Ten Supernova-rise in Binary Driven Gamma-ray Bursts

The observation of a gamma-ray burst (GRB) associated with a supernova (SN) coincides remarkably with the energy output from a binary system comprising a very massive carbon-oxygen (CO) core and an associated binary neutron star (NS) by the Binary-Driven Hypernova (BdHN) model. The dragging effect in the late evolution of such systems leads to co-rotation, with binary periods on the order of minutes, resulting in a very fast rotating core and a binary NS companion at a distance of $\sim {10}^5$ km. Such a fast-rotating CO core, stripped of its hydrogen and helium, undergoes gravitational collapse and, within a fraction of seconds, leads to a supernova (SN) and a newly born, fast-spinning neutron star ($\nu$NS), we name the emergence of the SN and the $\nu$NS as the SN-rise and $\nu$NS-rise. Typically, the SN energies range from ${10}^{51}$ to ${10}^{53}$ erg. We address this issue by examining 10 cases of Type-I BdHNe, the most energetic ones, in which SN accretion onto the companion NS leads to the formation of a black hole (BH). In all ten cases, the energetics of the SN events are estimated, ranging between $0.18$ and $12\times {10}^{52}$ erg. Additionally, in all 8 sources at redshift $z$ closer than $4.61$, a clear thermal blackbody component has been identified, with temperatures between $6.2$ and $39.99$ keV, as a possible signature of pair-driven SN. The triggering of the X-ray afterglow induced by the $\nu$NS-rise are identified in three cases at high redshift where early X-ray observations are achievable, benefits from the interplay of cosmological effects.