Magnetic topology in coupled binaries, spin-orbital resonances, and flares
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 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 F=T1S2 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 10 msec, the global resonance ω1+ω2= 2 (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 1044 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.