Early X-ray emission of short Gamma-Ray Bursts: insights into physics and multi-messenger prospects

Early X-ray emission of Gamma-Ray Bursts (GRBs) traces the transition between the prompt emission and the afterglow radiation, and its rapid flux decline is often interpreted as the tail of the prompt emission. As such, it can offer insights into the emission mechanisms active during the prompt emission and the physics of GRB jets. In this work, we focus on merger-driven GRBs, which are sources of gravitational waves (GWs) detectable by ground-based interferometers, such as LIGO, Virgo, and KAGRA. We present a systematic analysis of the early X-ray emission ($t < 10^3 \ \mathrm{s}$) of a sample of 16 merger-driven GRB candidates detected by the Neil Gehrels Swift Observatory (hereafter, Swift). We performed a time-resolved spectral analysis of soft and hard X-ray data (0.3-150 keV) by fitting two curved spectral models to the spectra: a physical synchrotron model and an empirical smoothly broken power law model. We characterized the evolution of the peak energy and bolometric flux, and derived the intrinsic properties of the 10 bursts with measured redshift. We discovered a tight correlation between the rest-frame peak energy of the spectra and the isotropic-equivalent luminosity. Specifically, we obtained $\nu_{c,z} \propto L_{\rm iso}^{(0.64 \pm 0.03)}$ when adopting the synchrotron model, and $E_{p,z} \propto L_{\rm iso}^{(0.58 \pm 0.04)}$ when adopting the smoothly broken power law. Both relations were extrapolated to the typical prompt emission energies and well describe the properties of short GRBs detected in the MeV gamma-rays. These results suggest a common origin for the prompt and steep-decay emissions in merger-driven GRBs, and rule out high-latitude emission as the dominant process shaping the early X-ray tails. Finally, we assessed the detectability of these sources with the Wide-field X-ray Telescope onboard the Einstein Probe mission.