Stellarpopulation models

Here I give a short overview of the method, which involves applying stellar populations to strengths of absorption lines tuned to decouple age and metallicity (and abundance ratios) in the spectra. A more complete description can be found in Trager (2004); for details the reader is referred to Trager et al. (2000a), with updates in Trager et al. (2008). An unfortunate drawback of this method at present is its inability to determine MDFs; only mean quantities (weighted in a peculiar way described below) can be determined.

At first glance, it might seem natural to use optical broad-band colours to determine rough abundances of galaxies: metal-poor stellar systems are blue and metal-rich ones are red. This is, of course, because the increasing opacity from metals removes light from the blue and moves it into the red, particularly on the RGB, which provides at least half of the optical light of galaxies. Unfortunately, age has the same effect: older populations are cooler because they have lower mass on the RGB and are therefore redder. One might expect to improve the situation by using metallic absorption lines like the Mg b feature, the MgH triplet (Mg2), or the Fe lines at 5270 A and 5335 A, which would allow a direct measurement of the metal-licity. Unfortunately, these lines have the same problem as broad-band colours: they are formed in the atmospheres of the cool RGB stars and are sensitive to their temperatures - and are therefore also subject to variations in stellar-population age. This age-metallicity degeneracy (e.g. O'Connell 1980) was finally broken by Worthey (1994) and Buzzoni et al. (1994), who independently showed that a plot of Balmer-line strength (such as Hp) as a function of metal-line strength could allow an independent measurement of stellar-population age and metallicity, a result first demonstrated by Rabin (1982). This is because the temperature of the main-sequence turn-off (MSTO) of a stellar population is more sensitive to age than to metallicity, and the Balmer lines of hydrogen are non-linearly sensitive to the temperature of the MSTO.

Stellar-population models that predict the metal- and Balmer-line strengths of stellar populations can then be built (e.g. Worthey 1994). Stellar-interior calculations, in the form of isochrones, are combined with stellar fluxes, determined either empirically or theoretically, and stellar absorption-line strengths, which are almost always determined empirically (but interpolation methods vary), to produce predicted line strengths as a function of stellar-population age and composition. Modern models (e.g. Trager et al. 2000a; Thomas et al. 2003) now allow for variations in abundance ratios like [a/Fe], since models based on line strengths of Solar-neighbourhood stars produce (for example) Mg b-line strengths too weak for a given (Fe) line strength relative to giant elliptical galaxies (e.g. Peterson 1976; O'Connell 1980; Peletier 1989; Worthey etal. 1992) (Figure 16.4).

3.2 Stellar-population analyses

Once stellar-population models are available, stellar-population ages, metallicities and abundance ratios can be read off diagrams like Figure 16.4. (Note, however,

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Mg b

Figure 16.4. Stellar populations of nearby early-type (elliptical and S0) galaxies. Data for elliptical galaxies in the field are taken from Gonzalez (1993), data for S0s in the field are from Fisher et al. (1996), and data for elliptical galaxies and S0s in the Fornax Cluster are from Kuntschner (2000). Data for ellipticals are squares and data for S0s are triangles. Model grids from Bruzual & Charlot (2003) as modified by Trager et al. (2008), see Serra & Trager (2007), for [a/Fe] = 0 are over-plotted. Solid lines are for constant age; dashed lines are for constant metallicity. In the left panel, [MgFe] = VMg b x (Fe> is a metallicity indicator reasonably free of non-Solar-abundance-ratio effects (Thomas et al. 2003). This means that SSP-equivalent age and metallicity can be read from this panel. In the right panel, model grids have [a/Fe] = 0 and +0.3 from left to right. This panel is used to estimate [a/Fe].

Mg b

Figure 16.4. Stellar populations of nearby early-type (elliptical and S0) galaxies. Data for elliptical galaxies in the field are taken from Gonzalez (1993), data for S0s in the field are from Fisher et al. (1996), and data for elliptical galaxies and S0s in the Fornax Cluster are from Kuntschner (2000). Data for ellipticals are squares and data for S0s are triangles. Model grids from Bruzual & Charlot (2003) as modified by Trager et al. (2008), see Serra & Trager (2007), for [a/Fe] = 0 are over-plotted. Solid lines are for constant age; dashed lines are for constant metallicity. In the left panel, [MgFe] = VMg b x (Fe> is a metallicity indicator reasonably free of non-Solar-abundance-ratio effects (Thomas et al. 2003). This means that SSP-equivalent age and metallicity can be read from this panel. In the right panel, model grids have [a/Fe] = 0 and +0.3 from left to right. This panel is used to estimate [a/Fe].

that stellar-population parameters are actually inferred from x 2 minimisation of the model line strengths against the observed line strengths.) All early-type galaxies span a range in metallicity and age (Trager et al. 2000b), with the mean age being older in clusters than in the field (Thomas et al. 2005). Early-type galaxies in all environments typically have -0.5 < [Z/H]SsP < +0.5 and 0 < [a/Fe]SSP < +0.4 (depending exactly on the stellar-population model used). There appears to be no significant difference in metallicity between different environments (Thomas etal. 2005; Sanchez-Blazquez etal. 2006), although small differences in [C/Fe] or [N/Fe] are possible (Sanchez-Blazquez et al. 2006).

