Systematics of RR Lyrae Statistical Parallax. II. Proper Motions and Radial Velocities

Abstract

We investigate whether a misestimate of proper motions or radial velocities could have been a source of substantial systematic errors in the statistical parallax determination of the absolute magnitude of RR Lyrae stars. In an earlier paper, we showed that the statistical parallax method is extremely robust and rather insensitive to various systematic effects. The main potential problem with this method would therefore arise from systematically bad observational inputs, proper motions, radial velocities, apparent magnitudes, and/or extinctions. Here we focus on the proper motions and radial velocities. We compare three different catalogs of proper motions: Lick, Hipparcos, and the one compiled by Wan et al. (WMJ). We find that the WMJ catalog is too heterogeneous to be a reliable source. We analyze a sample of 165 halo RR Lyrae stars with either Lick or Hipparcos proper motions. For the stars with both Lick and Hipparcos proper motions, we use the weighted means of reported values. Various possible biases are investigated through vigorous Monte Carlo simulations, and we evaluate the small corrections due to Malmquist bias, anisotropic positions of the stars on the sky, and non-Gaussian distribution of stellar velocities. The mean RR Lyrae absolute magnitude is MV = 0.74 ± 0.12 at the mean metallicity of the sample, [Fe/H] = -1.60, only 0.01 mag brighter than the value obtained in the previous study, which did not incorporate Hipparcos proper motions. To test for systematics in the RR Lyrae radial velocities, we analyze a non-kinematically selected sample ([Fe/H] ≤ -1.5) of 103 RR Lyrae stars with Hipparcos and/or Lick proper motions and 724 non-RR Lyrae stars from Beers & Sommer-Larsen. We find MV = 0.79 ± 0.12 at [Fe/H] = -1.79. Because the radial velocities in this sample are dominated by non-RR Lyrae stars, the agreement of the two determinations suggests that the pure RR Lyrae sample is not significantly affected by systematics in radial velocities. If the two determination are combined (taking into account the 0.45 correlation coefficient between them), the net result is MV = 0.77 ± 0.10 at [Fe/H] = -1.71. The faint absolute magnitudes of RR Lyrae stars confirmed by this analysis gives strong support to the short distance scale.