arXiv subjects

Joachim Stadel

Publications and source records attributed to Joachim Stadel.

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

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

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

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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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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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 ($γ\to 1$) 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

Mesh-free hydrodynamics in PKDGRAV3 for galaxy formation simulations

We extend the state-of-the-art N-body code PKDGRAV3 with the inclusion of mesh-free gas hydrodynamics for cosmological simulations. Two new hydrodynamic solvers have been implemented, the mesh-less finite volume and mesh-less finite mass methods. The solvers manifestly conserve mass, momentum and energy, and have been validated with a wide range of standard test simulations, including cosmological simulations. We also describe improvements to PKDGRAV3 that have been implemented for performing hydrodynamic simulations. These changes have been made with efficiency and modularity in mind, and provide a solid base for the implementation of the required modules for galaxy formation and evolution physics and future porting to GPUs. The code is released in a public repository, together with the documentation and all the test simulations presented in this work.

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arXiv2022

CosmoGridV1: a simulated $w$CDM theory prediction for map-level cosmological inference

We present CosmoGridV1: a large set of lightcone simulations for map-level cosmological inference with probes of large scale structure. It is designed for cosmological parameter measurement based on Stage-III photometric surveys with non-Gaussian statistics and machine learning. CosmoGridV1 spans the $w$CDM model by varying $Ω_m$, $σ_8$, $w_0$, $H_0$, $n_s$, $Ω_b$, and assumes three degenerate neutrinos with $\sum m_ν$ = 0.06 eV. This space is covered by 2500 grid points on a Sobol sequence. At each grid point, we run 7 simulations with PkdGrav3 and store 69 particle maps at nside=2048 up to $z$=3.5, as well as halo catalog snapshots. The fiducial cosmology has 200 independent simulations, along with their stencil derivatives. An important part of CosmoGridV1 is the benchmark set of 28 simulations, which include larger boxes, higher particle counts, and higher redshift resolution of shells. They allow for testing if new types of analyses are sensitive to choices made in CosmoGridV1. We add baryon feedback effects on the map level, using shell-based baryon correction model. The shells are used to create maps of weak gravitational lensing, intrinsic alignment, and galaxy clustering, using the UFalcon code. The main part of CosmoGridV1 are the raw particle count shells that can be used to create full-sky maps for a given $n(z)$. We also release projected maps for a Stage-III forecast, as well as maps used previously in KiDS-1000 deep learning constraints with CosmoGridV1. The data is available at www.cosmogrid.ai.

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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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arXiv2022

From EMBER to FIRE: predicting high resolution baryon fields from dark matter simulations with Deep Learning

Hydrodynamic simulations provide a powerful, but computationally expensive, approach to study the interplay of dark matter and baryons in cosmological structure formation. Here we introduce the EMulating Baryonic EnRichment (EMBER) Deep Learning framework to predict baryon fields based on dark-matter-only simulations thereby reducing computational cost. EMBER comprises two network architectures, U-Net and Wasserstein Generative Adversarial Networks (WGANs), to predict two-dimensional gas and HI densities from dark matter fields. We design the conditional WGANs as stochastic emulators, such that multiple target fields can be sampled from the same dark matter input. For training we combine cosmological volume and zoom-in hydrodynamical simulations from the Feedback in Realistic Environments (FIRE) project to represent a large range of scales. Our fiducial WGAN model reproduces the gas and HI power spectra within 10% accuracy down to ~10 kpc scales. Furthermore, we investigate the capability of EMBER to predict high resolution baryon fields from low resolution dark matter inputs through upsampling techniques. As a practical application, we use this methodology to emulate high-resolution HI maps for a dark matter simulation of a L=100 Mpc/h comoving cosmological box. The gas content of dark matter haloes and the HI column density distributions predicted by EMBER agree well with results of large volume cosmological simulations and abundance matching models. Our method provides a computationally efficient, stochastic emulator for augmenting dark matter only simulations with physically consistent maps of baryon fields.

