Gravitational Waves from the innermost parts of Core-Collapse Supernovae

Gravitational waves (GWs) from core-collapse supernovae (CCSNe) could offer a direct probe of the dense core of a proto-compact star (PCS), in which matter can reach densities of multiple times nuclear saturation density. We present axisymmetric simulations of CCSNe using two different models for the high-energy equations of state (EoS), the purely hadronic SFHx model and the CMF model with a smooth crossover to quark matter. We identify a distinct GW signature from a quadrupolar ${}^2\!g_1$-mode located in the PCS core. This mode is excited by PCS convection, and its frequency strongly depends on the EoS. We attribute the lower mode frequency to the stiffer CMF EoS and its higher sound speed at about twice nuclear saturation density, $\rho_0$. We summarize our semi-analytic expression that connects the mode frequency to PCS bulk parameters such as its mass, radius, and entropy profile, along with an EoS-dependent factor.