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Astron. Astrophys. 338, 581-591 (1998)

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3. Results

The observations are presented in Figs. 2 - 8a and b. The mean magnitude is used in the figures, when several observations are available for a star. In Figs. 4 - 8a and b only those stars are considered which, according to Wess87, are classified correctly and have a good period determined.

3.1. Magnitude distribution

At present we are mainly interested in the bulge stars. Therefore, disc stars are referred to as the foreground contamination.

If the stars were located in the disc, the magnitude distribution of the foreground contamination in PG3 will show a gradually, more or less linear, increase towards fainter magnitude (see for example Fig. 11 - 4, Ng et al. 1995). The roughly linear increase is a consequence of the increasing volume in the cone, when sampled towards larger distances. The distribution of stars in the bulge have in first approximation a peaked shape (see for example Fig. 11 - 3, Ng et al. 1995). This is a result of the density profile of the bulge stars, which increases towards the galactic centre, is highest near the galactic centre, and decreases afterwards.

Two interpretations are possible for the K-magnitude distributions displayed in Fig. 2.

1. There is a difference in the distribution of the foreground contamination (K [FORMULA] 6[FORMULA] between the SRVs and Miras. The foreground contamination of the Miras appears to be significantly larger than for the SRVs. The large fraction of foreground Miras was already noticed by Bl92, especially those which also have an IRAS 12 µm and 25 µm detection. Moreover, Fig. 2 shows that the peak of the SRVs (6[FORMULA] [FORMULA] K [FORMULA]9[FORMULA] is about 1.5 times broader than the Mira peak between 6[FORMULA] [FORMULA] K [FORMULA]8[FORMULA] This could indicate that part of the SRVs with 6[FORMULA] [FORMULA] K [FORMULA]8[FORMULA] are in fact Mira type variables. They were classified as SRVs, because of the amplitude of the variations in the lightcurves. In this case some of the SRVs with K [FORMULA] 8[FORMULA] represent a group of intrinsically fainter stars.

2. All the PG3 SRVs represent a group of stars with a distribution similar, but intrinsically fainter, to the Miras. A 1[FORMULA] shift towards brighter magnitudes is an empirical patch for the luminosity difference between SRVs and Miras. With this shift the foreground contamination for the SRVs is slightly smaller, but probably the difference is not significant anymore. In this case the PG3 SRVs are also contaminated with foreground stars.

In Sect. 4.6 we argue that the latter possibility is preferred, but that a fraction of the foreground contamination might be associated with the galactic bar.

[FIGURE] Fig. 2. Distribution of K-magnitudes for the SRVs (solid histogram; this paper) and the Miras (dot-shaded histogram; Bl92) observed in PG3

3.2. Periods and amplitudes

Fig. 3 gives the period distributions of the various samples, used for comparison with the PG3 SRVs. The PG3 SRVs have periods comparable with the short period tail of the PG3 Miras. Their periods further overlap with the `red' field SRVs distinguished by KH92 & KH94, but the PG3 SRVs have however a longer mean period.

[FIGURE] Fig. 3. Period distribution for the SRVs (solid, shaded histogram; this paper) and the Miras (dot-shaded histogram; Bl92) observed in PG3 together with the distributions for the field SRVs (dot-dashed histogram; KH94 and Kerschbaum 1995) and Miras (long dashed histogram; Catchpole et al. 1979)

There is no significant difference between the period distribution of the field and PG3 Miras, except for a deficiency of PG3 variables with periods larger than 300 days and is due to the spectral window for which the [FORMULA] plates (Wess87) were taken, see Sect. 2.1.

The mean photo-visual amplitude, estimated from Plaut (1971), for the PG3 SRVs is about 1[FORMULA] This is comparable to the V-amplitude of the field SRVs in the same period range, but much smaller than the amplitudes for the field Miras (5[FORMULA]

3.3. Period - K relation

Fig. 4 shows the apparent K magnitude versus log P diagram (hereafter referred to as PK0-relation). The PG3 SRVs obey the same PK0-relation as the PG3 Miras (Schultheis et al. 1996). This figure suggests a common origin for the two samples. Note that the straight line in Fig. 4 is not a fit to the data! It shows the PK0-relation for Sgr I (Eq. 5, Glass et al. 1995), transformed from the SAAO to the ESO photometric system. We further adopted an extinction (AV = 1[FORMULA] instead of AV = 1[FORMULA] for the Sgr I field. The resulting PK0-relation for Sgr I in the ESO photometric system is: [FORMULA]. The dashed lines above and below the Sgr I relation ([FORMULA]) are a combination of the expected scatter due to the depth of the bulge ([FORMULA] mag ) and the dispersion in the mag- nitudes (not averaged, [FORMULA] 0[FORMULA] of the PG3 variables. The stars above the dotted line are foreground stars, but see Sect. 4.6 for additional comments. A few stars lie under the period-luminosity relation. Ng & Schultheis (1997) argue that those stars are located at the edge of the Sagittarius dwarf galaxy. In the further analysis only those stars, which are located between the two dashed lines, are considered.

