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Diffusion coefficients for crystallized Coulomb plasmas are essential microphysics input for modeling white dwarf cores and neutron star crusts but are poorly understood. In this work we present a model for diffusion in Coulomb crystals. We show that melting and diffusion follow the same universal scaling such that diffusion is independent of screening. Our simulations show, contrary to prevailing wisdom, that the formation of vacancies is not suppressed by the large pressure. Rather, vacancy formation and hole diffusion is the dominant mode of self diffusion in Coulomb crystals., Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Lett

Nuclear Astrophysics is a field at the intersection of nuclear physics and astrophysics, which seeks to understand the nuclear engines of astronomical objects and the origin of the chemical elements. This white paper summarizes progress and status of the field, the new open questions that have emerged, and the tremendous scientific opportunities that have opened up with major advances in capabilities across an ever growing number of disciplines and subfields that need to be integrated. We take a holistic view of the field discussing the unique challenges and opportunities in nuclear astrophysics in regards to science, diversity, education, and the interdisciplinarity and breadth of the field. Clearly nuclear astrophysics is a dynamic field with a bright future that is entering a new era of discovery opportunities., Comment: 96 pages. Submitted to Journal of Physics G

Diffusion coefficients are essential microphysics input for modeling white dwarf evolution, as they impact phase separation at crystallization and sedimentary heat sources. Present schemes for computing diffusion coefficients are accurate at weak coupling ($\Gamma \ll 1$), but they have errors as large as a factor of two in the strongly coupled liquid regime ($1 \lesssim \Gamma \lesssim 200$). With modern molecular dynamics codes it is possible to accurately determine diffusion coefficients in select systems with percent-level precision. In this work, we develop a theoretically motivated law for diffusion coefficients which works across the wide range of parameters typical for white dwarf interiors. We perform molecular dynamics simulations of pure systems and two mixtures that respectively model a typical-mass C/O white dwarf and a higher-mass O/Ne white dwarf, and resolve diffusion coefficients for several trace neutron-rich nuclides. We fit the model to the pure systems and propose a physically motivated generalization for mixtures. We show that this model is accurate to roughly 15% when compared to molecular dynamics for many individual elements under conditions typical of white dwarfs, and is straightforward to implement in stellar evolution codes., Comment: 6 pages, 4 figures, accepted for publication in MNRAS Letters

Type-Ia supernovae (SN Ia) are powerful stellar explosions that provide important distance indicators in cosmology. There is significant tension between values of the Hubble constant (expansion rate of the universe) determined from SN Ia and from other data. Recently, we proposed a new SN Ia mechanism that involves a nuclear fission chain reaction in an isolated white dwarf [PRL 126, 1311010]. We find the average mass of an exploding star decreases with increasing enrichment f_5 -- the fraction of uranium that is the isotope U-235. As a result, the average SN Ia luminosity decreases with increasing f_5. Furthermore, f_5 is likely higher in the host galaxies of SN Ia observed at large redshift $z$ because of younger galaxy ages. This change of f_5 leads to the evolution of SN Ia properties with redshift. If f_5 increases with redshift this results in an increased SN Ia rate, but a lower average SN Ia luminosity., Comment: 9 pages, 7 figures, submitted to ApJ

Type-Ia supernovae (SN Ia) are powerful stellar explosions that provide important distance indicators in cosmology. Recently, we proposed a new SN Ia mechanism that involves a nuclear fission chain-reaction in an isolated white dwarf [PRL 126, 1311010]. Here we perform novel reaction network simulations of the actinide-rich first solids in a cooling white dwarf. The network includes neutron-capture and fission reactions on a range of U and Th isotopes with various possible values for U-235 enrichment. We find, for modest U-235 enrichments, neutron-capture on U-238 and Th-232 can breed additional fissile nuclei so that a significant fraction of all U and Th nuclei may fission during the chain-reaction. The resulting large energy release could ignite thermonuclear carbon burning and possibly trigger a SN Ia., Comment: 8 pages, 5 figures, revised introduction, accepted Phys. Rev. C

Do white dwarfs have inner cores made of iron? Neutron rich nuclei like $^{56}$Fe experience a net gravitational force and sediment toward the core. Using new phase diagrams and molecular dynamics simulations, we show that $^{56}$Fe should separate into mesoscopic Fe-rich crystallites due to its large charge relative to the background. At solar abundances, these crystallites rapidly precipitate and form an inner core of order 100 km and $10^{-3} M_\odot$ that may be detectable with asteroseismology. Associated cooling delays could be up to a Gyr for low mass white dwarfs but are only $\sim$0.1 Gyr for massive white dwarfs, so while this mechanism may contribute to the Q-branch the heating is insufficient to fully explain it., Comment: 8 pages, 5 figures, accepted for publication in ApJ Letters

