Missed opportunities: GRB 211211A and the case for continual gravitational-wave coverage with a single observatory

Gamma-ray burst GRB 211211A may have been the result of a neutron star merger at $\approx350$ Mpc. However, none of the LIGO-Virgo detectors were operating at the time. We show that the gravitational-wave signal from a \grb-like binary neutron star inspiral in the next LIGO-Virgo-KAGRA observing run (O4) would be below the conventional detection threshold, however a coincident gamma-ray burst observation would provide necessary information to claim a statistically-significant multimessenger observation. We calculate that with O4 sensitivity, approximately $11\%$ of gamma-ray bursts within 600 Mpc will produce a confident association between the gravitational-wave binary neutron star inspiral signature and the prompt gamma-ray signature. This corresponds to a coincident detection rate of $\unit[0.22^{+8.3}_{-0.22}]{yr^{-1}}$, where the uncertainties are the 90\% confidence intervals arising from uncertainties in the absolute merger rate, beaming and jet-launching fractions. These increase to approximately $34\%$ and $\unit[0.71^{+26.8}_{-0.70}]{yr^{-1}}$ with proposed O5 sensitivity. We show that the above numbers do not depend significantly on the number of gravitational-wave observatories operating with the specific sensitivity. That is, the number of confident joint gamma-ray burst and gravitational-wave detections is only marginally improved with two or three detectors operating compared to a single detector. It is therefore worth considering whether one detector with sufficient sensitivity (post O4) should remain in sky-watch mode at all times to elucidate the true nature of GRB 211211A-like events, a proposal we discuss in detail.