Scaling of impact-generated cavity-size for highly porous targets and its application to cometary surfaces

Detailed images of highly porous small bodies show variety of the surface. One of the interesting findings is that the depressions on comets look shallower than the simple craters such as on the moon, that is the depth-to-diameter ratio of the depressions is smaller than ∼0.2. Although the mechanisms for the formation of the depression are controversial; such as collapse after the sublimation of the sub-surface volatile or activities after impact such as sublimation and viscous relaxation, the shape of the cavity formed on the highly-porous surface by impact itself has not been studied much. We performed impact experiments of sintered glass-bead targets with porosities of ∼94% and 87%, as well as gypsum targets with a porosity of ∼50%, and pumice targets with that of 74%. The cavity formed in the porous target by the impact has maximum diameter at some depth from the target surface. This type of cavity is called bulb-shape cavity. In addition to the results of this study, we also compiled the results of previous impact experiments for cavity sizes in which the targets with porosity larger than 30% were used. Then new empirical scaling relations for the maximum diameter and the bulb depth for the wide range of target porosity were obtained. We applied the relations to comets and showed that the surface strength and the particle size of the comet 9P/Tempel 1 are estimated to be of the orders of 101-103 Pa, and, with the assumption of ice grains consisted of monodisperse spheres, to be larger than ∼90 µm, respectively. The ratio of bulb depth to the maximum diameter on a comet derived from the extrapolation of scaling relations expects that the ratio on the weak surface with the strength less than 102 Pa was 0.10 or below, which is smaller than the depth-to-diameter ratio of simple craters, ∼0.2. It suggests a possibility that shallow depressions on comets could be formed only by impact without the need for subsequent activities, such as sublimation and viscous relaxation.