Mass-radius relations for helium white dwarfs

In recent years, white dwarf stars are receiving increasing attension. The recent studies on the relation of M-R for the WDs are those of Wood (1990), Vennes et al. (1995) and Althaus and Benvenuto (1997, 1998). Vennes et al. (1995) computed static M-R relation for masses between 0.4 $M_\odot$ and 0.7 $M_\odot$ assuming non zero temperature effects. They assumed the luminosity is proportional to the mass which works for cool WDs but their results are in the range of high effective temperatures. As Althaus and Benvenuto (1997) mentioned, luminosity is not proportional to a constant for hot WD interiors because of neutrino emission. The purpose of this study is to present the effect of neutrino emission at finite temperatures. We considered fully degenerate configuration for WDs with pure helium composition to obtain static mass-radius relation for masses greater than 0.4 $M_\odot$ with luminosity mass ratio due to neutrino energy loss.