Application of superconducting-superfluid magnetohydrodynamics to nuclear “pasta” in neutron stars

Abstract

A mixture of superconducting and superfluid nuclear liquids of protons coupled to the ultrarelativistic electron gas, and neutrons is considered. In the magnetohydrodynamic (MHD) approximation, the energy-momentum (stress) tensor is derived, and the entrainment contribution is found in the explicit form. It is shown that this contribution generates a force density, when a superfluid velocity lag and the magnetic field are simultaneously present. This force may be important in the nuclear "pasta" phase in neutron stars, if the proton and neutron Cooper pairing in the pasta phase is taken into account. It is found that if the liquid-crystalline matter of the pasta phase is superfluid and superconducting, then magnitude of the forces acting upon element of matter at typical magnetic field and the superfluid velocity lag, under certain conditions may become large enough to induce a critical stress in the neutron star crust. As an application, the necessary conditions for triggering of a starquake are found in the pasta phase of neutron stars, assuming that the nuclei are flat slabs in parallel magnetic field. The present model includes two independent local parameters: the superfluid velocity lag and the magnetic field. Possible links between the entrainment force and the magnetar starquake triggering mechanism, and some open problems are discussed.