Thermodynamic Functions of Magnetized Coulomb Crystals

Abstract

Free energy, internal energy, and specific heat for each of the three phonon spectrum branches of a magnetized Coulomb crystal with body-centered cubic lattice are calculated by numerical integration over the Brillouin zone in the range of magnetic fields $B$ and temperatures $T$, such that $0 \le \omega_{\rm B}/\omega_{\rm p}\le 10^3$ and $10^{-4} \le T/T_{\rm p} \le 10^4$. In this case, $\omega_{\rm B}$ is the ion cyclotron frequency, $\omega_{\rm p}$ and $T_{\rm p}$ are the ion plasma frequency and plasma temperature, respectively. The results of numerical calculations are approximated by simple analytical formulas. For illustration, these formulas are used to analyze the behavior of the heat capacity in the crust of a neutron star with strong magnetic field. Thermodynamic functions of magnetized neutron star crust are needed for modeling various observational phenomena in magnetars and high magnetic field pulsars.