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Crucial information about the star formation history is encoded in the chemical composition of stars. The key observables are mean (luminosity-weighted) metallicities, abundance ratios, and the run of these quantities with sigma. It has long been known that the central regions of nearby massive galaxies are metal-rich (e.g., Spinrad & Taylor 1971). It was only far more recently that reliable metallicity estimates became possible for massive ETGs at cosmological distances, showing that they have comparably high metallicities, (e.g., Spinrad et al. 1997, Jørgensen et al. 2005, Schiavon et al. 2006), implying a relatively rapid early chemical enrichment. A more detailed knowledge of the history of star formation requires accurate estimates of detailed abundance patterns in a range of redshifts, but work on abundance ratios has so far been restricted to relatively nearby samples (but see Jørgensen et al. 2005 and Kelson et al. 2006).

3.1. Magnesium

The Mg I 517-518 nm doublet has been the chief metallicity indicator in early studies of the chemical composition of ETGs from integrated light, due to its strength and location in a spectral region where astronomical detectors were very sensitive. Early studies found evidence for an overabundance of Mg relative to Fe in ETGs (e.g., Peterson 1976). When Mg and Fe lines were finally compared with models of stellar population synthesis, it was found that [Mg/Fe] 2 is above solar in the centers of massive ETGs (Worthey et al. 1992). This was arguably one of the most influential results in the history of the field, and it has guided theoretical work to this day. Further studies showed that Mg enhancement is correlated with central velocity dispersion (sigma) and metallicity (e.g., Jørgensen 1999, Trager et al. 2000, Thomas et al. 2005, Schiavon 2007, Smith et al. 2009). At least three scenarios have been invoked to explain this finding, all involving the balance between Mg enrichment by SN II and Fe enrichment by SN Ia: short star formation timescale, top-heavy IMF, and selective winds (Faber et al. 1992). One popular interpretation of the data invokes the existence of a relation between star formation timescale and galaxy mass (e.g., Thomas et al. 2005). The data, however, did not allow one to rule out scenarios based on selective winds or IMF variations.

Some exciting new results have been presented in a series of papers, by G. Graves and collaborators. Analyzing a large sample of stacked SDSS 3 spectra, they mapped the spectroscopic ages, [Fe/H], [Mg/H], and [Mg/Fe] of ETGs onto the fundamental plane (FP) with particular attention to how these parameters are distributed along and across the FP (Graves et al. 2009, Graves & Faber 2010, Graves et al. 2010). Besides recovering the well known trends of age and abundances with sigma, Graves et al. showed that, at fixed sigma, star formation histories of ETGs correlate strongly with galaxy surface brightness. Galaxies with higher surface brightness have lower spectroscopic ages, higher [Fe/H] and [Mg/H], but lower [Mg/Fe]. Graves & Faber (2010) contend that the thickness of the FP is accounted for by departures of a constant dynamical-mass-to-light ratio (Mdyn / L), which may be due to variations in either dark-matter fraction or IMF, and not to effects due to passive evolution of the stellar populations. At fixed Mdyn, galaxies with higher surface brightness (located "above" the FP) have a higher surface stellar density and therefore are characterized by either a lower dark matter fraction or by a bottom-heavier IMF. They formed stars during a longer timescale, so that their metallicities are higher, but both their spectroscopic ages and [Mg/Fe]s are lower than their low-surface-brightness counterparts. Graves et al. propose a scenario where star formation in galaxies with same Mdyn was truncated at different times, with longer/shorter star formation timescales resulting in higher/lower stellar surface mass density and surface brightness, higher/lower metallicity, lower/higher [Mg/Fe], and younger/older spectroscopic ages. In short, these new results single-handedly explain the thickness of the FP and establish possible (and testable) correlations between the star formation histories of ETGs and such measurable quantities as dark-matter fraction and the shape of the low-mass end of the stellar IMF. Further progress will be determined by observational tests of these predictions, as well as more sophisticated chemodynamical modeling of ETG formation.

