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Astron. Astrophys. 336, 925-941 (1998)

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6. The ([FORMULA]) and ([FORMULA]) relations

The ([FORMULA]) and ([FORMULA]) relations for the Galactic Center variables are shown in Figs. 10 and 11, respectively. LPVs in the Baade's Window field of Glass et al. (1995) are also shown along with LMC OH/IR stars from Wood et al. (1992) and a line representing the position of optically visible LPVs in the LMC from Hughes & Wood (1990) (see also Feast et al. 1989). The LMC line is split into two parts, the shorter period end representing the LMC LPVs with masses [FORMULA]1.5M[FORMULA] while the longer period part of the line represents more massive LPVs with 1.5 [FORMULA] M/M[FORMULA] [FORMULA] 6. Distances of 8.9 kpc to the Galactic Center, 8.7 kpc to the Baade's Window field and 51.3 kpc (distance modulus 18.55) to the LMC have been used for consistency with the results of Glass et al. (1995).

[FIGURE] Fig. 10. The ([FORMULA]) diagram for LPVs near the Galactic Center and in Baade's Window and the LMC. The Galactic Center objects are shown as symbols whose shapes have the same meaning as in Fig. 6: the filled symbols are LPVs with (K-L)[FORMULA] [FORMULA] 1.3. The Baade's Window objects are shown as crosses. The line represents optically visible LPVs in the LMC from Hughes & Wood (1990) while the plus signs represent LMC OH/IR stars from Wood et al. (1992).

[FIGURE] Fig. 11. The ([FORMULA]) diagram for LPVs near the Galactic Center and in Baade's Window and the LMC. Symbols are as in Fig. 10

It is clear that the majority of the Galactic Center objects do not follow the LMC ([FORMULA]) relation for optically visible LPVs and nearly all lie well below it, with offsets of up to 6 magnitudes. This indicates that most of these objects are surrounded by cool, dense, dusty shells that obscure the central stars in K. On the other hand, the majority of the Baade's Window LPVs lie on the LMC ([FORMULA]) relation as expected (since the distance given by Glass et al. was derived by fitting to the LMC relation). However, the longest period Baade's Window LPVs, which are generally the dusty IRAS sources, lie well below the LMC relation. Similarly, the LMC OH/IR stars have much longer periods than the optically visible LPVs of similar K magnitude.

In the ([FORMULA]) diagram, the optically detected LPVs in Baade's Window and the LMC once again lie on the same relation, while most of the Galactic Center LPVs show a lower luminosity, although the offset is smaller than in the ([FORMULA]) diagram. Low [FORMULA] values were also found by Jones et al. (1994) and Blommaert et al. (1997) with much smaller samples of stars. At least some of the scatter in the ([FORMULA]) diagram is due to the scatter in the values of [FORMULA]. This scatter could be reduced by obtaining photometry at wavelengths longer than 3.6 µm (L).

It is usually assumed that low luminosities or, equivalently, very long periods for LPVs are a demonstration of the effect of mass loss on pulsation period. Before the superwind phase of mass loss starts, LPVs of a given metallicity seem to lie on a unique relation as demonstrated by the LMC and Baade's Window LPVs. Now, for LPVs in general, the pulsation period varies as R[FORMULA]/M[FORMULA], where [FORMULA] 1.5-2 and [FORMULA] 0.5-0.9 depending on whether the LPVs pulsate in the first overtone or fundamental mode (Fox & Wood 1982; Wood 1990). Once the stellar mass has been reduced significantly as a result of a superwind, the pulsation period increases due to the combined effects of the mass reduction and the increase in mean radius that results from structural readjustment (Vassiliadis & Wood 1993). In this situation, the LPVs evolve almost horizontally from their positions as optical variables in the ([FORMULA]) diagram to the positions found here for the Galactic Center OH/IR stars. This sample of stars is the first to clearly demonstrate this effect over a wide range of luminosities.

