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Bayesian inference of stellar parameters and interstellar extinction using parallaxes and multiband photometry
Astrometric surveys provide the opportunity to measure the absolutemagnitudes of large numbers of stars, but only if the individualline-of-sight extinctions are known. Unfortunately, extinction is highlydegenerate with stellar effective temperature when estimated frombroad-band optical/infrared photometry. To address this problem, Iintroduce a Bayesian method for estimating the intrinsic parameters of astar and its line-of-sight extinction. It uses both photometry andparallaxes in a self-consistent manner in order to provide anon-parametric posterior probability distribution over the parameters.The method makes explicit use of domain knowledge by employing theHertzsprung-Russell Diagram (HRD) to constrain solutions and to ensurethat they respect stellar physics. I first demonstrate this method byusing it to estimate effective temperature and extinction from BVJHKdata for a set of artificially reddened Hipparcos stars, for whichaccurate effective temperatures have been estimated from high-resolutionspectroscopy. Using just the four colours, we see the expected strongdegeneracy (positive correlation) between the temperature andextinction. Introducing the parallax, apparent magnitude and the HRDreduces this degeneracy and improves both the precision (reduces theerror bars) and the accuracy of the parameter estimates, the latter byabout 35 per cent. The resulting accuracy is about 200 K in temperatureand 0.2 mag in extinction. I then apply the method to estimate theseparameters and absolute magnitudes for some 47 000 F, G, K Hipparcosstars which have been cross-matched with Two-Micron All-Sky Survey(2MASS). The method can easily be extended to incorporate the estimationof other parameters, in particular metallicity and surface gravity,making it particularly suitable for the analysis of the 109stars from Gaia.
| A Hipparcos study of the Hyades open cluster. Improved colour-absolute magnitude and Hertzsprung-Russell diagrams
Hipparcos parallaxes fix distances to individual stars in the Hyadescluster with an accuracy of ~ 6 percent. We use the Hipparcos propermotions, which have a larger relative precision than the trigonometricparallaxes, to derive ~ 3 times more precise distance estimates, byassuming that all members share the same space motion. An investigationof the available kinematic data confirms that the Hyades velocity fielddoes not contain significant structure in the form of rotation and/orshear, but is fully consistent with a common space motion plus a(one-dimensional) internal velocity dispersion of ~ 0.30 kms-1. The improved parallaxes as a set are statisticallyconsistent with the Hipparcos parallaxes. The maximum expectedsystematic error in the proper motion-based parallaxes for stars in theouter regions of the cluster (i.e., beyond ~ 2 tidal radii ~ 20 pc) isla 0.30 mas. The new parallaxes confirm that the Hipparcos measurementsare correlated on small angular scales, consistent with the limitsspecified in the Hipparcos Catalogue, though with significantly smaller``amplitudes'' than claimed by Narayanan & Gould. We use the Tycho-2long time-baseline astrometric catalogue to derive a set of independentproper motion-based parallaxes for the Hipparcos members. The newparallaxes provide a uniquely sharp view of the three-dimensionalstructure of the Hyades. The colour-absolute magnitude diagram of thecluster based on the new parallaxes shows a well-defined main sequencewith two ``gaps''/``turn-offs''. These features provide the first directobservational support of Böhm-Vitense's prediction that (the onsetof) surface convection in stars significantly affects their (B-V)colours. We present and discuss the theoretical Hertzsprung-Russelldiagram (log L versus log T_eff) for an objectively defined set of 88high-fidelity members of the cluster as well as the delta Scuti startheta 2 Tau, the giants delta 1, theta1, epsilon , and gamma Tau, and the white dwarfs V471 Tau andHD 27483 (all of which are also members). The precision with which thenew parallaxes place individual Hyades in the Hertzsprung-Russelldiagram is limited by (systematic) uncertainties related to thetransformations from observed colours and absolute magnitudes toeffective temperatures and luminosities. The new parallaxes providestringent constraints on the calibration of such transformations whencombined with detailed theoretical stellar evolutionary modelling,tailored to the chemical composition and age of the Hyades, over thelarge stellar mass range of the cluster probed by Hipparcos.
| The Hyades: distance, structure, dynamics, and age
{We use absolute trigonometric parallaxes from the Hipparcos Catalogueto determine individual distances to members of the Hyades cluster, fromwhich the 3-dimensional structure of the cluster can be derived.Inertially-referenced proper motions are used to rediscuss distancedeterminations based on convergent-point analyses. A combination ofparallaxes and proper motions from Hipparcos, and radial velocities fromground-based observations, are used to determine the position andvelocity components of candidate members with respect to the clustercentre, providing new information on cluster membership: 13 newcandidate members within 20 pc of the cluster centre have beenidentified. Farther from the cluster centre there is a gradual mergingbetween certain cluster members and field stars, both spatially andkinematically. Within the cluster, the kinematical structure is fullyconsistent with parallel space motion of the component stars with aninternal velocity dispersion of about 0.3 km s(-1) . The spatialstructure and mass segregation are consistent with N-body simulationresults, without the need to invoke expansion, contraction, rotation, orother significant perturbations of the cluster. The quality of theindividual distance determinations permits the cluster zero-age mainsequence to be accurately modelled. The helium abundance for the clusteris determined to be Y =3D 0.26+/-0.02 which, combined with isochronemodelling including convective overshooting, yields a cluster age of625+/-50 Myr. The distance to the observed centre of mass (a conceptmeaningful only in the restricted context of the cluster memberscontained in the Hipparcos Catalogue) is 46.34+/-0.27 pc, correspondingto a distance modulus m-M=3D3.33+/-0.01 mag for the objects within 10 pcof the cluster centre (roughly corresponding to the tidal radius). Thisdistance modulus is close to, but significantly better determined than,that derived from recent high-precision radial velocity studies,somewhat larger than that indicated by recent ground-based trigonometricparallax determinations, and smaller than those found from recentstudies of the cluster convergent point. These discrepancies areinvestigated and explained. } Based on observations made with the ESAHipparcos astrometry satellite. Table~2 is also available in electronicform at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5)or via http://cdsweb.u-strasbg.fr/Abstract.html
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Member of following groups:
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Observation and Astrometry data
| Constellation: | Stier |
| Right ascension: | 03h30m59.75s |
| Declination: | -00°07'34.2" |
| Apparent magnitude: | 10.232 |
| Proper motion RA: | 62.1 |
| Proper motion Dec: | -0.9 |
| B-T magnitude: | 10.936 |
| V-T magnitude: | 10.291 |
Catalogs and designations:
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