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A relativistic jet has been produced in the single well-localised binaryneutron star (BNS) merger detected to date in gravitational waves (GWs), andthe local rates of BNS mergers and short gamma-ray bursts are of the same orderof magnitude. This suggests that jet formation is not a rare outcome for BNSmergers, and we show that this intuition can be turned into a quantitativeconstraint: at least about $1/3$ of GW-detected BNS mergers, and at least about$1/5$ of all BNS mergers, should produce a successful jet (90\% crediblelevel). Whether a jet is launched depends on the properties of the mergerremnant and of the surrounding accretion disc, which in turn are a function ofthe progenitor binary masses and equation of state (EoS). The incidence of jetsin the population therefore carries information about the binary component massdistribution and EoS. Under the assumption that a jet can only be produced by ablack hole remnant surrounded by a non-negligible accretion disc, we show howthe jet incidence can be used to place a joint constraint on the space of BNScomponent mass distributions and EoS. The result points to a broad massdistribution, with particularly strong support for masses in the$1.3-1.6\,\mathrm{M_\odot}$ range. The constraints on the EoS are shallow, butwe show how they will tighten as the knowledge on the jet incidence improves.We also discuss how to extend the method to include future BNS mergers, withpossibly uncertain jet associations.

Constraints on the merging binary neutron star mass distribution and equation of state based on the incidence of jets in the population