Pulsational Pair-Instability Supernovae

The final evolution of stars in the mass range 70 - 140 solar masses is explored. Depending upon their mass loss history and rotation rates, these stars will end their lives as pulsational pair-instability supernovae producing a great variety of observational transients with total durations ranging from weeks to millennia and luminosities from 10$^{41}$ to over 10$^{44}$ erg s$^{-1}$. No non-rotating model radiates more than $5 \times 10^{50}$ erg of light or has a kinetic energy exceeding $5 \times 10^{51}$ erg, but greater energies are possible, in principle, in magnetar-powered explosions which are explored. Many events resemble Type Ibn, Icn, and IIn supernovae, and some potential observational counterparts are mentioned. Some PPISN can exist in a dormant state for extended periods, producing explosions millennia after their first violent pulse. These dormant supernovae contain bright Wolf-Rayet stars, possibly embedded in bright x-ray and radio sources. The relevance of PPISN to supernova impostors like Eta Carinae, to super-luminous supernovae, and to sources of gravitational radiation is discussed. No black holes between 52 and 133 solar masses are expected from stellar evolution in close binaries.