A SURVEY OF THE PARAMETER SPACE OF THE COMPRESSIBLE LIQUID DROP MODEL AS APPLIED TO THE NEUTRON STAR INNER CRUST

Abstract

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