The dynamics of thermal capillary waves (CWs) on an ionic liquid's surface are studied at the transition from propagating to overdamped CWs by x-ray photon correlation spectroscopy. The analysis considers both homodyne and heterodyne contributions, and yields excellent full line-shape experiment-theory agreement for the structure factor. The CWs' Brillouin scattering becomes extinct at a critical temperature Tc JK ∼10 K above Tc LL, the propagating modes' hydrodynamic limit, in agreement with linear response theory. Surprisingly, the same power law applies at both Tc. The results rule out the presence of a suggested surface dipole layer.
