First Light of Neutron Star Mergers: Off-axis Cocoon Cooling X-ray Emission from Short Gamma-Ray Burst Jets

Neutron star mergers (NSMs) are confirmed gravitational wave sources. Identifying an early electromagnetic counterpart for these events is therefore crucial for rapid localization and multimessenger follow-up. However, the associated Gamma-Ray Bursts (GRBs) are highly collimated and are therefore easily missed by off-axis observers. An early, less beamed counterpart is essential for identifying the majority of mergers. In this Letter, we investigate the cooling emission from jet-driven cocoons produced by short gamma-ray burst jets propagating through merger ejecta. We perform hydrodynamic simulations and radiative post-processing to calculate the early X-ray emission over a wide range of viewing angles. We find that the mildly relativistic cocoon produces bright soft X-ray transients for off-axis observers, with luminosities of 10 46-48 erg,s-1 and durations of a few to ten seconds. The X-ray spectra are quasi-thermal with characteristic temperatures of 0.1 -- 1, keV. For observers at θ v=10, the cocoon emission is detectable by Einstein Probe (EP) out to z 0.3. For nearby events like GW170817, it remains detectable up to θ v 45. The predicted detection rate for EP is 0.5, yr-1 in the canonical model. In future multimessenger campaigns, rapid UV/optical/IR follow-up of such X-ray triggers can subsequently identify the associated kilonova and jet afterglow emission, which will confirm the origin.