Nuclear Pasta Research Articles

Nuclear pasta and symmetry energy in the relativistic point-coupling model

Nonuniform structure of low-density nuclear matter, known as nuclear pasta, is expected to appear not only in the inner crust of neutron stars but also in core-collapse supernova explosions and neutron-star mergers. We perform fully three-dimensional calculations of inhomogeneous nuclear matter and neutron-star matter in the low-density region using the Thomas-Fermi approximation. The nuclear interaction is described in the relativistic mean-field approach with the point-coupling interaction, where the meson exchange in each channel is replaced by the contact interaction between nucleons. We investigate the influence of nuclear symmetry energy and its density dependence on pasta structures by introducing a coupling term between the isoscalar-vector and isovector-vector interactions. It is found that the properties of pasta phases in the neutron-rich matter are strongly dependent on the symmetry energy and its slope. In addition to typical shapes like droplets, rods, slabs, tubes, and bubbles, some intermediate pasta structures are also observed in cold stellar matter with a relatively large proton fraction. We find that nonspherical shapes are unlikely to be formed in neutron-star crusts, since the proton fraction obtained in $\beta$ equilibrium is rather small. The inner crust properties may lead to a visible difference in the neutron-star radius.

Tasting nuclear pasta made with classical molecular dynamics simulations

Nuclear clusters or voids in the inner crust of neutron stars were predicted to have various shapes collectively nicknamed nuclear pasta. The recent review in Ref. \cite{Lopez1} by L\'opez, Dorso and Frank summarized their systematic investigations into properties especially the morphological and thermodynamical phase transitions of the nuclear pasta within a Classical Molecular Dynamics model, providing further stimuli to find more observational evidences of the predicted nuclear pasta in neutron stars.

Fast neutrino cooling of nuclear pasta in neutron stars: Molecular dynamics simulations

The direct URCA process of rapid neutrino emission can occur in nonuniform nuclear pasta phases that are expected in the inner crust of neutron stars. Here, the periodic potential for a nucleon in nuclear pasta allows momentum conservation to be satisfied for direct URCA reactions. We improve on earlier work by modeling a rich variety of pasta phases (gnocchi, waffle, lasagna, and anti-spaghetti) with large-scale molecular dynamics simulations. We find that the neutrino luminosity due to direct URCA reactions in nuclear pasta can be 3 to 4 orders of magnitude larger than that from the modified URCA process in the NS core. Thus neutrino radiation from pasta could dominate radiation from the core and this could significantly impact the cooling of neutron stars

Nuclear pasta in hot and dense matter and its influence on the equation of state for astrophysical simulations

We explore the properties of nuclear pasta appearing in supernova matter, i.e., matter at finite temperature with a fixed proton fraction. The pasta phases with a series of geometric shapes are studied using the compressible liquid-drop (CLD) model, where nuclear matter separates into a dense liquid phase of nucleons and a dilute gas phase of nucleons and $\alpha$ particles. The equilibrium conditions for two coexisting phases are derived by minimization of the total free energy including the surface and Coulomb contributions, which are clearly different from the Gibbs conditions for phase equilibrium due to the finite-size effects. Compared to the results considering only spherical nuclei, the inclusion of pasta phases can delay the transition to uniform matter and enlarge the region of nonuniform matter in the phase diagram. The thermodynamic quantities obtained in the present calculation with the CLD model are consistent with those in the realistic equation of state table for astrophysical simulations using the Thomas--Fermi approximation. It is found that the density ranges of various pasta shapes depend on both the temperature $T$ and the proton fraction $Y_p$. Furthermore, the nuclear symmetry energy and its density dependence may play crucial roles in determining the properties of pasta phases. Our results suggest that the pasta phase diagram is most sensitively dependent on the symmetry energy slope $L$ especially in the low-$Y_p$ and high-$T$ region.

