Next: Bibliography Up: Population Synthesis in the Previous: Conclusions

Tables

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**Figure 1:** a. Comparison of the line indices measured in our spectra for Lick/IDS standards with the values tabulated by Worthey et al. (1994) and Worthey & Ottaviani (1997). For all indices only minor zero-point corrections are needed to convert our data to the Lick/IDS system. Crosses mark stars removed from the zero-point estimate (see text for details).
$\begin{figure}\plotone{f1a.eps}\end{figure}$

**Figure 1:** b.
$\begin{figure}\plotone{f1b.eps}\end{figure}$

**Figure 2:** a. Comparison of the line indices measured in the Jones (1999) spectra for Lick standards with those obtained in Paper III (see text). Compare the scatter of the residuals with that seen in Figure 1. The much lower scatter seen here provides an assessment of the much better quality of the index measurements upon which our models are based.
$\begin{figure}\plotone{f2a.eps}\end{figure}$

**Figure 2:** b.
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**Figure 3:** Comparison of our stellar parameters with those determined by Jones & Worthey (1995) for dwarf stars. The systematic shift in [Fe/H] is due to a revision of the Schuster & Nissen (1989) metallicity scale by Clementini et al. (1999).
$\begin{figure}\plotone{f3.eps} \end{figure}$

**Figure 4:** Same as Figure 3, for giant stars. The systematic effects on [Fe/H] is due to updated stellar parameters by Soubiran et al. (1998)
$\begin{figure}\plotone{f4.eps} \end{figure}$

**Figure 5:** Abundance pattern of the input stellar library. Dwarfs and giants are marked by small dots and open squares, respectively. Nitrogen and carbon abundances are affected by stellar evolution, therefore they differ between dwarfs and giants. Overall, dwarf abundances are more homogeneous and present less scatter than values for giants, so we decide to discard the latter.

**Figure 6:** a. *Upper panels*: fitting functions over-plotted on $H\delta _A$ measurements for dwarfs and giants, as indicated on top of each panel. The data are color-coded according to metallicity. Red dots correspond to [Fe/H] $\geq$ -0.1, green dots correspond to -0.6 $\leq$ [Fe/H] -0.1, and blue dots correspond to [Fe/H] -0.6. The red curves correspond to fitting functions computed for [Fe/H] = +0.1, the green to [Fe/H] = -0.35, and the blue to [Fe/H]=-1.0. A $T_{\rm eff}$ vs $\log g$ relation from Girardi et al. (2000)'s 5 Gyr old isochrone for solar metallicity is assumed. Black dots and lines are adopted for stars in regions of parameter space where the fits are [Fe/H]-independent. *Bottom panels*: Residuals of the fits. $\theta_{\rm eff}$ = 5040/ $T_{\rm eff}$ . In all plots crosses indicate stars that were rejected by the fitting routine.

**Figure 6:** b.

**Figure 6:** c.

**Figure 6:** d.

**Figure 6:** e.
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**Figure 6:** f.
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**Figure 6:** g.
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**Figure 6:** h.
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**Figure 6:** i.
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**Figure 6:** j.
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**Figure 6:** k.
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**Figure 6:** l.
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**Figure 6:** m.
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**Figure 6:** n.
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**Figure 6:** o.
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**Figure 6:** p.
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**Figure 7:** a. Comparison of model predictions based on our fitting functions (solid lines) and on those of Worthey et al. (1994, dashed lines), computed with the same set of isochrones. Metallicities are [Fe/H] = -1.3, -0.7, -0.4, 0.0, and +0.2. The arrows indicate the direction of increasing [Fe/H]. For the lowest metallicities, the Worthey et al. (1994) fitting functions are not defined for ages lower than 5 Gyr, but we decided to keep the comparisons for completeness.
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**Figure 7:** b.
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**Figure 7:** c.
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**Figure 7:** d.
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**Figure 8:** *Top panel*: $H\beta$ against $T_{\rm eff}$ for giant stars in the Worthey et al. (1994) database. *Bottom panel:* Same for our data. *Open squares*: stars with [Fe/H] -0.3. *Filled squares*: stars with [Fe/H] 0. The improvement on both index measurements and stellar parameters allows us to estimate the dependence of the index on [Fe/H] more accurately.
$\begin{figure}\plotone{f8.eps}\end{figure}$