The first solids that form as a white dwarf (WD) starts to crystallize are expected to be greatly enriched in actinides. Previously [PRL 126, 1311010] we found that these solids might support a nuclear fission chain reaction that could ignite carbon burning and provide a new Type Ia supernova (SN Ia) mechanism involving an {\it isolated} WD. Here we explore this fission mechanism in more detail and calculate the final temperature and density after the chain reaction and discuss a number of open physics questions., Comment: 8 pages, 4 figures

Observations of galactic white dwarfs with Gaia have allowed for unprecedented modeling of white dwarf cooling, resolving core crystallization and sedimentary heating from neutron rich nuclei. These cooling sequences are sensitive to the diffusion coefficients of nuclei in Coulomb plasmas which have order 10\% uncertainty and are often not valid across coupling regimes. Using large scale molecular dynamics simulations we calculate diffusion coefficients at high resolution in the regime relevant for white dwarf modeling. We present a physically motivated law for diffusion with a semi-empirical correction which is accurate at the percent level. Implemented along with linear mixing in stellar evolution codes, this law should reduce the error from diffusion coefficients by an order of magnitude., Comment: 5 pages, 3 figures, MNRAS accepted

The first solids that form as a cooling white dwarf (WD) starts to crystallize are expected to be greatly enriched in actinides. This is because the melting points of WD matter scale as $Z^{5/3}$ and actinides have the largest charge $Z$. We estimate that the solids may be so enriched in actinides that they could support a fission chain reaction. This reaction could ignite carbon burning and lead to the explosion of an isolated WD in a thermonuclear supernova (SN Ia). Our mechanism could potentially explain SN Ia with sub-Chandrasekhar ejecta masses and short delay times., Comment: 8 pages, 6 figures total including Appendix, Phys. Rev. Let. in press

Recent observations of Galactic white dwarfs (WDs) with Gaia suggest there is a population of massive crystallizing WDs exhibiting anomalous cooling -- the Q branch. While single-particle $^{22}$Ne sedimentation has long been considered a possible heat source, recent work suggests that $^{22}$Ne must separate into clusters, enhancing diffusion, in order for sedimentation to provide heating on the observed timescale. We show definitively that $^{22}$Ne cannot separate to form clusters in C/O WDs using molecular dynamics simulations, and we further present a general C/O/Ne phase diagram showing that strong $^{22}$Ne enrichment is not achievable for $^{22}$Ne abundance $\lesssim 30\%$. We conclude that the anomalous heating cannot be due to $^{22}$Ne cluster sedimentation and that Q branch WDs may have an unusual composition, possibly rich with heavier elements., Comment: 7 pages, 4 figures, accepted for publication in ApJ Letters

In the far future long after star formation has ceased the universe will be populated by sparse degenerate remnants, mostly white dwarfs, though their ultimate fate is an open question. These white dwarfs will cool and freeze solid into black dwarfs while pycnonuclear fusion will slowly process their composition to iron-56. However, due to the declining electron fraction the Chandrasekhar limit of these stars will be decreasing and will eventually be below that of the most massive black dwarfs. As such, isolated dwarf stars with masses greater than $\sim 1.2 M_\odot$ will collapse in the far future due to the slow accumulation of iron-56 in their cores. If proton decay does not occur then this is the ultimate fate of about $10^{21}$ stars, approximately one percent of all stars in the observable universe. We present calculations of the internal structure of black dwarfs with iron cores as a model for progenitors. From pycnonuclear fusion rates we estimate their lifetime and thus delay time to be $10^{1100}$ years. We speculate that high mass black dwarf supernovae resemble accretion induced collapse of O/Ne/Mg white dwarfs while later low mass transients will be similar to stripped-envelope core-collapse supernova, and may be the last interesting astrophysical transients to occur prior to heat death., Comment: 6 pages, 1 figure, accepted for publication in MNRAS

Despite their astrophysical relevance, nuclear pasta phases are relatively unstudied at high temperatures. We present molecular dynamics simulations of symmetric nuclear matter with several topologies of `lasagna' at a range of temperatures to study the pasta-uniform transition. Using the Minkowski functionals we quantify trends in the occupied volume, surface area, mean breadth, and Euler characteristic. The amplitude of surface displacements of the pasta increase with temperature which produce short lived topological defects such as holes and filaments near melting, resulting in power laws for increasing surface curvature with temperature. We calculate the static structure factor and report the shear viscosity and thermal conductivity of pasta, finding that the shear viscosity is minimized at the melting temperature. These results may have implications for the thermoelastic properties of nuclear pasta and finite temperature corrections to the equation of state at pasta densities., Comment: 13 pages, 8 figures, PRC accepted

