Magnetic field amplification in proto-neutron stars -- The role of the neutron-finger instability for dynamo excitation

Abstract

During the first 40 s after their birth, proto-neutron stars are expected to be subject to at least two types of instability: the convective instability and the neutron-finger one. Both instabilities involve convective motions and hence can trigger dynamo actions which may be responsible for the large magnetic fields in neutron stars and magnetars. We have solved the mean-field induction equation in a simplified one-dimensional model of both the convective and the neutron-finger instability zones. Although very idealized, the model includes the nonlinearities introduced by the feedback processes which tend to saturate the growth of the magnetic field (alpha-quenching) and suppress its turbulent diffusion (eta-quenching). The possibility of a dynamo action is studied within a dynamical model of turbulent diffusivity where the boundary of the unstable zone is allowed to move. We show that the dynamo action can be operative and that the amplification of the magnetic field can still be very effective. Furthermore, we confirm the existence of a critical spin-period, below which the dynamo is always excited independently of the degree of differential rotation, and whose value is related to the size of the neutron-finger instability zone. Finally we provide a relation for the intensity of the final field as a function of the spin of the star and of its differential rotation. Although they were obtained by using a toy model, we expect that our results are able to capture the qualitative and asymptotic behaviour of a mean-field dynamo action developing in the neutron-finger instability zone. Overall, we find that such a dynamo is very efficient in producing magnetic fields well above equipartition and thus that it could represent a possible explanation for the large surface magnetic fields observed in neutron stars.

Accepted for publication in A&A - 10 pages; corrections after language editing included

References in corpus (2)

• Flux-transport dynamos with Lorentz force feedback on differential rotation and meridional flow: Saturation mechanism and torsional oscillations
• Protoneutron star dynamos: pulsars, magnetars, and radio-silent X-ray emitting neutron stars

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• Evolution of proto-neutron stars to pulsars, magnetars and central compact objects
• Phase transitions in the inner crust of neutron stars within the superfluid band theory: Competition between ${}^1{\text{S}}_0$ pairing and spin polarization under finite temperature and magnetic field