6 Discussion and concluding remarks

6.1 Summary

This work is dedicated to the presentation of theoretical isochrones in several photometric systems. It represents the continuation of a wide project of the Padova group, started with Bertelli et al. (1994) and then carried on by Chiosi et al. (1997), and more recently by Salasnich et al. (2000). It starts describing the formalism for converting synthetic stellar spectra into tables of bolometric corrections (Sect. 2), in such a way that it can be easily applied to different photometric systems, and with the possibility of including extinction in a self-consistent way.

Figure 4: Comparison of Girardi et al. (2000) isochrones transformed to Johnson-Cousins-Glass magnitudes and colours by using either present relations (continuous lines) or Bertelli et al. (1994) ones (dashed lines), in several CMDs. The isochrones have solar metallicity (Z=0.019) and ages 108, 109, and 1010 yr (from top to bottom).

Figure 5: Comparison of Girardi et al. (2000) isochrones as transformed to the WFPC2 VEGAmag system using either present relations (continuous lines) or Salasnich et al. (2000) ones (dashed lines). The isochrone ages and metallicities are the same as in Fig. 4.

Then, we describe the assemblage of an updated library of stellar spectra (Sect. 3). The library is quite extended in $T_{\rm eff}$ and $\log g$, and includes the crucial dependence of spectral features on metallicity. Of course, it suffers from some limitations: very hot stars and M-giants are not included among synthetic spectra, a situation which can be remediated by using blackbody and empirical spectra, respectively. The strinkingly different spectra of carbon stars will also have to be considered in the future (Marigo et al., in preparation). These are probably the points where the models can be most improved. Moreover, several problems may be affecting the ATLAS9 synthetic spectra we are using to simulate the broad-band colours of most stars (see Sect. 3.1). Although such spectra have been demonstrated to be suitable for synthetic photometry (mainly for the Johnson-Cousins-Glass system; e.g. Bessell et al. 1998), their accuracy has still to be sistematically evaluated for stars of all metallicities, temperatures and gravities. Anyway, we assume that they are good enough for simulating broad-band photometric systems in the visual-infrared wavelength region, whereas expect that the results in narrow-band systems, and in the ultraviolet pass-bands, will be affected by more significant errors. Another important aspect of synthetic spectra is that they are usually computed for scaled-solar chemical compositions, whereas the extension to peculiar and $\alpha$-enhanced mixtures would be of high interest. This latter problem will probably be alleviated in a near future, with the release of extensions to ATLAS9 spectra.

From the spectral library, we derive bolometric corrections for each pass-band mentioned in Sect. 4, and apply them to the Padova isochrones. In practice, only in few cases we present newly-constructed isochrones: the bulk of isochrone data is already described in previous papers by our group, and it is only the transformation from theoretical quantities to absolute magnitudes that changes compared to past releases. Section 5 summarizes the basic characteristics of the different sets of isochrones, indicating the full references.

6.2 Comparison with previous works

It is important to illustrate the differences between the present and previous transformations. The previous ones for UBVRIJHK are fully described in Bertelli et al. (1994), and were adopted by Girardi et al. (2000), Salasnich et al. (2000) and Marigo et al. (2001); for HST/WFPC2 photometry, they are the ones described in Salasnich et al. (2000).

The situation for Johnson-Cousins-Glass is tentatively illustrated in Fig. 4, which compares a set of Girardi et al. (2000) isochrones, transformed according to both present (continuous lines) and Bertelli et al. (1994; dashed lines) transformations. We point out that:

1.

For stars hotter than $\mbox{$T_{\rm eff}$ }\sim4000$ K, present transformations are very similar to those of Bertelli et al. (1994). The differences amount to just a few hundredths of a magnitude over most regions of the CMD, including the entire main sequence and subgiant branch, and most of the RGB. They can be entirely attributed to the slightly different pass-bands and zero-points, and to the use of more recent ATLAS9 "NOVER'' atmospheres instead of Kurucz (1993) ones;

2.

