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We present the first self-consistent, three-dimensional (3D) core-collapsesupernova simulations performed with the Prometheus-Vertex code for a rotatingprogenitor star. Besides using the angular momentum of the 15 solar-mass modelas obtained in the stellar evolution calculation with an angular frequency ofabout 0.001 rad/s (spin period of more than 6000 s) at the Si/Si-O interface,we also computed 2D and 3D cases with no rotation and with a ~300 times shorterrotation period and different angular resolutions. In 2D, only the nonrotatingand slowly rotating models explode, while rapid rotation prevents an explosionwithin 500 ms after bounce because of lower radiated neutrino luminosities andmean energies and thus reduced neutrino heating. In contrast, only the fastrotating model develops an explosion in 3D when the Si/Si-O interface collapsesthrough the shock. The explosion becomes possible by the support of a powerfulSASI spiral mode, which compensates for the reduced neutrino heating and pushesstrong shock expansion in the equatorial plane. Fast rotation in 3D leads to a"two-dimensionalization" of the turbulent energy spectrum (yielding roughly a-3 instead of a -5/3 power-law slope at intermediate wavelengths) with enhancedkinetic energy on the largest spatial scales. We also introduce ageneralization of the "universal critical luminosity condition" of Summa et al.(2016) to account for the effects of rotation, and demonstrate its viabilityfor a set of more than 40 core-collapse simulations including 9 and 20solar-mass progenitors as well as black-hole forming cases of 40 and 75solar-mass stars to be discussed in forthcoming papers.

Rotation-supported Neutrino-driven Supernova Explosions in Three Dimensions and the Critical Luminosity Condition