Evidence for an anticorrelation between the duration of the shallow decay phase and the burst energetics

Several studies have addressed the intrinsic properties of the X-ray shallow phase, in particular by testing whether a dependence exists between the intrinsic duration of the shallow phase and the burst energetics. Results obtained so far are discordant, possibly due to the large uncertainties affecting the burst energetics estimates and/or in modeling the X-ray shallow phase and estimating the temporal break between the shallow and the standard phases. In this work we have constructed a GRB sample according to the following selection criteria i) a 0.3-10 keV XRT lightcurve featuring shallow behavior with temporal index α<0.8 over a temporal interval greater than 0.5 ks (so that the power-law decay index can be measured accurately) ii) the shallow decay interval should not be dominated by features such as "bumps" or flares that may affect the measurement of the decay index. In addition, we requested well defined GRB prompt spectral properties that enable a secure energy (E_iso) estimate of the burst. Although a much larger sample is needed, our results favor the existence of a dependence of the intrinsic shallow phase duration from E_iso and from the X-ray luminosity at the end of the shallow phase. Considering also those GRBs with excellent XRT data monitoring with no evidence of shallow phase and with decay index consistent on average with the post-plateau phase, we find that these epochs are consistent with the extrapolation of the burst energy and X-ray luminosity anticorrelations found for those GRBs with evidence of a plateau in their X-ray light curves.