Magnetic topology in coupled binaries, spin-orbital resonances, and flares

TL;DR

This paper explores magnetic field configurations in coupled stellar binaries, identifying conditions for slow winding and energy release in flares, especially near topological bifurcations, with implications for neutron star mergers.

Contribution

It introduces a topological framework for understanding magnetic interactions in binary systems, highlighting slow winding conditions and resonance effects near bifurcation points.

Findings

Slow winding configurations can store magnetic energy for flares.

Global resonance occurs approximately a second before neutron star merger.

Flares can release up to 10% of magnetic energy, producing intense bursts.

Abstract

We consider topological configurations of the magnetically coupled spinning stellar binaries (e.g., merging neutron stars or interacting star-planet systems). We discuss conditions when the stellar spins and the orbital motion nearly `compensate' each other, leading to very {\it slow} overall winding of the coupled magnetic fields; slowly winding configurations allow gradual accumulation of magnetic energy, that is eventually released in a flare when the instability threshold is reached. We find that this slow winding can be global and/or local. We describe the topology of the relevant space $\mathbb{F}=T^1S^2$ as the unit tangent bundle of the two-sphere and find conditions for slowly winding configurations in terms of magnetic moments, spins and orbital momentum. These conditions become ambiguous near the topological bifurcation points; in certain cases they also depend on the relative phases of the spin and orbital motions. In the case of merging magnetized neutron stars, if one of the stars is a millisecond pulsar, spinning at $\sim$ 10 msec, the global resonance $\omega_1+\omega_2= 2 \Omega$ (spin-plus beat is two times the orbital period) occurs approximately a second before the merger; the total energy of the flare can be as large as $10\%$ of the total magnetic energy, producing bursts of luminosity $\sim 10^{44}$ erg s$^{-1}$. Higher order local resonances may have similar powers, since the amount of involved magnetic flux tubes may be comparable to the total connected flux.