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Astron. Astrophys. 330, 515-520 (1998)

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5. MV , [Fe/H] calibration and implications for the distance scale

Combining the results from Section 3 (the trigonometric parallax of RR Lyrae, which gives [FORMULA] =0.78 [FORMULA] 0.29 at [Fe/H]=-1.39) and Section 4 (the Statistical Parallax solution for 84 Halo RR Lyraes, which gives [FORMULA] =0.77 [FORMULA] 0.17 at [Fe/H]=-1.66) we obtain [FORMULA] =0.77 [FORMULA] 0.15 at [Fe/H]=-1.53. These results give no information about the slope of the [FORMULA],[Fe/H] relation, however this has recently been discussed by Fernley et al. (1997) who estimate a value of 0.18 [FORMULA] 0.03. Thus we obtain

[EQUATION]

5.1. Distance to the LMC

We show in Table 3 some recent determinations of the distance modulus of the LMC, both using RR Lyraes and other distance indicators.


[TABLE]

Table 3. LMC distance moduli


Below are some comments on the entries on Table 3.

RR Lyraes. There are observations of RR Lyraes in 5 LMC Clusters (Walker 1992, Reid and Freedman 1994) and combining the data from the clusters gives a mean dereddened magnitude [FORMULA] of 18.98 and a mean [Fe/H] of -1.8. From Eq. (1) we obtain a distance modulus (m-M) of 18.26 [FORMULA] 0.15.

Recently several groups have worked on Baade-Wesselink analyses of RR Lyrae stars (Liu and Janes 1990a, Jones et al. 1992, Cacciari et al. 1992, Skillen et al. 1993 and Fernley 1994) and results of the different groups are reasonably consistent. Taking a simple mean gives

[EQUATION]

where the error on the zero-point comes from both the random error, [FORMULA] 0.06, and the estimated systematic errors in the Baade-Wesselink method, [FORMULA] 0.12. At [Fe/H]=-1.53 Eq. (2) predicts [FORMULA] =0.73 [FORMULA] 0.14 which is in good agreement with the zero-point derived from the HIPPARCOS data in Eq. (1), which is itself based on two independent methods. In our opinion this agreement in the zero-point between three completely independent methods of analysis is the main result of this paper.

Nonetheless it is clear from Table 3 that the resulting LMC distance moduli from the RR Lyraes are in general lower than those from other distance indicators. Are there other factors which could be affecting the distance estimate ? One possibility is depth effects in the LMC. The observed diameter of the LMC is [FORMULA] and if the depth is comparable to the width this would be equivalent to [FORMULA] 0.14 in (m-M). However, this is unlikely to be significant in the present case since the mean [FORMULA] for the RR Lyraes is based on observations of RR Lyraes in 5 clusters which are spread evenly across the face of the LMC (Walker 1992).

Another possibility is that, for some reason, RR Lyraes in clusters are not the same as RR Lyraes in the field. Liu and Janes (1990b) did Baade-Wesselink analyses of 4 RR Lyraes in the Globular Cluster M4 ([Fe/H] [FORMULA] -1.4) and Storm et al. (1994) did Baade-Wesselink analyses of 2 RR Lyraes in M5 ([Fe/H] [FORMULA] -1.5) and 2 in M92 ([Fe/H] [FORMULA] -2.1). For the intermediate metallicity clusters M4 and M5 the absolute magnitudes derived by these authors were in the mean 0.03 mags fainter (M4) and 0.06 mags brighter (M5) than predicted by Eq. (2), which is the Baade-Wesselink relation for field stars. For the metal-poor cluster M92 the derived absolute magnitudes were 0.14 mags brighter than predicted by Eq. (2). Because of the difficulty of doing Baade-Wesselink analyses of such relatively faint stars the quoted error on these absolute magnitudes was [FORMULA] 0.20 mags. Certainly for the intermediate metallicity clusters the level of agreement between the field and cluster RR Lyraes is very good. For M92 the agreement is less good and we note here the discussion by Storm et al. concerning the relative fractions of "normal" and "evolved" RR Lyraes in the RR Lyrae Instability Strip as a function of metallicity. In intermediate metallicity clusters it is expected that the majority of RR Lyraes are "normal", i.e. stars on the zero-age Horizontal Branch. In more metal-poor clusters it is expected that there will be an increasing number of "evolved" RR Lyraes, i.e. stars with zero-age Horizontal Branch positions to the blue of the Instability Strip and which are now crossing the Instability Strip during their redward evolution towards the Asymptotic Giant Branch. In general the "evolved" RR Lyraes will be brighter than "normal" RR Lyraes. If this argument is correct then RR Lyraes in more metal-poor clusters will, in the mean, be brighter than predicted by Eqs. (1) and (2). A similar result was obtained by Lee et al. (1990) who constructed synthetic Horizontal Branches from grids of evolutionary tracks. These showed that, for more metal-poor clusters, the mean level of the Horizontal Branch was [FORMULA] 0.1 brighter than the zero-age level, this being due to the mixing of "normal" and "evolved" RR Lyraes. In the present context, any brightening of the mean level of the Horizontal Branch due to the presence of significant numbers of "evolved" stars, will increase the derived LMC distance.

