arXiv subjects

Christian Reinhardt

Publications and source records attributed to Christian Reinhardt.

At least 19 recordsLinked to original sources

arXiv2026

Three-dimensional SPH simulations of the Caloris basin-forming impact: basin scaling, the gravity anomaly, and antipodal effects

The Caloris basin is the largest well-preserved impact structure on Mercury, yet its formation conditions, the origin of its positive gravity anomaly, and its relation to the antipodal terrain remain poorly constrained. We present global, three-dimensional smoothed particle hydrodynamics simulations of the Caloris basin-forming impact with the pkdgrav3 code, including material strength. We survey 225 combinations of impactor radius, velocity, angle, and target thermal profile, complemented by simulations of up to two billion particles, which resolve the adopted 40 km crust by ten particle layers. At all resolutions, basin sizes are measured directly from the crust particles. The measured basin diameters follow a single power law in impactor radius, velocity, and angle, systematically steeper than idealized point-source crater scaling. The observed Caloris diameter is reproduced by a broad family of impactors favoring oblique incidence; sensitivity to resolution and crust thickness shifts this family toward smaller or slower impactors. All impactor material remaining in the basin region is vaporized, so our crust-like impactors leave no buried remnant. Instead, the impact thins the mantle and raises a local dome on Mercury's core. The dome's isolated gravity signal is positive and centered on the basin, supporting the mantle-uplift origin proposed for the observed mascon. At the antipode, single seismic pulses cannot loft surface material when strength is included, yet accumulated strain exceeds the elastic limit. A kilometer-scale equivalent thickness of impact-derived material then converges on this weakened surface. Ejecta convergence contributed at least as much as seismic shaking to forming the terrain.

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arXiv2026

A Formation-Stage Bottleneck for Exomoons around Close-in Rocky Planets

Massive moons around rocky exoplanets are expected outcomes of giant impacts, yet no exomoon has been securely confirmed. We address this problem using meshless finite-mass simulations of giant impacts between differentiated rocky planets that include stellar tidal and Coriolis forces in a local co-rotating frame for orbital periods of 1--300 days, and compare these simulations with otherwise identical collisions in isolation. We find that stellar perturbations impose a severe formation-stage bottleneck on moon-forming disks. Ultra-short-period impacts leave essentially no surviving circumplanetary disk, whereas 10-day systems retain only strongly depleted, radially truncated, and dynamically compact disks. High impact velocities, expected for close-in planets, are devastating for disk generation, while retrograde impacts can slightly compensate for disk mass depletion. These results show that stellar perturbations can suppress exomoon formation around close-in rocky planets, reshaping expectations for the demographics of exomoons.

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arXiv2026

A scaling relation for core heating by giant impacts and implications for dynamo onset

Accretional heating of Earth's interior during formation is pivotal to its subsequent thermal and chemical evolution. In particular, impact heating of Earth's core is expected, but its amplitude and radial distribution within the core is unknown and could influence the onset of the geodynamo. The uncertainty is due, in part, to the lack of constraints on the temperature of the interior following formation due to the difficulty of preserving a record of such a high energy environment, and the assertion that super-heating during formation would be rapidly lost through magma ocean cooling. Here we systematically investigate core heating due to giant impacts using a Smoothed Particle Hydrodynamics (SPH) code with simulations spanning a range of impact angles, velocities, and masses. From these simulations we derive a scaling relation for core heating that depends on the impact parameters and predicts the radial core temperature profile following the impact. Our findings show that a significant amount of heat is deposited into the core, with a canonical impact scenario resulting in an average core temperature increase of about 3000 K, approximately 500 K higher than that of the overlying mantle. In this case the heat distribution within the the core produces a strong thermal stratification. We use a parameterized cooling model to estimate that the core could have cooled to an adiabatic state 290 Myr after a canonical impact, which is consistent with the observed time span between the age of the Moon and evidence for an active geodynamo.

