Calculating the Potato Radius of Asteroids using the Height of Mt. Everest

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

Astromaterial Science and Nuclear Pasta

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 pres

The Elasticity of Nuclear Pasta

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 Letter

Thermal Fluctuations in Nuclear Pasta

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: 12 pages, 8 figure

Black Dwarf Supernova in the Far Future

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 MNRA

Structure of Multicomponent Coulomb Crystals

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 PR

Pasta Nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium

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 page

Simulating the Novel Phase Separation of a Rapid Proton Capture Ash Composition

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.

Nuclear Waffles

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 pres

Parking-garage structures in astrophysics and biophysics

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 figure