The shorter period stars at the top of the envelope of Galactic Center variable stars in Fig. 11, in particular the newly discovered variables, do not have the extremely red intrinsic colours that might be expected if these stars were surrounded by dense circumstellar shells produced by superwind mass loss. The pulsation periods of these stars are probably not greatly affected by mass reduction as described above. Such stars with K-[FORMULA] 1.3 are shown in Figs. 10 and 11 as filled symbols (we use this colour cutoff as it corresponds to the red limit of the optically-visible LPVs in Baade's Window). For [FORMULA] 300 days, these LPVs have [FORMULA] and [FORMULA] values in excellent agreement with those of LPVs in the LMC and Baade's Window. The short periods of these stars and the agreement of their luminosities with those of similar LMC LPVs suggest that they are old and of metallicity up to solar. For example, 47 Tuc with a metal abundance of [FORMULA]0.2 solar has three Miras of period [FORMULA]200 days while the globular clusters NGC5927 and NGC6553, which have near-solar metal abundances and lie in the inner parts of the Galaxy, appear to have Mira variables with periods near 300 days (Andrews et al. 1974). This situation is consistent with solar metallicity being attained in the Galactic Center region during the earliest star formation epoch.

For [FORMULA] 300 days, it is clear that the LPVs without thick dust shells generally fall below the LMC and Baade's Window period-luminosity relations. What we are seeing here is a clear demonstration of the fact that the ([FORMULA]) and ([FORMULA]) relations for LPVs are metallicity dependent, as predicted by Wood (1990). The long periods in high metallicity LPVs result from the giant branch being redder than for solar metallicity stars. Consequently, the stars will have a larger radius and longer period at a given luminosity. Note, however, that substantial metal abundance variations are required to make the metallicity dependence apparent: Wood(1995) found that the ([FORMULA]) relations for the LMC (metallicity [FORMULA]0.5 solar) and SMC (metallicity [FORMULA]0.25 solar) were consistent with each other.

A rough estimate of the metallicity required to produce the long periods seen for the less extreme stars in Fig. 11 (solid symbols) may be obtained as follows. Wood (1990) found that for LPVs pulsating in the fundamental mode (which we will assume here), [FORMULA] (note that this relation was derived for solar metallicity and below, so we will be extrapolating beyond the range of tested parameters here). From Fig. 11, it appears that the bluer Galactic Center stars with [FORMULA] 300 days are [FORMULA]0.4 mag. fainter than bulge or LMC stars of the same period. Ignoring any possible difference in mass, we then find from the equation above that we require the Galactic Center metallicity to be [FORMULA]3.6 times higher than the bulge metallicity in order to get the observed offset between the bulge stars and the bluest Galactic Center stars.

Another very important feature of the ([FORMULA]) diagram is that the luminosities of the main group of Galactic Center OH/IR stars extend considerably brighter than the luminosities of the LPVs in Baade's Window (we exclude the 4 Baade's Window stars that lie above the LMC line in Fig. 11 as they are almost certainly foreground objects). Since final AGB luminosities increase with initial mass (eg. Vassiliadis & Wood 1993) we interpret this to mean that there is a significant component of the intermediate age population of stars near the Galactic Center that does not exist in Baade's Window. If we take [FORMULA] [FORMULA] -6 as the upper limit to the AGB for the main distribution of Galactic Center LPVs, then Fig. 19 of Vassiliadis & Wood, with an assumed solar metal abundance, indicates a maximum initial mass of [FORMULA]4 [FORMULA] for this group of stars. The empirical calibration of AGB tip luminosities from LMC clusters (Frogel et al. 1990) suggests a similar or greater mass.

As well as the main population of LPVs with [FORMULA] -6, there are several more luminous objects. The presence of stars with an [FORMULA] -6 might be challenged by the suggestion that these are in the foreground and much closer to us than we have assumed. We noted in Sect. 1that at most a few of the LWHN stars should be foreground objects. The following argument gives strong evidence that at least one of these luminous stars is truely at the centre or beyond. In trying to measure the angular size of the OH masers of several of the LWHN stars, van Langevelde et al. (1992) and Frail et al. (1994) found that the size was unexpectedly large in directions close to the Galactic Center. They concluded that interstellar scattering in the region close the Galactic Center was the most likely cause of the large observed size. One of the sources observed to have a large size was LWHN 33 for which Blommaert et al. (1997) derive [FORMULA] -6.2. In this situation, LWHN 33 must be behind the scattering region and close to the Center and it cannot be a foreground object: its absolute bolometric magnitudes is truely [FORMULA]-6.2. This result supports our conclusion that other LWHN stars have a similar luminosity.

