Wide Jets or Low Rates: Reconciling Short GRB and Gravitational-Wave Neutron Star Merger Rates

Gravitational wave (GW) and short Gamma Ray Burst (sGRB) observations provide us with complementary views of compact object mergers. The paucity of binary neutron star merger (BNS) detections in the latest LIGO/Virgo/KAGRA (LVK) observing run raises the question of whether the GW merger rates are sufficient to explain the observed sGRB rate with compact object mergers alone. We investigate this connection using the latest merger rate constraints from the fourth LVK observing run (O4) and published estimates of the local sGRB rate density. For an observed sGRB rate density of $ \sim 1-7~\mathrm{Gpc^{-3}\,yr^{-1}}$, if $>55\%$ of BNS mergers can successfully launch a jet, we find that the current LVK BNS merger rate can be reconciled with a sGRB merger population containing a significant fraction of relatively wide jets with core half-opening angles $\theta_j \geq 10^\circ$. Meanwhile, a narrow jet population ($\theta_j \sim 6^\circ$) can only be matched with the O4 neutron star merger rate estimates for an observed sGRB rate density of $\lesssim 1~\mathrm{Gpc^{-3}\,yr^{-1}}$, which is broadly consistent with several of the latest available estimates. We also find that neutron star-black hole mergers (NSBH) are expected to be a subdominant component of the sGRB population compared to BNS mergers, and they cannot help reconcile some of the highest available sGRB rate ($ >7~\mathrm{Gpc^{-3}\,yr^{-1}}$) with the GW rate estimates. However, they can still substantially contribute to the sGRB population, comprising $\sim 6-16\%$ of it for an observed sGRB rate density of $\sim 1-3~\mathrm{Gpc^{-3}\,yr^{-1}}$. Overall, our results indicate that present GW and sGRB observations remain broadly consistent with BNS mergers as the main progenitors of sGRBs.