Validation of numerical codes for impact and explosion cratering: Impacts on strengthless and metal targets

Over the last few decades, rapid improvement of computer capabilities has allowed impact cratering to be modeled with increasing complexity and realism, and has paved the way for a new era of numerical modeling of the impact process, including full, three-dimensional (3D) simulations. When properly benchmarked and validated against observation, computer models offer a powerful tool for understanding the mechanics of impact crater formation. This work presents results from the first phase of a project to benchmark and validate shock codes. A variety of 2D and 3D codes were used in this study, from commercial products like AUTODYN, to codes developed within the scientific community like SOVA, SPH, ZEUS-MP, iSALE, and codes developed at U.S. National Laboratories like CTH, SAGE/RAGE, and ALE3D. Benchmark calculations of shock wave propagation in aluminum-on-aluminum impacts were performed to examine the agreement between codes for simple idealized problems. The benchmark simulations show that variability in code results is to be expected due to differences in the underlying solution algorithm of each code, artificial stability parameters, spatial and temporal resolution, and material models. Overall, the inter-code variability in peak shock pressure as a function of distance is around 10 to 20%. In general, if the impactor is resolved by at least 20 cells across its radius, the underestimation of peak shock pressure due to spatial resolution is less than 10%. In addition to the benchmark tests, three validation tests were performed to examine the ability of the codes to reproduce the time evolution of crater radius and depth observed in vertical laboratory impacts in water and two well-characterized aluminum alloys. Results from these calculations are in good agreement with experiments. There appears to be a general tendency of shock physics codes to underestimate the radius of the forming crater. Overall, the discrepancy between the model and experiment results is between 10 and 20%, similar to the inter-code variability.The Meteoritics & Planetary Science archives are made available by the Meteoritical Society and the University of Arizona Libraries. Contact [email protected] for further information.Migrated from OJS platform February 202

Plume Development of the Shoemaker-Levy 9 Comet Impact

We have studied plume formation after a Jovian comet impact using the ZEUS-MP 2 hydrodynamics code. The three-dimensional models followed objects with 500, 750, and 1000 meter diameters. Our simulations show the development of a fast, upward-moving component of the plume in the wake of the impacting comet that "pinches off" from the bulk of the cometary material ~50 km below the 1 bar pressure level, ~100 km above the depth of greatest mass and energy deposition. The fast-moving component contains about twice the mass of the initial comet, but consists almost entirely (>99.9%) of Jovian atmosphere rather than cometary material. The ejecta rise mainly along the impact trajectory, but an additional vertical velocity component due to buoyancy establishes itself within seconds of impact, leading to an asymmetry in the ejecta with respect to the entry trajectory. The mass of the upward-moving component follows a velocity distribution M(>v) approximately proportional to v^-1.4 (v^-1.6 for the 750 m and 500 m cases) in the velocity range 0.1 < v < 10 km/s.Comment: 5 pages, 4 figures. Accepted for publication in The Astrophysical Journa

The effect of an isothermal atmosphere on the propagation of three-dimensional waves in a thermally stratified accretion disk

We extend our analysis of the three-dimensional response of a vertically polytropic disk to tidal forcing at Lindblad resonances by including the effects of a disk atmosphere. The atmosphere is modeled as an isothermal layer that joins smoothly on to an underlying polytropic layer. The launched wave progressively enters the atmosphere as it propagates away from the resonance. The wave never propagates vertically, however, and the wave energy rises to a (finite) characteristic height in the atmosphere. The increase of wave amplitude associated with this process of wave channeling is reduced by the effect of the atmosphere. For waves of large azimuthal mode number m generated by giant planets embedded in a disk, the increase in wave amplitude is still substantial enough to be likely to dissipate the wave energy by shocks for even modest optical depths (tau greater than about 10) over a radial distance of a few times the disk thickness. For low-m waves generated in circumstellar disks in binary stars, the effects of wave channeling are less important and the level of wave nonlinearity increases by less than a factor of 10 in going from the disk edge to the disk center. For circumbinary disks, the effects of wave channeling remain important, even for modest values of optical depth.Comment: 11 pages, 4 figures, submitted to the Astrophysical Journa

