A Quark-Nova in the wake of a core-collapse Supernova: a unifying model for long duration Gamma-Ray Bursts and Fast Radio Bursts.

[Abridged] By appealing to a Quark-Nova (QN; the explosive transition of a neutron star to a quark star) in the wake of a core-collapse Supernova explosion of a massive star, we develop a unified model for long duration Gamma-ray Bursts (LGRBs) and Fast Radio Bursts (FRBs). The time delay (years to decades) between the SN and the QN and, the fragmented nature (i.e. millions of chunks) of the relativistic QN ejecta are key to yielding a robust LGRB engine. In our model, a LGRB light-curve exhibits the interaction of the fragmented QN ejecta with a turbulent (i.e. filamentary and magnetically saturated) SN ejecta which is shaped by its interaction with an underlying pulsar wind nebula (PWN). The afterglow is due to the interaction of the QN chunks, exiting the SN ejecta, with the surrounding medium. Our model can fit BAT/XRT prompt and afterglow light-curves, simultaneously with their spectra, thus yielding the observed properties of LGRBs (e.g. the Band function and the X-ray flares). We find that the Yonetoku law and the Amati law are not fundamental but phenomenological. FRBs result from coherent synchrotron emission when the QN chunks interact with non-turbulent weakly magnetized PWN-SN ejecta, where conditions are prone to the Weibel instability. Magnetic field amplification induced by the Weibel instability sets the bunching length for electrons and pairs to radiate coherently. The resulting emission frequency, luminosity, duration and dispersion measure in our model are consistent with FRB data. We find a natural unification of high-energy burst phenomena from FRBs to LGRBs including X-ray Flashes and X-ray rich GRBs as well as Super-Luminous SNe. We find a possible connection between Ultra-High Energy Cosmic Rays and FRBs and propose that a QN following a binary neutron star merger can yield a short GRB (SGRB) with fits to BAT/XRT light-curves.