Properties of Gamma-Ray Bursts Associated with Supernovae and Kilonovae

We systematically compare the temporal and spectral properties of 53 Supernova (SN)-associated and 15 Kilonova (KN)-associated Gamma-Ray Bursts (GRBs). We find that the spectral parameters of both types GRBs are identically and lognormally distributed, consistent with those normal GRBs. The bolometric luminosities of SN/GRBs and KN/GRBs have a triple form with the corresponding break luminosities of SN/GRBs are roughly two orders of magnitude larger than those of KN/GRBs. We build the power-law relations between the spectral lag and the luminosity of prompt $\gamma$-rays with indices of $-1.43\pm 0.33$ for SN/GRBs and $-2.17\pm 0.57$ for KN/GRBs in the laboratory frame, which are respectively coincident with the rest-frame values. We verify that both SN/GRBs and KN/GRBs comply with their own Amati relations that match those of long and short GRBs, respectively. Analyzing X-ray afterglows with good plateau segments, we build the power-law relations between the X-ray luminosity and the plateau time with an index of $-1.12\pm 0.17$ for KN/GRBs and $-1.08\pm 0.22$ for SN/GRBs, which can be well explained by the relativistic shock driven by an energy injection. The plots of luminosity-lag, Amati relation and luminosity-time show heavy overlap between the two types of GRBs, implying that they might share the same radiation mechanism despite originating from different progenitors or central engines.