Multi-disciplinary perspective on late accretion processes: from impact processes to early differentiation
Multi-disciplinary perspective on late accretion processes: from impact processes to early differentiation
Late accretion onto the terrestrial planets is of critical importance for understanding the early chemical differentiation processes and the evolution of the terrestrial planets in the solar system. This session aims at obtaining an integrated understanding of these processes from a multidisciplinary perspective. The session aims at bringing together geodynamics, (isotope) geo- and cosmochemistry, experimental petrology, and numerical modeling with a particular focus on the Earth, Moon and Mars.
We welcome contributions from any of these disciplines, especially contributions aimed at improving our current understanding of key processes involved in the early evolution of the terrestrial planets including the provenance and composition of late accreted bodies, the role of giant impacts in volatile loss processes and core formation, the formation and evolution of magma oceans, early convection processes in planetary mantles, and the cooling history of terrestrial planets.
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Laetitia Allibert, Nicole Güldemeister, Lukas Manske, Miki Nakajima, and Kai Wünnemann
Planetary collisions play an important role in the compositional and thermal evolution of planetary systems and such collisions are caracteristics of the final stage of planetary formation. The Moon-forming impact event is thought to (re)set the conditions for the subsequent thermochemical evolution of Earth and Moon. Large parts of proto-Earth are thought to melt as a consequence of the impact [e.g.1] and the extent of melting affects the evolution of the Earth’s interior and atmosphere. It is then critical to address the initial conditions of the proto-Earth and the volume and shape of a possible magma ocean after the impact. Previously, the Moon-forming giant impact was modeled with mesh-free so-called smoothed particle hydrodynamics (SPH [1, 2, 3]). In this study, we, in contrast, carried out numerical simulations of the Moon-forming impact event considering different impact scenarios with the three-dimensional (3D) iSALE code [4, 5], that tends to be more accurate in the description of thermodynamics and shock waves than SPH simulations. We also compare simulation results from our iSALE code with SPH models for benchmarking () because SPH uses self-gravity, whereas iSALE uses central gravity. We vary the impact angle (15° to 90°) and impact velocities (12 to 20 km/s). In order to quantify the volume of impact-induced melt, we use the so-called peak-shock pressure approach (‘Tracer method’) that has been used in several modeling studies [6,7] and is described in more detail by .
The benchmark study shows a good agreement of the two different numerical approaches with respect to pressure evolution. However the production of a magma ocean show some differences that need to be further explored, with notably the effects of considering central gravity instead of self-gravity into iSALE 3D simulations.
Acknowledgments: We gratefully thank the iSALE developers, including Gareth Collins, Kai Wünnemann, Dirk Elbeshausen, Boris Ivanov and Jay Melosh and Thomas Davison for the development of the pysaleplot tool. We also thank the Deutsche Forschungsgemeinschaft (SFB-TRR 170, subproject C2 and C4) for funding.
References: Nakajima M. and Stevenson D. J. (2015) EPSL, 427, 286-295.  Canup R. M. et al. (2013) ICARUS 222, 200-219.  Canup R, M. (2004) Science 338, 1052-1054.  Collins G. S. et al. (2004) Meteoritics & Planet. Sci., 39, 217-231.  Wünnemann K. (2006) ICARUS 180, 514-527.  Wünnemann K. et al. (2008) EPSL 269, 529-538.  Pierazzo et al. (1997) ICARUS 127, 408-423.  Manske L. et al. (2018) 49th LPSC, abstract# 2269. Pierazzo and Melosh (1999) EPSL 165, 163-176
How to cite:
Allibert, L., Güldemeister, N., Manske, L., Nakajima, M., and Wünnemann, K.: Numerical modeling of the thermal state of Earth after the Moon-forming impact event , Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-613, https://doi.org/10.5194/epsc2021-613, 2021.
