Modeling crater populations on Venus and Titan

摘要

We describe a model for crater populations on planets and satellites with dense atmospheres, like those of Venus and Titan. The model takes into account ablation (or mass shedding), pancaking, and fragmentation. Fragmentation is assumed to occur due to the hydrodynamic instabilities promoted by the impactors' deceleration in the atmosphere. Fragments that survive to hit the ground make craters or groups thereof. Crater sizes are estimated using standard laws in the gravity regime, modified to take into account impactor disruption. We use Monte Carlo methods to pick parameters from appropriate distributions of impactor mass, zenith angle, and velocity. Good fits to the Venus crater populations (including multiple crater fields) can be found with reasonable values of model parameters. An important aspect of the model is that it reproduces the dearth of small craters on Venus: this is due to a cutoff on crater formation we impose, when the expected crater would be smaller than the (dispersed) object that would make it. Hydrodynamic effects alone (ablation, pancaking, fragmentation) due to the passage of impactors through the atmosphere are insufficient to explain the lack of small craters. In our favored model, the observed number of craters (940) is produced by ～5500 impactors with masses > 10~(15) gm, yielding an age of 730 ± 110Myr (1-σ uncertainty) for the venusian surface. This figure does not take into account any uncertainties in crater scaling and impactor population characteristics, which probably increase the uncertainty to a factor of two in age. We apply the model with the same parameter values to Titan to predict crater populations under differing assumptions of impactor populations that reflect present conditions. We assume that the impactors (comets) are made of 50% porous ice. Predicted crater production rates are ≈ 190 craters (10~9 yr)~(-1). The smallest craters on Titan are predicted to be ≈ 2 km in diameter, and ≈ 5 crater fields (10~9 yr)~(-1) are expected. If the impactors are composed of solid ice (density 0.92 gmcm~(-3)), crater production rates increase by ≈ 70% and the smallest crater is predicted to be ≈ 1.6km in diameter. We give cratering rates for denser comets and atmospheres 0.1 and 10 times as thick as Titan's current atmosphere. We also explicitly address leading-trailing hemisphere asymmetries that might be seen if Titan's rotation rate were strictly synchronous over astronomical timescales: if that is the case, the ratio of crater production on the leading hemisphere to that on the trailing hemisphere is ≈ 4 : 1.