A class of long gamma-ray bursts (GRBs) with a plateau phase in their X-ray afterglows obeys a three-dimensional (3D) relation (Dainotti et al. 2016), between the rest-frame time at the end of the plateau, Ta, its corresponding X-ray luminosity, La, and the peak luminosity in the prompt emission, Lpeak. We extended the original analysis with X-ray data from July 2014 to July 2016 achieving a total sample of 183 Swift GRBs with afterglow plateaus and known redshifts. We added the most recent GRBs to the previous gold sample (now including 45 GRBs) and obtained a relation plane with intrinsic scatter compatible within one sigma with the previous result. We compared several GRB categories, such as short with extended emission, X-ray Flashes, GRBs associated with SNe, long-duration GRBs, and the gold sample, composed only by GRBs with light curves with good data coverage and relatively flat plateaus and evaluated their relation planes. We found that they are not statistically different from the fundamental plane derived from the gold sample and that the fundamental plane still has the smallest scatter. We compared the jet opening angles tabulated in literature with the angles derived using the Eiso-Egamma relation of the method in Pescalli et al. (2015) and calculated the relation plane for a sample of long GRBs accounting for the different jet opening angles. We observed that this correction does not significantly reduce the scatter. In an extended analysis, we found that the fundamental plane is independent from several prompt and afterglow parameters.
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