3.2. Calcium

Past studies suggest that Ca does not behave like Mg, with [Ca/Fe] being possibly solar (or lower) and not correlated with sigma. Trager et al. (1998) found the Lick/IDS Ca4227 index to be essentially independent of sigma. Accordingly, Thomas et al. (2003) concluded that [Ca/Fe] in their sample galaxies was also essentially constant with sigma. Saglia et al. (2002), on the other hand, found the Ca II triplet (CaT, 849, 855, 862 nm) to be mildly decreasing with sigma. Vazdekis et al. (2003) and Cenarro et al. (2004) compared new single stellar population synthesis models for the CaT with data for field and Coma galaxies, again finding very low [Ca/Fe]. While difficult to understand, given that both Ca and Mg are alpha elements manufactured in similar (though not identical) nucleosynthetic sites, the implications of these results are potentially important, giving theorists ample room for a wide range of speculations.

The unexpected behavior of Ca seems to be instead most likely caused by difficulties in the interpretation of the measurements, particularly because the two Ca indices employed in these studies do not respond to Ca abundance variations in a clean fashion. Prochaska et al. (2005) showed that the Ca4227 index is severely affected by a CN bandhead which contaminates the blue pseudocontinuum of the index, making it lower. Because CN is strongly correlated with sigma (Trager et al. 1998), the effect is stronger for higher sigma galaxies, offsetting any dependence of the Ca line strength itself on sigma, thus making the index sigma-independent. Prochaska et al. demonstrated this by defining a new index, Ca4227r, which is less affected by CN contamination. They showed that Ca4227r is as strongly correlated with sigma as Mg b.

While the issue of the slope of the Ca4227-sigma relation is seemingly resolved, models that account for the effect of CN on the Ca4227 index still indicate [Ca/Fe] ~ 0 in massive ETGs (Schiavon 2007, Graves et al. 2007). At face value, this confirms the abundance ratios found by previous studies. However, there may be non-negligible systematics in the Ca abundances derived by application of the Schiavon (2007) models. They are affected by uncertainties in age, and in the abundances of Fe, C, and N. They are also affected by uncertainties in the way models account for the contamination of Ca4227 by CN. So the matter should be considered far from settled.

Regarding the results based on CaT, one should bear in mind that the integrated spectra of metal-rich stellar populations in the CaT region is dominated by M giants (Schiavon & Barbuy 1999), and that fact has implications for both the zero point and the slope of the [Ca/Fe]-sigma relation. First let us consider the zero point. The stellar libraries employed in the models used to analyze CaT data in the past contain hardly any M giants with known metallicity, let alone known [Ca/Fe] (Cenarro et al. 2001a). Therefore, [Ca/Fe] in the models themselves is uncertain, which obviously makes it very hard for one to infer reliable [Ca/Fe] from comparison of those models with the data. As regards the slope of the CaT-sigma relation, we recall that the CaT lines are located in a region where opacity in the spectra of M giants is dominated by TiO lines. While the definition of the CaT* index employed in these studies is partly meant to account for TiO contamination (Cenarro et al. 2001b), the index has not been shown to be immune to variations in [Ti/Fe] 4 which may be important, given that there is evidence that Ti is enhanced in ETGs (Milone et al. 2000). Regarding the negative slope of the CaT* ~ sigma relation, that could be due to the effect of TiO opacity on the pseudocontinuum, because: 1) TiO is well correlated with sigma (Trager et al. 1998), and 2) TiO lines are more sensitive to metallicity than CaT lines (Schiavon et al. 2000, Schiavon & Barbuy 1999, Jørgensen et al. 1992). Finally, CN contamination of the CaT indices may also be important (Erdelyi-Mendes & Barbuy 1991).

In summary, we suggest that Ca abundances are far from well known in ETGs, and there is no compelling motivation to resort to extreme scenarios to account for the numbers currently available in the literature. More work is needed to produce reliable [Ca/Fe] measurements in ETGs.

3.3. Nitrogen & Carbon

While the behavior of C- and N-sensitive indices such as Lick CN1, CN2, G4300 and C24668 in ETG spectra has been well documented for over a decade, it was only after the Schiavon (2007) models and their implementation in EZ_Ages (Graves & Schiavon 2008) that these indices could be intepreted in terms of [N/Fe] and [C/Fe] (see also Kelson et al. 2006). Both abundance ratios are found to be super-solar and correlate strongly with sigma and metallicity (Schiavon 2007, Graves et al. 2007, Smith et al. 2009). This result has been called into question recently by Toloba et al. (2009), who found no correlation between the strength of the near-UV NH3360 feature and sigma in a sample of nearby galaxies. They argue that the NH3360 band is a clearer indicator of N abundance than the Lick CN features used by EZ_Ages, because the latter are also dependent on C abundance. The absence of a slope in the NH3360-sigma relation may be explained by the presence of metal-poor stars, whose contribution to the integrated light is highest in the UV. In fact, multiple stellar population models show that the inclusion of a small fraction of a metal-poor population flattens the NH3360-sigma relation, even in the presence of a [N/Fe]-sigma correlation (G. Worthey, 2010, private communication).

