Abstract
We use realistic Monte-Carlo simulations including both gravitational-wave and short gamma-ray burst selection effects to revisit the coincident rate of binary systems composed of two neutron stars or a neutron star and a black hole. We show that the fraction of GW triggers that can be observed in coincidence with sGRBs is proportional to the beaming factor at $z=0$, but increases with the distance, until it reaches 100 \% at the GW detector horizon distance. When this is taken into account the rate is improved by a factor of $~3$ compared to the simple beaming factor correction. We provide an estimate of the performance future GRB detectors should achieve in order to fully exploit the potentiality of the planned third generation GW antenna Einstein Telescope, and we propose a simple method to constrain the beaming angle of sGRBs.
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