Cepheids. It can be seen from Table 3 that the Cepheids produce a less consistent set of results. This is particularly striking in the applications of HIPPARCOS data. Feast and Catchpole (1997) used HIPPARCOS parallaxes of local field Cepheids to determine the zero-point of the Cepheid Period-Luminosity relation and hence derive an LMC distance modulus of 18.70 [FORMULA] 0.10. By contrast the Cluster Cepheids give a distance modulus of 18.33 [FORMULA] 0.10, based on the work of Feast (1995) corrected to the HIPPARCOS Pleiades distance modulus of 5.33 [FORMULA] 0.06 (Mermilliod et al. 1997). The work of Feast and Catchpole has also been criticised by Szabados (1997), who argues that the large number of binaries amongst the HIPPARCOS Cepheids leads to a systematic under-estimate of parallaxes (and hence too bright a zero-point and too large an LMC distance modulus). It is clear that the results from applying HIPPARCOS data to Cepheids are still in their early stages.

A more consistent set of values for the Cepheids comes from the Baade-Wesselink analyses of Gieren et al. (1993, 1997), the former using purely optical data and the latter using both optical and infrared data.

A simple mean of the 4 Cepheid distance moduli gives a value of 18.54, which is [FORMULA] 0.25 larger than given by the RR Lyraes. In this matter we note the recent work of Sekiguchi and Fukugita (1997) concerning the sensitivity of the zero-point of the Cepheid P-L relation to metallicity effects. They used the high quality abundances derived for 23 galactic Cepheids by Fry and Carney (1997) to show that the residuals from the Cepheid P-L relation are strongly correlated with metallicity, specifically [FORMULA] [FORMULA] = -2.15[Fe/H]. Assuming the Cepheids in the LMC are slightly metal-poor compared to Galactic Cepheids, [FORMULA] -0.15 dex (Feast and Walker 1985), then the relation found by Sekiguchi and Fukugita would reduce the Cepheid LMC distance modulus by 0.32.

Miras. van Leewuen et al. (1997) have used HIPPARCOS parallaxes of nearby Miras to calibrate the Mira P-L relations. Examination of the resulting plots (their Figs 2 and 3) shows a relatively poor fit, with 4 out of the 8 high-weight stars lying 2 or more sigma from the line. It seems clear that there are systematic effects that have not been completely dealt with in the analysis, possibly metallicity effects in the stars or biases in the parallaxes due to surface inhomogeneities on the stars (note that Miras have angular diameters that are typically an order of magnitude larger than their parallaxes).

SN1987A. Four papers published this year show a range of values between 18.37 and 18.67 for the LMC distance modulus derived from SN1987A. It is clear that the early hopes that SN1987A would give the definitive LMC distance are, as yet, unfulfilled.

5.2. Ages of the Globular Clusters

Chaboyer et al. (1996) discuss the ages of the Globular Clusters using the Yale isochrones and Globular Cluster observations from the literature. They derive ages using several different assumptions about the RR Lyrae [FORMULA], [Fe/H] relation. Interpolating amongst their relations in order to fit our Eq. (1) we obtain a mean age of 17.4 [FORMULA] 3.0 GYrs.

Reid (1997) has recently claimed a mean age of [FORMULA] 12 GYrs. The difference between the two ages is entirely due to the distance calibration. Reid obtains distances to the Globular Clusters by fitting their main sequences to local subdwarfs whose absolute magnitudes he determines from their HIPPARCOS trigonometric parallaxes. This distance scale is [FORMULA] 0.35 mags longer than the RR Lyrae distance scale given by Eq. (1). Two other groups have also analysed the HIPPARCOS trigonometric parallaxes of local subdwarfs. Fusi Pecci et al. (1997) obtain similar results to Reid, however Pont et al. (1997) make the subdwarfs fainter by [FORMULA] 0.30 mags, i.e. consistent with the RR Lyraes. At the present time the situation with the subdwarfs is not clear, in particular the important question of when to apply bias corrections to HIPPARCOS parallaxes is not settled.

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Online publication: January 16, 1998
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