The final core collapse of pulsational pair instability supernovae.

We present 3D core-collapse supernova simulations of massive Pop-III progenitor stars at the transition to the pulsational pair instability regime. We simulate two progenitor models with initial masses of $85\,\mathrm{M}_{\odot}$ and $100\,\mathrm{M}_\odot$ with the LS220, SFHo, and SFHx equations of state. The $85\,\mathrm{M}_{\odot}$ progenitor experiences a pair instability pulse coincident with core collapse, whereas the $100\,\mathrm{M}_{\odot}$ progenitor has already gone through a sequence of four pulses $1\mathord,500$ years before collapse in which it ejected its H and He envelope. The $85\,\mathrm{M}_{\odot}$ models experience shock revival and then delayed collapse to a black hole (BH) due to ongoing accretion within hundreds of milliseconds. The diagnostic energy of the incipient explosion reaches up to $2.7\times10^{51}\,\mathrm{erg}$ in the SFHx model. Due to the high binding energy of the metal core, BH collapse by fallback is eventually unavoidable, but partial mass ejection may be possible. The $100\,\mathrm{M}_\odot$ models have not achieved shock revival or undergone BH collapse by the end of the simulation. All models exhibit relatively strong gravitational-wave emission both in the high-frequency g-mode emission band and at low frequencies. The SFHx and SFHo models show clear emission from the standing accretion shock instability. For our models, we estimate maximum detection distances of up to $\mathord{\sim}46\,\mathrm{kpc}$ with LIGO and $\mathord{\sim} 850\,\mathrm{kpc}$ with Cosmic Explorer.