Papers by Christian Reinhardt
arXiv (Cornell University), Jul 12, 2023
In the leading theory of lunar formation, known as the giant impact hypothesis, a collision betwe... more In the leading theory of lunar formation, known as the giant impact hypothesis, a collision between two planet-size objects resulted in a young Earth surrounded by a circumplanetary debris disk from which the Moon later accreted. The range of giant impacts that could conceivably explain the Earth-Moon system is limited by the set of known physical and geochemical constraints. However, while several distinct Moon-forming impact scenarios have been proposed-from small, high-velocity impactors to low-velocity mergers between equal-mass objects-none of these scenarios have been successful at explaining the full set of known constraints, especially without invoking controversial post-impact processes. In order to bridge the gap between previous studies and provide a consistent survey of the Moon-forming impact parameter space, we present a systematic study of simulations of potential Moon-forming impacts. In the first paper of this series, we focus on pairwise impacts between non-rotating bodies. Notably, we show that such collisions require a minimum initial angular momentum budget of approximately 2 J EM in order to generate a sufficiently massive protolunar disk. We also show that low-velocity impacts (v ∞ ≲ 0.5 v esc) with high impactor-to-target mass ratios (γ → 1) are preferred to explain the Earth-Moon isotopic similarities. In a follow-up paper, we consider impacts between rotating bodies at various mutual orientations.
Protostars and Planets VI Posters, Jul 1, 2013
arXiv (Cornell University), May 28, 2021
The formation of Uranus' regular moons has been suggested to be linked to the origin of its enorm... more The formation of Uranus' regular moons has been suggested to be linked to the origin of its enormous spin axial tilt (~98 o). A giant impact between proto-Uranus and a 2-3 MEarth impactor could lead to a large tilt and to the formation of an impact generated disc, where prograde and circular satellites are accreted. The most intriguing features of the current regular Uranian satellite system is that it possesses a positive trend in the mass-distance distribution and likely also in the bulk density, implying that viscous spreading of the disc after the giant impact plays a crucial role in shaping the architecture of the final system. In this paper, we investigate the formation of Uranus' satellites by combining results of SPH simulations for the giant impact, a 1D semi-analytic disc model for viscous spreading of the post-impact disc, and N-body simulations for the assembly of satellites from a disc of moonlets. Assuming the condensed rock (i.e., silicate) remains small and available to stick onto the relatively rapid growing condensed water-ice, we find that the best case in reproducing the observed mass and bulk composition of Uranus' satellite system is a pure-rocky impactor with 3 MEarth colliding with the young Uranus with an impact parameter b = 0.75. Such an oblique collision could also naturally explain Uranus' large tilt and possibly, its low internal heat flux. The giant impact scenario can naturally explain the key features of Uranus and its regular moons. We therefore suggest that the Uranian satellite system formed as a result of an impact rather than from a circumplanetary disc. Our results also suggest that objects beyond the water snow-line could be dominated by rocky objects similar to Pluto and Triton. Future missions to Uranus and its satellite system would further constrain the properties of Uranus and its moons and provide further insight on their formation processes.
ANEOS material model for Gasoline and ballic
ANEOS material model for Gasoline and ballic
Monthly Notices of the Royal Astronomical Society, 2021
The origin of Uranus and Neptune remains a challenge for planet formation models. A potential exp... more The origin of Uranus and Neptune remains a challenge for planet formation models. A potential explanation is that the planets formed from a population of a few planetary embryos with masses of a few Earth masses which formed beyond Saturn’s orbit and migrated inwards. These embryos can collide and merge to form Uranus and Neptune. In this work, we revisit this formation scenario and study the outcomes of such collisions using 3D hydrodynamical simulations. We investigate under what conditions the perfect-merging assumption is appropriate, and infer the planets’ final masses, obliquities, and rotation periods, as well as the presence of proto-satellite discs. We find that the total bound mass and obliquities of the planets formed in our simulations generally agree with N-body simulations therefore validating the perfect-merging assumption. The inferred obliquities, however, are typically different from those of Uranus and Neptune, and can be roughly matched only in a few cases. In ad...
Monthly Notices of the Royal Astronomical Society
We investigate mantle stripping giant impacts (GI) between super-Earths with masses between 1 and... more We investigate mantle stripping giant impacts (GI) between super-Earths with masses between 1 and $20\, {\rm M}_{\oplus }$. We infer new scaling laws for the mass of the largest fragment and its iron mass fraction, as well as updated fitting coefficients for the critical specific impact energy for catastrophic disruption, $Q_{{\rm RD}}^{*}$. With these scaling laws, we derive equations that relate the impact conditions, i.e. target mass, impact velocity, and impactor-to-target mass ratio, to the mass and iron mass fraction of the largest fragment. This allows one to predict collision outcomes without performing a large suite of simulations. Using these equations we present the maximum and minimum planetary iron mass fraction as a result of collisional stripping of its mantle for a given range of impact conditions. We also infer the radius for a given mass and composition using interior structure models and compare our results to observations of metal-rich exoplanets. We find good ag...
