Magnetic susceptibility of a neutron star crust

Abstract

Abstract. The magnetic susceptibility of the degenerate free electrons in the crust of a neutron star is computed for a range of densities, temperatures, and field strengths. It is shown that when the temperature is low enough (typically less than 10' K for densities of about 1O'g and 10" G fields), the susceptibility undergoes large de Haas-van Alphen oscillations. The crust is then unstable to the formation of layers of domains of alternating magnetisation. Associated with these domains are magnetic field fluctuations of a few per cent amplitude and anisotropic magnetostrictive stresses which may be large enough to crumble the crust. It is argued that these domains are unlikely to directly influence the surface properties of the neutron star but may possibly be coupled indirectly to observable effects.

Anisotropy in the equation of state of magnetized quark matter

“…from which the leptonic density can be written as 24) where μ l represents the leptonic chemical potential. The quantities E l and l ± can be obtained from their quark counterparts by the replacements already mentioned.…”

“…The parallel and the perpendicular components of the pressure can be written in terms of the magnetization, M = ∂ P /∂B, as [24,31,37] …”

“…While some of the first works advocated that the pressure, having in mind the thermodynamical pressure obtained from the thermodynamical potential that relates pressure to density, should be isotropic [20][21][22][23], based on an interpretation given in Ref. [24], other works were based on the fact that the energy-momentum tensor gives different contributions for the parallel and perpendicular pressure [25][26][27][28] (see Ref.[29] for a discussion based on LQCD). If two different pressures are indeed present in the system, the usual way of using the equation of state as input to the Tolman-Oppenheimer-Volkoff equations (TOV) [30], which determine the structure of a spherically symmetric body of isotropic material in static gravitational equilibrium, to 0556-2813/2015/91(6)/065205 (12) 065205-1…”

“…While some of the first works advocated that the pressure, having in mind the thermodynamical pressure obtained from the thermodynamical potential that relates pressure to density, should be isotropic [20][21][22][23], based on an interpretation given in Ref. [24], other works were based on the fact that the energy-momentum tensor gives different contributions for the parallel and perpendicular pressure [25][26][27][28] (see Ref.…”

Physics of strongly magnetized neutron stars

“…These de Haas -van Alphen type oscillations arise as successive Landau levels are occupied with increasing density (or decreasing magnetic field). The oscillatory quantities are usually expressed as derivatives of the bulk quantities with respect to thermodynamic variables; examples include heat capacity, magnetization and magnetic susceptibility, adiabatic index (∂ ln P e /∂ ln ρ), sound speed, and electron screening length of an electric charge in the plasma (e.g., Ashcroft & Mermin 1976;Blandford & Hernquist 1982;Lai & Shapiro 1991;Yakovlev & Kaminker 1994). With increasing T , the oscillations become weaker because of the thermal broadening of the Landau levels; when T > ∼ T B , the oscillations are entirely smeared out, and the field-free results are recovered.…”