The Kinematics and Zero Point of the log P -- <M_K> Relation for Galactic Field RR Lyrae Variables via Statistical Parallax

Abstract

The kinematical parameters of the local field RR Lyrae population and the zero point of the log P--<M_K> relation for these variables are inferred by applying the statistical parallax (maximum-likelihood) technique to a sample of 182 RR Lyraes with known periods, radial-velocities, metallicities, K-band photometry, and absolute proper motions on the ICRS system. The K-band magnitudes were adopted from the list of Fernley et al. (1998) and the 2MASS Second Incremental Data Release. The parameters of the velocity distribution are found to be (U_0,V_0,W_0) = (-10 +/- 10, -51 +/- 8, -14 +/- 5) km/s, (sigma_U, sigma_V, sigma_W) = (62 +/- 10, 45 +/- 8, 28 +/- 6) km/s and (U_0,V_0,W_0) = (-23 +/- 13, -213 +/- 12, -5 +/- 8) km/s, (sigma_U, sigma_V, sigma_W) = (157 +/- 12, 98 +/- 8, 91 +/- 7) km/s for the thick-disk (41 stars) and halo (141 stars) objects, respectively. The zero point of the infrared PL relation of Jones et al. (1992) (based on the results obtained using the Baade-Wesselink method) is confirmed: we find <M_K> = -2.33 log P_F-0.82 +/- 0.12 compared to <M_K> = -2.33 log P_F-0.88 as inferred by Jones et al. (1992). A conversion of the resulting log P-<M_K> relation to V-band luminosities yields the metallicity-luminosity relation <M_V> = +1.04 + 0.14 [Fe/H] +/- 0.11. Our results imply a solar Galactocentric distance of R_0 = 7.6 +/- 0.4 kpc and an LMC distance modulus of DM_LMC = 18.18 +/- 0.12 (cluster RR Lyraes) or DM_LMC = 18.11 +/- 0.12 (field RR Lyraes), thereby favoring the so-called short distance scale.