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Register a new userEffect of topological defects on nuclear pasta observables
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Added by
Andre da Silva Schneider
Publication date
2016
fields
Physics
and research's language is
English
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[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 $Q_{text{imp}}sim30$.
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Nuclear pasta topology is an essential ingredient to determine transport properties in the inner crust of neutron stars. We perform semi-classical molecular dynamics simulations of nuclear pasta for proton fractions $Y_p=0.30$ and $Y_p=0.40$ near one third of nuclear saturation density, $n=0.05,mathrm{fm}^{-3}$, at a temperature $T=1.0,mathrm{MeV}$. Our simulations are, to our knowledge, the largest nuclear pasta simulations to date and contain up to $3,276,800$ nucleons in the $Y_p=0.30$ and $819,200$ nucleons in the $Y_p=0.40$ case. An algorithm to determine which nucleons are part of a given sub-domain in the system is presented. By comparing runs of different sizes we study finite size effects, equilibration time, the formation of multiple domains and defects in the pasta structures, as well as the structure factor dependence on simulation size. Although we find qualitative agreement between the topological structure and the structure factors of runs with $51,200$ nucleons and those with $819,200$ nucleons or more, we show that simulations with hundreds of thousands of nucleons may be necessary to accurately predict pasta transport properties.
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.
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: Exotic non-spherical nuclear pasta shapes are expected in nuclear matter at just below saturation density because of competition between short range nuclear attraction and long range Coulomb repulsion. Purpose: We explore the impact of nuclear pasta on nucleosynthesis, during neutron star mergers, as cold dense nuclear matter is ejected and decompressed. Methods: We perform classical molecular dynamics simulations with 51200 and 409600 nucleons, that are run on GPUs. We expand our simulation region to decompress systems from an initial density of 0.080 fm^{-3} down to 0.00125 fm^{-3}. We study proton fractions of Y_P=0.05, 0.10, 0.20, 0.30, and 0.40 at T =0.5, 0.75, and 1.0 MeV. We calculate the composition of the resulting systems using a cluster algorithm. Results: We find final compositions that are in good agreement with nuclear statistical equilibrium models for temperatures of 0.75 and 1 MeV. However, for proton fractions greater than Y_P=0.2 at a temperature of T = 0.5 MeV, the MD simulations produce non-equilibrium results with large rod-like nuclei. Conclusions: Our MD model is valid at higher densities than simple nuclear statistical equilibrium models and may help determine the initial temperatures and proton fractions of matter ejected in mergers.
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