SIMBAD references

The famous mass-radius relation of white dwarf stars is based on theoretical considerations. The structure of a white dwarf, and thereby its fundamental properties, are deduced from the physical properties of the degenerate electron gas. Numerical computations take temperature and evolution effects into consideration. However, the few cases in which the masses and the radii of white dwarfs were directly or indirectly determined from observations do not agree well with the theoretical relation. The often stated discrepancy between theory and observation is usually explained by observational errors. In this work, we present the current situation of the empirical mass-radius relation using spectroscopic determinations of T_eff and logg for a large number of white dwarfs. Using the best values for parallaxes and gravitational redshifts available, we calculate the masses and radii. In comparison with a theoretical mass-radius relation, the empirical masses and radii show a large scattering. Independent of the method used to determine masses and radii, i.e., whether via parallaxes, gravitational redshift, or a combination of both, it seems that the observations cannot confirm the theory. In other words, the scattering of masses and radii in the mass-radius diagram is so large, that the observations do not show a correlation between mass and radius as predicted by the theoretical mass-radius relation. On the other hand, it is shown that the observed masses and radii are, within their errors, in accordance with the theoretical relation. We demonstrate that the main reason for the discrepancy between theory and observation are the uncertainties of the observational quantities. Therefore, an empirical description of a relation between mass and radius can only be achieved by using the most reliable values. We also discuss the improvements of the empirical mass-radius relation expected from the parallax measurement of the HIPPARCOS satellite.