[FIGURE] Fig. 4. K0 vs log P relation for the PG3 SRVs (solid triangles; this paper) and PG3 Miras (open boxes; Bl92). The straight line shows the Sgr I relation given by Glass et al. (1995). The two dashed lines indicate the transition between bulge and non-bulge stars (see Sect. 3.3 for details)

3.4. Period - colour relation

In Figs. 5a-c the period-colour (PC) relations for the PG3 SRVs and Miras are shown for (J-K)0, (J-H)0, and (H-K)0, respectively. The thick straight lines indicate the LMC relation due to Feast et al. (1989) and Glass et al. (1995). In Fig. 5a all the stars are slightly offset above the P/(J-K)0 relation. In Fig. 5b the Miras are below the P/(J-H)0 relation, while the SRVs are located slightly above. The (J-H)0 colour for both the SRVs and Miras appears to be independent of the period. In Fig. 5c the PG3 SRVs appear to follow the LMC relation, while the PG3 Miras are offset above. It is also possible that a fraction of the SRVs follows the PG3 Mira P/(H-K)0 relation, which is steeper than the LMC relation. An other fraction of SRVs lies clearly above such a relation.

[FIGURE] Fig. 5a-c. Colour vs log P relations for the PG3 SRVs & Miras for respectively a (J-H)0, b (J-H)0, and c (H-K)0; only bulge stars are considered and the symbols are the same as those used in Fig. 4. The thick straight lines are the LMC relations (Glass et al. 1995) transformed from the SAAO(Mk3) to the ESO system (see Sect. 2.7). The dotted extension indicate an extrapolation of this relation for P [FORMULA] 420d

For the PG3 Miras the mean offset from the LMC PC-relation is [FORMULA] 0[FORMULA] Within the transformation uncertainty of the LMC relation this is comparable to the [FORMULA] 0[FORMULA] offset obtained by Bl92.

Fig. 6 shows the P/(J-K)0 relation for the field SRVs and the field Miras. The field Miras also follow the LMC relation, although there is a slight offset of [FORMULA] 0[FORMULA] towards redder (J-K)0. This offset is not conclusive with regard to possible differences to the LMC or PG3 stars, given the transformation uncertainties (field Mira and the LMC relation).

[FIGURE] Fig. 6. (J-K)0 vs log P relation for the field SRVs (crosses; KH94 and Kerschbaum 1995) and field Miras (filled circles; Catchpole et al. 1979). The thick straight line is the LMC relation due to Glass et al. (1995). The photometry of the field Miras and the LMC relation are transformed respectively from the SAAO(Mk1) and SAAO(Mk3) to the ESO system (see Sect. 2.7)

The 0[FORMULA] offset of the PG3 Miras translates with the theoretical period-colour relation from Wood et al. (1991; assuming comparable masses between the PG3 & the field versus the LMC Miras) in a mean metallicity of the PG3 and field Miras [FORMULA] 1.4 times as high as the LMC.

The majority of the field SRVs appear to follow a different PC-relation with a slope flatter than the field Miras. But this might be an artifact, if the field SRVs are a non-homogeneous sample of fundamental mode pulsators with longer periods and overtone pulsators with shorter periods. Since each mode has its own PC-relation, their combined distribution could well result in the flatter slope.

3.5. Colour - magnitude diagram

Fig. 7 shows the (K,J-K)0 CMD for the PG3 SRVs and Miras. Isochrones placed at 8 kpc distance for 5 and 10 Gyr old stellar populations with Z = 0.004 and Z = 0.020 are displayed in this figure. The isochrones from Bertelli et al. (1994) are used. They converted their isochrones from the theoretical to the observational plane by convolving the near-infrared bands, as provided by Bessell & Brett (1988), with the spectral energy distributions from Kurucz (1992) for temperatures higher then 4000 K. At lower temperatures they used observed spectra as described in Sect. 4 of Bertelli et al. (1994) and they combined the effective temperature scale from Ridgway et al. (1980) for the late M giants with the Lançon & Rocca-Volmerange (1992) scale for the early M giants. The lack of very red standards limits the near-infrared colour transformations (Bressan & Nasi 1995) and causes the colours of the Z = 0.02 isochrones to `saturate' around (J-K)0 [FORMULA] 1[FORMULA] We derived a new, empirical [FORMULA]-(J-K)0 colour relation by making a conservative fit through the [FORMULA] and (J-K)0 data available for cool giants (see Ng et al. 1998 for details). This relation was adopted to compute the near infrared colours of the isochrones shown in Fig. 7.

[FIGURE] Fig. 7. K0 vs (J-K)0 Colour-Magnitude Diagram for the PG3 SRVs and Miras, the symbols are the same as those used in Fig. 4. The `error' bars attached to the two symbols on the right side indicate the effects of variability, the symbols do not correspond to the actual data. Isochrones (Bertelli et al. 1994), placed at 8 kpc distance (Wesselink 1987, Reid 1993), are shown for 5 and 10 Gyr populations with Z = 0.004 and Z = 0.020. The near-infrared colours of those isochrones have been computed with an empirical [FORMULA]-(J-K)0 colour relation, see Ng et al. (1998; Table 1) for details about this relation.

