Instability-driven interfacial dynamo in protoneutron stars

TL;DR

This paper investigates the conditions under which an interfacial dynamo can operate in protoneutron stars, revealing that specific discontinuity placements and anisotropic diffusivity enable magnetic field growth.

Contribution

It applies solar interfacial dynamo analysis to protoneutron stars, identifying conditions for self-sustained magnetic field growth not previously understood.

Findings

Self-sustained dynamo growth depends on the placement of discontinuities in $eta$, $ au$, and shear.

Anisotropic magnetic diffusivity allows dynamo action even with coincident discontinuities.

Stronger shear and $eta$-effects are required compared to the Sun.

Abstract

The existence of a tachocline in the Sun has been proven by helioseismology. It is unknown whether a similar shear layer, widely regarded as the seat of magnetic dynamo action, also exists in a protoneutron star. Sudden jumps in magnetic diffusivity $\eta$ and turbulent vorticity $\alpha$, for example at the interface between the neutron-finger and convective zones, are known to be capable of enhancing mean-field dynamo effects in a protoneutron star. Here we apply the well-known, plane-parallel, MacGregor-Charbonneau analysis of the Solar interfacial dynamo to the protoneutron star problem and calculate the growth rate analytically under a range of conditions. It is shown that, like the Solar dynamo, it is impossible to achieve self-sustained growth if the discontinuities in $\alpha$, $\eta$, and shear are coincident and the magnetic diffusivity is isotropic. In contrast, when the jumps in $\eta$ and $\alpha$ are situated away from the shear layer, self-sustained growth is possible for $P\lesssim 49.8$ ms (if the velocity shear is located at $0.3R$) or $P\lesssim 83.6$ ms (if the velocity shear is located at $0.6R$). This translates into stronger shear and/or $\alpha$-effect than in the Sun. Self-sustained growth is also possible if the magnetic diffusivity if anisotropic, through the ${\bf{\Omega}}\times{\bf{J}}$ effect, even when the $\alpha$, $\eta$, and shear discontinuities are coincident.