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10 Macroscopic Model of Neutron Star Crusts

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 [15Jump To The Next Citation Point]).

Macroscopic models of neutron star crusts, taking into account the presence of the neutron superfluid at ρ > ρND (see Section 8), have been developed by Carter and collaborators. They have shown how to extend the two-fluid picture of neutron star cores [93Jump To The Next Citation Point] to the inner crust layers in the Newtonian framework [79Jump To The Next Citation Point94Jump To The Next Citation Point]. They have also discussed how to calculate the microscopic coefficients of this model [78Jump To The Next Citation Point77]. 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 [73Jump To The Next Citation Point85Jump To The Next Citation Point] and in the Newtonian limit [73Jump To The Next Citation Point72Jump To The Next Citation Point]. 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 [74Jump To The Next Citation Point75Jump To The Next Citation Point76Jump To The Next Citation Point]. 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

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