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Astron. Astrophys. 348, L33-L36 (1999)

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3. Discussion

For their preferred sample of 84 stars with [Fe/H] [FORMULA] F98 obtain a zero point of 1.05 [FORMULA] 0.15 mag for the [FORMULA]-[Fe/H] relation (assuming a slope of 0.18), in agreement with results from Baade-Wesselink methods. When applying the RP method to the same sample of stars, we find a zero point 0.28 mag brighter. An analogous result, which means a zero point [FORMULA]0.30 mag brighter than the Baade-Wesselink one, is derived for the [FORMULA]-[FORMULA] relation.

Even if within the error bar the results derived with the different methods formally agree, there appears to exist a systematic difference between zero points obtained using the parallaxes directly and zero points obtained by employing methods which are sensitive to proper motions and radial velocities (F98, T98, L98), especially if one also takes into account the results for the HIPPARCOS Cepheids. Also with the Cepheids one finds that methods where the results are mostly sensitive to the proper motions and radial velocities find dimmer zero points for the Cepheids PL-relation compared to methods which directly use the parallax. In particular, using the RP method Feast & Catchpole (1997) derived a zero point of [FORMULA] mag, and Lanoix et al. (1999) using a slightly bigger sample find [FORMULA] mag. Oudmaijer et al. (1998), using only the positive parallaxes but then correcting for the LK-bias, find [FORMULA] mag. On the other hand, L98 find a zero point of [FORMULA] mag using a maximum likelihood method that takes into account parallaxes, proper motions and velocity informations. As discussed by Pont (1999), in this technique the parallaxes do not influence the result to first order, and the method is similar to a statistical parallax analysis. A careful check of all assumptions implicit in the kinematical methods could be the key to understanding the nature of this puzzling disagreement. In the case of the RP method, as discussed extensively in the previous section, the condition for deriving the zero point without introducing a bias is to have [FORMULA] small with respect to the errors on the parallaxes; this condition appears to be fulfilled in the sample considered.

Our zero point for the [FORMULA]-[Fe/H] relation is in agreement with results from the Main Sequence fitting technique (Gratton et al. 1997), and from theoretical Horizontal Branch models. In particular, the Horizontal Branch models by Salaris & Weiss (1998) and Cassisi et al. (1999) give a zero point for the Zero Age Horizontal Branch (ZAHB) at the RR Lyrae instability strip in the range 0.74-0.77 mag. To compare the results for the ZAHB brightness with the [FORMULA]-[Fe/H] relations mentioned in this paper which consider the mean absolute brightness of the RR Lyrae stars population at a certain metallicity, one has to apply a correction by [FORMULA] mag (see, e.g., Caloi et al. 1997 and references therein) to the ZAHB result; this takes into account the evolution off the ZAHB of the observed RR Lyrae stars. Even after applying this correction the theoretical results are in good agreement with the results from the RP method. Moreover, the zero point derived with the RP method is also in agreement with the recent results by Kovacs & Walker (1999), who derive, by employing linear pulsation models, RR Lyrae luminosities that are brighter by 0.2-0.3 mag with respect to Baade-Wesselink results.

Finally, we want to derive the LMC distance implied by our zero point of the RR Lyrae distance scale. Table 2 collects the available data on RR Lyrae stars in LMC clusters: the name of the cluster, the observed mean V-magnitude, reddening, metallicity and the difference in distance modulus ([FORMULA]) between the cluster and the main body of the LMC. All these data are taken from the references listed. From them the dereddened magnitude at the centre of the LMC (Col. 7), and this value minus the quantity (0.18 [Fe/H]) (Col. 8) have been calculated for those clusters with [FORMULA]0.1 mag. At this point we have taken into account the difference in metallicity between the clusters before deriving the LMC distance. More in detail, we have derived the weighted mean of the values in Col. 8 to find an average of 19.38 with a rms dispersion of 0.10 mag, which can be compared directly to the zero point of the [FORMULA][Fe/H] relation to find a distance modulus of 18.61 [FORMULA] 0.28. This result turns out to be consistent with the Cepheids distance to the LMC as derived by Feast & Catchpole (1997) or Oudmaijer et al. (1998).


[TABLE]

Table 2. Data on RR Lyrae in LMC clusters


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© European Southern Observatory (ESO) 1999

Online publication: July 26, 1999
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