Although crystallized neutron star crust is responsible for many fascinating observational phenomena, its actual microscopic structure in tremendous gravitational and magnetic fields is not understood. Here we show that in a non-uniform magnetic field, three-dimensional ionic Coulomb crystals comprising the crust may stretch or shrink while their electrostatic pressure becomes anisotropic. The pressure depends non-linearly on the magnitude of the stretch, so that a continuous magnetic field evolution may result in an abrupt crystal elongation or contraction. This may provide a trigger for magnetar activity. A phonon mode instability is revealed, which sets the limits of magnetic field variation beyond which the crystal is destroyed. These limits sometimes correspond to surprisingly large deformations. It is not known what happens to crust matter subject to a pressure anisotropy exceeding these limits. We hypothesize that the ion system then possesses a long-range order only in one or two dimensions, that is becomes a liquid crystal.
We study breaking stress of deformed Coulomb crystals in a neutron star crust, taking into account electron plasma screening of ion-ion interaction; calculated breaking stress is fitted as a function of electron screening parameter. We apply the results for analyzing torsional oscillation modes in the crust of a non-magnetic star. We present exact analytic expression for the fundamental frequencies of such oscillations and show that the frequencies of all torsional oscillations are insensitive to the presence of the outer neutron star crust. The results can be useful in theoretical modeling of processes involving deformed Coulomb crystals in the crust of neutron stars, such as magnetic field evolution, torsional crustal or thermo-elastic quasi-periodic oscillations of flaring soft gamma-ray repeaters, pulsar glitches. The applicability of the results to soft gamma-ray repeaters is discussed.
We calculate electrostatic, spectral, and thermal properties of two-component Coulomb crystals of ions and determine the limits of applicability of the linear mixing theory to such systems.
Electrostatic energy, collective modes, and thermodynamic functions of a Coulomb crystal with equal number of ions of two different types and uniform charge-compensating electron background are studied using harmonic lattice model. Simple cubic and hexagonal lattices with two different ions in the elementary cell (we denote these lattices sc2 and h2, respectively) are considered. The static sc2 lattice is more tightly bound than the h2 one at any charge ratio of the constituent ions. The phonon spectra depend on the ion charge and mass ratio. An analysis shows that these binary Coulomb crystals are stable, if the charge ratio is not too different from 1 (about 3.6 for sc2 and 1.3 for h2 lattices) regardless of the mass ratio. Heat capacity of the sc2 lattice is obtained by numerical integration over the first Brillouin zone as a function of temperature and charge and mass ratios. Well known classic and quantum asymptotes of the heat capacity are reproduced, and the dependence of the coefficient in the Debye T 3 law on charge and mass ratios is presented.
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