Randolph Röhlen, Kai Wünnemann, Laetitia Allibert, Lukas Manske, Christian Maas, and Ulrich Hansen
Introduction: The origin of the relatively high concentration of highly siderophile elements in Earth’s mantle  is still debated. One possible explanation is the addition of iron rich cores of differentiated impactors during the late accretion phase . Since Earth has most likely had a magma ocean during this period , a quantitative understanding of impacts into such targets is of pivotal interest. In particular the answer to the question whether the impactor core material breaks into droplets or remains mostly in one piece is key, since this greatly affects the metal-silicate equilibration and mixing in the magma ocean . This topic has been examined by several experimental as well as numerical studies [5,6,7]. The latter include mesh-free methods like smoothed particle hydrodynamics (SPH [8,9]), which may suffer from insufficient resolution, as well as grid based approaches. To expand on previous studies with such grid based algorithms , we implemented a method to improve the resolution and tracking of small material fragments in the simulation. This approach lays the groundwork for detailed studies of the size-frequency distribution of impactor cores in dependency to the impact parameters (core size, impact velocity and angle), as well as target properties (depth, temperature, and viscosity of the magma ocean). In a next step our results can then be used as input for further models studying material mixing in a convecting magma ocean .
Methods: We performed simulations of asteroid impacts using the iSALE-2D shock physics code [11,12], utilizing an Euler grid. By adding Lagrangian tracers at defined position at the start of the simulation, more detailed tracking of the material flow is possible. However, the exact fate of the material has to be reconstructed from these tracers in a post processing step, like in the stretching ratio model in . In addition, this approach neglects the fact that small fragments tend to be underresolved and, thus, their motion in the model may suffer from numerical artifacts.
To address these limitations, we developed a method to reduce numerical artifacts as well as improve the tracking of smaller material chunks in iSALE. To this end, we identify and analyze fragments of a chosen material type, in this case the material of the impactor core, in the whole numerical grid during each simulation step. Based on predefined criteria, for example looking at the shape of a fragment or the strain in its individual cells, we determine if each individual fragment is still sufficiently well resolved. If this is not the case, the fragment will be broken up or completely removed by replacing the impactor core material in its cells with that of the surrounding magma ocean matter. The removed mass and volume will be saved in the nearest tracer, which approximates the movement of the fragment based on the surrounding velocities. By effectively freezing mass and volume of a fragment in this way, artificial distortion caused by insufficient numerical resolution for such small fragments is prevented.
The setup of our simulations consists of a 200 km diameter dunite projectile with a 100 km iron core, impacting a dunite half space. The upper 900 km of this target behave purely hydrodynamically without strength or viscosity, approximating a magma ocean. The resolution is varied between 20 and 80 cells per projectile radius (cppr).
Results:Figure 1 shows a comparison between simulations with and without the new method for a cppr of 80 at different time steps. It shows the impactor core material (yellow) as well as the tracers used to save information in the method (red dots). The left side (negative x) of each image shows the results with the new method. It is clearly visible that, as impactor material penetrates deeper into the magma ocean, its core fragments into more and more pieces, the smallest of which are removed into tracers when using the method.
Discussion and Conclusion: The results obtained so far show that the impactor core breaks into many fragments during and after the impact, similar to observations in other studies . The current criteria, based on the concentration in individual cells and their neighbors, as well as on a simplified approximation of the fragment shape, are not entirely sufficient to find all cases in which numerical artifacts occur. To achieve this, physical parameters like the strain inside the fragments have to be considered as well. It is also important to note that the current use of tracers to save the mass and volume of small fragments means that these cannot fragment further and that their interaction with other matter is strongly simplified - tracers follow the velocity field of the surrounding material. Some additional interaction will need to be implemented to evaluate how valid this approximation is.
Acknowledgements: We gratefully acknowledge the developers of iSALE-2D, including Gareth Collins, Kai Wünnemann, Dirk Elbeshausen, Tom Davison, Boris Ivanov and Jay Melosh. This work was funded by the Deutsche Forschungsgemeinschaft (SFB-TRR170, subproject C2 and C4).
