Dispersion and shattering strength of rocky and frozen planetesimals studied by laboratory experiments and numerical simulations

Abstract We have developed a method to investigate the whole mass–velocity distribution of impact fragments generated by catastrophic disruption of simulated planetesimals. Flash X-ray radiography including 12 iron particles for tracers was used to visualize the interior of the target, and the velocity distribution of the whole target was estimated by using the velocities of the tracers measured by X-ray images. High-velocity impact experiments in the laboratory and numerical simulations were conducted for four types of targets simulating rocky and frozen planetesimals at various specific energies, Q. These targets consisted of frozen clays with three different water contents ranging from 25 to 45 wt% and porous gypsum with a porosity of 51%. The shattering strength, QS⁎, and the mass–velocity distribution (MVD) were studied for these targets. The QS⁎ of the frozen clays varied by a factor of 3–4 times, depending on the water content, and the QS⁎ for porous gypsum was almost the same as that for the frozen clays with lower water contents. The numerical impact simulations led to slightly different QS⁎ and MVD values for the frozen clay targets, possibly because of the partly ductile behavior of these samples. The MVDs resulting from the porous gypsum targets were well reproduced in the simulations. The cumulative mass of fragments with an ejection velocity slower than a specific velocity was examined to introduce a median velocity, v⁎, charactering the mass–velocity distribution. The v⁎ is defined as the velocity at which the cumulative mass corresponds to a half of the original target mass in the distribution. The v⁎ values of the frozen clays were described by the empirical equation v∗ = e Qγ with almost the same e and γ, irrespective of the water content, but the v⁎ of porous gypsum was about 1/3 that of the frozen clays. These experimental results were well reproduced by the numerical simulations for both frozen clays and porous gypsum targets. The dispersion strength, QD⁎, could be derived by comparing v⁎ with the escape velocity, vesc, of a target body with an effective mass, M, and radius, R. From this, a semi-theoretical equation showing the dispersion strength was derived: Q D ∗ = 1 e 2 GM R 1 / 2 1 / γ . Numerical simulations of catastrophic disruptions including self-gravity were conducted to directly determine QD⁎ at large scale. These calculations showed that the effective mass of the target body, which is used in the computation of vesc = v⁎, should be a half of the original target mass, M = Mtarget /2. Our results suggest that this approach for computing the semi-theoretical dispersion strength is suitable for bodies larger than ~10 km.