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In the framework of the relativistic mean field model with Thomas-Fermi approximation, we study the structures of low density nuclear matter in a three-dimensional geometry with reflection symmetry. The numerical accuracy and efficiency are improved by expanding the mean fields according to fast cosine transformation and considering only one octant of the unit cell. The effect of finite cell size is treated carefully by searching for the optimum cell size. Typical pasta structures (droplet, rod, slab, tube, and bubble) arranged in various crystalline configurations are obtained for both fixed proton fractions and $beta$-equilibration. It is found that the properties of droplets/bubbles are similar in body-centered cubic (BCC) and face-centered cubic (FCC) lattices, where the FCC lattice generally becomes more stable than BCC lattice as density increases. For the rod/tube phases, the honeycomb lattice is always more stable than the simple one. By introducing an $omega$-$rho$ cross coupling term, we further examine the pasta structures with a smaller slope of symmetry energy $L = 41.34$ MeV, which predicts larger onset densities for core-crust transition and non-spherical nuclei. Such a variation due to the reduction of $L$ is expected to have impacts on various properties in neutron stars, supernova dynamics, and binary neutron star mergers.
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Nuclear matter under astrophysical conditions is explored with time-dependent and static Hartree-Fock calculations. The focus is in a regime of densities where matter segregates into liquid and gaseous phases unfolding a rich scenario of geometries, often called nuclear pasta shapes (e.g. spaghetti, lasagna). Particularly the appearance of the different phases depending on the proton fraction and the transition to uniform matter are investigated. In this context the neutron background density is of special interest, because it plays a crucial role for the type of pasta shape which is built. The study is performed in two dynamical ranges, one for hot matter and one at temperature zero to investigate the effect of cooling.
The formation of complex nonuniform phases of nuclear matter, known as nuclear pasta, is studied with molecular dynamics simulations containing 51200 nucleons. A phenomenological nuclear interaction is used that reproduces the saturation binding energy and density of nuclear matter. Systems are prepared at an initial density of 0.10fm$^{-3}$ and then the density is decreased by expanding the simulation volume at different rates to densities of 0.01 fm$^{-3}$ or less. An originally uniform system of nuclear matter is observed to form spherical bubbles (swiss cheese), hollow tubes, flat plates (lasagna), thin rods (spaghetti) and, finally, nearly spherical nuclei with decreasing density. We explicitly observe nucleation mechanisms, with decreasing density, for these different pasta phase transitions. Topological quantities known as Minkowski functionals are obtained to characterize the pasta shapes. Different pasta shapes are observed depending on the expansion rate. This indicates non equilibrium effects. We use this to determine the best ways to obtain lower energy states of the pasta system from MD simulations and to place constrains on the equilibration time of the system.
[Background] The pasta phase of nuclear matter may play an important role in the structure and evolution of neutron stars. Recent works suggest nuclear pasta has a high resistivity which could be explained by the presence of long lived topological defects. The defects act as impurities that decrease thermal and electrical conductivity of the pasta. [Purpose] To quantify how topological defects affect transport properties of nuclear pasta and estimate this effect using an impurity parameter $Q_{text{imp}}$. [Methods] Contrast molecular dynamics simulations of up to 409,600 nucleons arranged in parallel nuclear pasta slabs (perfect pasta) with simulations of pasta slabs connected by topological defects (impure pasta). From these simulations compare the viscosity and heat conductivity of perfect and impure pasta to obtain an effective impurity parameter $Q_{text{imp}}$ due to the presence of defects. [Results] Both the viscosity and thermal conductivity calculated for both perfect and impure pasta are anisotropic, peaking along directions perpendicular to the slabs and reaching a minimum close to zero parallel to them. In our 409,600 nucleon simulation topological defects connecting slabs of pasta reduce both the thermal conductivity and viscosity on average by about 37%. We estimate an effective impurity parameter due to the defects of order $Q_{text{imp}}sim30$. [Conclusions] Topological defects in the pasta phase of nuclear matter have an effect similar to impurities in a crystal lattice. The irregularities introduced by the defects reduce the thermal and electrical conductivities and the viscosity of the system. This effect can be parameterized by a large impurity parameter $Q_{text{imp}}sim30$.
We investigate the nuclear pasta phases in neutron star crusts by conducting a large number of three-dimensional Hartree-Fock+BCS calculations at densities leading to the crust-core transition. We survey the shape parameter space of pasta at constant pressure. Spaghetti, waffles, lasagna, bi-continuous phases and cylindrical holes occupy local minima in the resulting Gibbs energy surfaces. The bi-continuous phase, in which both the neutron gas and nuclear matter extend continuously in all dimensions and therefore protons are delocalized, appears over a large range of depths. Our results support the idea that nuclear pasta is a glassy system. Multiple pasta configurations coexist in a given layer of the crust. At a characteristic temperature, of order $10^8$-$10^9$K, different phases become frozen into domains whose sizes we estimate to be 1-50 times the lattice spacing and over which the local density and electron fraction can vary. Above this temperature, there is very little long-range order and matter is an amorphous solid. Electron scattering off domain boundaries may contribute to the disorder resistivity of the pasta phases. Annealing of the domains may occur during cooling; repopulating of local minima during crustal heating might lead to temperature dependent transport properties in the deep layers of the crust. We identify 4 distinct regions: (1) nuclear pasta first appears as a local minima, but spherical nuclei are the ground state; (2) nuclear pasta become the absolute minimum, but spherical nuclei are still a local minimum (3) only nuclear pasta appears in local minima, and protons are still localized in at least one dimension (4) only pasta appears, and protons are delocalized. The whole pasta region can occupy up to 70% of the crust by mass and 40% by thickness, and the layer in which protons are delocalized could occupy 45% of the crust mass and 25% of its thickness.
Determining the Equation of State (EOS) of dense neutron-rich nuclear matter is a shared goal of both nuclear physics and astrophysics. Except possible phase transitions, the density dependence of nuclear symmetry esym is the most uncertain part of the EOS of neutron-rich nucleonic matter especially at supra-saturation densities. Much progresses have been made in recent years in predicting the symmetry energy and understanding why it is still very uncertain using various microscopic nuclear many-body theories and phenomenological models. Simultaneously, significant progresses have also been made in probing the symmetry energy in both terrestrial nuclear laboratories and astrophysical observatories. In light of the GW170817 event as well as ongoing or planned nuclear experiments and astrophysical observations probing the EOS of dense neutron-rich matter, we review recent progresses and identify new challenges to the best knowledge we have on several selected topics critical for understanding astrophysical effects of the nuclear symmetry energy.
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