GRB 221009A with an unconventional precursor: a typical two-stage collapsar scenario?

As the brightest Gamma-Ray burst (GRB) ever detected, GRB 221009A may offer a chance that reveals some interesting features which are hidden in those bursts that are not so bright. There seems a very weak emission with a flux of $10^{-8}\sim10^{-7}$ erg cm$^{-2}$ s$^{-1}$ between the first pulse ($T_0\sim T_0+50$~s, $T_0$ is the trigger time) and the main burst (appears from $T_0+180$ s). Thus the gap time between them is not really quiescent, and the first pulse could be taken as an unconventional precursor, which may provide a peculiar case study for the GRB-precursor phenomena. A two-stage collapsar scenario is proposed as the most likely origin for this burst. In this model, the jet for the precursor is produced during the initial core-collapse phase, and should be weak enough not to disrupt the star when it breaks out of the envelope, so that the fallback accretion process and the forming of the disk could continue. We present an approach in which the duration and flux both provide constraints on the luminosity ($L_{\rm j}$) and the Lorentz factor at the breakout time ($\Gamma_{\rm b}$) of this weak jet. The estimated $L_{\rm j}\lesssim 10^{49}$ erg s$^{-1}$ and $\Gamma_{\rm b}$ has an order of ten, which are well consistent with the theoretical prediction. Besides, the weak emission in the gap time could be interpreted as a MHD outflow due to a magnetically driven wind during the period from the proto-neutron star phase to forming the accretion disk in this scenario.