Force on a neutron quantized vortex pinned to proton fluxoids in the superfluid core of cold neutron stars

Abstract

The superfluid and superconducting core of a cold rotating neutron star is expected to be threaded by a tremendous number of neutron quantised vortices and proton fluxoids. Their interactions are unavoidable and may have important astrophysical implications. In this paper, the various contributions to the force acting on a single vortex to which fluxoids are pinned are clarified. The general expression of the force is derived by applying the variational multifluid formalism developed by Carter and collaborators. Pinning to fluxoids leads to an additional Magnus type force due to proton circulation around the vortex. Pinning in the core of a neutron star may thus have a dramatic impact on the vortex dynamics, and therefore on the magneto-rotational evolution of the star.

Vortex pinning in the superfluid core of neutron stars and the rise of pulsar glitches

“…The non-vanishing of the radial component of the mean vortex velocity (albeit very small) actually highlights the non-exact stationarity of the space-time considered here. Finally, the Newtonian limit of equations (53)−(54) is found to match perfectly with results obtained from Sourie & Chamel (2020a), as shown in Appendix D.…”

“…Following the seminal work of Langlois et al (1998), we have adapted to the general-relativistic framework our recent Newtonian treatment (Sourie & Chamel 2020a) of the smooth-averaged mutual-friction force acting on the neutron superfluid and locally induced by the pinning of quantized neutron vortices to proton fluxoids in the outer core of superfluid NSs (or alternatively by the formation of vortex clusters of the kind proposed by Sedrakian & Sedrakian (1995)). Quite generally, the force can be written as mf = N n R p⊥ + A p n .…”

“…At such small scales, the space-time curvature is negligible (see, e.g., the discussion in Section 3.4 of Glendenning (1997)) and the fluid dynamics is essentially nonrelativistic. We have recently derived the Newtonian expression for the force per unit length exerted on a single vortex line in a mixture of superfluid neutrons, superconducting protons and degenerate electrons, as can be typically found in the outer core of NSs (Sourie & Chamel 2020a). Allowing for the possible presence of vortex pinning onto proton fluxoids or vortex clusters of the kind proposed by Sedrakian & Sedrakian (1995), we considered the force acting on a vortex line to which a given number p of fluxoids are anchored 3 .…”

“…No new data were generated or analysed in support of this research. 32In the present appendix, we use the covariant Newtonian formulation developed by Carter and Chamel (Carter & Chamel 2004, 2005a to match the global general-relativistic description with the local nonrelativistic dynamics of individual vortices discussed in Sourie & Chamel (2020a). We will write the speed of light explicitly since we are interested in the limit → +∞.…”

The impact of superconductivity and the Hall effect in models of magnetised neutron stars

“…Our model, however, shows that no toroidal field area is present in the core to allow for such pinning, as it is expelled to the 'normal' matter crust. The models we produce can, however, be used as a background for more realistic vortex pinning calculations (Sourie & Chamel 2020a;Sourie & Chamel 2020b), in order to fully investigate the effect of pinning in the core on pulsar glitch phenomenology. Note, however, that for very strong surface magnetic fields (e.g., B s > 10 15 G) like those seen in magnetars, the ratio B cc /H cc c1 is greater than unity and the toroidal flux is non-zero inside the core of the star (Lander 2014) All our computations produced a toroidal field which is less than 5% of the total magnetic energy, and both the structure and strength of the field appear to rapidly converge to a qualitatively stable regime as we increase the degree of non-linearity by increasing the parameter s. This is in line also with the results obtained from numerical MHD evolution by Sur et al (2020).…”