Magnetic Topology in Coupled Binaries, Spin-orbital Resonances, and Flares

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, which 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 = T 1 S2 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 ms, the global resonance ω 1 + ω 2 = 2Ω (spin-plus beat is two times the orbital period) occurs approximately one 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.