In the standard picture of the crust of a neutron star, matter there is simple: a body-centered-cubic lattice of nuclei immersed in an essentially uniform electron gas. We show that, at densities above that for neutron drip (∼4 × 10 11 g cm −3 or roughly one-thousandth of nuclear matter density), the interstitial neutrons give rise to an attractive interaction between nuclei that renders the lattice unstable. We argue that the likely equilibrium structure is similar to that in displacive ferroelectric materials such as BaTiO 3 . As a consequence, the properties of matter in the inner crust are expected to be much richer than previously appreciated, and we mention possible consequences for observable neutron star properties. DOI: 10.1103/PhysRevLett.112.112504 PACS numbers: 21.65.-f, 26.60.Gj, 67.10.Jn, 97.60.Jd Many technologically important properties of terrestrial metals are governed by the fact that these materials exhibit a variety of crystal structures. Pure metals have many different phases [1]. For alloys, even more possibilities exist, and these have far-reaching implications: e.g., the strength of steels is determined to a high degree by the existence of different crystal structures. Here we consider matter in the outer parts of a neutron star (its crust), which is important for interpreting observations of neutron stars even though it comprises only a small fraction of the total mass of the star. In the traditional view, this matter is simple, because correlations between electrons, which are crucial for terrestrial matter, play little role. However, at densities above one-thousandth of nuclear density, matter consists of a crystal lattice of atomic nuclei permeated by neutrons [2]. The neutrons behave like a second component in a binary alloy, and we argue that, as a consequence, the properties of matter are more similar to those of terrestrial solids than has been previously appreciated. Specifically, the neutrons give rise to an attractive interaction between nuclei which makes the lattice unstable to clumping of nuclei in a manner similar to the formation of inhomogeneous regions in metallic alloys (spinodal decomposition) [3]. While the attraction is insufficient to make matter unstable to long-wavelength distortions, it can destabilize matter at finite wavelengths where the effective interaction between nuclei due to their electrical charges is reduced. We describe a number of possible consequences for observable properties of neutron stars.To set the scene, we consider the condition for thermodynamic stability of the system of nuclei immersed in a sea of neutrons, together with a background of electrons whose average density is the same as that of the protons to ensure electrical neutrality. The system may thus be regarded as having two components: the neutrons (both those in nuclei and the interstitial ones) and the charged particles. For most of the life of a neutron star, the temperature is so low that thermal effects may be neglected. In that case, the condition for stability is that th...
The magnetically induced Richtmyer-Meshkov instability in a two-component Bose-Einstein condensate is investigated. We construct and study analytical models describing the development of the instability at both the linear and nonlinear stages. The models indicate new features of the instability: the influence of quantum capillary waves and the separation of droplets, which are qualitatively different from the classical case. We perform numerical simulations of the instability in a trapped Bose-Einstein condensate using the Gross-Pitaevskii equation and compare the simulation results to the model predictions.
We consider the hydrodynamics of the outer core of a neutron star under conditions when both neutrons and protons are superfluid. Starting from the equation of motion for the phases of the wave functions of the condensates of neutron pairs and proton pairs we derive the generalization of the Euler equation for a onecomponent fluid. These equations are supplemented by the conditions for conservation of neutron number and proton number. Of particular interest is the effect of entrainment, the fact that the current of one nucleon species depends on the momenta per nucleon of both condensates. We find that the nonlinear terms in the Euler-like equation contain contributions that have not always been taken into account in previous applications of superfluid hydrodynamics. We apply the formalism to determine the frequency of oscillations about a state with stationary condensates and states with a spatially uniform counterflow of neutrons and protons. The velocities of the coupled sound-like modes of neutrons and protons are calculated from properties of uniform neutron star matter evaluated on the basis of chiral effective field theory. We also derive the condition for the two-stream instability to occur.
The dynamics of an interface in a two-component Bose-Einstein condensate driven by a spatially uniform time-dependent force is studied. Starting from the Gross-Pitaevskii Lagrangian, the dispersion relation for linear waves and instabilities at the interface is derived by means of a variational approach. A number of diverse dynamical effects for different types of the driving force is demonstrated, which includes the Rayleigh-Taylor instability for a constant force, the Richtmyer-Meshkov instability for a pulse force, dynamic stabilization of the Rayleigh-Taylor instability and onset of the parametric instability for an oscillating force. Gaussian Markovian and non-Markovian stochastic forces are also considered. It is found that the Markovian stochastic force does not produce any average effect on the dynamics of the interface, while the non-Markovian force leads to exponential perturbation growth.
Elastic properties of the solid regions of neutron star crusts and white dwarfs play an important role in theories of stellar oscillations. Matter in compact stars is presumably polycrystalline and, since the elastic properties of single crystals of such matter are very anisotropic, it is necessary to relate elastic properties of the polycrystal to those of a single crystal. We calculate the effective shear modulus of polycrystalline matter with randomly oriented crystallites using a self-consistent theory that has been very successful in applications to terrestrial materials and show that previous calculations overestimate the shear modulus by approximately 28%.
We present calculations of the hydrodynamics of the inner crust of neutron stars, where a superfluid neutron liquid coexists with a lattice of neutron-rich nuclei. The long-wavelength collective oscillations are combinations of phonons in the lattice and phonons in the superfluid neutrons. Velocities of collective modes are calculated from information about effective nucleon-nucleon interactions derived from Lattimer and Swesty's microscopic calculations based on a compressible liquid drop picture of the atomic nuclei and the surrounding neutrons.
We consider a two-component Bose-Einstein condensate in a quasi-one-dimensional harmonic trap, where the immiscible components are pressed against each other by an external magnetic force. The zero-temperature nonstationary Gross-Pitaevskii equations are solved numerically; analytical models are developed for the key steps in the process. We demonstrate that if the magnetic force is strong enough, then the condensates may swap their places in the trap due to dynamic quantum interpenetration of the nonlinear matter waves. The swapping is accompanied by development of a modulational instability leading to quasiturbulent excitations. Unlike the multidimensional Rayleigh-Taylor instability in a similar geometry of two-component quantum fluid systems, quantum interpenetration has no classical analog. In a two-dimensional geometry a crossover between the Rayleigh-Taylor instability and the dynamic quantum interpenetration is investigated.
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