**Figure 9:** $T_{\rm eff}$ against Fe5270 for K-F dwarfs. Our data are shown as filled squares, and Worthey et al. data as open squares. Our fitting function is shown as a thick line and that of Worthey et al. as a thin line. Only stars with [Fe/H] = -0.4 $\pm$ 0.15 are displayed and the fitting functions were computed for [Fe/H] = -0.4.
$\begin{figure}\plotone{f9.eps}\end{figure}$

**Figure 10:** An Mg-magnitude diagram for stars from M 67. The thin line shows computations adopting the Girardi et al. (2000) isochrone for 3.5 Gyr and solar metallicity and the Worthey et al. fitting functions. The thick lines were obtained using our fitting functions.
$\begin{figure}\plotone{f10.eps}\end{figure}$

**Figure 11:** Comparison between the behavior of Mg (lower panel) and Mg as a function of $T_{\rm eff}$ and $\log g$ . In both panels, measurements taken in the spectra of the library stars are plotted as a function of $T_{\rm eff}$ for dwarf and giant stars, as indicated in the upper panel. For K stars (4000 $\mathrel {\copy \simlessbox }$ $T_{\rm eff}$ $\mathrel {\copy \simlessbox }$ 5500 K), the behavior of the two indices as a function of both stellar parameters is essentially the same. Both indices are strongly sensitive to temperature and tend to be stronger in dwarf stars. For cooler, M stars, Mg tends to be much stronger in giants, unlike Mg, which is less dependent on surface gravity. This is due to the effect of TiO bands on Mg . See text for details.
$\begin{figure}\plotone{f11.eps}\end{figure}$

**Figure 12:** Effect of adopting $\alpha$ -enhanced isochrone (dark lines), as opposed to solar-scaled ones (gray lines) on predictions for and Balmer lines for single stellar populations. The ages shown are, from top to bottom, 1.2, 1.5, 2.5, 3.5, 7.9, and 14.1 Gyr. The values for [Fe/H] are -0.8 (-0.7 for solid lines), -0.4, and 0.0. The $\alpha$ enhanced isochrones yield weaker Balmer lines and slightly weaker for the same age and metallicity. Note that the effect is stronger on $H\beta$ than on $H\delta _F$ .
$\begin{figure}\plotone{f12.eps}\end{figure}$

**Figure 13:** Comparison between solar-scaled (gray) and base models (dark) on a few representative index-index plots. *Upper Left:* Both $H\beta$ and Fe5270 are essentially insensitive to abundance ratio variations. *Upper Right:* G4300 is stronger in solar-scaled than in the base models for [Fe/H] $\leq$ -0.4, because the latter have higher oxygen abundances (see text). *Lower Left:* $H\delta _F$ is weaker in solar-scaled than in the base models for [Fe/H] $\mathrel {\copy \simlessbox }$ -0.4, because at these metallicities the base models have higher magnesium and calcium abundances, indicating that there are lines due to these two elements in the $H\delta _F$ index passband. *Lower Right:* The Ca4227 index is much weaker in solar-scaled than in the base models for [Fe/H] $\mathrel {\copy \simlessbox }$ -0.4, having similar strength for [Fe/H]=0 and +0.2. This reflects the fact that the base models have higher calcium abundance than solar-scaled models for metallicities below solar (see Table 6).
$\begin{figure}\plotone{f13.eps}\end{figure}$

**Figure 14:** Comparison between solar-scaled (gray) and carbon-enhanced (dark) models. *Upper Left:* This panel shows that $H\beta$ and Fe5270 are virtually insensitive to carbon abundance variations. *Upper Right:* As expected, C4668 is strongly sensitive to carbon abundance variations. It is the best carbon-abundance indicator modeled in this paper. *Lower Left:* $H\delta _F$ is very mildly sensitive to carbon abundance variations, in spite of its being surrounded by CN lines (see text). *Lower Right:* The Ca4227 index is very sensitive to carbon, being stronger in lower carbon-abundance models. This is due to the presence of a CN band-head on the index blue pseudo-continuum, as pointed out by Prochaska et al. (2005, see discussion in the text).
$\begin{figure}\plotone{f14.eps}\end{figure}$

