Colloquium: Astromaterial science and nuclear pasta

“Astromaterial science” is defined 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, although they may be organized in ways similar to more conventional materials. By analogy to terrestrial materials, this study of astromaterials is divided into hard and soft and one example of each is discussed. 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, how molecular dynamics simulations have been used to calculate the properties of astromaterials to interpret observations of white dwarfs and neutron stars is discussed. 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 ${10}^{14}\mathrm{g}/{\mathrm{cm}}^3$. Competition between nuclear attraction and Coulomb repulsion rearranges neutrons and protons into complex nonspherical shapes such as sheets (lasagna) or tubes (spaghetti). Semiclassical 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 used to interpret observations of supernova neutrinos, magnetic field decay, and crust cooling of accreting neutron stars. This Colloquium concludes by comparing nuclear pasta shapes with some similar shapes seen in biological systems.

Figure 1

Cross section of a cooling white dwarf star. The Coulomb crystals described in Sec. 3 are found in the solid core, while the mantle is liquid. The Coulomb parameter $\mathrm{\Gamma }$ describes the ratio of a typical Coulomb energy between ions to the thermal energy $kT$; see Eq. (3).

Figure 2

Cross section of a neutron star. The Coulomb crystals described in Sec. 3 are found in the inner and outer crusts, while the nuclear pasta, described in Sec. 4, may be found at the base of the inner crust.

Figure 3

Nuclear pasta configurations produced in our MD simulations with 51 200 nucleons: (a) gnocchi, (b) spaghetti, (c) waffles, (d) lasagna, (e) defects, (f) antispaghetti, and (g) antignocchi. From [78], [76], and [35].

Figure 4

The normalized Minkowski functionals $B/A$ and $X/A$ as a function of density for a simulation of 51 200 nucleons.

Figure 5

The angle-averaged proton static structure factor $S_p(q)$ vs momentum transfer $q$. This is for nuclear pasta with $n=0.050{\mathrm{fm}}^{-3}$, temperature $T=1\mathrm{MeV}$, and proton fractions $Y_P=0.10$, 0.20, 0.30, and 0.40. From [76].

Figure 6

Surface temperature of MXB 1659-29 vs time since accretion stopped. The dashed line shows the predicted cooling curve for a model without a resistive pasta layer while the solid line shows the predicted cooling curve for a model with a resistive pasta layer. From [35].

Figure 7

Comparison of helicoidal ramps in (a) electron micrograph of endoplasmic reticulum at a density near $1\mathrm{g}/{\mathrm{cm}}^3$. From [88]. (b) Nuclear pasta simulations at a density of ${10}^{14}\mathrm{g}/{\mathrm{cm}}^3$.