Gravitational waves ( GW ) generated during a core-collapse supernova open a window into the heart of the explosion .
At core bounce , progenitors with rapid core rotation rates exhibit a characteristic GW signal which can be used to constrain the properties of the core of the progenitor star .
We investigate the dynamics of rapidly rotating core collapse , focusing on hydrodynamic waves generated by the core bounce and the GW spectrum they produce .
The centrifugal distortion of the rapidly rotating proto-neutron star ( PNS ) leads to the generation of axisymmetric quadrupolar oscillations within the PNS and surrounding envelope .
Using linear perturbation theory , we estimate the frequencies , amplitudes , damping times , and GW spectra of the oscillations .
Our analysis provides a qualitative explanation for several features of the GW spectrum and shows reasonable agreement with nonlinear hydrodynamic simulations , although a few discrepancies due to non-linear/rotational effects are evident .
The dominant early postbounce GW signal is produced by the fundamental quadrupolar oscillation mode of the PNS , at a frequency 0.70 { kHz } \lesssim f \lesssim 0.80 { kHz } , whose energy is largely trapped within the PNS and leaks out on a \sim 10 ms timescale .
Quasi-radial oscillations are not trapped within the PNS and quickly propagate outwards until they steepen into shocks .
Both the PNS structure and Coriolis/centrifugal forces have a strong impact on the GW spectrum , and a detection of the GW signal can therefore be used to constrain progenitor properties .