Cooling theory of crystallized white dwarfs

Abstract

We examine extensively the effect of the different crystallization related to the presence of major and minor chemical species, on the binding energy and the cooling time of old white dwarfs. We use improved equations of state for the solid and the liquid, and crystallization diagrams calculated within the modern theory of freezing. We show that, in spite of their small abundance, trace elements severely alter the cooling process and lengthen the cooling time of the star for a given luminosity by several gigayears. In particular, Ne-22 is shown to provide enough gravitational energy at crystallization to sustain the star at the same luminosity for a time larger than the one due to the crystallization of C/O itself. These calculations demonstrate the necessity of including a proper treatment of crystallization in modern white dwarf cooling theory. We also consider the effect of an initial composition gradient in the distribution of carbon and oxygen throughout the star. Finally, we show that a substantial portion of the interior of massive white dwarfs is already in a quantum state in the fluid phase and that Debye cooling probably occurs prior to crystallization in these stars.