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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 $\gtrsim10$ 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.