A somewhat similar situation holds for dwarfs cooler than $\mbox{$T_{\rm eff}$ }\sim4000$ K (see bottom end of the main sequence in all panels, for $\mbox{$M_{V}$ }\ga7$, and $\mbox{$M_{K}$ }\ga5$). The differences are generally small and can be attributed to the change from Kurucz (1993) to Allard et al. (2000a) spectra. The exceptions are $U\!-\!B$ and $J\!-\!H$ colours, for which the differences between the two versions become sizeable;

3.

For giants cooler than 4000 K, present transformations become very different. This can be noticed in the upper-right corner of all diagrams. M-giants corresponding to the RGB-tip and TP-AGB, are now seen to fade by some magnitudes in V, due to a sort of rapid increase of visual BCs at $\mbox{$T_{\rm eff}$ }\la3500$ K. This effect is caused by the use of Fluks et al. (1994) spectra and their $T_{\rm eff}$ vs. $V\!-\!K$ scale. Such a bending of the RGB is indeed observed in CMDs of old metal-rich clusters (see e.g. Ortolani et al. 1990; and Rich et al. 1998), and seems to be better reproduced now than with previous transformations. Other differences appear in all colours: the most remarkable are the excursion of M-giants of latest type towards much bluer $U\!-\!B$, and the much smoother behaviour now obtained for $J\!-\!H$ and $H\!-\!K$.

A quite similar situation holds for HST/WFPC2 photometry, as illustrated in Fig. 5. This time, we compare the same isochrones as transformed with present (continuous lines) and Salasnich et al. (2000; dashed lines) transformations. It is evident that the present transformations ensure a more continuous behaviour of the colours for all low-temperature stars (both dwarfs and giants).

From the plots at the top row of Fig. 5, one can also appreciate the unusual appearance of isochrones in CMDs that involve ultraviolet WFPC2 pass-bands: Notice for instance that in F170W, F218W, F255W and F330W magnitudes, giants may be fainter than turn-off stars. Isochrones in the F218W vs. F170W-F218W and F255W vs. F218W-F255W diagrams are even "twisted'', because the $T_{\rm eff}$ vs. colour relations are not monotonic for these filters. These effects are related to the presence of a red leak in the ultraviolet HST filters (for both the present WFPC2 and the former FOC camera), and are extensively discussed by Yi et al. (1995) and Chiosi et al. (1997).

As a consequence of the great similarity between present and previous UBVRIJHK and HST/WFPC2 transformations, for most colours and over a large portion of the HR diagram, most results derived from previous Padova isochrones are not expected to change. Exceptions may show up for works that are concerned with the photometry of the reddest giants, with $\mbox{$T_{\rm eff}$ }\la3500$ K ( $\mbox{$B\!-\!V$ }\ga1.5$), or that deal with low-mass main-sequence stars in the $U\!-\!B$ and ultraviolet colours.

Figure 6: Isochrones in the CMDs of NICMOS ABmag photometry. Ages and metallicities are the same as in Fig. 4.

Figure 7: Isochrones in the T1 vs. C-T1 plane of Washington photometry. Left panel: from top to bottom, a sequence of Z=0.008 isochrones with ages 107, 108, 109, and 1010 yr. Right panel: from left to right, a sequence of 14 Gyr old isochrones with metallicities Z=0.0001, 0.0004, 0.001, 0.004, 0.008, 0.019, and 0.030.

6.3 New results

The greatest improvement of the present database is in the presentation of Padova isochrones in several photometric systems for which they were not available so far - including the case of brand-new systems. Three examples of theis kind are given in Figs. 6-8.

First, Fig. 6 presents the isochrones in NICMOS ABmag system. In a VEGAmag system, NICMOS isochrones would look similar to their equivalent Johnson-Cousins-Glass ones, shown in Fig. 4. In the ABmag system, however, they appear shifted to quite different colour and magnitude intervals.

