Using neutron star observations to determine crust thicknesses, moments of inertia, and tidal deformabilities

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 a 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 $6\times {10}^{36}\mathrm{g}{\mathrm{cm}}^2{\mathrm{s}}^2$ (to 95% confidence) for $M=1.4M_{\odot }$, 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 $M=1.4M_{\odot }$ 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.

Figure 1

Probability distributions for the moment of inertia of a $1.4\text{−}{M}_{\odot }$ NS (upper left), tidal deformability of a $1.4\text{−}{M}_{\odot }$ NS (upper right), radius of a $1.4\text{−}{M}_{\odot }$ NS (lower left), and pressure at about three times the saturation density (lower right) given the set of mass and radius observations. Black lines are for GCR, and red lines are for HLPS. Solid lines are for Model A, and dotted lines are for Model C. Each of the distributions was separately normalized to have a maximum at 1.

Figure 2

Probability distributions for four pairs of quantities with EOS model GCR and Model C at high densities. In the upper-left panel, $P_t$ is the pressure at the core-crust transition. All other quantities are defined in the text. The red density plot gives the probability distributions that assume the NS $M$ and $R$ data along with 68% contour lines (solid black) and 95% contour lines (dotted black). Also shown are the 68% (blue dashed) and 95% (blue dot-dashed) contour lines that correspond to the distribution given the third data set with only a measurement of $I=(70\pm 7)M_{\odot }{\mathrm{km}}^2$.