Mean Ages and the History of Star Formation of Early-type Galaxies

We start by looking at the mean ages estimated from the different Balmer lines. According to Figures 29 and 30, early-type galaxies have luminosity-weighted mean ages of 8 Gyr, and no correlation is found between mean age and luminosity. The method described in Section 4.4 uses $H\beta$ as the only age indicator, due to its outstanding insensitivity to spectroscopic abundance ratio effects (Section 4.3.2). It is reasonable to expect, however, that other line indices should yield consistent ages when data are compared with models computed for the right abundance pattern. The latter is an important precaution, as the $H\delta$ and $H\gamma$ indices studied here are susceptible to spectroscopic abundance ratio effects, so that these indices can only be used for age estimates using models computed for the abundance pattern estimated above (Figure 30). In Figure 31, where ages estimated from $H\beta$ and $H\delta _F$ are plotted against $<M_r>$. Ages according to $H\delta _F$ are consistently lower, with the difference ranging between 2 (25%) and 4 Gyr (50%). The differences are several times larger than the internal error bars (which are very small, thanks to the exceedingly high S/N of the stacked spectra).

It is interesting to verify how this effect manifests itself in index-index plots where Balmer and metal line indices are compared with models. Unfortunately, we cannot compare models and data for the different luminosity bins all in the same set of plots, as $H\delta$ and $H\gamma$ indices are strongly sensitive to abundance-ratio effects requiring different sets of single-stellar population models to be computed for each luminosity bin, so that plotting various sets of models in the same graph would make things look rather confusing. Therefore, we henceforth focus on the lowest luminosity bin, for which the age differences are the highest. In Figure 32, data for the bin are compared to best-fitting models in $<Fe>$-Balmer and C$_2$4668 planes. From this figure, we learn that the age according to $H\delta _F$ is $\sim$ 4 Gyr (the data are just below the 3.5 Gyr dashed line), while that according to $H\beta$ is twice as old. The age according to $H\gamma _F$ lies somewhere in-between those values. In order for the $H\delta _F$-based age to agree with that based on $H\beta$, $H\delta _F$ would have to be $\sim$ 0.45 ${\rm\AA}$ weaker than the measured value which is entirely ruled out by the very small error bars of the measurements (Table 28). We note that the models are a very good match to the C$_2$4668 and CN (not shown) indices, so that in principle abundance-ratio effects on $H\delta _F$, which are mostly due to carbon and nitrogen abundances, are accounted for. While the focus of this discussion is on $H\delta _F$, we emphasize that this trend is quite general, in that bluer Balmer lines tend to indicate younger ages.

No such inconsistency was found when models were confronted with cluster data (Section 5), especially in the case of M 67, whose age and metallicity are comparable with those of SDSS early-type galaxies. Therefore, model inconsistencies cannot be blamed for the age differences apparent in Figures 30 through 32. We must seek other explanations. It is conceivable that the corrections for emission line in-fill are introducing a systematic effect in our Balmer line indices, since the relative corrections depend on assumptions on the size of the Balmer decrement and on the absence of reddening. However, it is very hard to attribute this discrepancy to errors in the Balmer in-fill corrections, for the following reason. The corrections for $H\beta$ and $H\delta _F$ were respectively $\sim$ 0.3 and 0.1 ${\rm\AA}$. Supposing we have overestimated the correction, the discrepancy between the two ages would be enhanced. In the extreme case, of no correction at all, the age according to $H\beta$ would be $\sim$ 14 Gyr and that according to $H\delta _F$ would be about 5 Gyr, which would increase the age discrepancy from a factor of two to a factor of three. Admitting that our in-fill corrections were instead underestimated, we can compute the size of the correction needed to bring the $H\beta$ and $H\delta _F$-based ages into agreement. The result is that the correction to $H\beta$ would have to be $\sim$ 0.7 ${\rm\AA}$, or more than twice the correction adopted. That is clearly ruled out by the small errors in the [OII] equivalent widths, and continuum measurements, as well as reasonable assumptions for the uncertainties in the Balmer decrement. Moreover, it would drive all the ages to much lower values, below 3.5 Gyr for ages according to $H\beta$, which would be in stark disagreement with all previous work on stellar age estimates in early-type galaxies. Therefore we conclude that systematic errors in our emission line in-fill corrections cannot account for the age discrepancies found.

