Collapse of Rotating Massive Stars Leading to Black Hole Formation and Energetic Supernovae

We explore a possible explosion scenario resulting from core collapses of rotating massive stars that leave a black hole by performing radiation-viscous-hydrodynamics simulations in numerical relativity. We take moderately and rapidly rotating compact pre-collapse stellar models with zero-age main-sequence masses of 9M _⊙ and 20M _⊙ based on stellar evolution calculations as the initial conditions. We find that viscous heating in the disk formed around the central black hole is the power source for an outflow. The moderately rotating models predict a small ejecta mass of the order of 0.1M _⊙ and an explosion energy of ≲10⁵¹ erg. Due to the small ejecta mass, these models may predict a short-timescale transient with a rise time of 3-5 days. This can lead to a bright (~10⁴⁴ erg s^-1) transient, like superluminous supernovae in the presence of a dense massive circumstellar medium. For hypothetically rapidly rotating models that have a high mass-infall rate onto the disk, the explosion energy is ≳3 × 10⁵¹ erg, which is comparable to or larger than that of typical stripped-envelope supernovae, indicating that a fraction of such supernovae may be explosions powered by black hole accretion disks. The explosion energy is still increasing at the end of the simulations with a rate of >10⁵⁰ erg s^-1, and thus, it may reach ~10⁵² erg. A nucleosynthesis calculation shows that the mass of ⁵⁶Ni amounts to ≳0.1M _⊙, which, together with the high explosion energy, may satisfy the required amount for broad-lined type Ic supernovae. Irrespective of the models, the lowest value of the electron fraction of the ejecta is ≳0.4; thus, synthesis of heavy r-process elements is not found in our models.