  Using relativistic supernova simulations of massive progenitor stars with a
quark-hadron equation of state (EoS) and a purely hadronic EoS, we identify a
distinctive feature in the gravitational-wave signal that originates from a
buoyancy-driven mode (g-mode) below the proto-neutron star convection zone. The
mode frequency lies in the range $200\lesssim f\lesssim 800\,\text{Hz}$ and
decreases with time. As the mode lives in the core of the proto-neutron star,
its frequency and power are highly sensitive to the EoS, in particular the
sound speed around twice saturation density.

High Energy Astrophysical Phenomena;Solar and Stellar Astrophysics;Nuclear Theory