References:  Walker R. J. (2009) Chem. Erde-Geochem. 69, 101-125.  Wood B. J. et al. (2006) Nature 441, 825-833.  Tonks W. B. et al. (1993) J. Geophys. Res. 98, 5319-5333.  Rubie D. C. et al. (2003) Earth Planet Sc. Lett. 205, 239-255.  Daguen R. et al. (2014) Earth Planet Sc. Lett. 391, 274-287.  Landeau M. et al. (2016) Nat. Geosci. 9, 786-789.  Kendall J. D. et al. (2016) Earth Planet Sc. Lett. 448 24-33.  Marchi S. et al. (2020) Sci. Adv. 6(7) eaay2338.  Monaghan J.J. (1992) Annu. Rev. Astron. Astrophys. 30, 543-574.  Maas C. et al. (2021) Earth Planet Sc. Lett. 554.  Collins. G. S. et al. (2004) Meteorics & Planet. Sci. 39, 217-231.  Wünnemann K. et al. (2006) Icarus 180, 514-527.
How to cite:
Röhlen, R., Wünnemann, K., Allibert, L., Manske, L., Maas, C., and Hansen, U.: Core Fragmentation of Differentiated Bodies Upon Impacts Into Magma Oceans – Insights From Numerical Modelling, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-639, https://doi.org/10.5194/epsc2021-639, 2021.
Tim Lichtenberg, Robert J. Graham, Ryan Boukrouche, and Raymond T. Pierrehumbert
The earliest atmospheres of rocky planets originate from extensive volatile release during magma ocean epochs that occur during assembly of the planet. These establish the initial distribution of the major volatile elements between different chemical reservoirs that subsequently evolve via geological cycles. Current theoretical techniques are limited in exploring the anticipated range of compositional and thermal scenarios of early planetary evolution. However, these are of prime importance to aid astronomical inferences on the environmental context and geological history of extrasolar planets. In order to advance the potential synergies between exoplanet observations and inferrences on the earliest history and climate state of the solar system terrestial planets, I will present a novel numerical framework that links an evolutionary, vertically-resolved model of the planetary silicate mantle with a radiative-convective model of the atmosphere. Numerical simulations using this framework illustrate the sensitive dependence of mantle crystallization and atmosphere build-up on volatile speciation and predict variations in atmospheric spectra with planet composition that may be detectable with future observations of exoplanets. Magma ocean thermal sequences fall into three general classes of primary atmospheric volatile with increasing cooling timescale: CO, N2, and O2 with minimal effect on heat flux, H2O, CO2, and CH4 with intermediate influence, and H2 with several orders of magnitude increase in solidification time and atmosphere vertical stratification. In addition to these time-resolved results, I will present a novel formulation and application of a multi-species moist-adiabat for condensable-rich magma ocean and archean earth analog atmospheres, and outline how the cooling of such atmospheres can lead to exotic climate states that provide testable predictions for terrestrial exoplanets.
How to cite:
Lichtenberg, T., Graham, R. J., Boukrouche, R., and Pierrehumbert, R. T.: Coupled models of magma oceans and their primordial atmospheres: volatile speciation, cooling history, and impact of condensables, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-133, https://doi.org/10.5194/epsc2021-133, 2021.
Thomas Ruedas, Kai Wünnemann, and John Lee Grenfell
We constructed a system of parameterized or semi-analytical representations of impact-related processes such as crater formation, atmospheric erosion, and melt production due to the direct effects of the impact as well as the long-term thermal effects triggered in the mantle by very large impacts in order to model how impactors of different types and a large range of sizes affect the CO2-H2O atmosphere and the interior of a terrestrial planet similar to Mars, Venus, or the early Earth. Mass fluxes of carbon dioxide and water between the impactor/outer space, the atmosphere, and the interior of the target planet are calculated in order to assess under which conditions atmospheres and interiors are depleted or enriched by processes related to impacts, melting/magmatism on different time scales, or weathering.