The existence of a steep slope in the [N/Fe]-sigma relation, if confirmed, is an important result, as it may indicate secondary enrichment of N by stars ranging from 4-8 Modot (Chiappini et al. 2003). Because these stars last for ~ 108 years, the presence of a secondary-enrichment signature in the chemical composition of stars in ETGs may constrain the lower limit for the duration of star formation in the systems that formed the stars that live today in those galaxies, (Schiavon 2007) and, perhaps most importantly, their characteristic masses. The increasing evidence for the presence of multiple stellar populations in globular clusters (Piotto 2009) may be an important clue in this regard. It has been long known that there is a marked spread in N and C abundances in globular cluster stars (e.g., Smith & Norris 1982, Cannon et al. 1998, Carretta et al. 2005), which is roughly consistent with enrichment by intermediate mass stars going through the AGB phase (Ventura & D'Antona 2008). The presence of such CN inhomogeneities seems to be a function of both cluster mass and environment (Martell & Smith 2009), as predicted by recent models (Conroy & Spergel 2010).

One may reasonably speculate that the evidence above indicates that the stars we see in nearby ETGs were formed in the precursors of today's Galactic globular clusters. In that scenario, the signature of secondary N enrichment we see in ETGs today would have been established in those early systems, before they merged to form the massive, dynamically hot galaxies we see today. The Galactic halo can be used as a resolved proxy to test this scenario. The recent identification of CN bimodality in a sample of halo field stars by Martell & Grebel (2010) argues for a similar process in operation during the formation of the Galactic halo. Because CN-strong stars have almost certainly been formed in globular clusters (or their precursors in the distant past), their presence in the halo field is evidence of the early dissolution of those systems in the formation of the Galactic halo. Martell & Grebel estimate that as much as 50% of the halo mass may have been contributed by globular clusters and their precursors. If a similar process was responsible for the assembly of stellar mass in ETGs, one might wonder whether a similar fraction of the total mass would have been contributed by the globular cluster precursors. Could the slope of the [N/Fe] vs. [Fe/H] or sigma be used to constrain that number? What were the characteristic masses of those systems? Would it be possible to construct chemodynamical evolution models for those low-mass systems that are capable of reproducing all the abundance ratios measured in today's ETGs?

Inclusion of C and N in abundance analyses of ETGs is bringing interesting new insights on their star formation histories, which could potentially even lead to a reinterpretation of the data on [Mg/Fe]. Smith et al. (2009) analyzed a large data set for galaxies from the Coma cluster and Shapley supercluster, spanning a very wide range of sigma. They determined the abundances of several elements using EZ_Ages, then performed biparametric fits to the relation between [Mg,Ca,C,N/Fe] and both [Fe/H] and sigma, thus disentangling the dependence of abundance ratios on these two variables. Smith et al. found that both [Mg/Fe] and [Ca/Fe] decrease with [Fe/H], whereas [N/Fe] and [C/Fe] do not correlate with it. They suggest that the run of [Mg/Fe] and [Ca/Fe] with [Fe/H] indicates a short time scale for star formation. They consider that the lack of correlations of [N/Fe] and [C/Fe] with [Fe/H] is expected since, unlike Mg and Ca, C and N are contributed by low(er) mass stars, so that these elements should scale with Fe, not with Mg and Ca. Interestingly, on the other hand, all abundance ratios show a strong correlation with sigma. Smith et al. contend that this result is difficult to interpret in terms of a simple dependence of star formation timescale on galaxy mass (e.g., Thomas et al. 2005), because that would preclude a correlation between [C/Fe] and [N/Fe] with sigma. Clearly, more work is needed to clarify this issue.

2 More often than not, this result is phrased in the literature in terms of an overabundance of alpha elements relative to iron. Despite the many theoretical reasons in favor of the assumption that all alpha elements should vary in tandem, there is so far no firm evidence that any alpha element other than Mg is enhanced in ETGs, except perhaps for Ti (Milone et al. 2000). Back.

3 Sloan Digital Sky Survey Back.

4 TiO lines are very sensitive to variations in the abundance of Ti. Back.

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