Viewing Angle Constraints on S190425z and S190426c and the Joint Gravitational-wave/Gamma-Ray Detection Fractions for Binary Neutron Star Mergers

The Laser Interferometer Gravitational-Wave Observatory (LIGO) and Virgo scientific collaboration (LVC) detected two binary neutron star (BNS) merger candidates, S190425z and S190426c. The Fermi-Gamma-ray Burst Monitor (GBM) observed 55.6% (for S190425z) and 100% (for S190426c) of the probability regions of both events at the respective merger times, but no gamma-ray burst (GRB) was detected in either case. The derived luminosity upper limits suggest that a short GRB similar to GRB 170817A would not be detectable for both cases due to their distances, which are larger than that of GW170817. Assuming that the jet profile obtained from GW170817/GRB 170817A is quasi-universal for all BNS-GRB associations, we derive that the viewing angles of S190425z and S190426c should be >(0.11-0.41) and >(0.09-0.39), respectively. Through Monte Carlo simulations, we show that with the GRB 170817A-like jet structure, all sky gamma-ray detectors, such as GBM and the Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor, are expected to detect similar to 4.6%, 3.9%, 1.7%, and 6.6%, 5.7%, 2.8% of BNS mergers triggered by advanced LIGO, A+, and the Einstein Telescope, respectively. The joint detection fraction would be largely reduced for Swift-BAT, SVOM-ECLAIRS, and the Einstein Probe, whose sensitivities are better but whose FOVs are smaller.