4 Discussion

Figure 4 shows the computed values of the CaT for SSPs. At Z = 2.5 $Z_{\odot}$ (Fig. 4a) both grids predict similar values of EW(CaT). However, at lower metallicities, the empirical calibration (grid II) provides EW(CaT) that are systematically larger than those computed with the theoretical fitting functions (grid I). For ages older than 100 Myr, the average differences between both grids are 1.2, 1.5 and 2 Å for metallicities $Z_{\odot}$, 0.4 $Z_{\odot}$ and 0.2 $Z_{\odot}$ respectively.

JCJ92 suggested that the differences found between their models and DTT89's data could be due to the different abundance scale - we must remind that grid I scales the abundances with [Ca/H] since grid II does with [Fe/H] - In the present models, a solar abundance ratio [Ca/Fe] has been assumed, but this could not be the case. In fact, both observations and chemical evolution models show that for low abundances ([Fe/H] $\leq -1$) the $\alpha$ elements are enhanced with respect to the solar partition. In particular, the behaviour of [Ca/Fe] versus [Fe/H] is shown in Fig. 5c from Mollá & Ferrini (1995) for the galactic bulge: [Ca/Fe] keeps constant ($\simeq$0.5) for a low [Fe/H] abundance and thereafter it decreases towards the solar value.

The observed enhancement of alpha-elements is due to a lower proportion of iron group elements to alpha-elements at low Z when compared with the corresponding ratio at the solar Z value. In other words, stars of low Z (where Z is representative of alpha-elements) have a lower value of Fe/H than stars with higher Z, as clearly demonstrated by the study of globular clusters. In particular stars with subsolar Z have supersolar abundance ratios. To account for this in the comparison between the observational and predicted values of CaT, we should use stars of lower observed Z than the value of Z used in the theoretical isochrones. At lower metallicities, this effect is larger. We also performed several tests aimed to clarify the role of the [$\alpha$ /Fe] on the evolution of the star in the HR diagram and they confirmed that isochrones with the same global metallicity Z but a different enhancement of the $\alpha$ elements are almost indistinguishable in the HR diagram (see also Salaris et al. 1993). In summary, to compare both grids, we should use a non solar partition of the heavy elements for abundances lower than solar. The net effect would be a correction in the values of [Fe/H] adopted in Eq. (7).

The real effect of different [Ca/Fe] ratios has been taken into account by Idiart et al. (1997). These authors, by measuring the CaT index in a sample of stars whose [Ca/H] and [Fe/H] were known, found a weak dependence of CaT index with the [Ca/Fe] ratio.

In the galactic star sample used by DTT89 this effect only appears at low metallicity. Therefore it explains the differences between DTT89 and JCJ92 results found in panels c) and d), because the low abundance stars present in DTT89s sample have been used to compute our grid II. However, the same explanation cannot be invoke in the case of solar abundance, panel b), where the partition must be solar for the neighbourhood stars.

The differences found between the two grids in the oldest populations at Z = 0.008 could be due to the use, in grid II, of the solar M-late relation, Eq. (11), also at Z=0.008, producing values of EW(CaT) that could be overestimated. This does not occur in grid I, in which both $T_{\rm eff}$ and abundance dependence are consistently taken into account in the theoretical calibrations. For these reasons we consider grid I more reliable than grid II although, on the other hand, this last one rest on the extrapolation of the JCJ's relation for the coolest stars, for which unfortunately, we have not found observed values either theoretical models.

The above disagreement between the two grids notwithstanding, we may draw the following general conclusions.

At the higher metallicities the EW(CaT) shows a clear maximum around 10 Myr. This is due to the prominence of the RSG phase at these ages and metal content. At earlier stages massive stars evolve according to the O-BSG-WR sequence, while at lower metallicity the scheme followed is O-BSG-YSG-RSG, with the later phase being only a tiny fraction of the total lifetime.

The dependence on metallicity can be easily quantified. Synthetic values of the index higher than 7 Å are only found in models with metallicity $Z_{\odot}$ or higher, reaching values as high as 11 Å only for 2.5 $Z_{\odot}$ models. The variation with the metallicity is due, on one hand, to the intrinsic dependence of the index and, on the other, to the stellar evolution effect just described (see also Sect. 2.1)

From this maximum value the index decreases as the age increases up to a value of about 100 Myr. In the case of the two metal poor sets the index remains almost constant with time up to this age. Around 100 Myr the appearance of the AGB phase produces a sudden increase of the index which then decreases until 1 Gyr. At this stage the advent of the RGB induces another discontinuity which is more evident at the highest metallicity. As the increasing duration of the RGB phase at increasing age is compensated by a decrease of the evolutionary flux of stars and by a shortening of the AGB phase, the integrated value of the index becomes almost age-independent. In clusters older than a few Gyr the metallicity is the dominant parameter driving the integrated value of EW(CaT).

