A survey of the parameter space of the compressible liquid drop model as applied to the neutron star inner crust

TL;DR

This survey systematically explores how variations in nuclear model parameters affect predictions of neutron star inner crust properties, highlighting sensitivities and potential reductions in pasta phases due to surface energy uncertainties.

Contribution

It provides a comprehensive analysis of the parameter space of the compressible liquid drop model for neutron star crusts, incorporating recent constraints and uncertainties.

Findings

Inner crust composition is highly sensitive to surface energy at low proton fractions.

Transition densities depend strongly on the sub-saturation PNM EoS behavior.

Predicted pasta phases may be significantly reduced based on recent neutron drop energy calculations.

Abstract

We present a systematic survey the range of predictions of the neutron star inner crust composition, crust-core transition densities and pressures, and density range of the nuclear `pasta' phases at the bottom of the crust provided by the compressible liquid drop model in the light of current experimental and theoretical constraints on model parameters. Using a Skyrme-like model for nuclear matter, we construct baseline sequences of crust models by consistently varying the density dependence of the bulk symmetry energy at nuclear saturation density, $L$, under two conditions: (i) that the magnitude of the symmetry energy at saturation density $J$ is held constant, and (ii) $J$ correlates with $L$ under the constraint that the pure neutron matter (PNM) EoS satisfies the results of ab-initio calculations at low densities. Such baseline crust models facilitate consistent exploration of the $L$ dependence of crustal properties. The remaining surface energy and symmetric nuclear matter parameters are systematically varied around the baseline, and different functional forms of the PNM EoS at sub-saturation densities implemented, to estimate theoretical `error bars' for the baseline predictions. Inner crust composition and transition densities are shown to be most sensitive to the surface energy at very low proton fractions and to the behavior of the sub-saturation PNM EoS. Recent calculations of the energies of neutron drops suggest that the low-proton-fraction surface energy might be higher than predicted in Skyrme-like models, which our study suggests may result in a greatly reduced volume of pasta in the crust than conventionally predicted.