Rotochemical Heating of Neutron Stars: Rigorous Formalism with Electrostatic Potential Perturbations

The electrostatic potential that keeps approximate charge neutrality in neutron star matter is self-consistently introduced into the formalism for rotochemical heating presented in a previous paper by Fernandez and Reisenegger. Although the new formalism is more rigorous, we show that its observable consequences are indistinguishable from those of the previous one, leaving the conclusions of the previous paper unchanged.Comment: 14 pages, including 4 eps figures. Accepted for publication in The Astrophysical Journa

Damping of sound waves in superfluid nucleon-hyperon matter of neutron stars

We consider sound waves in superfluid nucleon-hyperon matter of massive neutron-star cores. We calculate and analyze the speeds of sound modes and their damping times due to the shear viscosity and non-equilibrium weak processes of particle transformations. For that, we employ the dissipative relativistic hydrodynamics of a superfluid nucleon-hyperon mixture, formulated recently [M.E. Gusakov and E.M. Kantor, Phys. Rev. D78, 083006 (2008)]. We demonstrate that the damping times of sound modes calculated using this hydrodynamics and the ordinary (nonsuperfluid) one, can differ from each other by several orders of magnitude.Comment: 15 pages, 5 figures, Phys. Rev. D accepte

On matrix realizations of the Lie superalgebra D(2, 1 ; \alpha)

We obtain a realization of the Lie superalgebra $D(2, 1 ; \alpha)$ in differential operators on the supercircle $S^{1|2}$ and in $4\times 4$ matrices over a Weyl algebra. A contraction of $D(2, 1 ; \alpha)$ is isomorphic to the universal central extension \hat{\p\s\l}(2|2) of \p\s\l(2|2). We realize it in $4\times 4$ matrices over the associative algebra of pseudodifferential operators on $S^1$. Correspondingly, there exists a three-parameter family of irreducible representations of \hat{\p\s\l}(2|2) in a $(2|2)$--dimensional complex superspace.Comment: 15 pages, to be published in Journal of Geometry and Physics 60 (2010), 1656-166