Anisotropic crystal structure of magnetized neutron star crust

Abstract

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.

Breaking properties of neutron star crust

“…Thus, an accurate knowledge of the crust strength is fundamental for NS physics and in this paper we analyse it, paying special attention to its anisotropy. Previous works in this field explored a shear deformation by MD simulation (Horowitz & Kadau 2009;Chugunov & Horowitz 2010Hoffman & Heyl 2012) and volume-conserving crystal stretching in two highly symmetric directions semianalytically (Baiko & Kozhberov 2017; Paper 1). Here we apply the approach proposed in the latter work to study stretching in arbitrary directions.…”

Electrostatic properties and stability of Coulomb crystals

“…The bcc lattice which stretched along its main diagonal (in the direction of the nearest neighbour) is stable when 0.92 < c d1 < 1.13, where c d1 is the ratio of the length of the diagonal along the deformation to the length of the undeformed diagonal. 24 Stretched along the diagonal of the base of the elementary cell cube (towards the third nearest neighbour), the bcc lattice is stable when c d3 lies between 0.9 and 1.06, where c d3 is the similar ratio as in the previous case but for the base diagonal.…”

“…It is widely done in Refs. 24,25 where it was found that no deformation can bring the bcc lattice to a state with a lower electrostatic energy. Thus, the bcc Coulomb lattice has the lowest electrostatic energy among all lattices under consideration.…”

“…The stability of deformed bcc and fcc lattices was widely studied in Refs. 24,25 where it was shown that the bcc lattice stretched 1.49 times along one of the elementary cell cube edges (towards the second nearest neighbour), remains stable. Hence, it is possible to translate the bcc lattice into the fcc lattice by continuous deformation.…”

Elastic properties of binary crystals in neutron stars and white dwarfs

“…Note that the bcc lattice can be turned into the fcc lattice by continuous deformation (Baiko & Kozhberov 2017). According to the linear mixing rule, µ eff of the binary fcc lattice is…”