We experimentally investigate the self-sustained, star-shaped oscillations of Leidenfrost drops. The drops levitate on a cushion of evaporated vapor over a heated, curved surface. We observe modes with n = 2 − 13 lobes around the drop periphery. We find that the wavelength of the oscillations depends only on the capillary length of the liquid, and is independent of the drop radius and substrate temperature. However, the number of observed modes depends sensitively on the liquid viscosity. The dominant frequency of pressure variations in the vapor layer is approximately twice the drop oscillation frequency, consistent with a parametric forcing mechanism. Our results show that the star-shaped oscillations are driven by capillary waves of a characteristic wavelength beneath the drop, and that the waves are generated by a large shear stress at the liquid-vapor interface.PACS numbers: 47.35.Pq, 47.15.gm, 47.85.mf The Leidenfrost effect can be easily observed by placing a millimeter-scale water drop onto a sufficiently hot pan. The drop will levitate on a thermally-insulating vapor layer and survive for minutes [1][2][3][4]. For small drops, the geometry and dynamics of the vapor layer have been recently characterized [5,6]. The complex interactions between the liquid, vapor, and solid interfaces have led to a broad range of applications such as turbulent dragreduction [7], self-propulsion of drops on ratcheted surfaces [8,9], green nanofabrication [10], fuel combustion [11], and thermal control of nuclear reactors [12].Large Leidenfrost drops are well-known to form selfsustained, star-shaped oscillations (Fig. 1a). Since the 1950's, a number of studies have investigated these oscillations, often with different conclusions as to their physical origin based on the complicated interplay between thermal and hydrodynamic effects in both the liquid and gas phases [13][14][15][16][17][18][19]. A simple underlying mechanism for the onset of star oscillations remains unknown. Drops subjected to external, periodic excitations can form star oscillations with a frequency half that of the external excitation due to a parametric coupling mechanism [20,21]. However, if a parametric mechanism causes Leidenfrost stars, then the source of the periodic excitation is unclear. Recently, Bouwhuis et al. investigated the star oscillations of drops levitated by an air flow over a porous surface [22]. They showed that the onset of star oscillations occurs when the flow rate of air beneath the drop reaches a threshold, suggesting that a hydrodynamic coupling between the gas flow and liquid interface initiates the oscillations.Here we report measurements of star-shaped oscillations of six different liquids on a hot, curved surface. We observe stars with n = 2 − 13 lobes around the drop periphery. Although the number of observed modes depends on the liquid viscosity and substrate temperature, we find that the wavelength and frequency of the modes only depend on the capillary length, l c = γ/ρ l g, where γ and ρ l are the surface tension and ...