We have performed our data analysis of the observations by Swift, NuStar and Fermi satellites in order to probe the induced gravitational collapse (IGC) paradigm for GRBs associated with supernovae (SNe), in the "terra incognita" of GRB 130427A. We compare and contrast our data analysis with those in the literature. We have verified that the GRB 130427A conforms to the IGC paradigm by examining the power law behavior of the luminosity in the early 10 4 s of the XRT observations. This has led to the identification of the four different episodes of the "binary driven hypernovae" (BdHNe) and to the prediction, on May 2, 2013, of the occurrence of SN 2013cq, duly observed in the optical band on May 13, 2013. The exceptional quality of the data has allowed the identification of novel features in Episode 3 including: a) the confirmation and the extension of the existence of the recently discovered "nested structure" in the late X-ray luminosity in GRB 130427A, as well as the identification of a spiky structure at 10 2 s in the cosmological rest-frame of the source; b) a power law emission of the GeV luminosity light curve and its onset at the end of Episode 2; c) different Lorentz Γ factors for the emitting regions of the X-ray and GeV emissions in this Episode 3. These results make it possible to test the details of the physical and astrophysical regimes at work in the BdHNe: 1) a newly born neutron star and the supernova ejecta, originating in Episode 1, 2) a newly formed black hole originating in Episode 2, and 3) the possible interaction among these components, observable in the standard features of Episode 3.

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Context. The induced gravitational collapse (IGC) paradigm addresses the very energetic (10 52 -10 54 erg) long gamma-ray bursts (GRBs) associated to supernovae (SNe). Unlike the traditional "collapsar" model, an evolved FeCO core with a companion neutron star (NS) in a tight binary system is considered as the progenitor. This special class of sources, here named "binary-driven hypernovae" (BdHNe), presents a composite sequence composed of four different episodes with precise spectral and luminosity features. Aims. We first compare and contrast the steep decay, the plateau, and the power-law decay of the X-ray luminosities of three selected BdHNe (GRB 060729, GRB 061121, and GRB 130427A). Second, to explain the different sizes and Lorentz factors of the emitting regions of the four episodes, for definiteness, we use the most complete set of data of GRB 090618. Finally, we show the possible role of r-process, which originates in the binary system of the progenitor. Methods. We compare and contrast the late X-ray luminosity of the above three BdHNe. We examine correlations between the time at the starting point of the constant late power-law decay t * a , the average prompt luminosity L iso , and the luminosity at the end of the plateau L a . We analyze a thermal emission (∼0.97-0.29 keV), observed during the X-ray steep decay phase of GRB 090618. Results. The late X-ray luminosities of the three BdHNe, in the rest-frame energy band 0.3-10 keV, show a precisely constrained "nested" structure. In a space-time diagram, we illustrate the different sizes and Lorentz factors of the emitting regions of the three episodes. For GRB 090618, we infer an initial dimension of the thermal emitter of ∼7 × 10 12 cm, expanding at Γ ≈ 2. We find tighter correlations than the Dainotti-Willingale ones. Conclusions. We confirm a constant slope power-law behavior for the late X-ray luminosity in the source rest frame, which may lead to a new distance indicator for BdHNe. These results, as well as the emitter size and Lorentz factor, appear to be inconsistent with the traditional afterglow model based on synchrotron emission from an ultra-relativistic (Γ ∼ 10 2 -10 3 ) collimated jet outflow. We argue, instead, for the possible role of r-process, originating in the binary system, to power the mildly relativistic X-ray source.