r-Mode Oscillations and Rocket Effect in Rotating Superfluid Neutron Stars. I. Formalism

Abstract

We derive the hydrodynamical equations of r-mode oscillations in neutron stars in the presence of a novel damping mechanism related to particle number changing processes. The change in the number densities of the various species leads to new dissipative terms in the equations that are responsible for the rocket effect. We employ a two-fluid model, with one fluid consisting of the charged components, while the second fluid consists of superfluid neutrons. We consider two different kinds of r-mode oscillations, one associated with comoving displacements, and the second associated with countermoving, out of phase, displacements.

r-Mode Oscillations and Rocket Effect in Rotating Superfluid Neutron Stars. II. Numerical Results

“…As was already shown in [1], all these processes lead to the appearance of dissipative terms in the hydrodynamical equations, and we have called the rocket effect the corresponding effect on the hydrodynamical evolution of the system.…”

“…We estimate the damping time scale of this mechanism for the "standard r-mode oscillations" and the "superfluid rmode oscillations," whose hydrodynamical equations have been derived in [1]. We find that the dissipative mechanism associated with the rocket term does not efficiently damp standard r-mode oscillations.…”

“…(19) of [1], and in the case where the Urca processes are allowed the value of Urca Γ = Ξ depends on the superfluid phase considered.…”

“…56, No. 1, March , 2013 1 Università di Bari and I.N.F.N. Sezione di Bari, Italy, e-mail: colucci@th.physik.uni-frankfurt.de 2 Departament d'Estructura i Constituents de la Matèria and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Spain I.N.F.N., Laboratori Nazionali del Gran Sasso, Assergi (AQ), Italy, e-mail: massimo@lngs.infn.it the accompanying paper [1] for two different kinds of r-mode oscillations.…”

“…1, March , 2013 1 Università di Bari and I.N.F.N. Sezione di Bari, Italy, e-mail: colucci@th.physik.uni-frankfurt.de 2 Departament d'Estructura i Constituents de la Matèria and Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Spain I.N.F.N., Laboratori Nazionali del Gran Sasso, Assergi (AQ), Italy, e-mail: massimo@lngs.infn.it the accompanying paper [1] for two different kinds of r-mode oscillations. We have considered the standard r-mode oscillations, which are predominantly toroidal comoving displacements of the superfluid and normal components, and the superfluid r-mode oscillations, which are associated to toroidal countermoving displacements of the two fluids.…”