K-band (2.2 µm) period-luminosity relation for RR Lyrae stars and the system of distance moduli for globular clusters

Astronomy and Astrophysics – Astronomy

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We analyze the published K-band (2.2 m) observations of RR Lyrae stars in nine Galactic globular clusters. After revealing and correcting several mistakes in the original data, we determined the slope of the Kband period-luminosity relation for RR Lyrae stars in the globular clusters from 173 stars: ( _2.338 +/- 0.067) log P_F. Using the zero point found by Jones et al. (1992) for RR Lyrae stars of the Galactic field, we adopted the relation (M_K) = _2.338log log P_F _0.88. This relation agrees with the modern relation between M_V and [Fe/H] and corresponds to the LMC distance modulus mod{^o_v}(RR) = 18.23 +/- 0.04, in excellent agreement with the most recent distance modulus of the LMC that was derived from Cepheids, mod{^o_v}(CEP) = 18.25 +/- 0.05 (Berdnikov et al. 1996). We used our K-band period-luminosity relation to determine the distance moduli mod{^o_v}(RR) for the globular clusters. Their comparison with the systems of distance moduli by Kukarkin (1974) and Harris (1996) shows general agreement with the former scale but systematic deviations from the latter scale, which increase with increasing metal deficiency in clusters. On average, mod{^o_v}(Harris)_mod{^o_v} = + 0.14m. Our method of determining the distances to globular clusters has several advantages. For example, a small number of observations is enough to reliably determine (K) for an RR Lyrae star, and the effect of the errors in the interstellar reddening is marginal, because A(K) = 0.1 A(V).

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