4.1. Miras: PG3 versus field, Sgr I and LMC
In Fig. 8a and b the PG3 Miras resemble more the Sgr I Miras than the field Miras and LMC LPVs. This is apparently in contradiction with Glass et al. (1995, Fig. 4c) who did not find any significant offset of the Sgr I Miras from the LMC P/(J-K)0 relation. Note however, that the extinction correction is actually the origin of this discrepancy. Using = 1 the Sgr I Miras will be 0 redder in (J-K)0. The estimated offset is now 0 and within the uncertainties comparable to PG3.
From Figs. 5a and 6 it is not clear if there is a significant offset from the field Miras with respect to either the LMC or PG3, while there is an offset between PG3 and the LMC. Fig. 8a and b however shows that the field and PG3 Miras are not comparable and that there are noticeable differences between all four groups of Miras: (i) in contrast to PG3 and Sgr I, the field and LMC Miras populate the region with (J-H)0 0 (ii) the PG3 Miras extend to redder (H-K)0 colours than all the other groups, and (iii) only the LMC Miras reach (J-H)0 0
The blue (J-H)0 limit of the LMC Mira box is only defined by a few objects. The last point above is probably not a real difference but induced by statistical fluctuations. Note that unidentified, hot carbon stars in the Reid et al. (1995) sample would be located in this area of the colour-colour diagram (see for example Fig. 5 from Costa & Frogel 1996). However, the Reid et al. stars are LPV's while the blue carbon stars are not known to be large amplitude variables and nothing is known about the variability of the blue carbon stars. This point can be clarified only by more observational data.
Statistical fluctuations can hardly be responsible for the other two differences between the four groups of Miras. The redder (H-K)0 colours of the PG3 Miras could be due to metallicities higher than solar but there is no evidence for this from the colour magnitude diagram. The majority of the field stars with solar metallicity have ages between 1 Gyr and 8 Gyr (see Figs. 3 & 4 from Ng & Bertelli 1998), while for PG3 our age estimates range from 5 Gyr to 10 Gyr (Sect. 3.5, Ng et al. 1995). Thus the redder colour could be due to an older age of the PG3 stars with Z 0.02.
The lack of PG3 stars with (J-H)0 0 and (H-K)0 0 cannot be accounted for by metallicity effects alone, because this region is populated in the field as well as in the LMC. Age differences might again be the reason. In the LMC the last major star formation occurred 6 - 8 Gyr ago in some regions, while in other it happened only 2 - 3 Gyr ago (Vallenari et al. 1996a,b). For field stars with Z = 0.008 the age ranges from 2 - 10 Gyr (see again Figs. 3 & 4 from Ng & Bertelli 1998). Thus the lack of PG3 stars could be due to a lack of stars with a metallicity in the range Z 0.008 and an age between 2 - 5 Gyr.
Although age is an attractive parameter to explain the differences between the various groups of Miras we want to emphasize that confirmation through a comparison with isochrones in the colour-colour diagram is still needed. This requires a proper calibration of the colours for the isochrones, possibly combined with an improved description of the AGB-phase (Ng et al. 1998).
All together the data are compatible with a metallicity range spanning from a quarter solar to approximately solar for the field and PG3 stars. The majority of the field stars with metallicities around solar may be considerably younger than their counterparts in PG3. This would explain the smaller colour offset of the field Miras from the LMC P/(J-K)0 relation in comparison to the colour offset for the PG3 Miras. In this respect the apparent bluer (H-K)0 colour in Fig. 8a and b of Sgr I versus PG3 might be an indication for a slightly younger age for the Miras in the Sgr I area.
4.2. SRVs: PG3 versus field and LMC
The PG3 SRVs are similar to `red' field SRVs in their periods and amplitudes. There are however marked differences: the slope of the PK0 and P/(J-K)0 relations for the PG3 SRVs is similar to that of the PG3 and LMC Miras, while this does not appear to be the case for the field SRVs (see KH92 and Fig. 4). In addition, the colours of the PG3 SRVs are slightly bluer than those of the `red' field SRVs. The most plausible explanation for the colour differences is a higher temperature of the PG3 SRVs compared to the field SRVs. A temperature difference could explain the different behaviour in the P/(J-K)0 relations, as outlined in Sect. 4.3.
The longer mean period of the PG3 stars is probably due to the larger homogeneity of this sample relative to the field stars. This homogeneity concerns both the variability classification and the pulsation mode (see below).
The result that the PG3 SRVs extend to redder colours than the LMC SRVs is due to their higher average metallicity.
