A New Kilohertz Gravitational-Wave Feature from Rapidly Rotating Core-Collapse Supernovae

We present self-consistent three-dimensional core-collapse supernova simulations of a rotating $20M_\odot$ progenitor model with various initial angular velocities from $0.0$ to $4.0$ rad s$^{-1}$ using a smoothed particle hydrodynamics code, SPHYNX, and a grid-based hydrodynamics code, FLASH. We identify two strong gravitational-wave features, with peak frequencies of $\sim300$ Hz and $\sim1.3$ kHz in the first $100$ ms postbounce. We demonstrate that these two features are associated with the $m=1$ deformation from the proto-neutron star (PNS) modulation induced by the low-$T/|W|$ instability, regardless of the simulation code. The $300$ Hz feature is present in models with an initial angular velocity between $1.0$ and $4.0$ rad s$^{-1}$, while the $1.3$ kHz feature is present only in a narrower range, from $1.5$ to $3.5$ rad s$^{-1}$. We show that the $1.3$ kHz signal originates from the high-density inner core of the PNS, and the $m=1$ deformation triggers a strong asymmetric distribution of electron anti-neutrinos. In addition to the $300$ Hz and $1.3$ kHz features, we also observe one weaker but noticeable gravitational-wave feature from higher-order modes in the range between $1.5$ and $3.5$ rad s$^{-1}$. Its peak frequency is around $800$ Hz initially and gradually increases to $900-1000$ Hz. Therefore, in addition to the gravitational bounce signal, the detection of the $300$ Hz, $1.3$ kHz, the higher-order mode, and even the related asymmetric emission of neutrinos, could provide additional diagnostics to estimate the initial angular velocity of a collapsing core.