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Register a new userThe influence of Equation of State on impact dynamics between Pluto-like bodies
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Impacts between planetary-sized bodies can explain the origin of satellites orbiting large ($R>500$~km) trans-Neptunian objects. Their water rich composition, along with the complex phase diagram of water, make it important to accurately model the wide range of thermodynamic conditions material experiences during an impact event and in the debris disk. Since differences in the thermodynamics may influence the system dynamics, we seek to evaluate how the choice of an equation of state (EOS) alters the systems evolution. Specifically, we compare two EOSs that are constructed by different approaches: either by a simplified analytic description (Tillotson), or by interpolation of tabulated data (Sesame). Approximately $50$ pairs of Smoothed Particle Hydrodynamics impact simulations were performed, with similar initial conditions but different EOSs, in the parameter space in which the Pluto-Charon binary is thought to form (slow impacts between Pluto-size, water rich bodies). Generally, we show that impact outcomes (e.g., circumplanetary debris disk) are consistent between EOSs. Some differences arise, importantly in the production of satellitesimals (large intact clumps) that form in the post-impact debris disk. When utilizing an analytic EOS, the emergence of satellitesimals is highly certain, while when using the tabulated EOS it is less common. This is because for the typical densities and energies experienced in these impacts, the analytic EOS predicts very low pressure values, leading to particles artificially aggregating by a tensile instability.
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The discovery of a large putative impact crater buried beneath Hiawatha Glacier along the margin of the northwestern Greenland Ice Sheet has reinvigorated interest into the nature of large impacts into thick ice masses. This circular structure is relatively shallow and exhibits a small central uplift, whereas a peak-ring morphology is expected. This discrepancy may be due to long-term and ongoing subglacial erosion but may also be explained by a relatively recent impact through the Greenland Ice Sheet, which is expected to alter the final crater morphology. Here we model crater formation using hydrocode simulations, varying pre-impact ice thickness and impactor composition over crystalline target rock. We find that an ice-sheet thickness of 1.5 or 2 km results in a crater morphology that is consistent with the present morphology of this structure. Further, an ice sheet that thick substantially inhibits ejection of rocky material, which might explain the absence of rocky ejecta in most existing Greenland deep ice cores if the impact occurred during the late Pleistocene. From the present morphology of the putative Hiawatha impact crater alone, we cannot distinguish between an older crater formed by a pre-Pleistocene impact into ice-free bedrock or a younger, Pleistocene impact into locally thick ice, but based on our modeling we conclude that latter scenario is possible.
Dynamical scenarios of terrestrial planets formation involve strong perturbations of the inner part of the solar system by the giant-planets, leading to enhanced impact velocities and subsequent collisional erosion. We quantitatively estimate the effect of collisional erosion on the resulting composition of Earth, and estimate how it may provide information on the dynamical context of its formation. We simulate and quantify the erosion of Earths crust in the context of Solar System formation scenarios, including the classical model and Grand Tack scenario that invokes orbital migration of Jupiter during the gaseous disk phase (Walsh et al., 2011; Raymond et al., 2018). We find that collisional erosion of the early crust is unlikely to produce an excess of about 6% of the Sm/Nd ratio in terrestrial rock samples compared to chondrites for most simulations. Only Grand Tack simulations in which the last giant impact on Earth occurred later than 50 million years after the start of Solar System formation can account for such an offset. However, this time frame is consistent with current cosmochemical and dynamical estimates of the Moon forming impact (Chyba, 1991; Walker, 2009; Touboul et al.,2007, 2009, 2015; Pepin and Porcelli, 2006; Norman et al., 2003; Nyquist et al., 2006; Boyet et al.,2015). Such a late fractionation in the Sm/Nd ratio is unlikely to be responsible for a 20-ppm $^{142}$Nd excess in terrestrial rocks due to the half life of the radiogenic system. Additionally, such a large and late fractionation in the Sm/Nd ratio would accordingly induce non-observed anomalies in the $^{143}$Nd/$^{144}$Nd ratio. Considering our results, the Grand Tack model with a late Moon-forming impact cannot be easily reconciled with the Nd isotopic Earth contents.
