The relevance of ambipolar diffusion for neutron star evolution

TL;DR

This paper investigates how ambipolar diffusion influences magnetic field evolution in neutron stars, considering effects of neutrino reactions and superfluidity, revealing conditions under which diffusion significantly impacts magnetic reorganization.

Contribution

It provides a detailed analysis of ambipolar diffusion in magnetized neutron stars, incorporating neutrino reaction rates and superfluid transitions, highlighting their effects on magnetic field evolution.

Findings

Ambipolar diffusion is significant at low core temperatures ($T \,\lesssim\, 1-2\times10^8$ K).

Fast neutrino reactions shorten the diffusion timescale, reducing magnetic support.

Superconducting cores exhibit short diffusion timescales for $T \,\lesssim\, 10^9$ K.

Abstract

We study ambipolar diffusion in strongly magnetised neutron stars, with special focus on the effects of neutrino reaction rates and the impact of a superfluid/superconducting transition in the neutron star core. For axisymmetric magnetic field configurations, we determine the deviation from $\beta-$equilibrium induced by the magnetic force and calculate the velocity of the slow, quasi-stationary, ambipolar drift. We study the temperature dependence of the velocity pattern and clearly identify the transition to a predominantly solenoidal flow. For stars without superconducting/superfluid constituents and with a mixed poloidal-toroidal magnetic field of typical magnetar strength, we find that ambipolar diffusion proceeds fast enough to have a significant impact on the magnetic field evolution only at low core temperatures, $T \lesssim 1-2\times10^8$ K. The ambipolar diffusion timescale becomes appreciably shorter when fast neutrino reactions are present, because the possibility to balance part of the magnetic force with pressure gradients is reduced. We also find short ambipolar diffusion timescales in the case of superconducting cores for $T \lesssim 10^9$ K, due to the reduced interaction between protons and neutrons. In the most favourable scenario, with fast neutrino reactions and superconducting cores, ambipolar diffusion results in advection velocities of several km/kyr. This velocity can substantially reorganize magnetic fields in magnetar cores, in a way that can only be confirmed by dynamical simulations.