Description of the Problem The Model and Sampling Program Results and Conclusions Bayesian Analysis of RR Lyrae Distances and Kinematics Thomas R. Jefferys 1 a Thomas G. Barnes III 1 b Andrei Dambis 2 William H. Jefferys 1 b , 3 1 a. Department of Mathematics, b. Department of Astronomy University of Texas at Austin 2 Sternberg Astronomical Institute Universitetskii pr. 13, Moscow, 119992 Russia 3 Department of Mathematics University of Vermont MaxEnt 2007 Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program Results and Conclusions Abstract We are using a hierarchical Bayes model to analyze the distances, luminosities, and kinematics of RR Lyrae stars. Our model relates these characteristics to the raw data of proper motions, radial velocities, apparent luminosities and metallicities of each star. A combination of Gibbs and Metropolis-Hastings sampling, using latent variables for the actual velocity and luminosity of each star, is used to draw a sample from the full posterior distribution of these variables, with consideration to admissibility and the properness of the hierarchical model, and draw inferences on the quantities of interest in the usual way. We have applied our model to the large HIPPARCOS database, and we have attempted to include metallicity and period in our model, which has not been done previously. Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions RR Lyrae Stars: A Short Introduction What are they? Why do we care? They are a class of pulsating variable stars. They are readily recognizable from their periods (0 . 75 ± 0 . 25 days) and characteristic light curves. Fairly bright (40 times as bright as the Sun) and so can be seen to fair distances in the galaxy. Their intrinsic mean visual-band luminosities are nearly constant. This is known from studies of RR Lyrae stars in clusters, where all the stars are at the same distance. Their consistent luminosities makes them useful as “standard candles” for estimating the distance of an object (like a star cluster) Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions RR Lyrae Stars: A Short Introduction What are they? Why do we care? They are a class of pulsating variable stars. They are readily recognizable from their periods (0 . 75 ± 0 . 25 days) and characteristic light curves. Fairly bright (40 times as bright as the Sun) and so can be seen to fair distances in the galaxy. Their intrinsic mean visual-band luminosities are nearly constant. This is known from studies of RR Lyrae stars in clusters, where all the stars are at the same distance. Their consistent luminosities makes them useful as “standard candles” for estimating the distance of an object (like a star cluster) Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions RR Lyrae Stars: A Short Introduction What are they? Why do we care? They are a class of pulsating variable stars. They are readily recognizable from their periods (0 . 75 ± 0 . 25 days) and characteristic light curves. Fairly bright (40 times as bright as the Sun) and so can be seen to fair distances in the galaxy. Their intrinsic mean visual-band luminosities are nearly constant. This is known from studies of RR Lyrae stars in clusters, where all the stars are at the same distance. Their consistent luminosities makes them useful as “standard candles” for estimating the distance of an object (like a star cluster) Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions RR Lyrae Stars: A Short Introduction What are they? Why do we care? They are a class of pulsating variable stars. They are readily recognizable from their periods (0 . 75 ± 0 . 25 days) and characteristic light curves. Fairly bright (40 times as bright as the Sun) and so can be seen to fair distances in the galaxy. Their intrinsic mean visual-band luminosities are nearly constant. This is known from studies of RR Lyrae stars in clusters, where all the stars are at the same distance. Their consistent luminosities makes them useful as “standard candles” for estimating the distance of an object (like a star cluster) Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions RR Lyrae Stars: A Short Introduction What are they? Why do we care? They are a class of pulsating variable stars. They are readily recognizable from their periods (0 . 75 ± 0 . 25 days) and characteristic light curves. Fairly bright (40 times as bright as the Sun) and so can be seen to fair distances in the galaxy. Their intrinsic mean visual-band luminosities are nearly constant. This is known from studies of RR Lyrae stars in clusters, where all the stars are at the same distance. Their consistent luminosities makes them useful as “standard candles” for estimating the distance of an object (like a star cluster) Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions Goals of Our Investigation Determine the mean absolute magnitude (log luminosity) of these stars Investigate the kinematics of the stars as a group Investigate the “cosmic scatter” of the magnitude (i.e., the variation about the mean unexplained by the covariates) Investigate any variation of absolute magnitude with “metallicity” (i.e., content of elements heavier than helium) and period Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions Goals of Our Investigation Determine the mean absolute magnitude (log luminosity) of these stars Investigate the kinematics of the stars as a group Investigate the “cosmic scatter” of the magnitude (i.e., the variation about the mean unexplained by the covariates) Investigate any variation of absolute magnitude with “metallicity” (i.e., content of elements heavier than helium) and period Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions Goals of Our Investigation Determine the mean absolute magnitude (log luminosity) of these stars Investigate the kinematics of the stars as a group Investigate the “cosmic scatter” of the magnitude (i.e., the variation about the mean unexplained by the covariates) Investigate any variation of absolute magnitude with “metallicity” (i.e., content of elements heavier than helium) and period Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions Goals of Our Investigation Determine the mean absolute magnitude (log luminosity) of these stars Investigate the kinematics of the stars as a group Investigate the “cosmic scatter” of the magnitude (i.e., the variation about the mean unexplained by the covariates) Investigate any variation of absolute magnitude with “metallicity” (i.e., content of elements heavier than helium) and period Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions Overview of the Method Our raw data: Proper motions µ (vector of angular motion across the sky per unit time) Radial velocities ρ (kilometers/second of the motions towards or away from the Sun, obtained via the Doppler shift) Apparent magnitudes m of the stars, assumed measured without error. Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions Overview of the Method Our raw data: Proper motions µ (vector of angular motion across the sky per unit time) Radial velocities ρ (kilometers/second of the motions towards or away from the Sun, obtained via the Doppler shift) Apparent magnitudes m of the stars, assumed measured without error. Jefferys, et al. RR Lyrae Distances and Kinematics
Description of the Problem The Model and Sampling Program RR Lyraes and Their Kinematics Results and Conclusions Overview of the Method Our raw data: Proper motions µ (vector of angular motion across the sky per unit time) Radial velocities ρ (kilometers/second of the motions towards or away from the Sun, obtained via the Doppler shift) Apparent magnitudes m of the stars, assumed measured without error. Jefferys, et al. RR Lyrae Distances and Kinematics
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