The SRVs and Miras follow the trend indicated by the isochrones. SRVs and Miras with similar age and metallicity, distributed around isochrones with comparable age and metallicity, belong to the same population. Note that variability moves the stars in an almost diagonal direction in the CMD. The upper limits for the variation of the J-K colour around the light cycle is about [FORMULA] 0[FORMULA] for a Mira and [FORMULA] 0[FORMULA] for a SRV (Hron & Kerschbaum 1994). For the SRVs the amplitudes are too small to explain the scatter, while for the Miras the scatter might be for a large fraction due to their variability.

The uncertainties in the interstellar reddening is according to Wess87 in the worst case 0[FORMULA] in [FORMULA], which translates in [FORMULA] 0[FORMULA] in K and [FORMULA] 0[FORMULA] in J-K. Interstellar reddening therefore cannot explain the observed spread of [FORMULA] 0[FORMULA] in J-K. This spread on the other hand might be related to the intrinsic width of the instability strip. The intrinsic spread of the LMC PC relation provides an upper limit. According to Kanbur et al. (1997) this spread amounts for oxygen rich stars to 0[FORMULA] in J-K. This is again smaller than the observed colour spread.

[FIGURE] Fig. 8a and b. (J-H)0 vs (H-K)0 Colour-Colour Diagram for the PG3 SRVs and Miras, the symbols are the same as those used in Fig. 4. The polygon boxes show the location of the SRVs the Miras in different galactic environments: a Field and b LMC. In frame a the solid line represents the location of the Sgr I Miras by Glass et al. (1995), the dot-shaded box the Miras (Feast et al. 1989), the dot-dashed box the `blue SRVs and the long-dashed box the `red' SRVs (KH92 & KH94). In frame b the dot-shaded box represents the approximate location of the SRVs and the solid box the Miras from the Reid et al. (1995) LPVs (see Sect. 2.6)

Independently the variability of the SRVs, the uncertainties in the interstellar reddening and the intrinsic width of the instability strip cannot account for the observed colour spread. In combination even an upper limit for the colour spread, which amounts to 0[FORMULA] is not sufficient to explain the observed scatter.

The isochrones show that the effect of a 5 Gyr age difference results merely in a shift of [FORMULA] 0[FORMULA] in the (J-K)0 colour. On the other hand, metallicity differences result in larger shifts in the (J-K)0 colour, e.g. [FORMULA] 0[FORMULA] in Fig. 7. One might argue that the depth of the bulge would invalidate an analysis with isochrones, but one can verify easily that a similar result is obtained by removing the differential distance effects. For example, through an absolute calibration of the magnitude from the periods of the variables with the PK0-relation at the distance of the galactic centre, i.e. 8 kpc (Wesselink 1987, Reid 1993). The reason for the similarity of the result is that it depends strongly on the colour range covered and less on the magnitude (apparent or absolute) of the stars.

The presence of a large spread in the metallicity could explain the distribution of the stars in the CMD. Due to the large spread in metallicity it is not possible to get a reliable age estimate. The red edge is due to stars around solar metallicity, while the stars at the blue edge have Z = 0.004.

3.6. Colour - colour Diagram

The colour-colour diagram in Fig. 8a and b demonstrates the difference between the Miras and SRVs in PG3. For comparison the different locations of the Sgr I Miras (Glass et al. 1995; note that we adopted an extinction in agreement with R0 = 8 kpc, see also Sect. 3.3), the LMC LPVs (Reid et al. 1995) and the field Miras and SRVs (Feast et al. 1989, KH92 & KH94) are indicated. However, the shape of the LMC box is not well defined due to the small number of stars used present in the region (J-H)[FORMULA] 0[FORMULA] The PG3 SRVs are shifted with respect to the PG3 Miras to bluer (H-K)0 and slightly redder (J-H)0.

From the large similarity in period and amplitude between field `red' SRVs and PG3 SRVs one might expect that the PG3 SRVs will be located in the region of the `red' field SRVs. Although there is some overlap, the PG3 SRVs appear to be on average bluer in both colours than the `red' field SRVs. The PG3 SRVs extend to redder colours than the LMC SRVs

The PG3 Miras are more similar to the Sgr I Miras than to the comparison samples of field and LMC Miras. The PG3 stars do not extend to (J-H)0 colours as red as the Sgr I Miras. This could be related with deficiency of PG3 Miras with periods longer than 320 days. Within the uncertainties in the adopted colour transformations PG3 and Sgr I are comparable to each other.

For (J-H)0 [FORMULA] 0[FORMULA] and (H-K)0 [FORMULA] 0[FORMULA] the LMC is compared to the field and PG3 abundant with relatively blue LPVs/Miras. In addition, the LMC and the field have in contrast to PG3 and Sgr I for (J-H)0 [FORMULA] 0[FORMULA] and (H-K)0 [FORMULA] 0[FORMULA] in this region a significant number of LPVs/Miras. In the following section we will argue that this is due to a combination of age and metallicity of the stars.

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© European Southern Observatory (ESO) 1998

Online publication: September 14, 1998