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We explore the joint detection prospects of short gamma-ray bursts (sGRBs)and their gravitational wave (GW) counterparts by the current and upcominghigh-energy GRB and GW facilities from binary neutron star (BNS) mergers. Weconsider two GW detector networks: (1) A four-detector network comprising LIGOHanford, Livingston, Virgo, and Kagra, (IGWN4) and (2) a future five-detectornetwork including the same four detectors and LIGO India (IGWN5). For the sGRBdetection, we consider existing satellites Fermi and Swift and the proposedall-sky satellite Daksha. Most of the events for the joint detection will beoff-axis, hence, we consider a broad range of sGRB jet models predicting theoff-axis emission. Also, to test the effect of the assumed sGRB luminosityfunction, we consider two different functions for one of the emission models.We find that for the different jet models, the joint sGRB and GW detectionrates for Fermi and Swift with IGWN4 (IGWN5) lie within 0.07-0.62$\mathrm{\yr^{-1}}$ (0.8-4.0$\mathrm{\ yr^{-1}}$) and 0.02-0.14$\mathrm{\ yr^{-1}}$(0.15-1.0$\mathrm{\ yr^{-1}}$), respectively, when the BNS merger rate is takento be 320$\mathrm{\ Gpc^{-3}~yr^{-1}}$. With Daksha, the rates increase to0.2-1.3$\mathrm{\ yr^{-1}}$ (1.3-8.3$\mathrm{\ yr^{-1}}$), which is 2-9 timeshigher than the existing satellites. We show that such a mission with highersensitivity will be ideal for detecting a higher number of fainter eventsobserved off-axis or at a larger distance. Thus, Daksha will boost the jointdetections of sGRB and GW, especially for the off-axis events. Finally, we findthat our detection rates with optimal SNRs are conservative, and noise in GWdetectors can increase the rates further.

Joint gravitational wave-short GRB detection of Binary Neutron Star mergers with existing and future facilities