An Argument for Weakly-Magnetized, Slowly-Rotating Progenitors of Long Gamma-Ray Bursts

Abstract

Using binary evolution with Case-C mass transfer, the spins of several black holes (BHs) in X$-$ray binaries (XBs) have been predicted and confirmed (three cases) by observations. The rotational energy of these BHs is sufficient to power up long gamma$-$ray bursts and hypernovae (GRBs/HNe) and still leave a Kerr BH behind. However, strong magnetic fields and/or dynamo effects in the interior of such stars deplete their cores from angular momentum preventing the formation of collapsars. Thus, even though binaries can produce Kerr BHs, most of their rotation is acquired from the stellar mantle, with a long delay between BH formation and spin up. Such binaries would not form GRBs. We study whether the conditions required to produce GRBs can be met by the progenitors of such BHs. Tidal-synchronization and Alfvén timescales are compared for magnetic fields of different intensities threading He stars. A search is made for a magnetic field range which allows tidal spin up all the way in to the stellar core but prevents its slow down during differential rotation phases. The energetics for producing a strong magnetic field during core collapse, which may allow for a GRB central engine, are also estimated. An observationally-reasonable choice of parameters is found ($B \lesssim10^2$ G threading a slowly-rotating He star) which allows Fe cores to retain substantial angular momentum. Thus, the Case-C-mass-transfer binary channel is capable of explaining long GRBs. However, the progenitors must have low initial spin and low internal magnetic field throughout their H-burning and He-burning phases.