Impact-Induced Climate Change on Titan

Titan's thick atmosphere and volatile surface cause it to respond to big impacts like the one that produced the prominent Menrva impact basin in a somewhat Earth-like manner. Menrva was big enough to raise the surface temperature by 100 K. If methane in the regolith is generally as abundant as it was at the Huygens landing site, Menrva would have been big enough to double the amount of methane in the atmosphere. The extra methane would have drizzled out of the atmosphere over hundreds of years. Conditions may have been favorable for clathrating volatiles such as ethane. Impacts can also create local crater lakes set in warm ice but these quickly sink below the warm ice; whether the cryptic waters quickly freeze by mixing with the ice crust or whether they long endure under the ice remains a open question. Bigger impacts can create shallow liquid water oceans at the surface. If Titan's crust is made of water ice, the putative Hotei impact (a possible 800-1200 km diameter basin, Soderblom et al 2009) would have raised the average surface temperature to 350-400 K. Water rain would have fallen and global meltwaters would have averaged 50 m to as much as 500 m deep. The meltwaters may not have lasted more than a few decades or centuries at most, but are interesting to consider given Titan's organic wealth

On the width and shape of the corotation region for low-mass planets

We study the coorbital flow for embedded, low mass planets. We provide a simple semi-analytic model for the corotation region, which is subsequently compared to high resolution numerical simulations. The model is used to derive an expression for the half-width of the horseshoe region, x_s, which in the limit of zero softening is given by x_s/r_p = 1.68(q/h)^(1/2), where q is the planet to central star mass ratio, h is the disc aspect ratio and r_p the orbital radius. This is in very good agreement with the same quantity measured from simulations. This result is used to show that horseshoe drag is about an order of magnitude larger than the linear corotation torque in the zero softening limit. Thus the horseshoe drag, the sign of which depends on the gradient of specific vorticity, is important for estimates of the total torque acting on the planet. We further show that phenomena, such as the Lindblad wakes, with a radial separation from corotation of ~ a pressure scale height H can affect x_s, even though for low-mass planets x_s << H. The effect is to distort streamlines and to reduce x_s through the action of a back pressure. This effect is reduced for smaller gravitational softening parameters and planets of higher mass, for which x_s becomes comparable to H.Comment: 15 pages, 11 figures, accepted for publication in MNRA

Three-dimensional waves generated at Lindblad resonances in thermally stratified disks

We analyze the linear, 3D response to tidal forcing of a disk that is thin and thermally stratified in the direction normal to the disk plane. We model the vertical disk structure locally as a polytrope which represents a disk of high optical depth. We solve the 3D gas-dynamic equations semi-analytically in the neighborhood of a Lindblad resonance. These solutions match asymptotically on to those valid away from resonances and provide solutions valid at all radii. We obtain the following results. 1) A variety of waves are launched at resonance. However, the f mode carries more than 95% of the torque exerted at the resonance. 2) These 3D waves collectively transport exactly the amount of angular momentum predicted by the 2D torque formula. 3) Near resonance, the f mode occupies the full vertical extent of the disk. Away from resonance, the f mode becomes confined near the surface of the disk, and, in the absence of other dissipation mechanisms, damps via shocks. The radial length scale for this process is roughly r_L/m (for resonant radius r_L and azimuthal wavenumber m), independent of the disk thickness H. This wave channeling process is due to the variations of physical quantities in r and is not due to wave refraction. 4) However, the inwardly propagating f mode launched from an m=2 inner Lindblad resonance experiences relatively minor channeling. We conclude that for binary stars, tidally generated waves in highly optically thick circumbinary disks are subject to strong nonlinear damping by the channeling mechanism, while those in circumstellar accretion disks are subject to weaker nonlinear effects. We also apply our results to waves excited by young planets for which m is approximately r/H and conclude that the waves are damped on the scale of a few H.Comment: 15 pages, 3 figures, 2 colour plates, to be published in the Astrophysical Journa