  

Figure 5: EW(CaT) versus [Fe/H]. Filled symbols are data measured in old galactic globular clusters compiled from the literature (Bica & Alloin 1986b, 1987; Armandroff & Da Costa 1991; Armandroff et al. 1992 and Geisler et al. 1995). Open symbols are our two grids of models as labelled in the plot

It would be desirable to compare these models with the equivalent widths of clusters at different ages and metallicities (SSP) making use of the same isochrones library.

The main body of available data is the one from Bica & Alloin (1986a,b) who presented a data-base of star clusters at different ages and metallicities. For the young metal-poor clusters in the Magellanic Clouds, Bica et al. (1986, 1990) give also the value of the CaT, but the error bars quoted for the age and metallicity are too large to provide a reliable test for our models.

In the case of old SSPs, for which we have shown that the CaT index is mainly a function of abundance, we have collected in Fig. 5 the observed values of the EW(CaT) against [Fe/H] for several globular clusters and we have compared them with the results from our models at an age of 13 Gyr. We must refer our results to [Fe/H] abundance scale. This is the case of grid II. However, since grid I uses [Ca/H], we must account for the enhacement of [$\alpha$-elements/Fe] as we have explained above. Therefore, we have assigned the value of [Fe/H] for every total abundance Z or [Ca/H] value, by using the [Ca/Fe] relation found by Mollá & Ferrini (1995) already quoted. This relation implies a correction of 0.0, -0.2 and -0.4 dex for values of [Ca/H] solar, 0.4 solar and 0.2 solar respectively.

Data in Fig. 5 shows that in old systems a narrow correlation between the CaT index and the metallicity over more than two orders of magnitude in [Fe/H] is found and, at the same time, they provide a significant reliability test for the theoretical models presented here.

Finally, a recent paper by Mayya (1997) presents CaT synthesis models to be applied to starburst regions. Therefore only young population results may be compared with our models. Mayya uses JCJ92 fitting functions for $Z \leq \thinspace\hbox{$Z_{\odot}$}$ and DTT89 empirical relations for higher metallicities. He uses the stellar evolutionary tracks from Geneva group. His results also show a primary peak due to the RSG phase, a secondary maximum and a low constant value for SSP older than 100 Myr. Both peaks occur at earlier ages than in our models, due to differences in the assumed stellar tracks, and the asymptotic value is lower than the one in our grid II. The most important difference appears at lower abundances: at Z=0.008 the first maximum disappears in our models, while it exists in Mayya's. The evolutionary tracks selected by Mayya (1997) with enhaced mass loss rates for low abundances produce this behaviour, not predicted with the Padova evolutionary models either previous generation of Geneve tracks. The convenience of the use of these enhanced mass loss rates is still a matter of debate.

4.1 CaT synthesis in composite-populations: Unveiling the presence of RSG in star-forming regions

CaT has been observed not only in star clusters and normal galaxies but also in Active Galaxies (Terlevich et al. 1990a; Nelson & Whittle 1995; Palacios et al. 1997) and star-forming regions like Starbursts (Terlevich et al. 1990a,b; García-Vargas et al. 1993; González-Delgado et al. 1995) and Giant Extragalactic HII Regions, GEHRs, (Pastoriza et al. 1993; González-Delgado et al. 1995; Terlevich et al. 1996).

There is a controversy related to the origin of the observed CaT in star-forming regions and AGNmostly because these regions are not spatially resolved from the ground. Therefore one of the key questions is if the observed CaT comes from a single stellar population RSG rich or from a result of a mixture of populations of varying age and possibly metallicity (including the RSG plus the underlying older population).

In the case of isolated GEHRs, and therefore not contaminated by an underlying old population, two possibilities can arise: (1) the production of the CaT is due to the same young burst that is ionizing the region and (2) the CaT is produced in a slightly older (10-15 Myr) population, coexisting in the same GEHR with the younger, ionizing, one. With respect to the first scenario, current theoretical models (Salasnich et al. 1997) predict a narrow range of age and metallicity in which an SSP can produce both ionizing stars (O and WR stars) and RSG, namely around 4-6 Myr and at solar metallicity. This has been proposed for the CaT observations in NGC 604 (Terlevich et al. 1996). However, some other GEHR need the existence of an older component, second scenario, such is the case of some GEHR in the circumnuclear region of NGC 7714 (García-Vargas et al. 1997).

