Hydrodynamics and Nucleosynthesis of Jet-Driven Supernovae I: Parameter Study of the Dependence on Jet Energetics

Rotating massive stars with initial progenitor masses $M_{\rm prog} \sim$ 25 $M_{\odot}$ -- $\sim$140 $M_{\odot}$ can leave rapidly rotating black holes to become collapsars. The black holes and the surrounding accretion disks may develop powerful jets by magneto-hydrodynamics instabilities. The propagation of the jet in the stellar envelope provides the necessary shock heating for triggering nucleosynthesis unseen in canonical core-collapse supernovae. Yet, the energy budget of the jet and its effects on the final chemical abundance pattern are unclear. In this exploratory work, we present a survey on the parameter dependence of collapsar nucleosynthesis on jet energetics. We use the zero-metallicity star with $M_{\rm prog} \sim$ 40 $M_{\odot}$ as the progenitor. The parameters include the jet duration, its energy deposition rate, deposited energy, and the opening angle. We examine the correlations of following observables: (1) the ejecta and remnant masses, (2) the energy deposition efficiency, (3) the $^{56}$Ni production and its correlation with the ejecta velocity, deposited energy, and the ejected mass, (4) the Sc-Ti-V correlation as observed in metal-poor stars, and (5) the [Zn/Fe] ratio as observed in some metal-poor stars. We also provide the chemical abundance table of these explosion models for the use of the galactic chemical evolution and stellar archaeology.