Prior Probability Distributions of Neutron Star Crust Models

Abstract

To make best use of multifaceted astronomical and nuclear data sets, probability distributions of neutron star models that can be used to propagate errors consistently from one domain to another are required. We take steps toward a consistent model for this purpose, highlight where model inconsistencies occur, and assess the resulting model uncertainty. Using two distributions of nuclear symmetry energy parameters—one uniform, the other based on pure neutron matter theory—we prepare two ensembles of neutron star inner crust models. We use an extended Skyrme energy density functional within a compressible liquid drop model (CLDM). We fit the surface parameters of the CLDM to quantum 3D Hartree–Fock calculations of crustal nuclei. All models predict that more than 50% of the crust by mass and 15% of the crust by thickness comprises pasta with medians of around 62% and 30%, respectively. We also present 68% and 95% ranges for the crust composition as a function of density. We examine the relationships between crust–core boundary and pasta transition properties, the thickness of the pasta layers, the symmetry energy at saturation and subsaturation densities, and the neutron skins of 208Pb and 48Ca. We quantify the correlations using the maximal information coefficient, which can effectively characterize nonlinear relationships. Future measurements of neutron skins, information from nuclear masses and giant resonances, and theoretical constraints on PNM will be able to place constraints on the location of the pasta and crust–core boundaries and the amount of pasta in the crust.

The Nuclear Matter Density Functional under the Nucleonic Hypothesis

“…where P(X) is the prior, and N is a normalization factor. The different constraints c k used in the present study are as follows: (a) nuclear mass measurements in the AME2016 mass table [27]; (b) the bands of allowed region in symmetric and pure neutron matter produced by many-body perturbation theory (MBPT) calculations from Reference [35] based on two-and three-nucleon chiral effective field-theory (EFT) interactions at next-to-next-tonext-to leading order (N3LO), which are interpreted as a 90% confidence interval; (c) mass measurement from radio-timing observations of pulsar PSR J0348+0432 [36], M J03 = 2.01 ± 0.04M , where M is the solar mass; (d) constraints on the tidal deformability of the binary NS system associated to the gravitational wave event GW170817, detected by the LIGO/Virgo Collaboration (LVC) [7]; (e) X-ray pulse-profile measurements of PSR J0030+0451's mass, M J00 = 1.44 +0.15 −0.14 M , and radius, R J00 = 13.02 +1.24 −1.06 km from Reference [2]; (f) the radius measurement with NICER and XMM-Newton data [4] of the PSR J0740+6620 pulsar of mass M J07 = 2.08 ± 0.07M [37], R J07 = 13.7 +2.6 −1.5 km [4]. Posterior distributions of different observables Y are calculated by marginalizing over the EoS parameters as:…”

“…It only accepts models satisfying all the following conditions: causality, thermodynamic stability, and non-negative symmetry energy at all densities. The second term in Equation ( 6), P(J03|X), is the likelihood probability from the mass measurement of PSR J0348+0432 [36], which is M J03 = 2.01 ± 0.04M . This likelihood is defined as the cumulative Gaussian distribution function with a mean value of 2.01 and a standard deviation of 0.04:…”

Ensembles of unified crust and core equations of state in a nuclear-multimessenger astrophysics environment

“…Explorations of the space of neutron star crust EOSs are not as developed as those of the core EOS. There exists only two attempts to systematically generate of crust model ensembles, using meta-models [74,75,48] and using an extended Skyrme EDF [76,77].…”

“…1. A large number of extended Skyrme EDFs [94,76] with three degrees of freedom J, L, K sym are generated, from which neutron skin predictions are calculated. 2.…”

“…The polytropic parameters can be adjusted to reproduce desired values of the moment of inertia I 1.338 of a 1.338M star -which may be measured accurately in the next few years [95] -and the maximum neutron star mass M max . We construct an ensemble of EOSs with uniform priors on J, L, K sym , I 1.338 , M max which match the uniform prior distribution of crust models presented in [76]. We conduct a simple initial demonstration that this set of EOSs can be used to constrain crust and core properties, including the extent of nuclear pasta in the neutron star crust, by consistently incorporating the neutron skin measurements of PREX and the neutron star tidal deformability measurements from LIGO.…”