Gamma ray-bursts (GRBs) are astrophysical events observed at a rate of about one per day. Despite being regularly observed and studied since the seventies, and the large number of models that could possibly describe the GRB physics, a clear comprehension of those events is far from being achieved. One class of GRBs, called "short GRBs" (sGRBs) due to their duration shorter than two seconds, is supposed to originate mainly during the merger of binary neutron stars (BNS) systems. The possibility of such a connection was confirmed when a gravitational wave (GW) signal from a BNS system, named GW170817, was observed unambiguously joint with a sGRB, named GRB 170817A. The aforementioned sGRB was extremely close and had an unexpectedly low measured luminosity, orders of magnitude lower than other observed GRBs, suggesting that there is a sub-luminous fraction of the GRB population which is undetected at the usual measured distances.
This work aims to charachterize the low-luminosity part of the sGRB population through a multimessenger GW-GRB Bayesian study. The sGRB population is described via its luminosity probability distribution, which is an extension of a broken power law whose parameters have already been constrained through mid-high luminosity sGRB observations. The parameters of the 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 modeled GW followup analysis of the short GRBs detected during the first three obsering runs of the LIGO/Virgo network. The prior probability distribution function is built starting from a constant rate probability over the low-luminosity parameters. Under the assumptions that BNS mergers are the predominant sGRB progenitors, the sGRB rate is limited in the prior by the BNS rate distribution. The likelihood is built as the probability of observing what has been seen during the first three observing runs, i.e. one BNS GW event associated to one and only one among the short GRBs detected during the runs, with the corresponding GRB having the GRB 170817A luminoisity and being situated at the same distance as the one of GW170817A's host galaxy.
The results obtained allow us to define the luminosity distribution at lower values for the sGRB population and it is found to be compatible with other distributions found in the literature. The sGRB local rate density is found to be close to the value found for the BNS one, around 320 per cubic Gigaparsec per year. The results obtained allow also to estimate the joint GW-GRB detection rate for the next observing runs, expecting between 0 and 2 joint detections during O4 and between 0 and 4 joint detections during O5. The dependence of the analysis on the NS mass distribution has been studied as well, highlighting a strong impact on the sGRB local rate density but a weak dependence of the GW-GRB joint detection rate. Finally, by varying the parameters originally inferred through mid-high luminosity sGRB observations, it is found that those parameters do not have a strong impact on the analysis.
