Hipparcos data and the mass-radius relation

While spectroscopic measurements of white dwarfs have made significant advances in our understanding of the composition and structure of white dwarf atmospheres, interpreting some of these results relies on theoretical models of the evolutionary paths the stars follow and, in particular, the theoretical mass-radius relation. This was first defined by Chandrasekhar in his Nobel prize winning work on white dwarf structure. However, he and later authors only considered a fully degenerate configuration. Recent work has realised that the non-degenerate envelope plays an important role, particularly in the hot white dwarfs which form the EUV and X-ray emitting samples. Whichever framework is used, the relationship between the mass and radius of a white dwarf remains a theoretical concept which has hardly been tested empirically due to the difficulty of making accurate measurements of mass and radius in such faint objects.

The Hipparcos mission has provided an opportunity of making parallax measurements of hitherto unsurpassed accuracy. Since several of the brightest white dwarfs are included in the Hipparcos catalogue, this data yields distance measurements from which mass and radius can than then be estimated more reliably than before. In collaboration with M. Cruise (Birmingham) and A. Penny (RAL), we obtained early release data from the Hipparcos project to study white dwarfs in the ROSAT WFC sample. Using new spectroscopic data to also improve temperature and gravity measurements we have been able to determine the mass and radius for five white dwarfs spanning a range of temperatures (from 25000K to 55000K) and surface gravities (from 7.2-8.2). There is good agreement between the observed mass-radius relation and the theoretical predictions, demonstrating that the latter are reliable and can be used to convert spectroscopically determined gravities to masses with confidence ( Barstow et al, MNRAS, 1997, vol 290, pg 505-514 ). This results is of great importance for studies of the white dwarf mass distribution. In addition, since the white dwarf cooling rates are very sensitive to radius, tests of the evolutionary models are important for verifying the stellar ages and the luminosity function, from which limits on the age of the Galactic disk are obtained.

The best fitting mass and radius for V471 Tau, together with the associated 1 and 2 sigma uncertainty contours, when mass estimates from the work of Bois et al is included as an additional constraint.