Coulomb plasmas crystallize in a number of physical systems, such as dusty plasmas, neutron star crusts, and white dwarf cores. The crystal structure of the one component and binary plasma has received significant attention in the literature, though the less studied multicomponent plasma may be most relevant for many physical systems which contain a large range of particle charges. We report on molecular dynamics simulations of multicomponent plasmas near the melting temperature with mixtures taken to be realistic X-ray burst ash compositions. We quantify the structure of the crystal with the bond order parameters and radial distribution function. Consistent with past work, low charge particles form interstitial defects and we argue that they are in a quasi-liquid state within the lattice. The lattice shows screening effects which preserves long range order despite the large variance in particle charges which may impact transport properties relevant to astrophysics., Comment: 10 pages, 8 figures, accepted to PRE

The elastic properties of neutron star crusts are relevant for a variety of currently observable or near-future electromagnetic and gravitational wave phenomena. These phenomena may depend on the elastic properties of nuclear pasta found in the inner crust. We present large scale classical molecular dynamics simulations where we deform nuclear pasta. We simulate idealized samples of nuclear pasta and describe their breaking mechanism. We also deform nuclear pasta that is arranged into many domains, similar to what is known for the ions in neutron star crusts. Our results show that nuclear pasta may be the strongest known material, perhaps with a shear modulus of $10^{30}\,\text{ergs/cm}^3$ and breaking strain greater than 0.1., Comment: 5 pages, 2 figures. Submitted to Physical Review Letters

The crust of accreting neutron stars plays a central role in many different observational phenomena. In these stars, heavy elements produced by H-He burning in the rapid proton capture (rp-) process continually freeze to form new crust. In this paper, we explore the expected composition of the solid phase. We first demonstrate using molecular dynamics that two distinct types of chemical separation occur, depending on the composition of the rp-process ashes. We then calculate phase diagrams for three-component mixtures and use them to determine the allowed crust compositions. We show that, for the large range of atomic numbers produced in the rp-process ($Z\sim 10$--$50$), the solid that forms has only a small number of available compositions. We conclude that accreting neutron star crusts should be polycrystalline, with domains of distinct composition. Our results motivate further work on the size of the compositional domains, and have implications for crust physics and accreting neutron star phenomenology., Comment: 8 pages, 4 figures, Submitted to ApJ, this article supersedes arXiv:1709.09260

Nucleosynthesis in the oceans of accreting neutron stars can produce novel mixtures of nuclides, whose composition is dependent on the exact astrophysical conditions. Many simulations have now been done to determine the nucleosynthesis products in the ocean, but the phase separation at the base of the ocean, which determines the composition of the crust, has not been as well studied. In this work, we simulate the phase separation of a composition, which was predicted to produce a crust enriched in light nuclei, in contrast with past work which predicts that crust is enriched in heavy nuclei. We perform molecular dynamics simulations of the phase separation of this mixture using the methods of Horowitz $\textit{et. al.}$ (2007). We find good agreement with the predictions of Mckinven $\textit{et al.}$ (2016) for the phase separation of this mixture. Moreover, this supports their method as a computationally efficient alternative to molecular dynamics for calculating phase separation for a wider regime of astrophysical conditions., Comment: 8 pages, 5 figures, Submitted to Phys. Rev. E

Nuclear pasta, with nucleons arranged into tubes, sheets, or other complex shapes, is expected in core collapse supernovae (SNe) at just below nuclear density. We calculate the additional opacity from neutrino-pasta coherent scattering using molecular dynamics simulations. We approximately include this opacity in simulations of SNe. We find that pasta slows neutrino diffusion and greatly increases the neutrino signal at late times of 10 or more seconds after stellar core collapse. This signal, for a galactic SN, should be clearly visible in large detectors such as Super-Kamiokande., Comment: 6 pages, 4 figures