The largest circumnuclear GEHRs usually show the CaT feature in their spectra. However, some contamination from the older underlying population in the host galaxy is expected and therefore it is not clear whether the CaT is originated in the GEHR or in the disk-bulge population (García-Vargas et al. 1997).

In the case of starburst galaxies and AGN the picture is even more difficult to interpret, and the need for models which include the CaT synthesis from different populations becomes a key issue. To study this problem we have computed composite models with a combination of three different kind of populations: (a) a young one, able to ionize the gas, and definitively present in the region, (b) an intermediate age one, RSG rich, and (c) a very old population representative of those present in ellipticals and bulges of spirals. The selected ages are, 2.5 and 5 Myr for the youngest population, 8 and 12 Myr for the intermediate component and 10 Gyr for the oldest one. Three types of models have been computed: (1) a combination of two coexisting bursts, young, and intermediate, contributing 50% each in mass, suitable to be used in GEHRs, without any underlying population; (2) a two-component model in which the young burst plus the old population are combined in different proportions, and (3) a three-component model in which two coexisting bursts, young and intermediate-age, plus the old underlying population are contributing to the light in different percentages. The metallicity of the old population has been chosen to be $Z_{\odot}$, 0.4 $Z_{\odot}$ and 0.2 $Z_{\odot}$ for young populations with 2.5 $Z_{\odot}$, $Z_{\odot}$ and 0.4 $Z_{\odot}$ respectively, according to what is predicted by chemical evolution models.

To define the relative proportions we use the ratio, P, of the continuum luminosity at 6500 Å (close to $\hbox{H}_\alpha$) of the young and intermediate population (when present) to the total light. As an example P = 0.10 indicates a model in which the population characteristic of the region (young or young + intermediate) is contributing 10% to the total light in the continuum at $\hbox{H}_\alpha$. This method allows a check of the adopted proportions by a direct inspection of the $\hbox{H}_\alpha$ images. We have computed models with P ranging from the ones typical of GEHRs (P = 0.10 - 1 going from the smallest to the largest regions) to the ones characteristic of the most powerful starburst galaxies (P= 1 - 100).

Tables 7, 8 (grid I) 9 and 10 (grid II) display the results of the composite-population models. Each table contains the results for three metallicities: 0.4 $Z_{\odot}$, $Z_{\odot}$ and 2.5 $Z_{\odot}$. The first column lists the proportion, P, defined above (including the two - Tables 7, 9 -- or three -- Tables 8, 10 -- populations considered). If P is not given, a single population, or a combination of two coexisting young populations contributing 50% in mass each, have been considered. Column 2 shows the age of the population(s), in Myr. Therefore 2.5 + 10⁴ correspond to a model in which a young burst of 2.5 Myr is combined with an old population of 10 Gyr. Column 3, EW(CaT), lists the value of the equivalent width of CaT in absorption, in Å, for each model. Finally Col. 4 is the equivalent width of $\hbox{H}_\beta$ Balmer line in emission. If this value is missing then the adopted population(s) is(are) too old to produce ionizing photons.

The predicted values of EW($\hbox{H}_\beta$) in emission have been computed without considering the dust associated to the ionized region. There exists a well known discrepancy between predicted and observed values of EW(H$_{\beta}$)(e.g. Viallefond & Goss 1986). In fact, only 3 out of 425 HII galaxies in the catalogue by Terlevich et al. (1991) show EW(H$_{\beta}$) comparable to the ones calculated for clusters younger than about 3 Myr (i.e. > 350 Å; Mas-Hesse & Kunth 1991; García-Vargas et al. 1995a; Stasinska & Leitherer 1996). Under the assumption of a single burst population and a radiation bound nebula, an explanation for this disagreement could be that the reddening affecting the emission lines is caused by dust inside the regions (associated to the gas) which therefore does not affect the continuum of the ionizing cluster (Mayya & Prabhu 1996). If this is the case, the measured EW(H$_{\beta}$) should be increased according to the reddening determined from the emission lines and taking into account the contribution of the nebular continuum (García-Vargas et al. 1997).

Columns 5, 6 ( $Z_{\odot}$) and 7, 8 (0.4 $Z_{\odot}$) contain the same as Cols. 3, 4 already described for the case of 2.5 $Z_{\odot}$.

