Type II superconductivity and magnetic flux transport in neutron stars

Abstract

The transition to a type II proton superconductor which is believed to occur in a cooling neutron star is accompanied by changes in the equation of hydrostatic equilibrium and by the formation of proton vortices with quantized magnetic flux. Analysis of the electron Boltzmann equation for this system and of the proton supercurrent distribution formed at the transition leads to the derivation of a simple expression for the transport velocity of magnetic flux in the liquid interior of a neutron star. This shows that flux moves easily as a consequence of the interaction between neutron and proton superfluid vortices during intervals of spin‐down or spin‐up in binary systems. The differences between the present analysis and those of previous workers are reviewed and an error in the paper of Jones is corrected.

Post-glitch exponential relaxation of radio pulsars and magnetars in terms of vortex creep across flux tubes

“…If present at all, type I superconductivity with an admixture of field free superconducting regions and magnetic normal matter domains exists near the centre of the star (Jones 2006). When the core protons underwent transition into type II superconductivity, Meissner currents in the crust-core interface played a boundary condition for the coupled evolution of the magnetic field within the normal matter crust and superconducting core which is unknown currently (Jones 2004).…”

“…Long term magnetic field evolution determines the presence and extent of the toroidal field region within the neutron star core. Following the formation of the neutron star the mixed magnetic field configuration with poloidal and toroidal components are inherited from progenitor star (Braithwaite 2009) and after the transition into superconducting state this field form is frozen into the neutron star plasma due to the enhanced electrical conductivity (Jones 2006). Flux tubes move out as a result of diffusion processes, forces acting on them and secular interaction with vortex lines.…”

Fermion zero-mode influence on neutron-star magnetic field evolution

“…In the low‐temperature limit, ω 0 τ≫ 1, only a small longitudinal component of the spectral flow force, given by , remains. Owing to the cancellation of the Magnus force, reduces to f B + f V + F sf ∥ = 0, showing that the movement of proton vortices, and hence expulsion of the field, occurs easily under the influence of buoyancy forces or of interaction with outward‐moving neutron vortices as the rotation of the star slows (Jones 2006). At higher temperatures, the existence of spectral flow radically changes this behaviour.…”

“…The distinct populations of superfluid quasi‐particles concerned are those localized in the cores of proton vortices and those delocalized in the continuum. Previous vortex velocity calculations (Jones 2006) assumed both the internal temperatures T < 10 8 K of typical radio pulsars and negligibly small neutron and proton quasi‐particle number densities. Under these conditions, proton vortices and therefore the internal flux distribution could be quickly expelled to the core‐crust boundary.…”

Rotational Coupling of the Pinned Core Superfluid

“…Likewise, the effective length scale d P of the pinning interaction is expected to be of the order of the coherence length ξ p or the London penetration depth λ p of the proton superconductor for the above two mechanisms, respectively. The effective pinning force (per intersection) f P = E P d P is therefore roughly the same for the two interaction mechanisms, since the value of E P due to the magnetic interaction is larger than that of the density perturbation by the same ratio as the inverse of their corresponding d P values, i.e., λ p ξ p ∼ 10 (Muslimov & Tsygan 1985;Sauls 1989;Jones 1991aJones , 2006.…”