Measuring spin in coalescing binaries of neutron stars that show double precursors

Abstract

Gamma-ray bursts resulting from binary neutron-star mergers are sometimes preceded by precursor flares. These harbingers can be ignited by quasi-normal modes, excited by orbital resonances, shattering the stellar crust of one of the inspiralling stars up to ≳10 s before coalescence. In the rare case when a system displays two precursors, successive overtones of either interface modes or g modes can be responsible for the overstrainings. Since the free-mode frequencies of these overtones have an almost constant ratio, and the inertial-frame frequencies for rotating stars are shifted relative to static ones, the spin frequency of the flaring component can be constrained as a function of the equation of state, the binary mass ratio, the mode quantum numbers, and the spin-orbit misalignment angle. As a demonstration of the method, we find that the precursors of GRB090510 hint at a spin frequency range of 2 ≲ ν⋆/Hz ≲ 20 for the shattering star if we allow for an arbitrary misalignment angle, assuming ℓ = 2 g modes account for the events.