We define `astromaterial science' as the study of materials in astronomical objects that are qualitatively denser than materials on earth. Astromaterials can have unique properties related to their large density, though they may be organized in ways similar to more conventional materials. By analogy to terrestrial materials, we divide our study of astromaterials into hard and soft and discuss one example of each. The hard astromaterial discussed here is a crystalline lattice, such as the Coulomb crystals in the interior of cold white dwarfs and in the crust of neutron stars, while the soft astromaterial is nuclear pasta found in the inner crusts of neutron stars. In particular, we discuss how molecular dynamics simulations have been used to calculate the properties of astromaterials to interpret observations of white dwarfs and neutron stars. Coulomb crystals are studied to understand how compact stars freeze. Their incredible strength may make crust "mountains" on rotating neutron stars a source for gravitational waves that the Laser Interferometer Gravitational-Wave Observatory (LIGO) may detect. Nuclear pasta is expected near the base of the neutron star crust at densities of $10^{14}$ g/cm$^3$. Competition between nuclear attraction and Coulomb repulsion rearranges neutrons and protons into complex non-spherical shapes such as sheets (lasagna) or tubes (spaghetti). Semi-classical molecular dynamics simulations of nuclear pasta have been used to study these phases and calculate their transport properties such as neutrino opacity, thermal conductivity, and electrical conductivity. Observations of neutron stars may be sensitive to these properties, and can be be used to interpret observations of supernova neutrinos, magnetic field decay, and crust cooling of accreting neutron stars. We end by comparing nuclear pasta shapes with some similar shapes seen in biological systems., Comment: 16 pages, 7 figures, added references and revised for clarity, Reviews of Modern Physics in press

[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 $Q_{\text{imp}}\sim30$., Comment: 9 pages, 5 figures, 3 tables

At approximate radii of 200-300 km, asteroids transition from oblong `potato' shapes to spheres. This limit is known as the Potato Radius, and has been proposed as a classification for separating asteroids from dwarf planets. The Potato Radius can be calculated from first principles based on the elastic properties and gravity of the asteroid. Similarly, the tallest mountain that a planet can support is also known to be based on the elastic properties and gravity. In this work, a simple novel method of calculating the Potato Radius is presented using what is known about the maximum height of mountains and Newtonian gravity for a spherical body. This method does not assume any knowledge beyond high school level mechanics, and may be appropriate for students interested in applications of physics to astronomy.

A striking shape was recently observed for the cellular organelle endoplasmic reticulum consisting of stacked sheets connected by helical ramps. This shape is interesting both for its biological function, to synthesize proteins using an increased surface area for ribosome factories, and its geometric properties that may be insensitive to details of the microscopic interactions. In the present work, we find very similar shapes in our molecular dynamics simulations of the nuclear pasta phases of dense nuclear matter that are expected deep in the crust of neutron stars. There are dramatic differences between nuclear pasta and terrestrial cell biology. Nuclear pasta is 14 orders of magnitude denser than the aqueous environs of the cell nucleus and involves strong interactions between protons and neutrons, while cellular scale biology is dominated by the entropy of water and complex assemblies of biomolecules. Nonetheless the very similar geometry suggests both systems may have similar coarse-grained dynamics and that the shapes are indeed determined by geometrical considerations, independent of microscopic details. Many of our simulations self-assemble into flat sheets connected by helical ramps. These ramps may impact the thermal and electrical conductivities, viscosity, shear modulus, and breaking strain of neutron star crust. The interaction we use, with Coulomb frustration, may provide a simple model system that reproduces many biologically important shapes., Comment: 5 pages, 3 figures

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., Comment: 13 pages

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 Q_{imp}. Predictions of light curves for the low mass X-ray binary MXB 1659-29, assuming a large Q_{imp}, 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)., Comment: 5 pages, 2 figures

The dense neutron-rich matter found in supernovae and neutron stars is expected to form complex nonuniform phases 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. We use two recently developed hybrid CPU/GPU codes to perform large scale molecular dynamics (MD) simulations with $51200$ and $409600$ nucleons of nuclear pasta. From the output of the MD simulations we characterize the topology and compute two observables, the radial distribution function $g(r)$ and the structure factor $S(q)$, for systems with proton fractions $Y_p=0.10, 0.20, 0.30$ and $0.40$ at about one third of nuclear saturation density and temperatures near $1.0$ MeV. We observe that the two lowest proton fraction systems simulated, $Y_p=0.10$ and $0.20$, equilibrate quickly and form liquid-like structures. Meanwhile, the two higher proton fraction systems, $Y_p=0.30$ and $0.40$, take a longer time to equilibrate and organize themselves in solid-like periodic structures. Furthermore, the $Y_p=0.40$ system is made up of slabs, lasagna phase, interconnected by defects while the $Y_p=0.30$ systems consist of a stack of perforated plates, the nuclear waffle phase. The periodic configurations observed in our MD simulations for proton fractions $Y_p\ge0.30$ 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 an hexagonal lattice at temperatures slightly lower than $1.0$ MeV., Comment: 16 pages, 12 figires, 6 tables, small changes with respect to previous version, Phys Rev C in press