Numerical simulations of sub-catastrophic porous planetesimal collisions

Introduction: Porosity is an important property of many small solar system objects. The bulk density of some asteroids and comets suggests that pore space may occupy as much as 60-80% by volume [e.g., 1,2]. Moreover, as planetesimals are expected to form via gentle aggregation of smaller bodies, the first generation of large solid bodies likely possessed significant (>50%) porosity [3-5]. It has long been known that porosity has a strong influence on shock wave attenuation and shock heating in hypervelocity impacts [6]. The compaction of a substantial volume of pore space can dramatically decrease the peak shock pressure and increase the postshock temperature of impact-processed materials. Hence, pore collapse may play a major role in disruption, melt and vapor production, momentum transfer and crater formation, when solar system bodies collide. Addressing the influence of porosity on impact heating, Davison et al. [7] demonstrated that impacts at speeds greater than 4 km/s could cause significant localised heating on planetesimals if they were porous. Statistical models [8], based on these results, suggest that impact heating may be an important secondary heat source in the early solar system (in addition to the decay of short-lived radionuclides), with most heat delivered to a surviving planetesimal in large subcatastrophic collisions (i.e., collisions in which just over half the original planetesimal mass is retained). Critical to understanding the importance of impact heating in the early solar system, therefore, is quantification of (a) the disruption threshold for weak, porous first-generation planetesimals; (b) the evolution of planetesimal porosity with time through impactinduced compaction; and (c) the redistribution and retention of heated material in sub-catastrophic collisions. Here we extend the work of [7,8] by simulating large sub-catastrophic planetesimal collisions to late times, quantifying global compaction as well as the ejection and redistribution of impact heated material. Methods: We used the 2D iSALE hydrocode [9,10] to simulate sub-catastrophic head-on collisions between porous planetesimals. ANEOS-derived equation of state tables for dunite were used to represent the thermodynamic response of non-porous planetesimal material. Pore-space compaction was modeled using the improved epsilon-alpha porosity model [9,11]. Material strength was modeled using the procedure described in [10] with parameters for weak rock. The target planetesimal was 500 km in diameter with a uniform initial temperature (300K) and porosity (50%). Impacting planetesimals of 50-150 km in diameter and with identical material properties to the target collided with the target at 4-7 km/s. The gravity field was updated periodically during the calculation using a self-gravity algorithm, inspired by [12], implemented and tested for the purposes of this study. During a gravity update the gravitational attraction of cells containing mass (actually rings of mass due to axial symmetry) is calculated for each vertex of the mesh. Computational efficiency is achieved with minimal loss of accuracy by combining cells into patches of 2 2/4 4/8 8/etc neighbouring cells when they are sufficiently far from the point of interest and computing the gravitational acceleration of the patch (ring) as a whole. The size of the patch h is determined by a user-defined accuracy parameter, the opening angle , times the distance l between the patch center and the vertex at which gravity is being computed, h = l [12]. Thus, large numbers of cells are combined to form massive patches (rings) when accounting for the gravitational acceleration of mass far from the point of interest. The algorithm was tested against benchmark problems discussed in [13]. Results: The compaction of pore space during a planetesimal collision increases shock heating and reduces ejection velocities relative to the non-porous case (Fig. 1). Hence, if planesimals are sufficiently porous, collisions can cause substantial heating and, even in large sub-catastrophic collisions, the vast majority of the heated material is retained on the target planetesimal.