We determine the phase diagram for dense carbon-oxygen mixtures in white dwarf (WD) star interiors using molecular dynamics simulations involving liquid and solid phases. Our phase diagram agrees well with predictions from Ogata et al. and from Medin and Cumming and gives lower melting temperatures than Segretain et al. Observations of WD crystallization in the globular cluster NGC 6397 by Winget et al. suggest that the melting temperature of WD cores is close to that for pure carbon. If this is true, our phase diagram implies that the central oxygen abundance in these stars is less than about 60%. This constraint, along with assumptions about convection in stellar evolution models, limits the effective S factor for the 12C(α,γ)16O reaction to S(300)≤170  keV b.

The equation of state (EOS) of dense matter is an essential ingredient for numerical simulations of core-collapse supernovae and neutron star mergers. The properties of matter near and above nuclear saturation density are uncertain, which translates into uncertainties in astrophysical simulations and their multimessenger signatures. Therefore, a wide range of EOSs spanning the allowed range of nuclear interactions are necessary for determining the sensitivity of these astrophysical phenomena and their signatures to variations in input microphysics. We present a new set of finite temperature EOSs based on experimentally allowed Skyrme forces. We employ a liquid-drop model of nuclei to capture the nonuniform phase of nuclear matter at subsaturation density, which is blended into a nuclear statistical equilibrium EOS at lower densities. We also provide a new, open-source code for calculating EOSs for arbitrary Skyrme parametrizations. We then study the effects of different Skyrme parametrizations on thermodynamical properties of dense astrophysical matter, the neutron star mass-radius relationship, and the core collapse of 15 and 40 solar mass stars.

The formation of complex nonuniform phases of nuclear matter, known as nuclear pasta, is studied with molecular dynamics simulations containing 51 200 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 0.10 fm −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.

Nuclear pasta, with non-spherical shapes, is expected near the base of the crust in neutron stars. Large scale molecular dynamics simulations of pasta show long lived topological defects that could increase electron scattering and reduce both the thermal and electrical conductivities. We model a possible low conductivity pasta layer by increasing an impurity parameter Qimp. Predictions of light curves for the low mass X-ray binary MXB 1659-29, assuming a large Qimp, find continued late time cooling that is consistent with Chandra observations. The electrical and thermal conductivities are likely related. Therefore observations of late time crust cooling can provide insight on the electrical conductivity and the possible decay of neutron star magnetic fields (assuming these are supported by currents in the crust).

Background:The dense neutron-rich matter found in supernovae and inside neutron stars is expected to form complex nonuniform phases, often referred to as nuclear pasta. The pasta shapes depend on density, temperature and proton fraction and determine many transport properties in supernovae and neutron star crusts. Purpose: To characterize the topology and compute two observables, the radial distribution function (RDF) g (r) and the structure factor S(q), for systems with proton fractions Yp = 0.10, 0.20, 0.30, and 0.40 at about one-third of nuclear saturation density, n = 0.050 fm 3, and temperatures near kT = 1 MeV. Methods:We use two recently developed hybrid CPU/GPU codes to perform large scale molecular dynamics (MD) simulations with 51 200 and 409 600 nucleons. From the output of the MD simulations we obtain the two desired observables. Results: We compute and discuss the differences in topology and observables for each simulation. We observe that the two lowest proton fraction systems simulated, Yp = 0.10 and 0.20, equilibrate quickly and form liquidlike structures. Meanwhile, the two higher proton fraction systems, Yp = 0.30 and 0.40, take a longer time to equilibrate and organize themselves in solidlike periodic structures. Furthermore, the Yp = 0.40 system is made up of slabs, lasagna phase, interconnected by defects while the Yp = 0.30 systems consist of a stack of perforated plates, the nuclear waffle phase. Conclusions:The periodic configurations observed in our MD simulations for proton fractions Yp ^ 0.30 have important consequences for the structure factors S(q) of protons and neutrons, which relate to many transport properties of supernovae and neutron star crust. A detailed study of the waffle phase and how its structure depends on temperature, size of the simulation, and the screening length showed that finite-size effects appear to be under control and, also, that the plates in the waffle phase merge at temperatures slightly above 1.0 MeV and the holes in the plates form a hexagonal lattice at temperatures slightly lower than 1.0 MeV.

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Uncertainties in our knowledge of the properties of dense ma er near and above nuclear saturation density are among the main sources of variations in multi-messenger signatures predicted for core-collapse supernovae (CCSNe) and the properties of neutron stars (NSs). We construct 97 new nite-temperature equations of state (EOSs) of dense ma er that obey current experimental, observational, and theoretical constraints and discuss how systematic variations in the EOS parameters a ect the properties of cold nonrotating NSs and the core collapse of a 20-M progenitor star. e core collapse of the 20-M progenitor star is simulated in spherical symmetry using the general-relativistic radiation-hydrodynamics code GR1D where neutrino interactions are computed for each EOS using the NuLib library. We conclude that the e ective mass of nucleons at densities above nuclear saturation density is the largest source of uncertainty in the CCSN neutrino signal and dynamics even though it plays a subdominant role in most properties of cold NS ma er. Meanwhile, changes in other observables a ect the properties of cold NSs, while having li le e ect in CCSNe. To strengthen our conclusions, we perform six octant three-dimensional CCSN simulations varying the e ective mass of nucleons at nuclear saturation density. We conclude that neutrino heating and, thus, the likelihood of explosion is signi cantly increased for EOSs where the e ective mass of nucleons at nuclear saturation density is large.PACS numbers: 21.65. Mn,26.50.+x,26.60.Kp