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Electrical conductivity of neutron star cores in the presence of a magnetic field
Authors:D G Yakovlev  D A Shalybkov
Institution:(1) A. F. Ioffe Institute of Physics and Technology, Leningrad, U.S.S.R.
Abstract:General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities rgrgaprgr0, where rgr0 = 2.8×1014 g cm–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of sum-hyperons at rgr>rgr c , where rgr c ap4rgr0. The electric resistivities along and acrossB, Rscrpar and Rscrbottom, and the Hall resistivity Rscr H are calculated and fitted by simple analytical formulae at rgrlergr c and rgr>rgr c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; Rscrpar is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If rgrlergr c , one has Rscrbottom = Rscrpar1 + (B/B 0)2] for the normal neutrons, and Rscrpar for the superfluid neutrons, while Rscr H = Rscrpar B/B e for both cases. HereB e sim109 T 8 2 G,B 0sim1011 T 8 2 G, andT 8 is temperature in units of 108 K. Accordingly for the normal neutrons atBGtB 0, the transverse resistivity Rscrpar suffers an enhancement, Rscr1/4 Lt Rscr1. When rgrgap5rgr0 andB varies from 0 toBsimB p infin 1013 T 8 2 G, Rscrbottom increases by a factor of about 103–104 and Rscr H changes sign. WhenBGtB p , Rscrbottom remains constant for the superfluid neutrons, and Rscr H infinB 2 for the normal neutrons, while Rscr H infinB for any neutron state. Strong dependence of resistivity onB, T, and rgr may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of Rscrbottom at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.
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