Rates and beaming angles of GRBs associated with compact binary coalescences

Some, if not all, binary neutron star (BNS) coalescences, and a fraction of neutron - star black hole (NSBH) mergers, are thought to produce sufficient mass-ejection to power Gamma-Ray Bursts (GRBs). However, this fraction, as well as the distribution of beaming angles of BNS-associated GRBs, are poorly constrained from observation. Recent work applied machine learning tools to analyze GRB light curves observed by {\textit{Fermi}}/GBM and {\it Swift}/BAT. GRBs were segregated into multiple distinct clusters, with the tantalizing possibility that one of them (BNS cluster) could be associated with BNSs and another (NSBH cluster) with NSBHs. As a proof of principle, assuming that all GRBs detected by {\it Fermi}/GBM and {\it Swift}/BAT associated with BNSs (NSBHs) lie in the BNS (NSBH) cluster, we estimate their rates ($\mathrm{Gpc}^{-3}\mathrm{yr}^{-1}$). We compare these rates with corresponding BNS and NSBH rates estimated by the LIGO-Virgo-Kagra (LVK) collaboration from the first three observing runs (O1, O2, O3). We find that the BNS rates are consistent with LVK's rate estimates, assuming a uniform distribution of beaming fractions ($f_b \in [0.01, 0.1]$). Conversely, using the LVK's BNS rate estimates, assuming all BNS mergers produce GRBs, we are able to constrain the beaming angle distribution to $\theta_j \in [0.8^{\circ}, 33.5^{\circ}]$ at $90\%$ confidence. We similarly place limits on the fraction of GRB-Bright NSBHs as $f_B \in [1.3\%, 63\%]$ ($f_B \in [0.4\%, 15\%]$) with {\it Fermi}/GBM ({\it Swift}/BAT) data.