Neutron Star Merger Rates from Multi-messenger Observations: Clues to the Physical Origin of the Short and Long-short Gamma-ray Bursts

Short and long-short gamma-ray bursts (GRBs) are widely believed to be powered by neutron star mergers. In this work, we calculate local rate of such GRBs and find a relatively high value of $\sim 786-2468~{\rm Gpc^{-3}~yr^{-1}}$ when including the very narrow collimation event GRB 061201. Considering that its redshift is not very reliable, after excluding this event, the rate is $\sim 195-666~{\rm Gpc^{-3}~yr^{-1}}$. We also calculate the electromagnetically (EM) bright neutron star merger rate inferred from the LIGO/Virgo/KAGRA observations up to the end of the first epoch of the O4 run, and derive a rate of $\sim 66-347~{\rm Gpc^{-3}~yr^{-1}}$. This rate is somewhat lower than the value obtained from the GRBs, even after excluding GRB 061201. The non-detection of any viable EM bright merger in the O4b and O4c observing runs favors an even lower rate, which starts to challenge the neutron star merger origin of the short and long-short GRBs and may suggest additional contribution from the mergers of other compact object (like the neutron star-white dwarf) binaries, as speculated initially by King et al. (2007) in interpreting the long-short event GRB 060614.