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arXiv2026

Recent advances in modelling of global-scale collisions using smoothed particle hydrodynamics

Impacts play a fundamental role in shaping the physical and chemical properties of the objects in our Solar System. Given the challenges in replicating such collisions through laboratory experiments, computer simulations are an important tool to investigate their outcomes. Accurately modelling material properties such as shear strength, porosity, and the formation of cracks is crucial for understanding impacts on small bodies like asteroids and comets. Very large and massive objects are dominated by self-gravity and can be approximated as a fluid. In this regime the equation of state used to model the behaviour of the constituent materials plays a key role. However, for bodies of several hundred kilometres, which are already spheroidal due to self-gravity, shear strength must still be considered. This impact regime is most challenging to model and therefore often overlooked in publications. In this review we present different impact regimes and the relevant physics that must be included. We then discuss their application to a variety of Solar System objects and assess how recent observations and numerical simulations, focussing on the Smoothed Particle Hydrodynamics method, can be used to inform our understanding of impact processes and solar system formation.

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arXiv2026

Giant Planet Formation by Disk Instability

The disk instability (DI) model for giant planet formation remains an attractive alternative in explaining the formation of giant planets at early times, giant planets at large radial distances, and giant planets orbiting M-stars. In this review, we present recent developments in the disk instability model including hydrodynamical as well as magneto-hydrodynamical (MHD) disk simulations, populations synthesis models, and simulations of clump-clump collisions. We also discuss advances in observations that can be used to constrain and test this formation scenario.

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arXiv2026

Smoothed Particle Hydrodynamics in pkdgrav3 for Shock Physics Simulations. II. Shear Strength

Material strength effects have been recently shown to be significant in giant impacts even at scales of planetary collisions. Despite this, their effects are often neglected in numerical giant impact simulations. We present an implementation of a basic strength model (pressure dependent shear strength) in the massively parallel smoothed particle hydrodynamics code pkdgrav3. The model includes elastic deviatoric stresses, plasticity with pressure-dependent yield strength, and thermal softening, and is fully integrated into the GPU-accelerated framework introduced in Paper I, preserving its scalability and performance characteristics. We validate the implementation against laboratory experiments of granular cliff collapse and our simulation results are in excellent agreement. We then determine the catastrophic disruption threshold, $Q_{RD}^*$, over a wide mass range of the colliding bodies using simulations performed both with and without material strength. Consistent with prior work, we find that strength substantially increases $Q_{RD}^*$ in the low-mass regime, while convergence toward the fluid limit occurs only near $R_{C1} \sim 10^7$ m ($\sim 0.7,M_\oplus$), well above the often assumed $\sim 100$ km size limit. Entropy production and remnant morphology likewise remain sensitive to rheology at intermediate masses. Performance measurements show that including strength introduces only modest computational overhead while maintaining favorable scaling, thereby enabling realistic solid mechanics in large-scale impact simulations.

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arXiv2025

Smoothed Particle Hydrodynamics in pkdgrav3 for Shock Physics Simulations. I. Hydrodynamics

We present pkdgrav3, a high-performance, fully parallel tree-SPH code designed for large-scale hydrodynamic simulations including self-gravity. Building upon the long development history of pkdgrav, the code combines an efficient hierarchical tree algorithm for gravity and neighbor finding with a modern implementation of Smoothed Particle Hydrodynamics (SPH) optimized for massively parallel hybrid CPU/GPU architectures. Its hybrid shared/distributed memory model, combined with an asynchronous communication scheme, allows pkdgrav3 to scale efficiently to thousands of CPU cores and GPUs. We validate the numerical accuracy of pkdgrav3 using a suite of standard tests, demonstrating excellent agreement with analytic or reference solutions. The code was already used in several peer-reviewed publications to model planetary-scale impacts, where SPH's Lagrangian nature allows accurate tracking of material origin and thermodynamic evolution. These examples highlight pkdgrav3's robustness and efficiency in simulating highly dynamical, self-gravitating systems. pkdgrav3 thus provides a powerful, flexible, and scalable platform for astrophysical and planetary applications, capable of exploiting the full potential of modern heterogeneous high-performance computing systems.

