Two Component Charged Condensate in White Dwarfs

Abstract

The possibility of the formation of a condensate of charged spin-0 nuclei inside white dwarf cores, studied in arXiv:0806.3692 and arXiv:0904.4267, is pursued further. It has been shown, for cores composed mainly of one element (Helium or Carbon), that after condensation phonons become massive and the specific heat drops by about two orders of magnitude. In this note we extend that analysis by considering the coexistence of the nuclei of both types (Helium and Carbon), whose condensation points are generically different. An effective field theory is developed to describe the system when both elements are condensed. The spectrum of fluctuations of this two component charged condensate possesses a collective massless mode with $\omega \propto {\bf k}^2$. Assuming that the fraction of the less abundant element is greater than about 1/100, the thermal history changes as follows: There is a softer discontinuity in the average specific heat after the condensation of first sector, resulting in slower cooling and a milder drop in luminosity function. The specific heat remains almost constant until the condensation of the second sector, then starts to declines as $T^{3/2}$.