The unambiguous joint detection of GRB 170817A and GW170817 has been the long-awaited smoking gun for the association between short gamma-ray bursts (sGRBs) and the merger of binary neutron stars (BNS) systems. The aforementioned sGRB, however, was extremely close and had an unexpectedly low measured luminosity when compared to the other observed sGRBs, suggesting that there is a sub-luminous fraction of the GRB population which is undetected at the usually measured distances.

This work aims to characterize the low-luminosity part of the sGRB population through a multi-messenger GW-GRB Bayesian study. The sGRB population is described via its luminosity probability distribution, modelled through an extension of a broken power law whose parameters have already been constrained through mid-high luminosity sGRB observations. The parameters of this power-law extension, i.e. the low luminosity power index and the low-luminosity cutoff, are constrained through a Bayesian analysis which exploits the results from the modelled GW follow-up analysis of the short GRBs detected during the first three observing runs of the International Gravitational-Wave observatory Network (IGWN).

The results obtained allow us to define the luminosity distribution at lower values for the sGRB population and to give an estimate of the value found for the astrophysical sGRB rate and the joint GW-GRB detection rate for the next IGWN observing runs. There are, nonetheless, some upgrades to the method used for this study that could give a more precise and complete outline of the astrophysical sGRB population.