Survey of nuclear pasta in the intermediate-density regime: Structure functions for neutrino scattering

Background: Nuclear pasta matter, emerging due to the competition between the long-range Coulomb force and the short-range strong force, is believed to be present in astrophysical scenarios, such as neutron stars and core-collapse supernovae. Its structure can have a high impact, e.g., on neutrino transport or the tidal deformability of neutron stars.Purpose: We investigate the impact of nuclear pasta on neutrino interactions and compare the results to uniform matter.Method: We calculate the elastic and inelastic static structure factors for nuclear pasta matter, using density functional theory (DFT), which contain the main nuclear input for neutrino scattering.Results: Each pasta structure leaves a unique imprint in the elastic structure factor and it is largely enhanced. The inelastic structure factors are very similar for all configurations.Conclusion: Nuclear pasta has a noticeable impact on neutrino neutral-current scattering opacities. While for inelastic reactions the cross section is reduced, the elastic coherent scattering increases dramatically. The effect can be of importance for the cooling of neutron stars as well as for core-collapse supernova models.

Fluctuations in the composition of nuclear pasta in symmetric nuclear matter at finite temperature

The equilibrium distributions of the different pasta geometries and their linear sizes are calculated from the mean field Gibbs energy functional in symmetric nuclear matter at finite temperature. The average sizes and shapes coincide approximately with the ones predicted by a standard pasta calculation in the coexisting phase approximation, but fluctuations are additionally calculated and seen to increase with temperature and baryonic density. The different pasta shapes are shown to coexist in a wide domain of density and temperature, in qualitative agreement with the findings of large scale molecular dynamics simulations, but with a much less expensive computational cost.

Warming nuclear pasta with dark matter: kinetic and annihilation heating of neutron star crusts

Neutron stars serve as excellent next-generation thermal detectors of dark matter, heated by the scattering and annihilation of dark matter accelerated to relativistic speeds in their deep gravitational wells. However, the dynamics of neutron star cores are uncertain, making it difficult at present to unequivocally compute dark matter scattering in this region. On the other hand, the physics of an outer layer of the neutron star, the crust, is more robustly understood. We show that dark matter scattering solely with the low-density crust still kinetically heats neutron stars to infrared temperatures detectable by forthcoming telescopes. We find that for both spin-independent and spin-dependent scattering on nucleons, the crust-only cross section sensitivity is 10−43 − 10−41 cm2 for dark matter masses of 100 MeV − 1 PeV, with the best sensitivity arising from dark matter scattering with a crust constituent called nuclear pasta (including gnocchi, spaghetti, and lasagna phases). For dark matter masses from 10 eV to 1 MeV, the sensitivity is 10−39 − 10−34 cm2, arising from exciting collective phonon modes in a neutron superfluid in the inner crust. Furthermore, for any s-wave or p-wave annihilating dark matter, we show that dark matter will efficiently annihilate by thermalizing just with the neutron star crust, regardless of whether the dark matter ever scatters with the neutron star core. This implies efficient annihilation in neutron stars for any electroweakly interacting dark matter with inelastic mass splittings of up to 200 MeV, including Higgsinos. We conclude that neutron star crusts play a key role in dark matter scattering and annihilation in neutron stars.

Survey of nuclear pasta in the intermediate-density regime: Shapes and energies

Background: Nuclear pasta, emerging due to the competition between the long-range Coulomb force and the short-range strong force, is believed to be present in astrophysical scenarios, such as neutron stars and core-collapse supernovae. Its structure can have a high impact e.g. on neutrino transport or the tidal deformability of neutron stars. Purpose: We study several possible pasta configurations, all of them minimal surface configurations, which are expected to appear in the mid-density regime of nuclear pasta, i.e. around 40% of the nuclear saturation density. In particular we are interested in the energy spectrum for different pasta configurations considered. Method: Employing the density functional theory (DFT) approach, we calculate the binding energy of the different configurations for three values of the proton content XP = 1/10, 1/3 and 1/2, by optimizing their periodic length. We study finite temperature effects and the impact of electron screening. Results: Nuclear pasta lowers the energy significantly compared to uniform matter, especially for $X_P \geq 1/3$. However, the different configurations have very similar binding energies. For large proton content, $X_P \geq 1/3$, the pasta configurations are very stable, for lower proton content temperatures of a few MeV are enough for the transition to uniform matter. Electron screening has a small influence on the binding energy of nuclear pasta, but increases its periodic length. Conclusion: Nuclear pasta in the mid-density regime lowers the energy of the matter for all proton fractions under study. It can survive even large temperatures of several MeV. Since various configurations have very similar energy, it is to expected that many configurations can coexist simultaneously already at small temperatures.

