Abstract
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.