  We explore the joint detection prospects of short gamma-ray bursts (sGRBs)
and their gravitational wave (GW) counterparts by the current and upcoming
high-energy GRB and GW facilities from binary neutron star (BNS) mergers. We
consider two GW detector networks: (1) A four-detector network comprising LIGO
Hanford, Livingston, Virgo, and Kagra, (IGWN4) and (2) a future five-detector
network including the same four detectors and LIGO India (IGWN5). For the sGRB
detection, we consider existing satellites Fermi and Swift and the proposed
all-sky satellite Daksha. Most of the events for the joint detection will be
off-axis, hence, we consider a broad range of sGRB jet models predicting the
off-axis emission. Also, to test the effect of the assumed sGRB luminosity
function, we consider two different functions for one of the emission models.
We find that for the different jet models, the joint sGRB and GW detection
rates 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 taken
to be 320$\mathrm{\ Gpc^{-3}~yr^{-1}}$. With Daksha, the rates increase to
0.2-1.3$\mathrm{\ yr^{-1}}$ (1.3-8.3$\mathrm{\ yr^{-1}}$), which is 2-9 times
higher than the existing satellites. We show that such a mission with higher
sensitivity will be ideal for detecting a higher number of fainter events
observed off-axis or at a larger distance. Thus, Daksha will boost the joint
detections of sGRB and GW, especially for the off-axis events. Finally, we find
that our detection rates with optimal SNRs are conservative, and noise in GW
detectors can increase the rates further.
