Black-Hole Formation Accompanied by the Supernova Explosion of a 40-M$_{\odot}$ Progenitor Star

We have simulated the collapse and evolution of the core of a solar-metallicity 40-M$_{\odot}$ star and find that it explodes vigorously by the neutrino mechanism. This despite its very high "compactness". Within $\sim$1.5 seconds of explosion, a black hole forms. The explosion is very asymmetrical and has a total explosion energy of $\sim$1.6$\times$10$^{51}$ ergs. At black hole formation, its baryon mass is $\sim$2.434 M$_{\odot}$ and gravitational mass is 2.286 M$_{\odot}$. Seven seconds after black hole formation an additional $\sim$0.2 M$_{\odot}$ is accreted, leaving a black hole baryon mass of $\sim$2.63 M$_{\odot}$. A disk forms around the proto-neutron star, from which a pair of neutrino-driven jets emanates. These jets accelerate some of the matter up to speeds of $\sim$45,000 km s$^{-1}$ and contain matter with entropies of $\sim$50. The large spatial asymmetry in the explosion results in a residual black hole recoil speed of $\sim$1000 km s$^{-1}$. This novel black-hole formation channel now joins the other black-hole formation channel between $\sim$12 and $\sim$15 M$_{\odot}$ discovered previously and implies that the black-hole/neutron-star birth ratio for solar-metallicity stars could be $\sim$20\%. However, one channel leaves black holes in perhaps the $\sim$5-15 M$_{\odot}$ range with low kick speeds, while the other leaves black holes in perhaps the $\sim$2.5-3.0 M$_{\odot}$ mass range with high kick speeds. However, even $\sim$8.8 seconds after core bounce the newly-formed black hole is still accreting at a rate of $\sim$2$\times$10$^{-2}$ M$_{\odot}$ s$^{-1}$ and whether the black hole eventually achieves a significantly larger mass over time is yet to be determined.