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Heat capacity of low density neutron matter: from quantum to classical regimes

Abstract : The heat capacity of neutron matter is studied over the range of densities and temperatures prevailing in neutron-star crusts, allowing for the transition to a superfluid phase at temperatures below some critical temperature $T_{sf}$ and including the transition to the classical limit. Finite temperature Hartree-Fock-Bogoliubov equations (FTHFB) are solved and compared to existing approximate expressions. In particular, the formula given by Levenfish and Yakovlev is found to reproduce the numerical results with a high degree of accuracy for temperatures $T\leq T_{sf}$. In the non-superfluid phase, $T\geq T_{sf}$, the linear approximation is valid only at temperature $T\ll T_{{\rm F} n}$ ($T_{{\rm F} n}$ being the Fermi temperature of the neutron gas) which is rarely the case in the shallow layers of the neutron star's crust. A non-perturbative interpolation between the quantal and the classical regimes is proposed here. The heat capacity, conveniently parametrized solely in terms of $T_{sf}$, $T_{{\rm F} n}$, and the neutron number density $n_n$, can be easily implemented in neutron-star cooling simulations.
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Contributor : Dominique Girod <>
Submitted on : Tuesday, March 31, 2015 - 10:51:39 AM
Last modification on : Tuesday, November 19, 2019 - 2:43:56 AM

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A. Pastore, N. Chamel, J. Margueron. Heat capacity of low density neutron matter: from quantum to classical regimes. Monthly Notices of the Royal Astronomical Society, Oxford University Press (OUP): Policy P - Oxford Open Option A, 2015, 448, pp.1887-1892. ⟨10.1093/mnras/stv095⟩. ⟨in2p3-01137677⟩



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