Astronomical engineering: a strategy for modifying planetary orbits

The Sun's gradual brightening will seriously compromise the Earth's biosphere within ~ 1E9 years. If Earth's orbit migrates outward, however, the biosphere could remain intact over the entire main-sequence lifetime of the Sun. In this paper, we explore the feasibility of engineering such a migration over a long time period. The basic mechanism uses gravitational assists to (in effect) transfer orbital energy from Jupiter to the Earth, and thereby enlarges the orbital radius of Earth. This transfer is accomplished by a suitable intermediate body, either a Kuiper Belt object or a main belt asteroid. The object first encounters Earth during an inward pass on its initial highly elliptical orbit of large (~ 300 AU) semimajor axis. The encounter transfers energy from the object to the Earth in standard gravity-assist fashion by passing close to the leading limb of the planet. The resulting outbound trajectory of the object must cross the orbit of Jupiter; with proper timing, the outbound object encounters Jupiter and picks up the energy it lost to Earth. With small corrections to the trajectory, or additional planetary encounters (e.g., with Saturn), the object can repeat this process over many encounters. To maintain its present flux of solar energy, the Earth must experience roughly one encounter every 6000 years (for an object mass of 1E22 g). We develop the details of this scheme and discuss its ramifications.Comment: 21 pgs, 7 figs. Paper to appear in Astrophysics and Space Scienc

Big Impacts and Transient Oceans on Titan

We have studied the thermal consequences of very big impacts on Titan [1]. Titan's thick atmosphere and volatile-rich surface cause it to respond to big impacts in a somewhat Earth-like manner. Here we construct a simple globally-averaged model that tracks the flow of energy through the environment in the weeks, years, and millenia after a big comet strikes Titan. The model Titan is endowed with 1.4 bars of N2 and 0.07 bars of CH4, methane lakes, a water ice crust, and enough methane underground to saturate the regolith to the surface. We assume that half of the impact energy is immediately available to the atmosphere and surface while the other half is buried at the site of the crater and is unavailable on time scales of interest. The atmosphere and surface are treated as isothermal. We make the simplifying assumptions that the crust is everywhere as methane saturated as it was at the Huygens landing site, that the concentration of methane in the regolith is the same as it is at the surface, and that the crust is made of water ice. Heat flow into and out of the crust is approximated by step-functions. If the impact is great enough, ice melts. The meltwater oceans cool to the atmosphere conductively through an ice lid while at the base melting their way into the interior, driven down in part through Rayleigh-Taylor instabilities between the dense water and the warm ice. Topography, CO2, and hydrocarbons other than methane are ignored. Methane and ethane clathrate hydrates are discussed quantitatively but not fully incorporated into the model

Transient Climate Effects of Large Impacts on Titan

Titan's thick atmosphere and volatile-rich surface cause it to respond to big impacts in a somewhat Earth-like manner. Here we construct a simple globally-averaged model that tracks the flow of energy through the environment in the weeks, years, and millenia after a big comet strikes Titan. The model Titan is endowed with 1.4 bars of N2 and 0.07 bars of CH4, methane lakes, a water ice crust, and enough methane underground to saturate the regolith to the surface. We find that a nominal Menrva impact is big enough to raise the surface temperature by approx. 80 K and to double the amount of methane in the atmosphere. The extra methane drizzles out of the atmosphere over hundreds of years. An upper-limit Menrva is just big enough to raise the surface to water's melting point. The putative Hotei impact (a possible 800-1200 km diameter basin, Soderblom et al., 2009) is big enough to raise the surface temperature to 350-400 K. Water rain must fall and global meltwaters might range between 50 m to more than a kilometer deep, depending on the details. Global meltwater oceans do not last more than a few decades or centuries at most, but are interesting to consider given Titan's organic wealth. Significant near-surface clathrate formation is possible as Titan cools but faces major kinetic barriers