4.3. SRVs versus Miras
Most field SRVs with pulsation periods below are cooler and partly brighter than field Miras with the same period (see Fig. 6 and KH92). This favours fundamental mode pulsation for the Miras and overtone pulsation for the SRVs. Similar evidence for variables in the LMC was presented by Wood & Sebo (1996, hereafter WS96). Their results indicate that the fundamental mode pulsation is consistent with stellar masses . This might be in contradiction with the results obtained by van Leeuwen et al. (1997). Their analysis indicate that the majority of the Miras are first overtone pulsators. However, their sample did not include SRVs and is furthermore biased to stars with large radii. For stars in fundamental mode with shorter periods (like the PG3 SRVs) the data for the smaller radii are lacking, due to observational limitations. Therefore, the results from van Leeuwen et al. are not necessarily in disagreement with WS96. An interpretation of the PG3 stars in terms of pulsation modes has to be in agreement with the behaviour of the SRVs and Miras in the PK0 and P/(J-K)0 diagrams. The PG3 SRVs would be brighter and redder than the Miras at a given period, if the PG3 Miras are fundamental mode pulsators and the PG3 SRVs are overtone pulsators. If Miras and SRVs pulsate in the same mode, a systematically lower metallicity of the SRVs would increase their temperature and make them bluer, but at the same time their periods would be smaller at a given luminosity. This would introduce a luminosity difference relative to the Miras at a given period but would only shift the SRVs along their P/(J-K)0 relation. Therefore, our result that the PG3 SRVs are an extension of the PG3 Mira PK0 and P/(J-K)0 relations, can only be explained by adopting the same metallicity range and pulsation mode for the Miras and SRVs. In view of the similarities between field and PG3 Miras, fundamental mode pulsation is more plausible for the PG3 stars.
4.4. The metallicity of PG3 Miras and SRVs
From star counts and metal-rich globular cluster studies (Ng 1994; Bertelli et al. 1995, 1996; Minniti 1995) one expects a gradient of metal-rich stars towards the galactic centre. BW is located closer to the galactic centre and has a larger number of high metallicity stars with respect to PG3 (Ng et al. 1996a, 1997). The period-colour relation indicates that the mean metallicity of the PG3 variables is about 1.4 times larger than the LMC mean metallicity. A comparison of both the PG3 and Sgr I (Glass et al. 1995) period-(J-K)0 relation relative to the LMC relation shows that a small trend might be present. But the uncertainties in the extinction correction for Sgr I are larger than in PG3. An uncertainty in the extinction of 0 in one filter would give an error in the colour, i.e. (J-K)0, of a few hundredth of a magnitude. Together with the uncertainties in the transformation, the remaining difference between Sgr I and PG3 period-colour relation is not significant to conclude from the present data, that there is a metallicity gradient towards the galactic centre.
The PG3 SRVs and Miras extend to redder (H-K)0 than the LMC LPVs. This indicates that the mean metallicity for the PG3 LPVs is slightly larger than for the LMC which is also consistent with Fig. 7. The bulk of PG3 Miras cover the same position as the Sgr I Miras by Glass et al. (1995). They should have a similar age and metallicity as the Sgr I Miras, which presumably have solar-type metallicity. This implies that the whole metallicity range from intermediate to solar is possible in PG3 and the LMC, but as mentioned in Sect. 4.1 there are perhaps differences in age between PG3 and LMC stars of comparable metallicity.
4.5. Hints from galactic structure
The field SRVs have a scale height of 230 pc (KH92). This is slightly smaller than the scale height of 260 30 pc for the PG3 Miras with a detection in IRAS (Bl92). These values are comparable with the 250 pc obtained by Habing (1988) for AGB stars and they are consistent with the scale height for disc giants. The whole PG3 Mira sample, on the other hand, has a scale height of 300 50 pc. Although the previous values are within the uncertainties one has to consider, that differentially there is a noticeable difference between the Miras with and without an IRAS detection. With the ages and scale heights, determined for the stellar populations in the disc (Ng 1994; Ng et al. 1995, 1996a, 1997), the age of the field SRVs and the PG3 Miras with an detection in IRAS is between 4.5 - 7.0 Gyr with a metallicity ranging from Z = 0.008 - 0.015. The age range for the whole PG3 Mira sample is estimated 4.5 - 7.5 Gyr. These ages appears to be in agreement with an age considerably less than 10 Gyr, estimated by Harmon & Gilmore (1988) for the bulge IRAS sources with initial masses larger than 1.3 . But Whitelock et al. (1991) showed, that their lower limit estimate for the initial mass is more likely an upper limit for the majority of the stars. This gives a lower age limit 4 Gyr (Bertelli et al. 1994), which is consistent with the age deduced from the scale heights.
