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. 
T. Ohkubo, H. Umeda, K. Maeda, K. Nomoto, T. Suzuki, S. Tsuruta, M. J.   Rees