Evidence for the transition of a Jacobi ellipsoid into a Maclaurin spheroid in gamma-ray bursts

Abstract: In the binary-driven hypernova (BdHN) scenario, long gamma-ray bursts (GRBs) originate in a cataclysmic event that occurs in a binary system composed of a carbon-oxygen (CO) star and a neutron star (NS) companion in close orbit. The collapse of the CO star generates at its center a newborn NS ($\nu$NS), and a supernova (SN) explosion. Matter from the ejecta is accreted both onto the $\nu$NS because of fallback and onto the NS companion, leading to the collapse of the latter into a black hole (BH). Each of the ingredients of the above system leads to observable emission episodes in a GRB. In particular, the $\nu$NS is expected to show up (hereafter $\nu$NS-rise) in the early GRB emission, nearly contemporary or superimposed to the ultrarelativistic prompt emission (UPE) phase, but with a different spectral signature. Following the $\nu$NS-rise, the $\nu$NS powers the afterglow emission by injecting energy into the expanding ejecta leading to synchrotron radiation. We here show that the $\nu$NS-rise and the subsequent afterglow emission in both systems, GRB 180720B and GRB 190114C, are powered by the release of rotational energy of a Maclaurin spheroid, starting from the bifurcation point to the Jacobi ellipsoid sequence. This implies that the $\nu$NS evolves from a triaxial Jacobi configuration, prior to the $\nu$NS-rise, into the axially symmetric Maclaurin configuration observed in the GRB. The triaxial $\nu$NS configuration is short-lived (less than a second) due to a copious emission of gravitational waves, before the GRB emission, and it could be in principle detected for sources located at distances closer than $100$ Mpc. This appears to be a specific process of emission of gravitational waves in the BdHN I powering long GRBs.