There are two LPVs of long period in our sample (LWHN 28, P = 806 days; LWHN 116, P = 985) which have [FORMULA]-6.5, consistent with them being young AGB stars with masses [FORMULA] (using the Vassiliadis & Wood results). We also note that the two objects LWHN 70 and 90 are exceptionally red and bright in L although they are relatively faint in K so that periods could not be determined. However, Van Langevelde et al. (1993) determined periods [FORMULA]1000 days for these two objects (the periods belong to category 2, which are uncertain). Our photometry suggests that LWHN 70 is not particularly luminous ([FORMULA] -3.1) but Blommaert et al. (1997) derive [FORMULA] = -6 suggesting this is an AGB star with [FORMULA]. LWHN 90 is far too red for our bolometric correction to be applied. If we use our [FORMULA] colour and L magnitude with the bolometric correction of Blommaert et al. (1997) for such a red star, we derive [FORMULA] [FORMULA] -7 as expected for a massive AGB star with [FORMULA]. However, Blommaert et al. (1997) derived a modest luminosity [FORMULA] = -4.7. Two other stars with category 2 periods [FORMULA]1000 days are listed by Van Langevelde et al. (1993). For one of these, LWHN 21, we derive an unambiguous period of 692 days (compared to 1733 derived by Van Langevelde et al.). Blommaert et al. (1997) give a low bolometric luminosity of -3.7 for the other one (LWHN 72). In summary, it appears that there are 2 to 5 massive (4-7[FORMULA]) AGB stars currently in the OH/IR phase in the Galactic Center fields studied by LWHN. Since the superwind or OH/IR phase of evolution in stars of [FORMULA]5[FORMULA] lasts about 105 years (Vassiliadis & Wood 1993; Tanabé et al. 1997) while the corresponding main-sequence lifetime is [FORMULA]108 years, there should be about 1000 main-sequence stars of [FORMULA]5[FORMULA] near the Galactic Center for each OH/IR star with initial mass [FORMULA]5[FORMULA]. The existence of such stars near the Galactic Center is consistent with a situation where there is ongoing star formation occurring there.

A cautionary note regarding the quantitative estimates of AGB mass is appropriate here. There are no theoretical computations of AGB tip luminosities for stars with metallicity of [FORMULA]3.6 times solar, as estimated above for the Galactic Center LPVs. The results of Vassiliadis & Wood (1993) suggest that AGB tip luminosities for a given initial mass actually reduce with increased metal abundance, which would suggest that the initial masses derived above for AGB stars are underestimates. However, the theoretical results are highly dependent on the mass loss scheme used and need to be treated with caution. In fact, there are good reasons to believe that the mass estimates of up to [FORMULA]7[FORMULA] given above are too high. Firstly, in the LMC, the OH/IR stars with luminosity near the AGB limit of [FORMULA] and probable masses of 5-7[FORMULA] attain periods of up to [FORMULA]1500 days (Wood et al. 1992) whereas the maximum period attained near the Galactic Center is [FORMULA]1100 days (see the next section). Secondly, in the plane of our Galaxy, the variable OH/IR stars attain pulsation periods of up to [FORMULA]2800 days (Herman & Habing 1985; Van Langevelde 1990), this period presumably representing the most advanced stage in the evolution of the most massive AGB stars ([FORMULA]). Once again the maximum periods in the Galactic Center region are less than in the Galactic plane. Although the maximum mass for the Galactic Center AGB stars remains uncertain, the high luminosities (see above) and long periods (see next section) of these stars leave little doubt that the maximum mass is greater than in the bulge.

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© European Southern Observatory (ESO) 1998

Online publication: July 27, 1998
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