Title: GRB-SN Association within the Binary-Driven Hypernova Model

Abstract: The observations of supernovae (SNe) Ic occurring after the prompt emission of long gamma-ray bursts (GRBs) are addressed within the binary-driven hypernova (BdHN) model where GRBs originate from a binary composed of a $\sim10M_\odot$ carbon-oxygen (CO) star and a neutron star (NS). The CO core collapse gives the trigger, leading to a hypernova with a fast-spinning newborn NS ($\nu$NS) at its center. The evolution depends strongly on the binary period, $P_{\rm bin}$. For $P_{\rm bin}\sim5$min, BdHNe I occur with energies $10^{52}$--$10^{54}$erg. The accretion of SN ejecta onto the NS leads to its collapse, forming a black hole (BH) originating the MeV/GeV radiation. For $P_{\rm bin}\sim 10$min, BdHNe II occur with energies $10^{50}$--$10^{52}$erg and for $P_{\rm bin}\sim$hours, BdHN III occurs with energies below $10^{50}$erg. {In BdHNe II and III,} no BH is formed. The $1$--$1000$ms $\nu$NS originates, in all BdHNe, the X-ray-optical-radio afterglows by synchrotron emission. The hypernova follows an independent evolution, becoming an SN Ic, powered by nickel decay, observable after the GRB prompt emission. We report $24$ SNe Ic associated with BdHNe. Their optical peak luminosity and time of occurrence are similar and independent of the associated GRBs. {From previously identified $380$ BdHN I comprising redshifts up to $z=8.2$, we analyze} four examples with their associated hypernovae. By multiwavelength extragalactic observations, we identify seven new Episodes, theoretically explained, fortunately not yet detected in galactic sources, opening new research areas. Refinement of population synthesis simulations is needed to map the progenitors of such short-lived binary systems inside our galaxy.