*Astron. Astrophys. 330, 515-520 (1998)*
## 5. M_{V} , [Fe/H] calibration and implications for the distance scale
Combining the results from Section 3 (the trigonometric parallax of
RR Lyrae, which gives =0.78
0.29 at [Fe/H]=-1.39) and Section 4 (the
Statistical Parallax solution for 84 Halo RR Lyraes, which gives
=0.77 0.17 at
[Fe/H]=-1.66) we obtain =0.77
0.15 at [Fe/H]=-1.53. These results give no
information about the slope of the ,[Fe/H]
relation, however this has recently been discussed by Fernley et al.
(1997) who estimate a value of 0.18 0.03. Thus
we obtain
### 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 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
of 18.98 and a mean [Fe/H] of -1.8. From
Eq. (1) we obtain a distance modulus (m-M) of 18.26
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
where the error on the zero-point comes from both the random error,
0.06, and the estimated systematic errors in the
Baade-Wesselink method, 0.12. At [Fe/H]=-1.53
Eq. (2) predicts =0.73
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
and if the depth is comparable to the width this would be equivalent
to 0.14 in (m-M). However, this is unlikely to
be significant in the present case since the mean
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] -1.4) and Storm et al. (1994) did
Baade-Wesselink analyses of 2 RR Lyraes in M5 ([Fe/H]
-1.5) and 2 in M92 ([Fe/H]
-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 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
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 0.10. By
contrast the Cluster Cepheids give a distance modulus of 18.33
0.10, based on the work of Feast (1995)
corrected to the HIPPARCOS Pleiades distance modulus of 5.33
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 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
= -2.15[Fe/H]. Assuming
the Cepheids in the LMC are slightly metal-poor compared to Galactic
Cepheids, -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 , [Fe/H] relation. Interpolating
amongst their relations in order to fit our Eq. (1) we obtain a
mean age of 17.4 3.0 GYrs.
Reid (1997) has recently claimed a mean age of
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
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 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.
© European Southern Observatory (ESO) 1998
Online publication: January 16, 1998
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