In the absence of systematic effects introduced by our in-fill corrections, another very likely possibility is that stellar populations that are unaccounted by the models may be affecting the line indices differentially. It is conceivable that the trend seen in Figure 32 may be caused by the contribution of warm stars (spectral types A to early-F), which are characterized by strong Balmer lines. The contribution by these stars to the integrated light peaks in the far blue, and falls steeply longward, so that they tend to affect more strongly higher order Balmer lines, located further into the blue. A similar effect was found by Schiavon et al. (2004b) in data for Galactic globular clusters. In that case, the warm star component was identified with blue HB stars, but young/intermediate-age stars are likely to have the same effect on the integrated light of galaxies. Abundance ratios that are not accounted for in our models could in principle also generate this type of systematic effect. In what follows we consider four possible explanations for this trend of mean ages with Balmer line: 1) Contamination of the integrated light by a small fraction, by mass, of a young/intermediate-age stellar population; 2) Contamination by blue stragglers; 3) Metal-poor stellar populations with a blue horizontal branch; and 4) Abundance-ratio effects. In what follows we examine briefly each one of these scenarios.

Young/Intermediate-age Stars: In order to test this possibility, we extended our model calculations to ages as low as 0.1 Gyr, for [Fe/H]=0 and +0.2. These computations should be taken with caution, because the fitting functions underlying our models did not take into account the effect of metallicity for stars hotter than $\sim$ 7500 K. The latter effect, however, is likely to be small, so we can adopt these calculations at least for a first examination of our working hypothesis. We generate families of two-component models, whose input parameters are the age and metallicity of the old component, the age of the young component and the fractional contribution of the latter to the total mass. The abundance pattern assumed for the old component is that listed in Table 29, and both the metallicity and abundance pattern of the young component are assumed to be solar. The input ages considered for the old component varied between 10 and 14 Gyr and [Fe/H] varied between -0.4 and 0. The age of the young component was varied between 0.1 and 1.2 Gyr. The fractional contribution of the young component to the total mass of the system was varied between 0 and 20%. A $\chi$-square minimization procedure was adopted to find the model that best matches the data for the Balmer and Fe indices. For simplicity, indices which are prime indicators of other abundances than iron were not included in the minimization, in order to avoid having to include the abundance ratios of the young component as another parameter in the two-component models. In Figure 33 the gray lines show the predictions of the family of two-component models, containing the best fitting model. The gray open circles indicate increments of the mass fraction allocated to the young component in steps of 0.5%. One can see that, as that fraction increases, Balmer lines get stronger and metal lines get weaker, due to the increasing contribution to the integrated light by hot stars. It is also apparent that the bluer indices are more strongly affected. For instance, when the young stars make up 2% of the total mass (fourth open circle from the bottom up) $H\delta _F$ indicates a single stellar population age lower than 3.5 Gyr, while the $H\beta$-based age would be $\sim$ 5 Gyr. The old component of the best fitting model has an age of 11.2 Gyr and [Fe/H]=-0.15, whereas the young component is 0.8 Gyr-old, contributing $\sim$ 0.5-1% of the total mass of the system. We note that this result is somewhat degenerate, as other families of models provide an equally good fit. If one increases the age of the young component, a good match can still be found to the data if its contribution to the total mass budget is increased by an adequate factor. This degeneracy is well known from studies of post-starbust galaxies and it can be broken by introducing age indicators further to the blue (Leonardi & Rose 1996). Most importantly, we note that the two-component model is a better match to the data than single stellar population models. It is also a better match to the data than the alternative models considered below. We note that a similar result was obtained by Sánchez-Blázquez et al. (2006a), who estimated younger ages from r.m.s. fitting of the blue part of their galaxy data. They interpreted their result as being due to a spread of stellar population ages in their sample galaxies. Interestingly, we find that the age discrepancy is larger for lower luminosity galaxies. If our interpretation is correct, this result tells us that star formation was more extended in lower mass galaxies, which is in agreement with findings by other authors (e.g., Caldwell et al. 2003, Bernardi et al. 2005, Gallazzi et al. 2006) and seems to lend support to the downsizing scenario (Cowie et al. 1996).