**Figure 15:** Figure 14 continued. *Upper Left:* This panel shows that the Fe5335 index is also essentially insensitive to carbon abundance variations. *Upper Right:* As expected, CN is very sensitive to carbon, being substantially stronger for higher carbon abundances. This index is also sensitive to nitrogen, but not as strongly as to carbon. *Lower Left:* This plot shows how $H\gamma _F$ is affected by carbon abundance variations. It gets weaker for higher carbon, due to contamination of the index pseudo-continuum by CH lines. *Lower Right:* The Fe4383 index is almost insensitive to carbon. The index becomes only slightly stronger for higher carbon abundances. This effect is also due to the presence of CH lines in the index passband.
$\begin{figure}\plotone{f15.eps}\end{figure}$

**Figure 16:** Comparison between solar-scaled and $\alpha$ -enhanced models. *Upper Left:* This panel shows that $H\beta$ is insensitive to spectroscopic $\alpha$ -enhancement, while Fe5270 is only very mildly sensitive, and only at very low [Fe/H]. *Upper Right:* As expected, the Mg index is very sensitive to variations of [Mg/Fe]. It is the chief magnesium abundance indicator in our models. *Lower Left:* The $H\delta _F$ index is sensitive to $\alpha$ -enhancement, being slightly stronger for higher $\alpha$ -element abundances. This is due to contamination by magnesium and silicon lines in the index passband. *Lower Right:* The Ca4227 index is extremely sensitive to [Ca/Fe]. It is the only calcium abundance indicator in our models.
$\begin{figure}\plotone{f16.eps}\end{figure}$

**Figure 17:** Figure 16 continued. *Upper Left:* The Fe5335 index is shown to be only very mildly sensitive to $\alpha$ -enhancement, only for high [Fe/H]. *Upper Right:* As expected, Mg is very sensitive to [Mg/Fe], but not as strongly as Mg . *Lower Left:* The $H\gamma _F$ index shows some sensitivity to $\alpha$ -enhancement, mostly because of the decreased strength of CN lines, due to enhanced oxygen abundances. *Lower Right:* The Fe4383 index is mildly sensitive to $\alpha$ -enhancement, being weaker for higher $\alpha$ -element abundance, mostly due to the presence of magnesium and calcium lines in the index pseudo-continua.
$\begin{figure}\plotone{f17.eps}\end{figure}$

**Figure 18:** Data on M 67 (star) and NGC 6528 (filled square) compared to solar-scaled model predictions. Same-age models are connected by dotted lines, except for the 3.5 Gyr models, which are connected by dashed lines, for clarity. Same-[Fe/H] lines are solid. The ages of the models displayed are, from top to bottom, 1.2 (barely visible), 1.5, 2.5, 3.5, 7.9, and 14.1 Gyr. The values for [Fe/H] are, from left to right, -0.7, -0.4, 0.0, and +0.2. The best-fitting model for M 67 has an age of $\sim$ 3.8 Gyr and [Fe/H]=-0.08. Note the consistency with which all indices are matched by the models at essentially the same position on the grid.
$\begin{figure}\plotone{f18.eps} \end{figure}$

**Figure 19:** Figure 18 continued. Model age and [Fe/H] are the same as in Figure 18. Note the outstanding consistency with which all the indices from M 67 are matched by the models (i.e., same age and [Fe/H] everywhere). Due to a spectral blemish in the Schiavon et al. (2005) data, the Fe5015 is not available for NGC 6528.
$\begin{figure}\plotone{f19.eps}\end{figure}$

**Figure 20:** Figure 18 continued, now showing comparisons between models and data for indicators of carbon, nitrogen, and magnesium abundances. Again, data for M 67 are matched consistently for the same age and [Fe/H] as for indices in the previous figures.
$\begin{figure}\plotone{f20.eps}\end{figure}$

**Figure 21:** Figure 18 continued, now showing comparisons between models and data for indices sensitive to iron, calcium and carbon. The G4300 index is the one for which the models are the poorest match to the data (almost 0.2 dex too metal-rich, according to the models).
$\begin{figure}\plotone{f21.eps}\end{figure}$