An important caveat must be understood when reading diagrams like Figure 16.4. The ages and compositions inferred from these diagrams are those of the equivalent single stellar population (SSP) (we call them the 'SSP-equivalent' parameters). That is, these are the ages and compositions that the objects would have if they were composed solely of a single population formed in a single burst at the SSP-equivalent age with a chemical composition given by the SSP-equivalent metallicity and abundance ratio(s). This means that the composite populations of real galaxies are treated in terms of their line-strength-weighted mean population parameters. In the case of

Figure 16.5. The variation of stellar-population parameters with age and velocity dispersion (a). The plots are for, from left to right, the velocity-dispersion-metallicity plane, the age-metallicity plane, and the velocity-dispersion-abundance-ratio plane. Points are as in Figure 16.4. Stellar-population parameters were inferred from models of Worthey (1994) altered as described in Trager et al. (2006). Lines in the left and middle panels are projections of the Z-plane (Trager et al. 2000b). In the left panel, the lines correspond to ages of 5, 10 and 15 Gyr from top to bottom; in the middle panel, the lines correspond to a = 50, 150, 250 and 350 km s-1. The line in the right panel is the [E/Fe]-a relation of Trager et al. (2000b).

Figure 16.5. The variation of stellar-population parameters with age and velocity dispersion (a). The plots are for, from left to right, the velocity-dispersion-metallicity plane, the age-metallicity plane, and the velocity-dispersion-abundance-ratio plane. Points are as in Figure 16.4. Stellar-population parameters were inferred from models of Worthey (1994) altered as described in Trager et al. (2006). Lines in the left and middle panels are projections of the Z-plane (Trager et al. 2000b). In the left panel, the lines correspond to ages of 5, 10 and 15 Gyr from top to bottom; in the middle panel, the lines correspond to a = 50, 150, 250 and 350 km s-1. The line in the right panel is the [E/Fe]-a relation of Trager et al. (2000b).

M32, we can study what effect the MDF has on the inferred SSP-equivalent metal-licity. The light-weighted mean metallicity from the MDF is [Fe/H] = -0.25, as can be inferred from Figure 16.3 (left). Using absorption-line measurement extrapolated (slightly) to precisely the same position in the galaxy, [Fe/H]SSP = -0.32 (Trager et al. 2000b). This excellent agreement between the metallicities inferred from the integrated light and the CMD is possible only in the absence of a metal-poor tail in the MDF, since hot stars corrupt the abundances inferred from line strengths (Trager et al. 2005). More extensive analyses using synthetic star-formation histories and chemical-evolution models show that the inferred SSP-equivalent metallicities and [a/Fe] ratios are very close to their light-weighted or even mass-weighted mean values (Serra & Trager 2007; Trager & Somerville, in preparation). This is certainly not the case for the SSP-equivalent ages, which can easily be skewed towards young ages by the presence of very small amounts of young stars.

Using long-slit spectra of M32 and sophisticated stellar-population models that include in a limited way the variation of individual elements as a function of Fe abundance, Worthey (2004) finds [Fe/H] = +0.02, [C/Fe] = +0.08, [N/Fe] = -0.13 and [Mg/Fe] = -0.18 near the nucleus. This confirms the generally held notion that M32 has an abundance pattern very much like that of the Sun (O'Connell 1980; Grillmair et al. 1996; Trager et al. 2000a). The inferred nitrogen abundance appears to be too low compared with the nitrogen abundances of the PNe (Stasinska et al. 1998), but this could be due to self-enrichment of nitrogen in the PNe.

With this caveat in mind, the variations of stellar-population parameters with velocity dispersion (as a tracer of the mass) can be examined. The left panel of Figure 16.5 shows the mass-metallicity relation for field galaxies. That a narrower mass-metallicity relation is not apparent in this plot is due to the real anticorrela-tion between SSP-equivalent age and metallicity of galaxies in this sample (middle panel): older field galaxies have lower metallicities at fixed velocity dispersion. The dispersion in ages causes a broadening of the mass-metallicity relation. A narrow mass-metallicity relation is, however, seen clearly in cluster samples (e.g. Nelan et al. 2005; Trager et al. 2008), because these samples have small age spreads. At the same time, there is a clear mass-[a/Fe] relation in all environments, which is only weakly dependent on (Thomas et al. 2005; Nelan et al. 2005) or independent of (Trager et al. 2000b) SSP-equivalent age. The physical mechanisms driving these relations are likely to be a combination of rapid star formation, so that SNe II products dominate over SNe Ia products, and metal-enriched outflows, in which high-mass galaxies retain their SNe II products - which dominate the overall metallicity of the systems - more easily than low-mass galaxies do (Trager et al. 2000b); see also Chapters 28 and 44 in this volume.

3.3 Continuing annoyances

Nothing is easy, of course. Besides the effects of composite populations on the inferred stellar-population parameters and the fact that MDFs cannot (currently) be determined from the integrated light, two major annoyances persist when trying to infer abundances from absorption-line measurements. The first is the unknown oxygen abundances of early-type galaxies. The oxygen abundance controls the temperature of the MSTO (Salaris & Weiss 1998), and so the inferred age - and therefore metallicity - is dependent on the oxygen abundance. It is not yet clear whether a good tracer of oxygen abundance is available in the optical (but see below). The second is the hot-star content of these galaxies. Trager etal. (2005) have shown that these stars, such as BHB and blue straggler stars, not only corrupt age measurements for the oldest objects (e.g. Maraston & Thomas 2000) but also corrupt abundance measurements. Correcting for this effect requires excellent models and data with sensitivity in the blue, but this has been done for very few galaxies.

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