  

Figure 6: Diagnostic Diagram of EW(CaT) - in absorption - versus EW(H$_{\beta}$) - in emission - used as a tool to unveil the presence of RSG in star-forming regions. Triangles correspond to three component models, and asterisks are the two-component models, in which the CaT is contributed by the old population (10 Gyr in the models). Additionally, squares indicate models in which only a young and an intermediate component are considered. These two latest models should be applied to isolated GEHRs in which if CaT was detected it would be necessarily due to the presence of RSG

To summarize the results, we plot in Fig. 6 the value of EW(CaT) against that of EW(H$_{\beta}$). This figure can be used as a diagnostic diagram to unveil the presence of an intermediate population RSG rich, when analyzing data of star-forming regions which are located over an older underlying population. This is usually the case of AGN, nuclear starbursts and circumnuclear GEHRs. The results for the grid I are divided in in four panels. These panels simulate four different types of star-forming regions: a) AGN, corresponding to solar metallicity and large P values, b) circumnuclear high metallicity HII regions with solar metallicity but low P values, c) nuclear starbursts having half solar metallicity and high P, and d) circumnuclear GEHR with moderate metallicity (0.4 $Z_{\odot}$) and low P values.

Inspection of Tables 7, 8 and Fig. 6 shows that for powerful starburst galaxies (with values of P larger than 1.00) values of EW(CaT) higher than 3.8 Å are predicted only if RSG are present in the region and, in this case, the two-component models (ionizing burst+bulge) would not be able to reproduce the observations. García-Vargas et al. (1993) gave values of CaT in starbursts ranging between 2.5 and 8 Å. As can be seen in Fig. 6c a value as low as 2.5 Å can imply a low metallicity, an older age or simply the absence of RSG, and only a detailed study of other observational constraints could provide the solution. On the contrary, values as high as 8 Å would necessarily imply the presence of RSG and a metallicity at least solar, therefore somewhat higher than the average metallicity found in starburst galaxies.

The same method can be applied to AGN. In this case, a detection of CaT higher than 5 Å implies the presence of RSG inside the region sampled by the slit, probably larger than the nucleus and including also the subarcsec circumnuclear rings as shown by HST observations of some of the nearest AGN (Colina et al. 1997). Terlevich et al. (1990a) showed that all AGN in their sample had values of EW(CaT) $\geq$ 5 Å, therefore implying the presence of RSG.

In the case of circumnuclear GEHRs the discrimination between the presence or absence of RSG is a difficult task, particularly at moderate metallicity (see Figs. 6b and 6d). A more detailed study with further observational constraints is needed to discriminate between the two possibilities, such as the analysis of the whole optical spectrum to constrain the age of the young burst and an image near $\hbox{H}_\alpha$ to determine P (García-Vargas et al. 1997)

4.2 CaT in old populations: A strong metallicity constraint

We now turn to old populations, namely elliptical galaxies and bulges of spirals. Terlevich et al. (1990a) present a sample of 14 objects, whose EW(CaT) are between 6.1 and 8.1 Å (typical error bar of $\pm$ 0.8 Å) measured as in DTT89 and thus directly comparable to our models. Delisle & Hardy (1992) give central values (and also gradients) for 12 galaxies, with CaT equivalent widths ranging between 6.4 and 7.7 Å (typical error bar of $\pm$ 0.2 Å). In spite of different spectral band-passes than DTT89, but also free from TiO bands contamination, the comparison of three common objects, M 31, M 81 and NGC 1700, gives values of 6.4, 7.3 and 7.0 Å in Delisle & Hardy (1992) and 6.1, 7.7 and 6.1 in Terlevich et al. (1990a) respectively, which are consistent within the errors. In summary the available observed values of the CaT index in old populations (elliptical and bulges of spirals) are between 6 and 8 Å. These numbers compare well with our old SSP models of solar metallicity (Fig. 4b) and suggest a quite uniform average metallicity for these systems in agreement with what is derived by detailed galactic models of narrow band indices (Bressan et al. 1996).

Vazdekis et al. (1996, V96) compute evolutionary synthesis models for early-type galaxies, with metallicities 0.4 $Z_{\odot}$, $Z_{\odot}$, and 2.5 $Z_{\odot}$ and ages 1, 4, 8, 12 and 17 Gyr. They consider different hypotheses about the IMF, the chemical evolution and the star formation history, producing a set of models which includes colours and line indices, in particular CaT. Since the evolutionary scheme is the same as the one assumed in our models, we present in Table 11 a comparison between V96 models and our grid II for the SSP with common ages and metallicities.

