Vortex buoyancy in superfluid and superconducting neutron stars

Abstract

Buoyancy of proton vortices is considered as one of the important mechanisms of magnetic field expulsion from the superconducting interiors of neutron stars. Here we show that the generally accepted expression for the buoyancy force is not correct and should be modified. The correct expression is derived for both neutron and proton vortices. It is argued that this force is already contained in the coarse-grained hydrodynamics of Bekarevich & Khalatnikov and its various multifluid extensions, but is absent in the hydrodynamics of Hall. Some potentially interesting buoyancy-related effects are briefly discussed.

On the magnetic field evolution time-scale in superconducting neutron star cores

“…Surprisingly, although the momentum equations given by Glampedakis et al (2011) and Gusakov & Dommes (2016) are equivalent, Dommes & Gusakov (2017) find that their evolution timescales differ by several orders of magnitude from the results of Glampedakis et al (2011). We now discuss the cause of this discrepancy.…”

“…As shown by Dommes & Gusakov (2017), the vector field T also contains the contribution of the buoyancy force. Equation (23) has the same mathematical form as Ampère's law in the normal case, with the difference that the magnetic induction B is replaced by the vector Hc1b, where Hc1 is the lower critical magnetic field (Tinkham 2004).…”

“…The coefficients α and β are related to the dimensionless drag coefficient R (typically R ∼ 10 −4 ) by (Dommes & Gusakov 2017) …”

“…The electric field determined by Gusakov & Dommes (2016) has an extra contribution of the fluxtube tension which is absent in the derivation of Glampedakis et al (2011) and Graber et al (2015). As further emphasized in Dommes & Gusakov (2017), this leads to a difference of several orders of magnitude in the estimated evolution timescales.…”

Magnetic-field evolution in a plastically failing neutron-star crust

“…Core-field evolution is a much more vexed issue, mainly due to the uncertain role played by superfluid components (which are present even in magnetars younger than any observed to date; Ho et al (2012)). There are debates about whether any core process is fast enough to be relevant to magnetars; providing arbitration of the dispute is beyond the scope of this paper, but for a flavour of the recent literature see, e.g., Jones (2006); Glampedakis et al (2011b); Graber et al (2015); Gügercinoglu & Alpar (2016); Dommes & Gusakov (2017); Passamonti et al (2017); Castillo et al (2017); Ofengeim & Gusakov (2018). There is also little understanding about how core and crust are linked, and the physics at the boundary that separates them.…”