Nucleosynthesis of Ni in wind-driven Supernova Explosions and Constraints on the Central Engine of Gamma-Ray Bursts

Theoretically expected natures of a supernova driven by a wind/jet are discussed. Approximate analytical formulations are derived to clarify basic physical processes involved in the wind/jet-driven explosions, and it is shown that the explosion properties are characterized by the energy injection rate (Ėiso) and the mass injection rate (Ṁiso). To explain observations of SN 1998bw associated with Gamma-Ray Burst (GRB) 980425, the following conditions are required: ĖisoṀiso & 10 51 erg M⊙ s −2 and Ėiso & 2 × 10 52 erg s (if the wind Lorentz factor Γw ∼ 1) or Ėiso & 7 × 10 52 erg s (if Γw ≫ 1). In SN 1998bw, Ni (∼ 0.4M⊙) is probably produced in the shocked stellar mantle, not in the wind. The expected natures of SNe, e.g., ejected Ni masses and ejecta masses, vary depending on Ėiso and Ṁiso. The sequence of the SN properties from high Ėiso and Ṁiso to low Ėiso and Ṁiso is the following: SN 1998bw-like – intermediate case – low mass ejecta (. 1M⊙) where Ni is from the wind – whole collapse. This diversity may explain the diversity of supernovae associated with GRBs. Our result can be used to constrain natures of the wind/jet, which is linked to the central engine of GRBs, by studying properties of the associated supernovae.