Crust-cooling Models Are Insensitive to the Crust–Core Transition Pressure for Realistic Equations of State

Abstract Neutron stars cooling after sustained accretion outbursts provide unique information about the neutron star crust and underlying dense matter. Comparisons between astronomical observations of these cooling transients and model calculations of neutron star crust cooling have frequently been used to constrain neutron star properties such as the mass, radius, crust composition, and presence of nuclear pasta. These calculations often use a fixed pressure at which the crust–core transition happens, though this quantity depends on the dense matter equation of state. We demonstrate that varying the crust–core transition pressure in a manner consistent with adopting various equations of state results in modest changes to the crust-cooling light curve. This validates the approach adopted in most crust-cooling studies to date, where the neutron star mass and radius are varied while leaving the crust–core transition pressure constant.

Domains and defects in nuclear pasta

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.

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} ergs/cm^{3} and a breaking strain greater than 0.1.

Phase transitions and symmetry energy in nuclear pasta

Cold and isospin-symmetric nuclear matter at sub-saturation densities is known to form the so-called pasta structures, which, in turn, are known to undergo peculiar phase transitions. Here we investigate if such pastas and their phase changes survive in isospin asymmetric nuclear matter, and whether the symmetry energy of such pasta configurations is connected to the isospin content, the morphology of the pasta and to the phase transitions. We find that indeed pastas are formed in isospin asymmetric systems with proton to neutron ratios of x=0.3, 0.4 and 0.5, densities in the range of 0.05 fm−3<ρ<0.08 fm−3, and temperatures T<2 MeV. Using tools (such as the caloric curve, Lindemann coefficient, radial distribution function, Kolmogorov statistic, and Euler functional) on the composition of the pasta, determined the existence of homogeneous structures, tunnels, empty regions, cavities and transitions among these regions. The symmetry energy was observed to attain different values in the different phases showing its dependence on the morphology of the nuclear matter structure.

Calculation of the transport coefficients of the nuclear pasta phase

We calculate the transport coefficients of low-density nuclear matter, especially the nuclear pasta phase, using quantum molecular dynamics simulations. The shear viscosity as well as the thermal and electrical conductivities are determined by calculating the static structure factor of protons for all relevant density, temperature and proton fractions, using simulation data. It is found that all the transport coefficients have similar orders of magnitude as found earlier without considering the pasta phase. Our results are thus in contrast to the common belief that the pasta layer is highly resistive and therefore have important astrophysical consequences.

Nuclear pasta in hot dense matter and its implications for neutrino scattering

We find that the abundance of large clusters of nucleons in neutron-rich matter at sub-nuclear density is greatly reduced by finite temperature effects when matter is close to beta-equilibrium. Large nuclei and exotic non-spherical nuclear configurations called pasta, favored in the vicinity of the transition to uniform matter at $T=0$, dissolve at relatively low temperature. For matter close to beta-equilibrium we find that the pasta melting temperature is $T_m^\beta\simeq 4\pm 1$~MeV for realistic equations of state. The mechanism for pasta dissolution is discussed, and in general $T_m^\beta$ is shown to be sensitive to the proton fraction. We find that coherent neutrino scattering from nuclei and pasta makes a modest contribution to the opacity under the conditions encountered in supernovae and neutron star mergers. Implications for neutrino signals from galactic supernovae are briefly discussed.

