We present for the first time an analysis of high-frequency gravitational wave emission from proto-neutron star (PNS) in core collapse supernovae (CCSNe) that combines spatial decomposition and modal decomposition to both source and characterize the emission using three-dimensional CCSN simulations. Our analysis is based on three-dimensional CCSN simulations initiated from a solar-metallicity $15\text{−}{M}_{\odot }$ progenitor and a zero-metallicity $25\text{−}{M}_{\odot }$ progenitor. We decompose the gravitational wave strains into five spatial regions, and find that strains are initially largest in the PNS surface layers from accretion and later largest from the Ledoux convective and convective overshoot regions deep within the PNS. We compute the fractional gravitational wave luminosity as a function of enclosed radius and observe that the majority of the luminosity moves from the PNS surface at $\sim 100$ ms after bounce to deep within the PNS at later times. Using a self-consistent perturbative analysis, we investigate the evolution of the quadrupolar, nonradial, quasinormal oscillation modes of the PNS. We find that the frequency of the evolving high-frequency component of the gravitational wave signal is well matched to the eigenfrequency evolution of the ${{}^{2}g}_2$ mode initially, then the ${{}^{2}g}_1$ mode, and finally the ${}^{2}f$ mode, as labeled by the Generalized Cowling Nomenclature. We show that the ${}^{2}g$ modes emit most of their power in gravitational waves initially from the PNS surface region, but within a few 100 ms after bounce, it is the convective overshoot region of the PNS, just above the region of sustained Ledoux convection, that emits the most gravitational wave power for the ${{}^{2}g}_1$ mode. Eventually, the ${}^{2}f$ mode is the dominant mode producing gravitational waves, and these waves are emitted primarily from the convective overshoot region. Thus, with three interconnected analyses, we show that, while the gravitational wave emission is global, stemming from multiple regions in and around the PNS, it nonetheless remains possible to source the dominant contributions to it. We find that the source of the high-frequency gravitational wave emission from the PNS in CCSNe is more complex than assessed by other methods, as well as time dependent, first emitted mainly by ${}^{2}g$ modes driven by accretion onto the PNS and later emitted by the ${}^{2}f$ mode driven by sustained Ledoux convection.

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• Gravitational wave sources
• Gravitational waves
• Novae & supernovae