On the investigation of the closure relations for Gamma-Ray Bursts observed by Swift in the post-plateau phase and the GRB fundamental plane

Gamma-Ray Bursts (GRBs) are the most explosive phenomena in the Universe after the Big Bang. A large fraction of GRB lightcurves (LCs) shows X-ray plateaus. We perform the most comprehensive analysis of all GRBs (with known and unknown redshifts) with plateau emission observed by The Neil Gehrels Swift Observatory from its launch until August 2019. We fit 455 LCs showing a plateau and explore whether these LCs follow closure relations, relations between the temporal and spectral indices of the afterglow, corresponding to 2 distinct astrophysical environments and cooling regimes within the external forward shock (ES) model, and find that the ES model works for the majority of cases. The most favored environments are a constant density interstellar or wind medium with slow cooling. We also confirm the existence of the fundamental plane relation between the rest-frame time and luminosity at the end of the plateau emission and the peak prompt luminosity for this enlarged sample, and test this relation on groups corresponding to the astrophysical environments of our known redshift sample. The plane becomes a crucial discriminant corresponding to these environments in terms of the best fitting parameters and dispersions. Most GRBs for which the closure relations are fulfilled with respect to astrophysical environments have an intrinsic scatter sigma compatible within 1 sigma of that of the Gold GRBs, a subset of long GRBs with relatively flat plateaus. We also find that GRBs satisfying closure relations indicating a fast cooling regime have a lower sigma than ever previously found in literature.