Exponentially Decaying Extended Emissions Following Short Gamma-Ray Bursts with a Possible Luminosity–E-folding Time Correlation

Abstract

Abstract The origin of extended emissions following prompt emissions of short gamma-ray bursts (SGRBs) is a mystery. The long-term activity of the extended emission is responsible for promising electromagnetic counterparts to gravitational waves, thus it may be a key to uncovering the progenitor of SGRBs. We investigate the early X-ray light curves of 26 SGRBs with known redshifts observed with the X-Ray Telescope on board the Neil Gehrels Swift Observatory (Swift). We find that the exponential temporal decay model is able to describe the extended emission comprehensively, with a rest-frame e-folding time of 20–200 s. We also estimate the isotropic equivalent energies of the extended emission with the exponential decay model and of the prompt emission, and compare with those of the prompt emission. Then, it is revealed that the extended emission is 0–3 orders of magnitude less powerful than the prompt emission. We find a strong correlation between the expected maximum luminosity and e-folding time, which can be described by a power law with an index of −3.3 and whose chance probability is 8.2 × 10−6 if there is no observation bias of Swift. The exponential temporal decay may be interpreted as coming from the spin-down timescale of the rotation energy of a highly magnetized neutron star, and/or fallback accretion onto a disk surrounding a black hole with an exponentially decaying magnetic flux by magnetic reconnection.