 

Table 11: Comparison between V96 and grid II for old populations

V96 give values higher than grid II at Z=0.02 and 0.05, and lower at Z=0.008 (except at 1 Gyr). For the highest metallicity, a source of the discrepancy could be the different assumed fitting function for the index (although both based on DTT89, they use a single fit for any abundance, as in DTT89, since we use Eqs. (8) and (9) for $Z_{\odot}$ and 2.5 $Z_{\odot}$. The rest should be due to the inclusion in our models of the coolest late-type stars, Z91, and therefore a different modelization of CaT index for cool stars, important in old populations. This comparison stress the need of observations of cool stars to test the present calibrations.

Idiart et al. (1997) also compute synthetic values of CaT in old populations. They use a calibration based on their own star sample, with a different index definition, which includes the three calcium lines. They also include in their models late-type stars from Z91 but not high metallicity RSG stars (although these stars are not present in such old populations, the lack of high metallicity RSG in their star sample implies that their values would be definitively lower than ours in RSG-rich populations at metallicities solar or higher than solar). In the range-age (1-12 Gyr) in which we can compare our models with Idiart's, their resulting EW(CaT) for SSP are slightly lower than those from our grid II models. However, the values agree quite well (as an example, at 0.3 $Z_{\odot}$ their values are 5.53 and 6.50 Å for populations at 1 Gyr and 12 Gyr, since ours (as calculated as an average value of 0.2 and 0.4 $Z_{\odot}$) are 5.69 and 7.19 Å respectively. At $Z_{\odot}$ Idiart's values are 6.57 and 7.55 Å again for the extreme ages 1 Gyr and 12 Gyr, since ours are 6.84 and 8.60 Å at the same ages. Differences can come not only from the calculations in the CaT index but from the different assumptions adopted in the low-mass limit of the IMF and in the evolution of the low-mass stars.

An important point is the relatively low sensitivity of the CaT index to the age above a few Gyr, makes it a very powerful tool for discriminating among the metallicity of the stellar systems. It is well known that due to the similar response of the isochrone turn-off to variations in age or metallicity it is difficult to disentangle age and metallicity effects by the sole analysis of the integrated properties of the spectra in old populations. Different diagnostic diagrams have been adopted, as can be seen in González (1993) and Bressan et al. (1996) none of which is fully adequate to overcome this difficulty. The quantity

$$\frac {\delta {\rm log CaT}/\delta ({\rm log\, age}) } {\delta {\rm log CaT}/\delta {\rm log} Z}$$ (12)

is a measure of the relative sensitivity to age and metallicity. At t=13 Gyr and Z= $Z_{\odot}$ this quantity is 2.876, but the average value between 2 and 13 Gyr is 6.4. Among the narrow band indices considered so far in the literature (Gorgas et al. 1993; Worthey et al. 1994; Bressan et al. 1996) this is the one with the highest sensitivity to the metal content. Jones & Worthey (1995) claimed that the Fe₄₆₆₈ index has a large sensitivity to the metallicity with a value $\delta$ (log age)/$\delta$ $({\rm log} Z)=4.9$, that is lower than our mean result of 6.4. These same authors use the index H$_{\rm \gamma_{HR}}$ as an age discriminator, due to its total independence of the metallicity: $\delta$ (log age)/$\delta$ $({\rm log} Z)=0.0$. We have not calculated it, but a suitable combination of the CaT index with another whose age sensitivity is higher, such as the H$_{\beta}$ index (the following one with low sensitivity to the metallicity with a $\delta$ (log age)/$\delta$ $({\rm log} Z)=0.6$, could definitively separate age from metallicity and solve the age-metallicity dilemma in early-type galaxies (Bressan et al. 1996). Thus, as a preliminary step and awaiting for our own complete galaxy models, we can generate mixed diagnostic diagrams using our models for CaT index and the narrow band indices from Bressan et al. (1996), that are computed adopting the same library of stellar evolutionary tracks.

  

Figure 7: EW(CaT) (grid I, this work) versus the computed values for the logarithm of $\hbox{H}_\beta$ index (Bressan et al. 1996) in old populations

Figure 7 shows the synthetic values of the EW(CaT) plotted against the logarithm of $\hbox{H}_\beta$ index as modelled by Bressan et al. (1996). It can be seen that curves of constant age are almost orthogonal to curves of constant metallicity, making this diagram one of the most powerful tools to solve the problem of the age-metallicity degeneracy in elliptical galaxies in a similar way to Fig. 2 from Jones & Worthey (1995).

Although more theoretical work has to be made to assess the importance of the study of CaT in old systems, the use of the later index as a straightforward metallicity indicator in early-type galaxies is very promising (Gorgas et al. 1997).