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arXiv2025

The possibility of a giant impact on Venus

Giant impacts were common in the early evolution of the Solar System, and it is possible that Venus also experienced an impact. A giant impact on Venus could have affected its rotation rate and possibly its thermal evolution. In this work, we explore a range of possible impacts using smoothed particle hydrodynamics (SPH). We consider the final major collision, assuming that differentiation already occurred and that Venus consists of an iron core (30% of Venus' mass) and a forsterite mantle (70% of Venus' mass). We use differentiated impactors with masses ranging from 0.01 to 0.1 Earth masses, impact velocities between 10 and 15 km/s, various impact geometries (head-on and oblique), different primordial thermal profiles, and a range of pre-impact rotation rates of Venus. We analyse the post-impact rotation periods and debris disc masses to identify scenarios that can reproduce Venus' present-day characteristics. Our findings show that a wide range of impact scenarios are consistent with Venus' current rotation. These include head-on collisions on a non-rotating Venus and oblique, hit-and-run impacts by Mars-sized bodies on a rotating Venus. Importantly, collisions that match Venus' present-day rotation rate typically produce minimal debris discs residing within Venus' synchronous orbit. This suggests that the material would likely reaccrete onto the planet, preventing the formation of long-lasting satellites - consistent with Venus' lack of a moon. We conclude that a giant impact can be consistent with both Venus' unusual rotation and lack of a moon, potentially setting the stage for its subsequent thermal evolution.

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arXiv2025

On the origin of Jupiter's fuzzy core: constraints from N-body, impact and evolution simulations

It has been suggested that Jupiter's fuzzy core could be a result of a giant impact. Here, we investigate the expected impact conditions from N-body simulations. We then use state-of-the-art SPH simulations to investigate the results of impacts with different conditions including various impactor masses and composition, different formation stages in Jupiter's growth, and different resolutions. We next simulate the long-term thermal evolution of Jupiter post-impact. We find that 3D N-body simulations predict rather oblique impacts, and that head-on collisions are rare. Moreover, our results show that even under a head-on collision, Jupiter's fuzzy core cannot be formed. We next simulated Jupiter's thermal evolution and showed that unless post-impact temperatures are extremely low, a giant impact would not lead to an extended dilute core as inferred by interior models. We conclude that Jupiter's fuzzy core is not caused by an impact and is likely to be an outcome of its formation process.

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arXiv2024

The Moon-forming Impact as a Constraint for the Inner Solar System's Formation

The solar system planets are benchmarks for the planet formation theory. Yet two paradigms coexist for the four terrestrial planets: the prolonged collisional growth among planetesimals lasting $>100$ million years (Myr) and the fast formation via planetesimals accreting pebbles within 10 Myr. Despite their dramatic difference, we can hardly tell which theory is more relevant to the true history of the terrestrial planets' formation. Here, we show that the Moon's origin puts stringent constraints on the pebble accretion scenario, rendering it less favourable. In the pebble accretion model, the one-off giant impact between proto-Earth and Theia rarely (probability $<$ 1\textperthousand) occurs at the right timing and configuration for the Moon formation. Even if a potential impact happens by chance, giant impact simulations reveal perfect mixing between proto-Earth and Theia, leaving no room for the observed primordial Earth mantle heterogeneity and the compositional difference, though small, between Earth and the Moon. Thus, the Earth-Moon system along other terrestrial planets should preferably form from chaotic collisional growth in the inner solar system.

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arXiv2024

The Outcome of Collisions between Gaseous Clumps formed by Disk Instability

The disk instability model is a promising pathway for giant planet formation in various conditions. At the moment, population synthesis models are used to investigate the outcomes of this theory, where a key ingredient of the disk population evolution are collisions of self-gravitating clumps formed by the disk instabilities. In this study, we explore the wide range of dynamics between the colliding clumps by performing state-of-the-art Smoothed Particle Hydrodynamics simulations with a hydrogen-helium mixture equation of state and investigate the parameter space of collisions between clumps of different ages, masses (1--10 Jupiter mass), various impact conditions (head-on to oblique collisions) and a range of relative velocities. We find that the perfect merger assumption used in population synthesis models is rarely satisfied and that the outcomes of most of the collisions lead to erosion, disruption or a hit-and-run. We also show that in some cases collisions can initiate the dynamical collapse of the clump. We conclude that population synthesis models should abandon the simplifying assumption of perfect merging. Relaxing this assumption will significantly affect the inferred population of planets resulting from the disk instability model.

