The length of lunar crater rays explained using secondary crater scaling

The relationship between the length of crater rays and primary crater radius is still poorly understood. In this study we mapped the ray systems of 27 lunar craters, ranging from 10 m to 84 km in diameter. For each ray system, we measured the number, length, and optical maturity index (OMAT) of the rays. Our mapping effort shows that ray length scales to primary crater radius (R) with a power-law of R1.22, except for the smallest and freshest rays (<10 m diameter craters, less than ∼40 years old), which were ∼10 radii longer than expected. We also undertook an analytical modeling exercise in an attempt to better understand the physical processes that control ray length. The model suggests that the empirical relationship (R1.22) can be explained as resulting from the combination of 1) the relationship between ejecta fragment size and ejected distance, and 2) the scaling of secondary crater diameters, which create rays by excavating bright material from below the dark space-weathered layer, as a function of ejected velocity. When the ejecta fragments are large enough, they are able to excavate bright material from beneath the mature space-weathered layer, while smaller ejecta fragments simply mix the dark mature lunar soil. We then use this secondary crater scaling relationship to predict the ray length for different depths of well-weathered lunar soil. The anomalously long rays for the smallest, freshest craters may be due to the fact that their bright ejecta fragments are not traveling fast enough to excavate below the space-weathered surface layer, and simply become deposited on the surface. We suggest observations that will help refine many of the poorly constrained assumptions of our model.