Blue Stragglers: Another family of warm stars which can potentially enhance Balmer lines in integrated spectra of galaxies are the blue stragglers. In paper III we showed that blue stragglers have a strong impact on the integrated spectrum of M 67, by markedly increasing the Balmer lines strengths in the cluster spectrum, which indicates substantially younger ages ($\sim$ 1.5 Gyr) than the known 3.5 Gyr age of the cluster. We also found that, as in the case of the galaxy spectra discussed here, the age of the cluster seems younger according to bluer Balmer lines. In order to test the blue straggler hypothesis, we perform the following test. We extracted colors and magnitudes of blue stragglers from the VI color-magnitude diagram of the metal-rich globular cluster NGC 6553 by Zoccali et al. (2001). Blue stragglers are known to be very abundant in this cluster (e.g., Beaulieu et al. 2001). We choose to use the Zoccali et al. data because these authors used observations at different epochs in order to measure the proper motion of the cluster, so that we can minimize foreground contamination of our blue straggler selection. Stars were considered as blue stragglers in NGC 6553 if they met the following criteria: $V > 19.4$, , and relative proper motion smaller than 0.1 arcsec (see Zoccali et al. for details). The resulting blue straggler sample consisted of 50 stars, whose colors and magnitudes were de-reddened and converted into absolute magnitudes adopting E(V-I) = 0.90 (Barbuy et al. 1998) and (m-M)$_0$=13.64 (Zoccali et al. 2001). The latter were used to compute effective temperatures and surface gravities using the Lejeune et al. (1998) calibrations and assuming [Fe/H]=-0.2 (Cohen et al. 1999, Barbuy et al. 2004) and 1$M_\odot$. The latter stellar parameters were used to generate line indices using the fitting functions presented in Section 3 for each blue-straggler star. The latter were integrated using the stars' absolute magnitudes and colors in order to generate integrated indices of the blue straggler stars. The blue straggler indices were then used to generate a family of two-component models, by ``contaminating'' a reference old stellar population model with blue straggler light, assuming a range of blue straggler specific frequencies. The best match to the data was obtained when the old component was assumed to be 12.5 Gyr old, with [Fe/H]=-0.1. These models are compared with the observations in Figure 34, where the blue straggler specific frequency was varied from 0 to 1000 blue stragglers per 10$^4$ $L_\odot$. The gray open symbols indicate steps of 100/10$^4$ $L_\odot$. Figure 34 shows that adding blue stragglers to an old stellar population can also account for the trends observed in the data. However, the specific frequency needed to match the data is very high, ranging between 100 and 200 blue stragglers per 10$^4$ $L_\odot$. As noted by Trager et al. (2000), typical specific frequencies found in Galactic globular clusters, whose characteristic core densities are much higher than those of early-type galaxies, range from a few to a few tens of stars per 10$^4$$L_\odot$ (Ferraro, Fusi Pecci & Belazzini 1995). The case of M 67 is also definitely very extreme. In Paper III we saw that the spectrum of M 67 that includes blue stragglers has much stronger Balmer lines than the BS-free spectrum. But that spectrum includes star # 6481 (ID from Montgomery et al. 1993), with $T_{\rm eff} \mathrel{\copy\simgreatbox}12,000K$ (Landsman et al. 1998) and several stars hotter than $\sim$ 8500 K. Such high temperatures are not expected to be found among lower mass blue stragglers characteristic of old, metal-rich, stellar populations. Moreover, M 67 has a specific blue straggler frequency that far exceeds that of other open clusters with the same central density (Landsman et al. 1998, Ahumada & Lapasset 1995), which is possibly the result of severe mass-segregation followed by evaporation of low mass stars (Hurley et al. 2001). In summary, while we cannot rule out the blue stragglers as the responsible for the apparent younger ages we are getting from higher-order Balmer lines, we deem this a less likely scenario, given the extreme conditions required to satisfy the data.

Old, Metal-Poor Populations: This scenario has been examined recently by Trager et al. (2005), so we will address it very briefly. It has been proposed by Maraston & Thomas (2000) that an old metal-poor stellar population component with a blue horizontal branch can account for the strong Balmer lines observed in integrated spectra of early-type galaxies. Moreover, their signature would be very similar to that found here, where higher order Balmer lines are more strongly affected (Schiavon et al. 2004b). In order to test this scenario, we adopt the line indices measured in the integrated spectrum of M 5, which were discussed in Section 5, and the integrated UBV colors of the cluster, taken from Van den Bergh (1967). The old, metal-poor, single stellar population thus produced is added to the old, metal-rich fiducial adopted in the previous exercises, to produce the two-component models shown in Figure 35. The open symbols indicate increments of 5% of the mass fraction of the metal-poor component, which is varied from 0 to 50%. While this model matches reasonably well the data for $H\beta$, it fails to satisfy the observations for $H\gamma _F$ and in particular those for $H\delta _F$. (see Trager et al. 2005 for a more detailed discussion). Varying the age of the prevalent old metal-rich population allows accommodating the data for one Balmer lines, at the expense of deteriorating the match to the others. We also tried using data for other globular clusters in the Schiavon et al. (2005) spectral library (NGC 2298 and 5986), but the quality of the match did not improve. The reason, we speculate, is that the temperature distribution of the warm stars in these old metal-poor stellar populations is not the one needed to match the data. We conclude that an old metal-poor component can not explain the behavior of Balmer lines in the data.