The impactor flux onto a planetary target is a stochastic process in terms of time, magnitude and location, which we describe with a size-frequency distribution of impactors and a cratering chronology. The temporal aspect, in combination with the complexities of the various effects of a single impact, cause the evolution to depend on its own history. In the absence of unique information about the impact sequence of a target, the evolution should therefore not be uniquely determined by cratering statistics, and the possible paths are expected to vary within a certain range. Thus, we aim to deduce a range of evolutionary paths for the volatile content of the atmosphere and, within limits, of the interior.
We consider rocky S-type and icy-rocky C-type asteroids as well as comets, covering a range of impactor-target density contrasts from about 1/6 to about 4/5 as well as a range of (absolute) impact velocities from a little less than 10 to almost 65 km/s. Impactor size ranges from 1 m to half the planetary radius. Atmospheric (surface) densities cover almost five orders of magnitude, ranging from a few millibars (modern Mars) to 95 bar (modern Venus).
With regard to atmospheric effects, there is a fundamental distinction to be made between blast-producing and crater-forming impacts; the boundary that separates these two regimes is mostly defined by the deceleration of the impactor and its resistance to breakup under the ram pressure during its traversal of the atmosphere. The direct effects of the former leave the interior essentially unaffected and interact only with the atmosphere. We use the formalism by Svetsov (2007) to assess the bulk mass transfer and balance resulting from mechanical erosion of the atmosphere and the disintegration of the impactor and estimate the balance for the individual volatiles from estimates of the impactor composition. In crater-forming impacts, there are additional effects that need to be included. Ejecta can contribute to the mechanical erosion of the atmosphere (e.g., Shuvalov et al., 2014) and also produce layers of porous material with a large, reactive surface that can absorb CO2 from the atmosphere by weathering in the long-term aftermath of an impact. Moreover, they produce a crater that opens up the interior to mass exchange with the atmosphere. A key process in this context is the production of impact melt, which can serve as a vehicle for volatiles between the atmosphere and the interior by either releasing or removing (by dissolution) CO2 and water, depending mostly on the pressure conditions at the interface; generally outgassing is expected to be more common, but still these two volatiles may behave quite differently. We find that CO2 is expelled from the melt much more easily than water and will therefore enter the atmosphere under all conditions considered, whereas water may be retained in the melt at high atmospheric pressures. In addition to these common effects, very large impacts cause perturbations at sublithospheric depths and implant local thermal anomalies into the mantle that subsequently turn into upwellings and can cause longer-term magmatism and the local degassing from the deep interior.
How to cite:
Ruedas, T., Wünnemann, K., and Grenfell, J. L.: Temporal evolution of impact-atmosphere-interior interactions in terrestrial planets, Europlanet Science Congress 2021, online, 13–24 Sep 2021, EPSC2021-496, https://doi.org/10.5194/epsc2021-496, 2021.
Irene Bernt, Ana-Catalina Plesa, Sabrina Schwinger, Max Collinet, and Doris Breuer
During the early stages of lunar evolution, the large amount of heat available from the lunar forming impact led to extensive melting of the Moon’s silicate mantle giving rise to a magma ocean. The fractional crystallization of the latter resulted in an inhomogeneous mantle with cumulate layers of increasing density towards the surface, due to iron enrichment in the residual magma ocean . Such an unstable density distribution is prone to overturn and sets the stage for the subsequent thermo-chemical history of the mantle. In particular, this initial stage can significantly affect mixing of mantle material and the partial melt production, as well as the melt composition during the later stages of lunar evolution. The melt composition is directly linked to the composition of lunar basalts, whose variability at the lunar surface indicates complex melting processes and the presence of various mantle reservoirs.