Gravity inversion allows us to constrain the interior mass distribution of a planetary body using the observed shape, rotation, and gravity. Traditionally, techniques developed for gravity inversion can be divided into Monte Carlo methods, matrix inversion methods, and spectral methods. Here we employ both matrix inversion and Monte Carlo in order to explore the space of exact solutions, in a method which is particularly suited for arbitrary shape bodies. We expand the mass density function using orthogonal polynomials, and map the contribution of each term to the global gravitational field generated. This map is linear in the density terms, and can be pseudo-inverted in the under-determined regime using QR decomposition, to obtain a basis of the affine space of exact interior structure solutions. As the interior structure solutions are degenerate, assumptions have to be made in order to control their properties, and these assumptions can be transformed into scalar functions and used to explore the solutions space using Monte Carlo techniques. Sample applications show that the range of solutions tend to converge towards the nominal one as long as the generic assumptions made are correct, even in the presence of moderate noise. We present the underlying mathematical formalism and an analysis of how to impose specific features on the global solution, including uniform solutions, gradients, and layered models. Analytical formulas for the computation of the relevant quantities when the shape is represented using several common methods are included in the Appendix.
Molecular kinetic simulations are typically used to accurately describe the tenuous regions of the upper atmospheres on planetary bodies. These simulations track the motion of particles representing real atmospheric atoms and/or molecules subject to collisions, the objects gravity, and external influences. Because particles can end up in very large ballistic orbits, upper boundary conditions (UBC) are typically used to limit the domain size thereby reducing the time for the atmosphere to reach steady-state. In the absence of a clear altitude at which all molecules are removed, such as a Hill sphere, an often used condition is to choose an altitude at which collisions become infrequent so that particles on escape trajectories are removed. The remainder are then either specularly reflected back into the simulation domain or their ballistic trajectories are calculated analytically or explicitly tracked so they eventually re-enter the domain. Here we examine the effect of the choice of the UBC on the escape rate and the structure of the atmosphere near the nominal exobase in the convenient and frequently used 1D spherically symmetric approximation. Using Callisto as the example body, we show that the commonly used specular reflection UBC can lead to significant uncertainties when simulating a species with a lifetime comparable to or longer than a dynamical time scale, such as an overestimation of escape rates and an inflated exosphere. Therefore, although specular reflection is convenient, the molecular lifetimes and bodys dynamical time scales need to be considered even when implementing the convenient 1D spherically symmetric simulations in order to accurately estimate the escape rate and the density and temperature structure in the transition regime.
Aims: The secondary atmospheres of terrestrial planets form and evolve as a consequence of interaction with the interior over geological time. We aim to quantify the influence of planetary bulk composition on the interior--atmosphere evolution for Earth-sized terrestrial planets to aid in the interpretation of future observations of terrestrial exoplanet atmospheres. Methods: We used a geochemical model to determine the major-element composition of planetary interiors (MgO, FeO, and SiO2) following the crystallization of a magma ocean after planet formation, predicting a compositional profile of the interior as an initial condition for our long-term thermal evolution model. Our 1D evolution model predicts the pressure-temperature structure of the interior, which we used to evaluate near-surface melt production and subsequent volatile outgassing. Volatiles are exchanged between the interior and atmosphere according to mass conservation. Results: Based on stellar compositions reported in the Hypatia catalog, we predict that about half of rocky exoplanets have a mantle that convects as a single layer (whole-mantle convection), and the other half exhibit double-layered convection due to the presence of a mid-mantle compositional boundary. Double-layered convection is more likely for planets with high bulk planetary Fe-content and low Mg/Si-ratio. We find that planets with low Mg/Si-ratio tend to cool slowly because their mantle viscosity is high. Accordingly, low-Mg/Si planets also tend to lose volatiles swiftly through extensive melting. Moreover, the dynamic regime of the lithosphere (plate tectonics vs. stagnant lid) has a first-order influence on the thermal evolution and volatile cycling. These results suggest that the composition of terrestrial exoplanetary atmospheres can provide information on the dynamic regime of the lithosphere and the thermo-chemical evolution of the interior.
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