Figure 7 illustrates how Padova isochrones look like in the T₁ vs. C-T₁ CMD of Washington photometry, both for varying age at constant metallicity (left panel), and for varying metallicity at constant age (right one). The striking feature in these plots is the excellent separation in metallicity offered by the C-T₁ colour, from the main sequence up to red giant phases. This feature, combined to the excellent throughput in the C filter (Fig. 3), is among the advantages that make the Washington system a very competitive one if compared to Johnson-Cousins (see also Paltoglou & Bell 1994; Geisler & Sarajedini 1999).

Preliminary comparisons point to a good agreement between our Washington isochrones and real data for LMC fields from Bica et al. (1998). Just to mention an example, we notice that C-T₁ for giants "saturates'' at $\sim$3.4, both in the models and in the LMC data.

Figure 8: Comparison between the same set of Z=0.019 isochrones as seen in the UBVI CMDs using either Johnson-Cousins (dashed lines) or WFI filters (continuous lines). VEGAmag systems are used in both cases. Ages are the same as in Fig. 4.

An example of "new'' photometric system is provided by the WFI, which has broad-band filters very different from Johnson-Cousins ones. To illustrate the effect in colours, Fig. 8 shows exactly the same isochrones as seen in BVI CMDs using either Johnson-Cousins or WFI filters, and applying in both cases the VEGAmag definition of zero-points. The differences are striking. In particular, since the BV WFI filters represent a wavelength baseline shorter than the Johnson ones, they provide a more modest separation of stars in $\mbox{$B\!-\!V$ }$ colour. It is evident from this plot that the normal Johnson-Cousins isochrones cannot be used to interpret WFI data that has been converted to VEGAmag or ABmag systems, as for most of EIS data (e.g. Arnouts et al. 2001; Groenewegen et al. 2002).

6.4 Retrieval of electronic tables

All the data here mentioned are available at the WWW site http://pleiadi.pd.astro.it. The database already includes a very large number of files, and is expected to increase further as we publish data for other photometric systems. Thus, it is hard to describe here both the structure of the database, and the content of each file. Moreover, this kind of information is probably useful just to whom actually accesses the database. Thus, we opt to provide all the relevant information in readme.txt files inserted in the database.

To the general reader, suffice it to briefly mention the kind of data which is available:

• Tables of bolometric corrections for each metallicity: they contain the quantities $BC_{S_\lambda}$ for each filter, and as a function of stellar $T_{\rm eff}$ and $\log g$. Metallicities available are $\mbox{\rm [{\rm Fe}/{\rm H}]}=-2.0$, -1.5, -1.0, -0.5, 0, +0.5. The values of $T_{\rm eff}$ and $\log g$ are not exactly the same for all metallicities, but correspond quite well to the regions indicated in Fig. 1;
• Tables of isochrones: they include all metallicities and cases indicated in Sect. 5. The various photometric systems are separated in different directories. For each isochrone file, the information and structure are the same as already presented in Girardi et al. (2000), Salasnich et al. (2000), and Marigo & Girardi (2001), with the obvious difference that instead of UBVRIJHK absolute magnitudes, in each file we tabulate the absolute magnitudes for the photometric system under consideration;
• Tables of integrated colours of single-burst stellar populations: a table of this kind is present for each isochrone table. They provide integrated magnitudes in each pass-band, as a function of age.

Acknowledgements

L.G. thanks the many people who helped by providing filter transmission curves and zero-points information (in particular E. Bica, D. Geisler, J. Holtzman, D. Figer, E. Grebel, M. Gregg, M. Rich, S. Arnouts, and L. da Costa). Particularly appreciated are the availability (R. Kurucz, F. Allard) and help with (I. Baraffe) on-line spectral data, the useful comments by B. Plez regarding cool giants, and the many useful remarks by R. Bell and M.S. Bessell, which greatly helped to improve this paper. Also acknowledged are those who kindly pointed out some mistakes in our preliminar releases of data. L.G. acknowledges a stay at MPA funded by the European TMR grant ERBFMRXCT 960086. This work was partially funded by the Italian MURST.