred from new generation spectroscopy. Carigi, Hernandez & Gilmore (2002) analysed Carina, Ursa Min, Leo I, and Leo II and suggested a relation between the duration of the star formation activity and the size of the dark matter halo. Lanfranchi & Matteucci (e.g., Lanfranchi, Matteucci & Cescutti 2008 and references therein) devoted a series of papers to the chemical evolution of Carina, Draco, Sgr, Sextans, Scl and Ursa Min reaching the conclusion that, to reproduce the observed stellar abundance ratios and age-metallicity relations, they need low star formation and high wind efficiencies. They suggest that a connection between dSphs and BCDs is unlikely.

Due to the lack of stellar spectroscopy available for more distant dI galaxies chemical evolution models with the detailed approach applied to nearby dSphs have been computed only for NGC 6822 (Carigi, Colín & Peimbert 2006), the closest dI in the Local Group beyond the Clouds. Models assuming the SFH derived from HST CMDs have been computed also for the starburst dwarfs NGC 1569 and NGC 1705 (Romano, Tosi & Matteucci 2006), a few Mpc outside the Local Group. Projects are in progress to model the chemical evolution of the Magellanic Clouds with the level of detail and reliability achieved so far only for the solar neighbourhood, as soon as their SFHs and age-metallicity relations are derived (e.g., Tosi et al. 2008). The situation is expected to improve significantly with the advent of new generation instruments on HST, VLT and eventually Extremely Large Telescopes, which will allow to measure reliable stellar metallicities at larger distances.

5.3.2 CHEMO-DYNAMICAL MODELS    To date chemo-dynamical models have mainly been used to study the effects of feedback from supernovae explosions in a variety of conditions. They can analyse in detail the heating and cooling processes and put important constraints on the onset and fate of galactic winds, stripping and ram pressure. However, they are not yet able to follow the evolution of a galaxy over the entire Hubble time assuming empirically derived SFHs. They have been applied to resolved starburst dwarfs with SFH derived from HST photometry (e.g., Recchi et al. 2004, 2006) for I Zw 18 and NGC 1569) and to a few nearby dSphs (see Fenner et al. 2006, Marcolini et al. 2006, Marcolini et al. 2008) for Draco, and Scl and Fnx).

5.3.3 MODEL PREDICTIONS AND OBSERVED ABUNDANCES The different time scales for the chemical enrichment of elements produced by different stellar processes are particularly useful to constrain chemical evolution models. This is especially true for r- and s- process elements, and for Ba in particular. Only a few models (Fenner et al. 2006, Lanfranchi, Matteucci & Cescutti 2008) and references therein) are recent enough to have their predictions compared with the abundance patterns measured in dwarfs (as shown in Section 4). They thus deserve a few more words of comment. Both types of models reproduce fairly well the observed properties of the galaxies they are applied to, although sometimes they need to assume chemical yields different from those available in the literature (Lanfranchi, Matteucci & Cescutti 2008 and references therein )

[Ba/Fe] is one of the few elements known to have a very large spread at low metallicities (e.g., François et al. 2007), see Fig. 16. At early times Ba is produced by the r-process which must be a rare occurrence and thus sensitive probe of enrichment timescales. The strong rise of [Ba/Fe] seen in Fnx or Sgr (and the LMC, Pompeia et al. 2008) is clearly attributable to the s-process, that is AGB stellar wind pollution. This is currently not well predicted by chemical evolution models of dSphs such as those of Lanfranchi, Matteucci & Cescutti (2008), and Fenner et al. (2006), probably because of the lack of adequate stellar yields. In these models, the galactic wind removes the gas and makes the SFR drop suddenly, preventing high-mass stars from contributing to the enrichment and thereby lowering the r-process contribution to the neutron capture elements. But the wind does not prevent low and intermediate mass AGBs from contributing significantly to the ISM. The decreasing r-process contribution is indeed observed in Fig. 14 with the continuous rise of [Ba/Eu] in Fnx in the range [Fe/H] > -0.8, but this decrease of the r process also acts to prevent [Ba/Fe] from rising: in fact, in these models, [Ba/Fe] (or [La/Fe]) decrease slightly at high metallicities. The models of Fenner et al. (2006) aim to reproduce the abundances of the Scl dSph, and indeed there is a turn up of [Ba/Fe] that is linked to the rise of the s-process, but [Ba/Fe] at low metallicities in Scl is strongly underestimated in the models compared to observations. This is probably due to the strong winds in these models, efficiently removing metals produced by massive stars, including the r-process that makes Ba at low metallicities. These models also predict low alpha elements down to the lowest metallicities in the systems, which is also not observed. In these models, the low-metallicity AGB stars that produce the s-process responsible for the [Ba/Fe] upturn, also produce the right [Ba/Y].

Finally, Fig. 14 shows that, in the domain where the neutron-capture enrichment is dominated by the s-process, [Y/Ba] in dSphs are exceedingly low. The most straight-forward interpretation assumes that low-metallicity AGB stars dominate the s-process. Suggesting that in these stars nucleosynthesis favours high-mass nuclei over lower mass ones, as the result of less numerous seed nuclei (iron mostly) being bombarded by similar neutron fluxes to those at higher metallicities. However, this simple minded explanation has so far lacked any quantitative prediction to be tested against observations, owing largely to the uncertainties plaguing the detailed s-process computations (thermal pulses in AGBs are a challenge to model). Another interpretation put forward by Lanfranchi, Matteucci & Cescutti (2008) is that low [Y/Ba] is reached by simply decreasing the r-/s- fractions at late times (as above, due to galactic winds loosing preferentially r-process elements). Again, the models are not able to reproduce the steep rise in heavier s-process elements such as Ba. This shows us that yields inferred from the solar neighbourhood are not adequate. Although they can reproduce the abundance patterns in the halo and disk of the MW, they cannot easily also reproduce the abundances of dSphs, such as Fnx and Sgr, nor the LMC.

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