Icarus, 2022
The formation of Uranus' regular moons has been suggested to be linked to the origin of its enorm... more The formation of Uranus' regular moons has been suggested to be linked to the origin of its enormous spin axial tilt (~98 o). A giant impact between proto-Uranus and a 2-3 MEarth impactor could lead to a large tilt and to the formation of a debris disc, where prograde and circular satellites are accreted. The most intriguing features of the current regular Uranian satellite system is that it possesses a positive trend in the mass-distance distribution and likely also in the bulk density, implying that viscous spreading of the debris disc after the giant impact plays a crucial role in shaping the architecture of the final system. In this paper, we investigate the formation of Uranus' satellites by combining results of SPH simulations for the giant impact, a 1D semi-analytic disc model for viscous spreading of the post-impact debris disc, and N-body simulations for the assembly of satellites from a disc of moonlets. Assuming the condensed rock (i.e., silicate) remains small and available to stick onto the relatively rapid growing condensed water-ice, we find that the best case in reproducing the observed mass and bulk composition of Uranus' satellite system is a pure-rocky impactor with 3 MEarth colliding with the young Uranus with an impact parameter b = 0.75. Such an oblique collision could also naturally explain Uranus' large tilt and possibly, its low internal heat flux. The giant impact scenario can naturally explain the key features of Uranus and its regular moons. We therefore suggest that the Uranian satellite system formed as a result of an impact rather than from a circumplanetary disc. Our results also suggest that objects beyond the water snow-line could be dominated by rocky objects similar to Pluto and Triton. Future missions to Uranus and its satellite system would further constrain the properties of Uranus and its moons and provide further insight on their formation processes.
Acta Geochimica, 2021
The Earth’s accretion process is accompanied by a large number of collisions. It is widely accept... more The Earth’s accretion process is accompanied by a large number of collisions. It is widely accepted that collisions dominate the Earth’s late accretion stage. Among all these collisions, there is a special type of collision called Core-merging giant impact (CMGI), in which much or most the impactor’s core merges directly with the proto-Earth’s core. This core-merging scenario plays an important role in the Earth’s accretion process and deeply affects the formation of the Earth’s core and mantle. However, because CMGI is a small probability event, it has not been fully studied. Here we use the SPH method to comprehensively study all possible CMGIs in the Earth’s accretion history. We find that CMGI only occurs in the initial conditions with small impact angle, small impact velocity and big impactor. We further discuss the implications of CMGI. We are confident that CMGI inevitably causes the chemical disequilibrium of the Earth's core and mantle. The CMGI process also brings many light elements into the Earth’s core. In particular, if the Moon-forming giant impact is a CMGI, then CMGI can also explain the abnormal content of HSEs in the Earth’s current mantle.
First public release, no licensing info
arXiv: Earth and Planetary Astrophysics, 2019
The Earths core formation process has decisive effect in the chemical differentiation between the... more The Earths core formation process has decisive effect in the chemical differentiation between the Earths core and its mantle. Here, we propose a new core formation model which is caused by a special giant impact. This model suggests that the impactors core can be kept intact by its own sticky mantle under appropriate impacting conditions and let it merge into the targets core without contact with the targets mantle. We call this special giant impact that caused the new core formation mode as glue ball impact model (GBI). By simulating hundreds of giant impacts with the sizes from planetesimals to planets, the conditions that can lead to GBI have been found out. If with small impact angle (i.e., less than 20 degree), small impact velocity and small impactors mass but larger than 0.07 Mearth, there is a good chance to produce a GBI at the final stage of the Earths accretion. We find that it will be much easier to have GBIs at the late stage of the Earths accretion rather than at the e...
Monthly Notices of the Royal Astronomical Society, 2021
We investigate how the choice of equation of state (EOS) and resolution conspire to affect the ou... more We investigate how the choice of equation of state (EOS) and resolution conspire to affect the outcomes of giant impact (GI) simulations. We focus on the simple case of equal-mass collisions of two Earth-like 0.5-M⊕ proto-planets showing that the choice of EOS has a profound impact on the outcome of such collisions as well as on the numerical convergence with resolution. In simulations where the Tillotson EOS is used, impacts generate an excess amount of vapour due to the lack of a thermodynamically consistent treatment of phase transitions and mixtures. In oblique collisions this enhances the artificial angular momentum (AM) transport from the planet to the circum-planetary disc reducing the planet’s rotation period over time. Even at a resolution of 1.3 × 106 particles, the result is not converged. In head-on collisions, the lack of a proper treatment of the solid/liquid-vapour phase transition allows the bound material to expand to very low densities, which, in turn, results in v...