Abundance Ratios: Our models are a good match to the galaxy data for a number of spectral indices, which poses constraints on the abundances of iron, magnesium, carbon, nitrogen and calcium. Those are the elemental abundances that influence the most strongly the line indices studied in this paper. However, abundances of other elements such as oxygen, titanium, silicon, and sodium are largely unconstrained. Titanium, silicon, and sodium are spectroscopically active in the atmospheres of the stars that dominate the light in the systems under study, and the sensitivities of line indices as a function of these elements (Tripicco & Bell 1995, Korn et al. 2005) can be used as a guide to gauge the possible effects on the Balmer lines studied. These studies tell us that $H\beta$ is largely unaffected by abundance variations of elements other than iron, so we turn to $H\delta _F$. In order to bring the $H\delta _F$-based age into agreement with that based on $H\beta$, $H\delta _F$ would have to be decreased by roughly 0.45 ${\rm\AA}$. Of the three spectroscopically active elements, titanium is the one which affects $H\delta _F$ the most strongly. Inspection of the Korn et al. (2005) tables shows that a +0.3 dex variation in [Ti/Fe] causes $H\delta _F$ to drop by 0.31 ${\rm\AA}$ in the spectrum of a super-metal-rich giant star, 0.09 ${\rm\AA}$ for a turn-off star, and 0.22 ${\rm\AA}$ for a cool main sequence star. Therefore, in order to increase the model predictions to match $H\delta _F$ through a change in [Ti/Fe], the latter would have to be decreased by more than -0.7 dex (if we can trust linear extrapolations of the Korn et al. sensitivities). This sounds extreme. Similar reasoning poses even stronger lower limits on variations of silicon and sodium. Oxygen is more complicated, because it indirectly affects the line strengths via the dissociation equilibrium of CO and its impact on the strengths of more spectroscopically active carbon molecules, like CN and CH. This is accounted for in Korn et al.'s calculations, and consulting their tables we verify that only extreme variations of [O/Fe] can explain the $H\delta _F$ ages. However, oxygen can also play a role through its impact on stellar evolution. We saw in Section 4.3.1 that this effect is stronger on $H\beta$ than on $H\delta _F$ and found a slight, similar age trend on our comparisons with NGC 6528 data in Section 5.3, which we attribute to a slight mismatch between the oxygen abundances of the cluster and that of the isochrones. The trend is such that, in order to match $H\beta$ without affecting $H\delta _F$ substantially, [O/Fe] would have to be increased. Figure 12 shows how $H\beta$ changes when [O/Fe] varies from 0 to +0.5. Such a variation would account for about half of the effect seen in Figure 32, so that in order to account for the $H\delta _F$/$H\beta$ age mismatch [O/Fe] would probably need to be raised to $\sim$ +1.0 (again if linear extrapolations are to be trusted). While [O/Fe]=+1.0 may sound contriving, it cannot be ruled out. However, abundance determinations of stars in our closest proxy to the cores of early-type galaxies, the Galactic bulge field, seem to indicate much lower values for [O/Fe] (Fulbright et al. 2005). Therefore we conclude that, unless there is an important opacity source missing in the Korn et al. (2005) tables, and/or the effect of oxygen abundances on the evolutionary tracks of low-mass stars is quite substantially underestimated in the Padova isochrones, abundance ratio effects are a unlikely explanation for the differences we are finding between the ages determined from different Balmer lines.

In summary, while neither the blue straggler nor the abundance ratio scenarios can be completely ruled out, they seem to require extreme conditions in order to satisfy the observations. We conclude that contamination of the integrated light of the cores of galaxies by small mass fractions of young/intermediate-age stellar populations is the most likely scenario to account for the trends found. If this result is confirmed, the inference is that stellar population synthesis models are now able to constrain not only the mean ages of the stellar populations of galaxies from their integrated light, but also their distribution. This has been possible because the models adopted are extended to a wider baseline than previously considered and also because they match the data for known systems spanning the relevant range of stellar population parameters in an accurate and consistent fashion. This result also implies that the early-type galaxies studied have undergone a prolonged history of star formation, possibly with a small fraction of their stars being formed in the very recent past, as proposed in a number of previous works (e.g., O'Connell 1976, O'Connell 1980, Trager et al. 2000, to name a few). The ideal way of testing this scenario involves extending model and data accuracy towards an even wider baseline, preferably including the far blue and the ultraviolet.