Abstract
Context. The interior of a neutron star is usually assumed to be made of cold catalyzed matter. However, the outer layers are unlikely to remain in full thermodynamic equilibrium during the formation of the star and its subsequent cooling, especially after crystallization occurs. Aims. We study the cooling and the equilibrium composition of the outer layers of a non-accreting neutron star down to crystallization. Here the impurity parameter, generally taken as a free parameter in cooling simulations, is calculated self-consistently using a microscopic nuclear model for which a unified equation of state has recently been determined. Methods. We follow the evolution of the nuclear distributions of the multi-component Coulomb liquid plasma fully self-consistently, adapting a general formalism originally developed for the description of supernova cores. We calculate the impurity parameter at the crystallization temperature as determined in the one-component plasma approximation. Results. Our analysis shows that the sharp changes in composition obtained in the one-component plasma approximation are smoothed out when a full nuclear distribution is allowed. The Coulomb coupling parameter at melting is found to be reasonably close to the canonical value of 175, except for specific values of the pressure for which supercooling occurs in the one-component plasma approximation. Our multi-component treatment leads to non-monotonic variations of the impurity parameter with pressure. Its values can change by several orders of magnitude reaching about 50, suggesting that the crust may be composed of an alternation of pure (highly conductive) and impure (highly resistive) layers. The results presented here complement the recent unified equation of state obtained within the same nuclear model. Conclusions. Our self-consistent approach to hot dense multi-component plasma shows that the presence of impurities in the outer crust of a neutron star is non-negligible and may have a sizeable impact on transport properties. In turn, this may have important implications not only for the cooling of neutron stars, but also for their magneto-rotational evolution.
Highlights
Formed in the aftermath of gravitational core-collapse supernova explosions, neutron stars (NSs) are initially very hot
The Coulomb coupling parameter at melting is found to be reasonably close to the canonical value of 175, except for specific values of the pressure for which supercooling occurs in the one-component plasma approximation
We took into account the coexistence of different nuclear species in a self-consistent nuclear statistical equilibrium treatment using the latest experimental atomic mass data supplemented with the microscopic nuclear mass table HFB-24
Summary
Formed in the aftermath of gravitational core-collapse supernova explosions, neutron stars (NSs) are initially very hot. It is generally assumed that as the NS cools down by emitting neutrinos and photons, this multi-component plasma (MCP), which crystallizes at the temperature Tm, remains in full thermodynamic equilibrium (with respect to all possible processes) until the ground state at T = 0 K is eventually reached. According to this so-called “cold catalyzed matter” hypothesis, the outer crust of a mature NS is, expected to be stratified into pure layers, each of which consists of a one-component Coulomb crystal (except, possibly, at the boundaries between adjacent layers; see Chamel & Fantina 2016a for a discussion). In Appendix A, we derive the expression for the pressure of the MCP, while in Appendices B and C, we report for completeness the expressions used in this work for the free energy and pressure of the uniform electron gas and for the free energy of the Coulomb plasma of ions, respectively
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