The very large metallicity spread causes that age estimates are very susceptible. Even ages as old as 16 Gyr estimated by Bl92 are possible. With such an old age the bluest SRVs and Miras should be very metal-poor. This would lead to a contradiction that long period variables cannot be present, because they are not found in old, metal-poor globular clusters. Therefore, the PG3 Miras and SRVs cannot be old and very metal-poor, but this does not rule out the intermediate and solar metallicity cases. The period for the PG3 Miras ranges from 180 - 320 days, which is comparable with the periods of the Miras found in metal-rich globular clusters (Feast & Whitelock 1987, Whitelock et al. 1991). The 8 - 9 Gyr age of these clusters (Ng et al. 1996c,d) gives an initial mass of about 1 , which is consistent with the upper limit obtained from the scale height for these stars.
On the other hand, if the disc density towards the galactic centre is lower than expected from a double exponential density profile (Bertelli et al. 1995; Kiraga et al. 1997; Ng 1994& 1997a; Ng et al. 1995, 1996a; Paczynski & Udalski 1997; Paczynski et al. 1994), this could imply that the PG3 SRVs and Miras are not due to a disc population. As argued above they are also not related to a very old, metal-poor population. With an upper age of about 8 Gyr, the PG3 Miras are in that case likely related with the `bar' population identified by Ng et al. (1996a,b). The age and metallicity spread for this population (t = 8 - 9 Gyr; Z = 0.005 - 0.03) might imply that the variables in PG3 are located in the outer regions of the `bar'. A complication is that one should be careful with the semantics related with the `bar'. If the stars of this population can be found in PG3, i.e. 1.5 kpc out of the galactic plane, this population cannot be originating from a bar as found in bar-like galaxies. Strictly spoken, this should be referred to as a triaxial structure. The bluest SRVs and Miras might have a metallicity of Z 0.005 with an age 9 Gyr. Although the uncertainty in the ages is between 1 - 3 Gyr, the large metallicity spread seems to indicate that all ages between 5 - 10 Gyr are possible in the metallicity range Z = 0.005 - 0.03. The great similarity in Fig. 8b between the distributions of the variables from PG3 and the LMC suggests a comparable age and metallicity for both samples. Vallenari et al. (1996a,b) find indications for enhancements of the star formation rate in the LMC at ages as old as 6 - 8 Gyr, but in other regions the bulk of star formation has occurred only 2 - 3 Gyr ago.
This raises the question if stars younger than 5 Gyr are present in the galactic bulge/bar. The bluer (J-H)0 colour of the Sgr I Miras with respect to those from PG3 might indicate a younger age for the former, but as pointed out in Sect. 3.6 the colour difference is probably due to uncertainties in the colour transformations.
The presence of carbon stars could be an indication for a young age, because the work from Marigo et al. (1996ab and references cited therein) indicates that carbon stars cannot be much older than 4 Gyr. The carbon stars (L199,S283) identified in our sample of LPVs and those identified by Azzopardi et al. (1991) might therefore be an indication for the presence of stars younger than 5 Gyr in the bulge/bar. Ng & Schultheis (1997) argue that S283 is actually related to the Sagittarius dwarf galaxy found by Ibata et al. (1994). Possibly the same argument holds for PG3 variable L199. Furthermore it was argued that the sample of carbon stars from Azzopardi et al. (1991) is probably not associated with the bulge. In the bulge they would be bolometrically 2 too faint, but associated with the Sagittarius dwarf galaxy their luminosities are comparable to carbon stars found in other dwarf galaxies.
If all the bulge carbon stars are related to the Sagittarius dwarf galaxy (Ng 1997b, 1998) this would imply that they are absent in the bulge. In contrast to the field and LMC sample this implies the absence of a major star formation epoch less than 4 Gyr ago.
4.6. PG3 and the foreground stars
As already described in Sect. 3.1 the foreground contamination of PG3 Miras is either significantly larger or comparable with the PG3 SRVs. Fig. 7 hints that both groups belong to the same population and a similar fraction of foreground stars is therefore expected. This implies that the SRVs are one magnitude fainter than the Miras. The K magnitude distribution of the two groups are in this case comparable. The asymmetry suggests that more stars are found nearby. This could imply a high foreground contamination as suggested by BL92, but most likely it is due to stars located in the nearby side of the triaxial structure mentioned above. Some of the nearby stars in the sample belongs therefore to the same population as the bulge SRVs and Miras and should not have been treated as foreground contamination.
© European Southern Observatory (ESO) 1998
Online publication: September 14, 1998