Using Neutron Star Observations to Determine Crust Thicknesses, Moments of Inertia, and Tidal Deformabilities

Abstract: We perform a systematic assessment of models for the equation of state (EOS) of dense matter in the context of recent neutron star mass and radius measurements to obtain a broad picture of the structure of neutron stars. We demonstrate that currently available neutron star mass and radius measurements provide strong constraints on moments of inertia, tidal deformabilities, and crust thicknesses. A measurement of the moment of inertia of PSR J0737-3039A with 10% error, without any other information from observations, will constrain the EOS over a range of densities to within 50%$-$60%. We find tidal deformabilities between 0.6 and $6\times 10^{36}$ g cm$^{2}$ s$^{2}$ (to 95% confidence) for $M=1.4~\mathrm{M}{\odot}$, and any measurement which constrains this range will provide an important constraint on dense matter. The crustal fraction of the moment of inertia can be as large as 10% for $M=1.4~\mathrm{M}{\odot}$ permitting crusts to have a large enough moment of inertia reservoir to explain glitches in the Vela pulsar even with a large amount of superfluid entrainment. Finally, due to the uncertainty in the equation of state, there is at least a 40% variation in the thickness of the crust for a fixed mass and radius, which implies that future simulations of the cooling of a neutron star crust which has been heated by accretion will need to take this variation into account.