The understanding of many observed phenomena occurring in neutron stars (and briefly reviewed in Section 12, for instance, pulsar glitches or torsional oscillations in Soft Gamma Repeaters) requires modeling the dynamic evolution of the crust. So far theoretical efforts have been mainly devoted to modeling the dynamic evolution of the liquid core by considering a mixture of superfluid neutrons and superconducting protons (see, for instance, the recent review by Andersson & Comer [15]).

Macroscopic models of neutron star crusts, taking into account the presence of the neutron superfluid at (see Section 8), have been developed by Carter and collaborators. They have shown how to extend the two-fluid picture of neutron star cores [93] to the inner crust layers in the Newtonian framework [79, 94]. They have also discussed how to calculate the microscopic coefficients of this model [78, 77]. More elaborate models treating the crust as a neutron superfluid in an elastic medium and taking into account the effects of a frozen-in magnetic field have been very recently developed both in general relativity [73, 85] and in the Newtonian limit [73, 72]. All these models are based on an action principle that will be briefly reviewed in Section 10.1. We will consider a simple nonrelativistic two-fluid model of neutron star crusts in Section 10.2 using the fully-4D covariant formulation of Carter & Chamel [74, 75, 76]. Entrainment effects and superfluidity will be discussed in Sections 10.3 and 10.4, respectively.

10.1 Variational formulation of multi-fluid hydrodynamics

10.2 Two-fluid model of neutron star crust

10.3 Entrainment and effective masses

10.4 Neutron superfluidity

10.2 Two-fluid model of neutron star crust

10.3 Entrainment and effective masses

10.4 Neutron superfluidity

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