Core-Collapse Very Massive Stars: Evolution, Explosion, and Nucleosynthesis of Population III 500 -- 1000 $M_{\odot}$ Stars

We calculate evolution, collapse, explosion, and nucleosynthesis of Population III very-massive stars with 500$M_{\odot}$ and 1000$M_{\odot}$. Presupernova evolution is calculated in spherical symmetry. Collapse and explosion are calculated by a two-dimensional code, based on the bipolar jet models. We compare the results of nucleosynthesis with the abundance patterns of intracluster matter, hot gases in M82, and extremely metal-poor stars in the Galactic halo. It was found that both 500$M_{\odot}$ and 1000$M_{\odot}$ models enter the region of pair-instability but continue to undergo core collapse. In the presupernova stage, silicon burning regions occupy a large fraction, more than 20% of the total mass. For moderately aspherical explosions, the patterns of nucleosynthesis match the observational data of both intracluster medium and M82. Our results suggest that explosions of Population III core-collapse very-massive stars contribute significantly to the chemical evolution of gases in clusters of galaxies. For Galactic halo stars, our [O/Fe] ratios are smaller than the observational abundances. However, our proposed scenario is naturally consistent with this outcome. The final black hole masses are $\sim 230M_{\odot}$ and $\sim 500M_{\odot}$ for the $500M_{\odot}$ and 1000$M_{\odot}$ models, respectively. This result may support the view that Population III very massive stars are responsible for the origin of intermediate mass black holes which were recently reported to be discovered.