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Register a new userThermal conductivity and impurity scattering in the accreting neutron star crust
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We calculate the thermal conductivity of electrons for the strongly correlated multi-component ion plasma expected in the outer layers of neutron stars crust employing a Path Integral Monte Carlo (PIMC) approach. This allows us to isolate the low energy response of the ions and use it to calculate the electron scattering rate and the electron thermal conductivity. We find that the scattering rate is enhanced by a factor 2-4 compared to earlier calculations based on the simpler electron-impurity scattering formalism. This findings directly impacts the interpretation of thermal relaxation observed in transiently accreting neutron stars and has implications for the composition and nuclear reactions in the crust that occur during accretion.
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Recently, crust cooling times have been measured for neutron stars after extended outbursts. These observations are very sensitive to the thermal conductivity $kappa$ of the crust and strongly suggest that $kappa$ is large. We perform molecular dynamics simulations of the structure of the crust of an accreting neutron star using a complex composition that includes many impurities. The composition comes from simulations of rapid proton capture nucleosynthesys followed by electron captures. We find that the thermal conductivity is reduced by impurity scattering. In addition, we find phase separation. Some impurities with low atomic number $Z$ are concentrated in a subregion of the simulation volume. For our composition, the solid crust must separate into regions of different compositions. This could lead to an asymmetric star with a quadrupole deformation that radiates gravitational waves. Observations of crust cooling can constrain impurity concentrations.
To make best use of multi-faceted 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 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 sub-saturation densities and the neutron skins of 208Pb and 48Ca. We quantify the correlations using the maximal information coefficient, which can effectively characterize non-linear 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.
In this book chapter we review plasma crystals in the laboratory, in the interior of white dwarf stars, and in the crust of neutron stars. We describe a molecular dynamics formalism and show results for many neutron star crust properties including phase separation upon freezing, diffusion, breaking strain, shear viscosity and dynamics response of nuclear pasta. We end with a summary and discuss open questions and challenges for the future.
Fusion reactions in the crust of an accreting neutron star are an important source of heat, and the depth at which these reactions occur is important for determining the temperature profile of the star. Fusion reactions depend strongly on the nuclear charge $Z$. Nuclei with $Zle 6$ can fuse at low densities in a liquid ocean. However, nuclei with Z=8 or 10 may not burn until higher densities where the crust is solid and electron capture has made the nuclei neutron rich. We calculate the $S$ factor for fusion reactions of neutron rich nuclei including $^{24}$O + $^{24}$O and $^{28}$Ne + $^{28}$Ne. We use a simple barrier penetration model. The $S$ factor could be further enhanced by dynamical effects involving the neutron rich skin. This possible enhancement in $S$ should be studied in the laboratory with neutron rich radioactive beams. We model the structure of the crust with molecular dynamics simulations. We find that the crust of accreting neutron stars may contain micro-crystals or regions of phase separation. Nevertheless, the screening factors that we determine for the enhancement of the rate of thermonuclear reactions are insensitive to these features. Finally, we calculate the rate of thermonuclear $^{24}$O + $^{24}$O fusion and find that $^{24}$O should burn at densities near $10^{11}$ g/cm$^3$. The energy released from this and similar reactions may be important for the temperature profile of the star.
The form of the nuclear symmetry energy $E_s$ around saturation point density leads to a different crust-core transition point in the neutron star and affect the crust properties. We show that the knowledge about $E_s$ close to the saturation point is not sufficient, because the very low density behaviour is relevant. We also claim that crust properties are strongly influenced by the very high density behavior of $E_s$, so in order to conclude about the form of low density part of the symmetry energy one must isolate properly the high density part.
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