Gravitational waves from very massive stars collapsing to a black hole

We compute gravitational waves emitted by the collapse of a rotating very massive star (VMS) core leading directly to a black hole in axisymmetric numerical-relativity simulations. The evolved rotating VMS is derived by a stellar evolution calculation and its initial mass and the final carbon-oxygen core mass are $320M_{\odot }$ and $\approx 150M_{\odot }$, respectively. We find that for the moderately rapidly rotating cases, the peak strain amplitude and the corresponding frequency of gravitational waves are $\sim {10}^{-22}$ and $f \approx 300$--600Hzforaneventatthedistanceof$D=50$~Mpc. Such gravitational waves will be detectable only for $D\lesssim 10$~Mpc by second generation detectors, advanced LIGO, advanced VIRGO, and KAGRA, even if the designed sensitivity for these detectors is achieved. However, third-generation detectors will be able to detect such gravitational waves for an event up to $D \sim 100$~Mpc. The detection of the gravitational-wave signal will provide a potential opportunity for verifying the presence of VMSs with mass $\gtrsim 300M_\odot$ and their pair-unstable collapse in the universe.