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arXiv2024

A Systematic Survey of Moon-Forming Giant Impacts. II. Rotating bodies

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 one or more controversial post-impact processes. Allowing for pre-impact rotation of the colliding bodies has been suggested as an avenue which may produce more promising collision outcomes. However, to date, only limited studies of pre-impact rotation have been conducted. Therefore, in the second paper of this series, we focus on pairwise impacts between rotating bodies. Using non-rotating collisions as a baseline, we systematically study the effects of rotation on collision outcomes. We consider nine distinct rotation configurations and a range of rotation rates up to the rotational stability limit. Notably, we identify a population of collisions that can produce low post-impact angular momentum budgets and massive, iron-poor protolunar disks. Furthermore, even when pre-impact rotation is included, we demonstrate that the canonical Moon-forming impact can only generate sufficiently massive protolunar disks in the presence of excessive post-impact angular momentum budgets; this casts doubt on the canonical impact scenario.

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arXiv2023

A systematic survey of Moon-forming giant impacts: Non-rotating bodies

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 ($v_{\infty} \lesssim 0.5~v_{esc}$) with high impactor-to-target mass ratios ($\gamma \to 1$) are preferred to explain the Earth-Moon isotopic similarities. In a follow-up paper, we consider impacts between rotating bodies at various mutual orientations.

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arXiv2022

Forming Iron-rich Planets with Giant Impacts

We investigate mantle stripping giant impacts (GI) between super-Earths with masses between 1 M$_{\oplus}$ and 20 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, $Q_{RD}^{*}$. 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 agreement between the data and the simulated planets suggesting that GI could have played a key role in their formation. Furthermore, using our scaling laws we can further constrain the impact conditions that favour their masses and compositions. Finally, we present a flexible and easy-to-use tool that allows one to predict mass and composition of a planet after a GI for an arbitrary range of impact conditions which in turn allows to assess the role of GI in observed planetary systems.

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arXiv2021

Did Uranus' regular moons form via a rocky giant impactor?

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 M_Earth 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 M_Earth 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.

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arXiv2021

The EOS/Resolution Conspiracy: Convergence in Proto-Planetary Collision Simulations

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 $0.5\,M_\oplus$ 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 $1.3 \times 10^6$ 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 very slow numerical convergence of the critical specific impact energy for catastrophic disruption $Q_{RD}^*$ with increasing resolution as reported in prior work. The simulations where ANEOS is used for oblique impacts are already converged at a modest resolution of $10^5$ particles, while head-on collisions converge when they evidence the post-shock formation of a dense iron-rich ring, which promotes gravitational re-accumulation of material. Once sufficient resolution is reached to resolve the liquid-vapour phase transition of iron in the ANEOS case, and this ring is resolved, the value of $Q_{RD}^*$ has then converged.

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arXiv2020

Could Uranus and Neptune form by collisions of planetary embryos?

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 disks. 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 addition, we find that in most cases the planets formed in this scenario rotate faster than Uranus and Neptune, close to break-up speed, and have massive disks. We therefore conclude that forming Uranus and Neptune in this scenario is challenging, and further research is required. We suggest that future planet formation models should aim to explain the various physical properties of the planets such as their masses, compositions, obliquities, rotation rates and satellite systems.

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arXiv2019

Bifurcation in the history of Uranus and Neptune: the role of giant impacts

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 disk, 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 disk where the regular satellites are formed. Some of the disks 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 to an adiabatic temperature profile, which may explain its larger flux and higher moment of inertia value. We find that massive and dense projectiles can penetrate towards the centre and deposit mass and energy in the deep interior, leading to a less centrally concentrated interior for Neptune. We conclude that the dichotomy between the ice giants can be explained by violent impacts after their formation.

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