**Figure 22:** a. Data for M 5 (left) and 47 Tuc. The arrow indicates how the predictions for M 5 change when the contribution due to blue HB stars is ``removed'' from the cluster data. Ages are 1.2, 1.5, 2.5, 3.5, 7.9, and 14.1 Gyr, and metallicities are [Fe/H]=-1.3, -0.7, -0.4, 0.0, and +0.2. The models for 3.5 Gyr are connected by a dashed line, to guide the eye. The models for [Fe/H]=-1.3 are not shown in Figure 22e. See detailed discussion in the text.
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**Figure 22:** b.
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**Figure 22:** c.
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**Figure 22:** d.
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**Figure 22:** e.
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**Figure 22:** f.
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**Figure 23:** Effects of mass function on the predictions for the Mg indices. *Upper panels*: a dwarf-depleted IMF is adopted, consistent with the clusters' heavy mass-segregation. *Lower panels*: Same as the top panels of Figure 22d, where a Salpeter IMF is adopted in the computations. Note the improved agreement between model and data for Mg in the upper panels.
$\begin{figure}\plotone{f23.eps}\par \end{figure}$

**Figure 24:** Comparison, between data for 47 Tuc and models in iron vs. CN-sensitive data plots. Models shown are all for an age of 14.1 Gyr. Gray lines: base models from Table 24. Dark lines: models computed for the abundance pattern of 47 Tuc. Dotted lines connect same-[Fe/H] models (from left to right, [Fe/H]=-1.3, -0.7, -0.4, 0.0, +0.2). The models with [Fe/H]=-0.7 and the cluster abundance pattern reproduce very well all indices except for G4300. See text.
$\begin{figure}\plotone{f24.eps}\end{figure}$

**Figure 25:** Comparison of data for NGC 6528 with model predictions assuming the input parameters listed in Table 27. Note the consistency with which models match all indices for the same age and [Fe/H]. Ages plotted are 1.5, 2.5, 3.5 (dashed), 7.9, and 14.1 Gyr, and metallicities are [Fe/H] = -0.7, -0.4, 0.0, and +0.2.
$\begin{figure}\plotone{f25.eps}\end{figure}$

**Figure 26:** Figure 25 continued. Here the models are compared to data for indices sensitive to the abundances of calcium, carbon, nitrogen, and magnesium. Note that the best matching models have the same age and [Fe/H] as those in Figure 25 (except for G4300, which is matched for a slightly too young age--see text).
$\begin{figure}\plotone{f26.eps}\end{figure}$

**Figure 27:** Comparison of our models to data by Trager et al. (2000). *Bottom panels:* solar-scaled models; *Upper panels:* models with [Mg/Fe]=+0.3. The labels on the left (right) panels show [Fe/H] ([Mg/H]). The bulk (3/4) of the sample galaxies have mean ages between 7 and 14 Gyr (lower left panel). Solar-scaled models cannot match and Mg for the same age and metallicity (lower panels). The upper panels show that Mg-enhanced models are a much better match to the data, as they match both and Mg for the same age and [Fe/H] (roughly solar).
$\begin{figure}\plotone{f27.eps}\end{figure}$

**Figure 28:** Trager et al. data compared with our models in -Mg diagrams. *Left Panel:* All galaxies are compared with solar-scaled (gray) and Mg-enhanced models. Galaxies with mean stellar ages younger than $\sim$ 7 Gyr ( $H\beta > 2 {\rm \AA}$ ) are plotted with open symbols. Older galaxies (solid squares) tend to have higher [Mg/Fe] than their younger counterparts. *Right panel:* Same plot, comparing only galaxies with ages lower than $\sim$ 7 Gyr with models for younger single stellar populations with solar-scaled (gray) and Mg-enhanced abundance patterns. Galaxies with younger mean stellar ages in the Trager et al. sample tend to have lower [Mg/Fe].
$\begin{figure}\plotone{f28.eps}\end{figure}$

**Figure 29:** Comparison of Lick indices measured in SDSS stacked spectra (``All'' from Eisenstein et al. 2003) and our predictions for single stellar populations. Galaxy absolute luminosity increases from left to right (see values in Table 28). Errorbars are always smaller than symbol size. *Upper left:* The SDSS sample under study has a mean age of $\sim$ 8 Gyr (regardless of luminosity) and [Fe/H] just below solar (slightly dependent on luminosity) *Upper right:* In this and the remaining panels, galaxies are compared with solar-scaled (gray lines) and enhanced models (enhanced elements indicated in the labels). SDSS galaxies are Mg-enhanced, with more luminous galaxies being slightly more enhanced. *Lower left:* Galaxies are C-enhanced, with more luminous galaxies being more enhanced. *Lower right:* Three model predictions are shown: solar scaled (gray), C-enhanced (thin), and C,N-enhanced (thick). C-enhancement alone is not enough to match CN data, which require N-enhancement as well. More luminous galaxies are clearly more enhanced here.
$\begin{figure}\plotone{f29.eps} \end{figure}$