Monthly Notices of the Royal Astronomical Society, 2019
Despite many similarities, there are significant observed differences between Uranus and Neptune:... more Despite many similarities, there are significant observed differences between Uranus and Neptune: While Uranus is tilted and has a regular set of satellites, suggesting their accretion from a disc, Neptune’s moons are irregular and are captured objects. In addition, Neptune seems to have an internal heat source, while Uranus is in equilibrium with solar insulation. Finally, structure models based on gravity data suggest that Uranus is more centrally condensed than Neptune. We perform a large suite of high-resolution SPH simulations to investigate whether these differences can be explained by giant impacts. For Uranus, we find that an oblique impact can tilt its spin axis and eject enough material to create a disc where the regular satellites are formed. Some of the discs are massive and extended enough, and consist of enough rocky material to explain the formation of Uranus’ regular satellites. For Neptune, we investigate whether a head-on collision could mix the interior, and lead ...
The Astrophysical Journal, 2019
ulating discussions. We acknowledge support from the Swiss National Science Foundation via the NC... more ulating discussions. We acknowledge support from the Swiss National Science Foundation via the NCCR PlanetS. Contributions H.D. conceived the idea of linking the moon formation impact to the Earth mantle heterogeneity and planned the project. C.R. built the equation of state (EOS) library and F.B. prepared the EOS lookup table. H.D. and C.R. incorporated the EOS library into the hydrodynamical code and prepared the initial conditions. H.D. ran the simulations and did the visualisation and interpretation. C.R., L.M., J.S. also helped in the interpretation. M.B. and M.M. contributed to the geodynamic and cosmochemistry argument, respectively. H.D., M.B. and M.M. prepared the manuscript. L.M. reviewed the manuscript and all authors commented on it.
The Astrophysical Journal, 2018
The origin of Mercury's high iron-to-rock ratio is still unknown. In this work we investigate Mer... more The origin of Mercury's high iron-to-rock ratio is still unknown. In this work we investigate Mercury's formation via giant impacts and consider the possibilities of a single giant impact, a hit-and-run, and multiple collisions, in one theoretical framework. We study the standard collision parameters (impact velocity, mass ratio, impact parameter), along with the impactor's composition and the cooling of the target. It is found that the impactor's composition affects the iron distribution within the planet and the final mass of the target by up to 25%, although the resulting mean iron fraction is similar. We suggest that an efficient giant impact has to be head-on at high velocity, while in the hit-and-run case the impact can occur closer to the most probable collision angle (45°). It is also shown that Mercury's current iron-to-rock ratio can be a result of multiple collisions, with their exact number depending on the collision parameters. Mass loss is found to be more significant when the collisions are close together in time.
The Astrophysical Journal, 2019
Giant impacts (GIs) are common in the late stage of planet formation. The Smoothed Particle Hydro... more Giant impacts (GIs) are common in the late stage of planet formation. The Smoothed Particle Hydrodynamics (SPH) method is widely used for simulating the outcome of such violent collisions, one prominent example being the formation of the Moon. However, a decade of numerical studies in various areas of computational astrophysics has shown that the standard formulation of SPH suffers from several shortcomings such as artificial surface tension and its tendency to promptly damp turbulent motions on scales much larger than the physical dissipation scale, both resulting in the suppression of mixing. In order to estimate how severe these limitations are when modeling GIs we carried out a comparison of simulations with identical initial conditions performed with the standard SPH as well as with the novel Lagrangian Meshless Finite Mass (MFM) method using the multi-method code, GIZMO (Hopkins 2015). We confirm the lack of mixing between the impactor and target when SPH is employed, while MFM is capable of driving vigorous subsonic turbulence and leads to significant mixing between the two bodies. Modern SPH variants with artificial conductivity, a different formulation of the hydro force or reduced artificial viscosity, do not improve mixing as significantly. Angular momentum is conserved similarly well in both methods, but MFM does not suffer from spurious transport induced by artificial viscosity, resulting in a slightly higher angular momentum of the protolunar disk. Furthermore, SPH initial conditions unphysically smooth the core-mantle boundary which is easily avoided in MFM.
Monthly Notices of the Royal Astronomical Society, 2017
In this paper, we present solutions to three short comings of smoothed particles hydrodynamics (S... more In this paper, we present solutions to three short comings of smoothed particles hydrodynamics (SPH) encountered in previous work when applying it to giant impacts. First we introduce a novel method to obtain accurate SPH representations of a planet's equilibrium initial conditions based on equal area tessellations of the sphere. This allows one to imprint an arbitrary density and internal energy profile with very low noise which substantially reduces computation because these models require no relaxation prior to use. As a consequence one can significantly increase the resolution and more flexibly change the initial bodies to explore larger parts of the impact parameter space in simulations. The second issue addressed is the proper treatment of the matter/vacuum boundary at a planet's surface with a modified SPH density estimator that properly calculates the density stabilizing the models and avoiding an artificially low-density atmosphere prior to impact. Further we present a novel SPH scheme that simultaneously conserves both energy and entropy for an arbitrary equation of state. This prevents loss of entropy during the simulation and further assures that the material does not evolve into unphysical states. Application of these modifications to impact simulations for different resolutions up to 6.4 × 10 6 particles show a general agreement with prior result. However, we observe resolution-dependent differences in the evolution and composition of post-collision ejecta. This strongly suggests that the use of more sophisticated equations of state also demands a large number of particles in such simulations.
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Papers by Christian Reinhardt