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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

Parameter inference with non-linear galaxy clustering: accounting for theoretical uncertainties

We implement EuclidEmulator (version 1), an emulator for the non-linear correction of the matter power spectrum, into the MCMC forecasting code MontePython. We compare the performance of Halofit, HMCode, and EuclidEmulator1, both at the level of power spectrum prediction and at the level of posterior probability distributions of the cosmological parameters, for different cosmological models and different galaxy power spectrum wave number cut-offs. We confirm that the choice of the power spectrum predictor has a non-negligible effect on the computed sensitivities when doing cosmological parameter forecasting, even for a conservative wave number cut-off of $0.2\,h\,{\rm Mpc}^{-1}$. We find that EuclidEmulator1 is on average up to $17\%$ more sensitive to the cosmological parameters than the other two codes, with the most significant improvements being for the Hubble parameter of up to $42\%$ and the equation of state of dark energy of up to $26\%$, depending on the case. In addition, we point out that the choice of the power spectrum predictor contributes to the risk of computing a significantly biased mean cosmology when doing parameter estimations. For the four tested scenarios we find biases, averaged over the cosmological parameters, of between 0.5 and 2$σ$ (from below $1σ$ up to $6σ$ for individual parameters). This paper provides a proof of concept that this risk can be mitigated by taking a well-tailored theoretical uncertainty into account as this allows to reduce the bias by a factor of 2 to 5, depending on the case under consideration, while keeping posterior credibility contours small: the standard deviations are amplified by a factor of $\leq1.4$ in all cases.

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arXiv2021

The terrestrial planet formation paradox inferred from high-resolution N-body simulations

Recent improvements to GPU hardware and the symplectic N-body code GENGA allow for unprecedented resolution in simulations of planet formation. In this paper, we report results from high-resolution N-body simulations of terrestrial planet formation that are mostly direct continuation of our previous 10 Myr simulations (Woo et al. 2021a) until 150 Myr. By assuming that Jupiter and Saturn have always maintained their current eccentric orbits (EJS), we are able to achieve a reasonably good match to the current inner solar system architecture. However, due to the strong radial mixing that occurs in the EJS scenario, it has difficulties in explaining the known isotopic differences between bodies in the inner solar system, most notably between Earth and Mars. On the other hand, assuming initially circular orbits for Jupiter and Saturn (CJS) can reproduce the observed low degree of radial mixing in the inner solar system, while failing to reproduce the current architecture of the inner solar system. These outcomes suggest a possible paradox between dynamical structure and cosmochemical data for the terrestrial planets within the classical formation scenario.

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arXiv2021

Decaying Dark Matter: Simulations and Weak-Lensing Forecast

Despite evidence for the existence of dark matter (DM) from very high and low redshifts, a moderate amount of DM particle decay remains a valid possibility. This includes both models with very long-lived yet unstable particles or mixed scenarios where only a small fraction of dark matter is allowed to decay. In this paper, we investigate how DM particles decaying into radiation affect non-linear structure formation. We look at the power spectrum and its redshift evolution, varying both the decay lifetime ($τ$) and the fraction of decaying-to-total dark matter ($f$), and we propose a fitting function that reaches sub-percent precision below $k\sim10$ h/Mpc. Based on this fit, we perform a forecast analysis for a Euclid-like weak lensing (WL) survey, including both massive neutrino and baryonic feedback parameters. We find that with WL observations alone, it is possible to rule out decay lifetimes smaller than $τ=75$ Gyr (at 95 percent CL) for the case that all DM is unstable. This constraint improves to $τ=182$ Gyr if the WL data is combined with CMB priors from the Planck satellite and to $τ=275$ Gyr if we further assume baryonic feedback to be fully constrained by upcoming Sunyaev-Zeldovich or X-ray data. The latter shows a factor of 3.2 improvement compared to constraints from CMB data alone. Regarding the scenario of a strongly decaying sub-component of dark matter with $τ\sim 30$ Gyr or lower, it will be possible to rule out a decaying-to-total fraction of $f>0.49$, $f>0.21$, and $f>0.13$ (at the 95 percent CL) for the same three scenarios. We conclude that the upcoming stage-IV WL surveys will allow us to significantly improve current constraints on the stability of the dark matter sector.

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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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