In this study we model the solid-state convection, mixing and partial melt production in the lunar mantle. We investigate the effects of an initially layered mantle as a consequence of the fractional crystallization of the lunar magma ocean. To this end, we combine geodynamical models using the mantle convection code GAIA with petrological calculations that provide information about the composition and structure at the end of lunar magma ocean (LMO) solidification.
While previous mantle convection studies investigated lunar mantle melting in a purely homogeneous mantle  or with a localized KREEP layer [3,4], here we combine petrological and geodynamical models to investigate the degree of heterogeneity that can be produced by melting and mixing an initially heterogeneous lunar mantle.
The petrological model computes the crystallization sequence of the LMO. For the calculations in the deeper part of the mantle we use FOXMTR, for the shallower part alphaMELTS, as this approach is in good agreement with experimental data for the whole solidification process. We assume fractional crystallization of a spherical shell with an initial thickness of 1350 km, and a bulk lunar mantle composition from .
During crystallization the temperature is lowered stepwise and all minerals (except plagioclase) are assumed to accumulate at the bottom of the LMO and equilibrate with the melt at the respective pressure conditions. Plagioclase is assumed to float to the surface and form anothoritic crust.
The resulting mantle structure is characterized by 5 compositional layers, where the predominant minerals are olivine, orthopyroxene, clinopyroxene, clinopyroxene and ilmenite (ilmenite bearing cumulates = IBC) and plagioclase (crust), respectively. For each of those layers an average density is calculated from the density profile after crystallization, as well as the change in density as a function of depletion. The solidus and liquidus temperature profiles are calculated for the average layer compositions using alphaMELTS.
The depths and densities of the compositional layers, the initial temperature profile, the solidus and liquidus profiles for each layer and the density-depletion functions of each layer composition are provided in the form of read-out tables.
The results from the petrological model are shown in figure 1. The densities of the mantle layers increase with radius due to the enrichment of iron in the melt during crystallization. The crust has a comparative low density (figure 1a).
The temperature profile follows the crystallization temperatures of the cumulates. In figure 1b the temperature profile is shown together with the individual layers and their corresponding solidi and liquidi. From olivine to IBC the solidus and liquidus temperatures decrease because of the crystallization sequence (figure 1b).
We use the mantle convection code GAIA  in a 2D quarter cylinder geometry to model the thermochemical evolution of the compositionally heterogeneous lunar mantle. The nondimensional conservation equations of mass, momentum, thermal energy, and composition are solved under the extended Boussinesq approximation. We use an Arrhenius law to calculate the temperature- and depth-dependent viscosity.
To track the composition of the mantle we use a particle-in-cell (PIC) method , where tracer particles carry information about material properties such as density, melting temperature, degree of depletion, amount of heat producing elements etc. Our models use between 35 to 50 particles per cell that are advected at each time step according to the velocity field.
In our simulations we account for core cooling and radioactive decay, as well as mechanical mixing. In addition, we consider the effects of melting by accounting for the latent heat during mantle melting, as well as solidus and density increase/decrease due to mantle depletion . During melting, low melting point components are extracted from the mantle as the melt rises to the surface to form the basaltic crust. This leads to an increase of the solidus temperature requiring a higher temperature to further melt the residual mantle material. Gradual changes in density and solidus temperatures are extracted from the precomputed read-out tables of the petrological modelling.
Summary and Outlook
Our coupled petrological-geodynamical model of mantle convection and melt production will be used to investigate the thermochemical evolution of an initially heterogeneous lunar mantle structure (figure 2). Preliminary results show a smaller amount of melt produced in a heterogeneous mantle in comparison to a homogeneous one. We will present the distribution of the compositional layers as a function of time and compare the amount of melting produced from each individual component.
With this approach we aim to provide a link between melting processes in the interior of the Moon and the compositional diversity of basalts observed at the lunar surface. This in turn will help us to put constraints on the LMO crystallization and the subsequent thermochemical history of the Moon.