Viewing angle constraints on S190425z and S190426c and the joint gravitational-wave/gamma-ray detection fractions for binary neutron star mergers

The LIGO and Virgo scientific collaboration (LVC) alerted two binary neutron star (BNS) merger candidates, S190425z and S190426c. Fermi-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 larger distances than GW170817. Assuming that the jet profile obtained from the 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 GECAM, are expected to detect $\sim 4.6%$,$3.9%$,$1.7%$and$6.6%$,$5.7%$,$2.8%$ BNS mergers triggered by aLIGO, aLIGO A+ and ET, respectively. The joint detection fraction would be largely reduced for Swift-BAT, SVOM-ECLAIRS and Einstein Probe, whose sensitivities are better but fields of view are smaller.