On binary-driven hypernovae and their nested late X-ray emission

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 (similar to 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 similar to 7 x 10(12) cm, expanding at Gamma approximate to 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 (Gamma similar to 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.