Measuring spin in coalescing binaries of neutron stars showing double precursors

Abstract

Gamma-ray bursts resulting from binary neutron-star mergers are sometimes preceded by precursor flares. These harbingers may be ignited by quasi-normal modes, excited by orbital resonances, shattering the stellar crust of one of the inspiralling stars up to $\gtrsim 10$ seconds before coalescence. In the rare case that a system displays two precursors, successive overtones of either interface- or $g$-modes may 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 $2\lesssim {\nu }_{\star }/\text{Hz}\lesssim 20$ for the shattering star if we allow for an arbitrary misalignment angle, assuming $\ell =2$ $g$-modes account for the events.

11 pages, 6 figures, 2 tables with an appendix containing 1 figure. Accepted for publication in A&A

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