Using molecular dynamics simulations, we determine the structure of neutron star crust made of rapid proton capture nucleosynthesis material. We find a regular body centered cubic lattice, even with the large number of impurities that are present. Low charge $Z$ impurities tend to occupy interstitial positions, while high $Z$ impurities tend to occupy substitutional lattice sites. We find strong attractive correlations between low $Z$ impurities that could significantly increase the rate of pycnonuclear (density driven) nuclear reactions. The thermal conductivity is significantly reduced by electron impurity scattering. Our results will be used in future work to study the effects of impurities on mechanical properties such as the shear modulus and breaking strain.
Deep Dive into The structure of accreted neutron star crust.
Using molecular dynamics simulations, we determine the structure of neutron star crust made of rapid proton capture nucleosynthesis material. We find a regular body centered cubic lattice, even with the large number of impurities that are present. Low charge $Z$ impurities tend to occupy interstitial positions, while high $Z$ impurities tend to occupy substitutional lattice sites. We find strong attractive correlations between low $Z$ impurities that could significantly increase the rate of pycnonuclear (density driven) nuclear reactions. The thermal conductivity is significantly reduced by electron impurity scattering. Our results will be used in future work to study the effects of impurities on mechanical properties such as the shear modulus and breaking strain.
Neutron stars, collapsed objects half again more massive than the sun, are thought to have solid crusts about a kilometer thick. Detailed properties of this crust are important for many X-ray, radio, and gravitational wave observations. Because of the great densities, the electronic structure of the crust is likely very simple, consisting of an extremely degenerate relativistic Fermi gas. The system can be modeled as nearly classical ions interacting via screened Coulomb, or Yukawa, interactions, where the screening length λ depends on the electron density.
Indeed many condensed matter systems can be modeled with Yukawa interactions and much is known about the properties of a single component Yukawa system. See for example ref. [1]. Because the ion-ion interaction is purely repulsive, there is no liquid-gas phase transition. However there is a liquid solid phase transition at a melting temperature T m that depends primarily on the Coulomb parameter Γ,
Here the ions have charge Z, T is the temperature and the ion sphere radius a is a = 3 4πn 1/3 (2) with n the ion density.The system melts at a temperature for which Γ ≈ 175 (assuming the screening length is relatively large).
Neutron stars, that accrete material from a binary companion, form new crust from the ashes of nuclear reactions. Simulations of rapid proton capture nucleosynthesis [2][3] find a complex composition with many different ion species. These species then undergo electron capture as the material is buried by further accretion to greater densities [4]. This still leaves a complex composition of very neutron rich isotopes with many different chemical elements. In this paper, we investigate the structure of the resulting solid crust when this complex mixture freezes.
Monte Carlo simulations [5] of the freezing of a classical one component plasma (OCP) indicate that it can freeze into imperfect body centered cubic (bcc) or face-centered cubic (fcc) microcrystals. Unfortunetly not much has been published on the freezing of a multi-component plasma (MCP), although Wunsch et al. study the structure of a MCP liquid [6]. There are many possibilities for the state of a cold MCP [7]. It can be a regular MCP lattice; or microcrystals; or an amorphous, uniformly mixed structure; or a lattice of one phase with random admixture of other ions; or even an ensemble of phase separated domains.
One possibility is that impurities could become frozen into random configurations that only relax on very long time scales. This could lead to the formation of a glass. For example, the binary Lennard-Jones system, with two species of different sizes, can form a glass [8]. Here the hard core of the interaction keeps the different species from diffusing. However the screened coulomb interaction has a relatively soft 1/r core. This may allow impurities to diffuse and prevent the formation of a glass.
In this paper we use molecular dynamics simulations to calculate radial distribution functions g(r) and static structure factors S(q) to determine the structure of the crust. In previous work we determined the chemical separation that takes place as the crust freezes. We found that the liquid phase is greatly enriched in low charge Z ions while the solid is enriched in high Z ions [9]. The distribution of low Z (impurity) ions in the crust may be important for the rate of strongly screened thermonuclear or pycnonuclear (density driven) reactions. In ref. [10] we found that fusion of 24 O + 24 O could be an important heat source in the crust.
In ref. [11] we calculated the thermal conductivity of the crust. We found the crust to be a regular crystal with a relatively high thermal conductivity. Recently the cooling of two neutron stars has been observed after extended outbursts [12,13]. These outbursts heat the stars’ crusts out of equilibrium and then the cooling time is measured as the crusts return to equilibrium. The surface temperature of the neutron star in KS 1731-260 decreased with an exponential time scale of 325 ± 100 days while MXB 1659-29 has a time scale of 505 ± 59 days [13]. Comparing these observations, of rapid cooling, to calculations by Rutledge et al. [14], Shternin et al. [15], and Brown et al. [16] strongly suggest that the crust has a high thermal conductivity.
The shear modulus of a single component system was calculated in ref. [17] where electron screening was found to reduce the shear modulus by about 10% compared to a pure 1/r Coulomb system [18]. The shear modulus determines the frequency of shear oscillations of the neutron star crust. These may have been observed as quasiperiodic oscillations in magnetar giant flares [19]. In the future, we will use the results of this paper to calculate the effects of impurities on the shear modulus.
The breaking strain is the deformation of the crust when it fails. This determines the maximum height of mountains on the surface of neutron stars. These may be important sources of gravitational waves for ra
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