Phase diagrams of binary ionic mixtures and white dwarf cooling

Abstract

Phase diagrams of fully ionized binary ionic mixtures are considered within the framework of the linear mixing formalism taking into account recent advances in understanding quantum one-component plasma thermodynamics. We have followed a transformation of azeotropic phase diagrams into peritectic and eutectic types with increase of the charge ratio. For solid $^{12}$C/$^{16}$O and $^{16}$O/$^{20}$Ne mixtures, we have found extensive miscibility gaps. Their appearance seems to be a robust feature of the theory. The gaps evolve naturally into two-solid regions of eutectic phase diagrams at higher $Z_2/Z_1$. They do not depend on thermodynamic fit extensions beyond their applicability limits. The gaps are sensitive to binary mixture composition and physics, being strongly different for C/O and O/Ne mixtures and for the three variants of corrections to linear-mixing solid-state energies available in the literature. When matter cools to its miscibility gap temperature, the exsolution process takes place. It results in a separation of heavier and lighter solid solutions. This may represent a significant reservoir of gravitational energy and should be included in future white dwarf (WD) cooling simulations. Ion quantum effects mostly resulted in moderate modifications, however, for certain $Z_2/Z_1$, these effects can produce qualitative restructuring of the phase diagram. This may be important for the model with $^{22}$Ne distillation in cooling C/O/Ne WD proposed as a solution for the ultramassive WD cooling anomaly.