How do gamma-ray bursts associated with supernovae avoid baryon contamination?

Current hypernova models for y-ray bursts (GRBs) associated with supernovae suffer from the baryon contamination problem, which prevents formation of relativistic shocks and emission of gamma-rays. Here we present a possible solution to this difficulty. Our model can be divided into two steps. In the first step, the core collapse of a star with mass > 19M. leads to a massive neutron star and a supernova (SN), and subsequently, one jet produced via neutrino annihilation during hypercritical accretion of the neutron star will push out of its front matter, resulting in a small cone relatively tree of baryons. In the second step, once the mass of the neutron star reaches the maximum value, it will promptly implode to a rapidly rotating black hole surrounded by a torus. The gravitational binding energy of the torus will convert to the expansion energy of the SN ejecta, thus yielding a hypernova, while the rotational energy of the black hole will be extracted via the Blandford-Znajek process to generate another jet responsible for a GRB. We show that the mass of baryons loading with the second jet is smaller than 10^3M . and the Lorentz factor of this jet is larger than 100. Thus our model can avoid the baryon contamination problem suffered from in the hypernova models.