A Study of the Gamma-Ray Burst Fundamental Plane

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, an extension of the two-dimensional Dainotti relation. This 3D relation identifies a GRB fundamental plane whose existence we here confirm. We extend the original analysis with X-ray data untill July 2016 gathering 183 Swift GRBs with afterglow plateaus and known redshifts. We compare several GRB categories, such as shorts with extended emission, SEE, X-ray Flashes, GRBs associated with SNe, a sample of only long-duration GRBs (132), selected from the total sample by excluding GRBs of the previous categories, and the gold sample, composed by GRBs with light curves with good data coverage and relatively flat plateaus. The relation planes for each of these categories are not statistically different from the gold fundamental plane, with the exception of the SEE, which are hence identified as a physically distinct class of objects. The gold fundamental plane has an intrinsic scatter smaller than any plane derived from the other sample categories. Thus, the distance of any particular GRB category from this plane becomes a key parameter. Additionally, we tested this 3D relations by using GRBs observed at high energy, namely the peak luminosity values derived by the Fermi-Gamma Ray Burst Monitor (GBM). The 3D relation is also confirmed for GRBs observed by the GBM, thus showing its independence from the energy range. Furthermore, we computed the several category planes with T*a as a dependent parameter obtaining for each category smaller intrinsic scatters (reaching a reduction of $24\%$ for the long GRBs). The fundamental plane is independent from several prompt and afterglow parameters.