**Figure 30:** Mean luminosity-weighted metal abundances and ages of the stellar populations in the SDSS galaxies from the Eisenstein et al. (2003) ``All'' sample, as a function of absolute magnitude in the SDSS band. Note that $M^\star _r \approx -20.8$ at the involved redshifts. All panels have a vertical scale of 0.5 dex. Iron abundances are slightly below solar for all luminosities, and abundance ratios are above solar for all elements in almost all luminosity bins. All abundances and all abundance ratios appear to be correlated with luminosity at different levels. Nitrogen is the most strongly enhanced element and also the one whose enhancement appears to be the most strongly correlated with galaxy luminosity. We find no correlation between mean age and luminosity (but see Figure 31).
$\begin{figure}\plotone{f30.eps}\end{figure}$

**Figure 31:** Mean ages of SDSS galaxies in the Eisenstein et al. (2003) sample, estimated from models including the abundance ratios from Figure 30 and Table 6.2.2. *Upper panel:* Ages according to $H\beta$ and $H\delta _F$ . As expected from Figure 29, mean ages according to $H\beta$ are $\sim$ 8 Gyr, regardless of luminosity. On the other hand, ages according to $H\delta _F$ are substantially (2-4 Gyr) younger, with ages according to $H\gamma _F$ (not shown) lying somewhere inbetween. *Lower panel:* Differences between $H\delta _F$ -based and $H\beta$ -based ages, as a function of luminosity. The mismatch between $H\beta$ and $H\delta _F$ -based ages is very luminosity dependent, being larger for lower luminosity galaxies.
$\begin{figure}\plotone{f31.eps} \end{figure}$

**Figure 32:** Data for the lowest luminosity bin ( = -20.8) compared with single stellar population models in Balmer-metal line planes. Model ages are the same as upper left panel of Figure 29. To help guiding the eye, the 3.5 Gyr models are connected by dashed lines. The models were computed for the best-matching abundance pattern (Table 6.2.2), as can be seen by the good match to C4668 (see Section 6.2.4 and Figure 30). Therefore, abundance-ratio effects on $H\gamma _F$ and $H\delta _F$ are accounted for. The bluer the Balmer line, the younger the mean age that is estimated. The effect is independent of the metal index adopted.
$\begin{figure}\plotone{f32.eps}\end{figure}$

**Figure 33:** Comparison between data for the lowest luminosity bin and a family of composite two-population models, consisting of an old single stellar population with an age of 11.2 Gyr and [Fe/H]=-0.2 combined with a young population with age 0.8 Gyr and solar metallicity. The contribution of the young population to the total mass budget is varied in steps of 0.5%, indicated by the gray open symbols. The largest the contribution of the young population to the mass budget, the stronger (weaker) the Balmer (metal) index for the composite population. A best match is obtained when the mass allocated in the young population is somewhere between $\sim$ 0.5 and 1% of the total mass. A similarly good match is obtained when the young component is $\sim$ 1 Gyr old, but in that case the mass fraction is an order of magnitude higher. See discussion in text.
$\begin{figure}\plotone{f33.eps}\end{figure}$

**Figure 34:** Comparison between data for the lowest luminosity bin and a family of composite two-population models, consisting of an old single stellar population with an age of 11.2 Gyr and [Fe/H]=-0.2 combined with blue stragglers from the metal-rich Galactic globular cluster NGC 6553. The specific frequency of blue stragglers is varied in steps of 100 stars per 10 $L_\odot$ . Adding blue stragglers to an old population, one can match the data reasonably well, but only for extremely high blue-straggler specific frequencies. See details in text.
$\begin{figure}\plotone{f34.eps}\end{figure}$

**Figure 35:** Comparison between data for the lowest luminosity bin and a family of composite two-population models, consisting of an old single stellar population with an age of 11.2 Gyr and [Fe/H]=-0.2 combined with an old metal-poor population, represented by data from a Galactic globular cluster (M 5/NGC 5904). The contribution of the metal-poor population to the total mass budget is varied in steps of 5%, indicated by the gray open symbols. The match to the data is very poor, as these models cannot reproduce the strengths of all Balmer lines.
$\begin{figure}\plotone{f35.eps}\end{figure}$

Next: Bibliography Up: Population Synthesis in the Previous: Conclusions

Ricardo Piorno Schiavon 2006-11-15