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Sublimation-driven morphogenesis of Zen stones on ice surfaces

Significance Zen stones are fascinating natural structures consisting of a stone standing on a slender ice pedestal, whose origin had long been misunderstood. We demonstrate that they are caused by a variation in the sublimation rate of the surrounding ice, which leads to the slow formation of a pedestal, adding to the very few reports of sublimation-driven pattern formation. Understanding this process sheds light on other differential ablation processes encountered on ice surfaces, such as debris-covered glaciers, whose existence is threatened by global warming, and icy bodies in space. Indeed, NASA’s Europa Lander project aims to seek biosignatures on Jupiter’s ice-covered moon, on the surface of which differential sublimation may threaten the lander stability, and this needs to be fully understood. In this article, the formation of Zen stones on frozen lakes and the shape of the resulting pedestal are elucidated. Zen stones are natural structures in which a stone, initially resting on an ice surface, ends up balanced atop a narrow ice pedestal. We provide a physical explanation for their formation, sometimes believed to be caused by the melting of the ice. Instead, we show that slow surface sublimation is indeed the physical mechanism responsible for the differential ablation. Far from the stone, the sublimation rate is governed by the diffuse sunlight, while in its vicinity, the shade it creates inhibits the sublimation process. We reproduced the phenomenon in laboratory-scale experiments conducted in a lyophilizer and studied the dynamics of the morphogenesis. In this apparatus, which imposes controlled constant sublimation rate, a variety of model stones consisting of metal disks was used, which allows us to rule out the possible influence of the thermal conduction in the morphogenesis process. Instead, we show that the stone only acts as an umbrella whose shade hinders the sublimation, hence protecting the ice underneath, which leads to the formation of the pedestal. Numerical simulations, in which the local ablation rate of the surface depends solely on the visible portion of the sky, allow us to study the influence of the shape of the stone on the formation of the ice foot. Finally, we show that the far-infrared black-body irradiance of the stone itself leads to the formation of a depression surrounding the pedestal.