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T. G. Barnes (McDonald Observatory, University of Texas at Austin), T. R. Jefferys, W. H. Jefferys (Dept. of Astronomy, University of Texas at Austin)
We have undertaken a study of RR Lyrae distances, luminosities, and kinematics through the statistical parallax method. Unlike previous maximum likelihood approaches, we construct a hierarchical Bayes model to describe the data. Using an assumed absolute magnitude for RR Lyrae stars, a distance for each star is determined from its reddening-corrected apparent magnitude; the proper motion and radial velocity data are converted into observed space velocities relative to the Sun. Latent variables for the actual velocity of each star are introduced and a multivariate normal likelihood function is assumed (the three components of the velocity of each star are characterized by a variance-covariance matrix, assumed known). A multivariate normal prior on the velocities is introduced with parameters being the velocity of the Sun relative to the group of stars as a whole and the variance-covariance matrix of the peculiar velocities of the RR Lyrae stars. Priors on the solar velocity and the variance-covariance matrix are introduced. Latent variables are also introduced to represent the individual magnitudes of the stars, with a normal prior centered on the group mean absolute magnitude with an informative variance. By a combination of Gibbs and Metropolis-Hastings sampling, we draw a sample from the full posterior distribution and draw inferences on the quantities of interest in the usual way.
Initially we are applying our model to a dataset earlier analyzed by maximum likelihood techniques (Hawley et al. 1986, ApJ, 302, 626) As far as we know, ours is the first application of a fully Bayesian analysis to this problem, and we wish compare our results with the earlier analyses to see how they differ. The HIPPARCOS satellite has provided a much larger database of highly accurate proper motions for these objects, and there has been considerable augmentation and improvement of the radial velocity database (see Dambis & Vozyakova, 2004, ``Variable Stars in the Local Group", ASP Conf. Ser., in press). Thus we plan eventually to apply our model to this much better database. We also plan to include metallicity explicitly in our model, which has not been done previously as other methods do not provide an effective way to study this dependence.
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Bulletin of the American Astronomical Society, 36 #2
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