Nuclear Pasta Formation

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.

Direct MD simulation of liquid-solid phase equilibria for three-component plasma

The neutron rich isotope 22Ne may be a significant impurity in carbon and oxygen white dwarfs and could impact how the stars freeze. We perform molecular dynamics simulations to determine the influence of 22Ne in carbon-oxygen-neon systems on liquid-solid phase equilibria. Both liquid and solid phases are present simultaneously in our simulation volumes. We identify liquid, solid, and interface regions in our simulations using a bond angle metric. In general we find good agreement for the composition of liquid and solid phases between our MD simulations and the semi analytic model of Medin and Cumming. The trace presence of a third component, neon, does not appear to strongly impact the chemical separation found previously for two component carbon and oxygen systems. This suggests that small amounts of 22Ne may not qualitatively change how the material in white dwarf stars freezes. However, we do find systematically lower melting temperatures (higher Gamma) in our MD simulations compared to the semi analytic model. This difference seems to grow with impurity parameter Q_imp and suggests a problem with simple corrections to the linear mixing rule for the free energy of multicomponent solid mixtures that is used in the semi analytic model.

Neutron Star Crust and Molecular Dynamics Simulation

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.

Direct MD simulation of liquid-solid phase equilibria for two-component plasmas

We determine the liquid-solid phase diagram for carbon-oxygen and oxygen-selenium plasma mixtures using two-phase MD simulations. We identified liquid, solid, and interface regions using a bond angle metric. To study finite size effects, we perform 27648 and 55296 ion simulations. To help monitor non-equilibrium effects, we calculate diffusion constants $D_i$. For the carbon-oxygen system we find that $D_O$ for oxygen ions in the solid is much smaller than $D_C$ for carbon ions and that both diffusion constants are 80 or more times smaller than diffusion constants in the liquid phase. There is excellent agreement between our carbon-oxygen phase diagram and that predicted by Medin and Cumming. This suggests that errors from finite size and non-equilibrium effects are small and that the carbon-oxygen phase diagram is now accurately known. The oxygen-selenium system is a simple two-component model for more complex rapid proton capture nucleosynthesis ash compositions for an accreting neutron star. Diffusion of oxygen, in a predominately selenium crystal, is remarkably fast, comparable to diffusion in the liquid phase. We find a somewhat lower melting temperature for the oxygen-selenium system than that predicted by Medin and Cumming. This is probably because of electron screening effects.

Diffusion in Coulomb Crystals

Diffusion in coulomb crystals can be important for the structure of neutron star crusts. We determine diffusion constants $D$ from molecular dynamics simulations. We find that $D$ for coulomb crystals with relatively soft-core $1/r$ interactions may be larger than $D$ for Lennard-Jones or other solids with harder-core interactions. Diffusion, for simulations of nearly perfect body-centered-cubic lattices, involves the exchange of ions in ring-like configurations. Here ions hop in unison without the formation of long lived vacancies. Diffusion, for imperfect crystals, involves the motion of defects. Finally, we find that diffusion, for an amorphous system rapidly quenched from coulomb parameter $Gamma=175$ to coulomb parameters up to $Gamma=1750$, is fast enough so that the system starts to crystallize during long simulation runs. These results strongly suggest that coulomb solids in cold white dwarf stars, and the crust of neutron stars, will be crystalline and not amorphous.

Diffusion of Neon in White Dwarf Stars

Sedimentation of the neutron rich isotope $^{22}$Ne may be an important source of gravitational energy during the cooling of white dwarf stars. This depends on the diffusion constant for $^{22}$Ne in strongly coupled plasma mixtures. We calculate self-diffusion constants $D_i$ from molecular dynamics simulations of carbon, oxygen, and neon mixtures. We find that $D_i$ in a mixture does not differ greatly from earlier one component plasma results. For strong coupling (coulomb parameter $Gamma>$ few), $D_i$ has a modest dependence on the charge $Z_i$ of the ion species, $D_i propto Z_i^{-2/3}$. However $D_i$ depends more strongly on $Z_i$ for weak coupling (smaller $Gamma$). We conclude that the self-diffusion constant $D_{rm Ne}$ for $^{22}$Ne in carbon, oxygen, and neon plasma mixtures is accurately known so that uncertainties in $D_{rm Ne}$ should be unimportant for simulations of white dwarf cooling.

Molecular Dynamics Simulation of Shear Moduli for Coulomb Crystals

Torsional (shear) oscillations of neutron stars may have been observed in quasiperiodic oscillations of Magnetar Giant Flares. The frequencies of these modes depend on the shear modulus of neutron star crust. We calculate the shear modulus of Coulomb crystals from molecular dynamics simulations. We find that electron screening reduces the shear modulus by about 10% compared to previous Ogata et al. results. Our MD simulations can be extended to calculate the effects of impurities and or polycrystalline structures on the shear modulus.