Dynamics of fragment formation in neutron-rich matter

Background: Neutron stars are astronomical systems with nucleons submitted to extreme conditions. Due to the longer range coulomb repulsion between protons, the system has structural inhomogeneities. Several interactions tailored to reproduce nuclear matter plus screened Coulomb term reproduce these inhomogeneities known as nuclear pasta. These structural inhomogeneities, located in the crust of neutron stars, can also arise in expanding systems depending on the thermodynamic conditions (temperature, proton fraction, ...) and the expansion velocity. Purpose: We aim to find the dynamics of the fragments formation for expanding systems simulated according to the little big bang model. This expansion resembles the evolution of neutron stars merger. Method: We study the dynamics of the nucleons with semiclassical molecular dynamics models. Starting with an equilibrium configuration, we expand the system homogeneously until we arrive to an asymptotic configuration (i. e. very low final densities). We study, with four different cluster recognition algorithms, the fragment distribution throughout this expansion and the dynamics of the cluster formation. Results: Studying the topology of the equilibrium states, before the expansion, we reproduced the known pasta phases plus a novel phase we called pregnocchi, consisting of proton aggregates embedded in a neutron sea. We have identified different fragmentation regimes, depending on the initial temperature and fragment velocity. In particular, for the already mentioned pregnocchi, a neutron cloud surrounds the clusters during the early stages of the expansion, resulting in systems that give rise to configurations compatibles with the emergence of r-proccess. Conclusions: These calculations pave the way to a comparision between Earth experiments and neutron star studies.

Transport Properties of the Nuclear Pasta Phase with Quantum Molecular Dynamics

Abstract We study the transport properties of nuclear pasta for a wide range of density, temperature, and proton fractions, relevant for different astrophysical scenarios adopting a quantum molecular dynamics model. In particular, we estimate the values of shear viscosity as well as electrical and thermal conductivities by calculating the static structure factor S(q) using simulation data. In the density and temperature range where the pasta phase appears, the static structure factor shows irregular behavior. The presence of a slab phase greatly enhances the peak in S(q). However, the effect of irregularities in S(q) on the transport coefficients is not very dramatic. The values of all three transport coefficients are found to have the same orders of magnitude as found in theoretical calculations for the inner crust matter of neutron stars without the pasta phase; therefore, the values are in contrast to earlier speculations that a pasta layer might be highly resistive, both thermally and electrically.

Colloquium: 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.

Hyperons in the nuclear pasta phase

We have investigated under which conditions hyperons (particularly $\Lambda$s and $\Sigma^-$s) can be found in the pasta phase. The larger the density and the temperature and the smaller the electron fraction the higher the probability that these particles appear but always in very small amounts. $\Lambda$-hyperons only occur in the gas and in smaller amounts than would occur if matter were homogeneous, never with abundancies above 10$^{-5}$. The amount of $\Sigma^-$ in the gas is at least two orders of magnitude smaller and can be disregarded in practical calculations.

Topological analysis of nuclear pasta phases

In this paper the analysis of the result of numerical simulations of pasta phases using algebraic topology methods is presented. These considerations suggest that some phases can be further split into (sub)phases and therefore should be more refined in numerical simulations. The results presented in the paper can also be used to relate the Euler characteristic from numerical simulations to the geometry of the phases. The Betti numbers are used as they provide finer characterization of the phases. It is also shown that different boundary conditions give different outcomes.

Structure of neutron star crusts from new Skyrme effective interactions constrained by chiral effective field theory

We investigate the structure of neutron star crusts, including the crust-core boundary, based on new Skyrme mean field models constrained by the bulk-matter equation of state from chiral effective field theory and the ground-state energies of doubly-magic nuclei. Nuclear pasta phases are studied using both the liquid drop model as well as the Thomas-Fermi approximation. We compare the energy per nucleon for each geometry (spherical nuclei, cylindrical nuclei, nuclear slabs, cylindrical holes, and spherical holes) to obtain the ground state phase as a function of density. We find that the size of the Wigner-Seitz cell depends strongly on the model parameters, especially the coefficients of the density gradient interaction terms. We employ also the thermodynamic instability method to check the validity of the numerical solutions based on energy comparisons.