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.
Numerical aspects of giant impact simulations Reinhardt, Christian; Stadel, Joachim
Monthly notices of the Royal Astronomical Society,
06/2017, Letnik:
467, Številka:
4
Journal Article
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Abstract
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 × 106 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.
ABSTRACT
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 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.
We describe an open source GPU implementation of a hybrid symplectic N-body integrator, GENGA (Gravitational ENcounters with Gpu Acceleration), designed to integrate planet and planetesimal dynamics ...in the late stage of planet formation and stability analyses of planetary systems. GENGA uses a hybrid symplectic integrator to handle close encounters with very good energy conservation, which is essential in long-term planetary system integration. We extended the second-order hybrid integration scheme to higher orders. The GENGA code supports three simulation modes: integration of up to 2048 massive bodies, integration with up to a million test particles, or parallel integration of a large number of individual planetary systems. We compare the results of GENGA to Mercury and pkdgrav2 in terms of energy conservation and performance and find that the energy conservation of GENGA is comparable to Mercury and around two orders of magnitude better than pkdgrav2. GENGA runs up to 30 times faster than Mercury and up to 8 times faster than pkdgrav2. GENGA is written in CUDA C and runs on all NVIDIA GPUs with a computing capability of at least 2.0.
Abstract
We present a new power spectrum emulator named EuclidEmulator that estimates the nonlinear correction to the linear dark matter power spectrum depending on the six cosmological parameters ...ωb, ωm, ns, h, $w$0, and σ8. It is constructed using the uncertainty quantification software UQLab using a spectral decomposition method called polynomial chaos expansion. All steps in its construction have been tested and optimized: the large high-resolution N-body simulations carried out with PKDGRAV3 were validated using a simulation from the Euclid Flagship campaign and demonstrated to have converged up to wavenumbers $k\approx 5\, h\, {\rm Mpc}^{-1}$ for redshifts $z$ ≤ 5. The emulator is based on 100 input cosmologies simulated in boxes of (1250 Mpc/h)3 using 20483 particles. We show that by creating mock emulators it is possible to successfully predict and optimize the performance of the final emulator prior to performing any N-body simulations. The absolute accuracy of the final nonlinear power spectrum is as good as one obtained with N-body simulations, conservatively, ${\sim } 1$ per cent for $k\lesssim 1\, h\, {\rm Mpc}^{-1}$ and $z$ ≲ 1. This enables efficient forward modelling in the nonlinear regime, allowing for estimation of cosmological parameters using Markov Chain Monte Carlo methods. EuclidEmulator has been compared to HALOFIT, CosmicEmu, and NGenHalofit, and shown to be more accurate than these other approaches. This work paves a new way for optimal construction of future emulators that also consider other cosmological observables, use higher resolution input simulations, and investigate higher dimensional cosmological parameter spaces.
Forming iron-rich planets with giant impacts Reinhardt, Christian; Meier, Thomas; Stadel, Joachim G ...
Monthly notices of the Royal Astronomical Society,
10/2022, Letnik:
517, Številka:
3
Journal Article
Recenzirano
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ABSTRACT
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 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.
Abstract
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 nonrotating 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.
Abstract
We present recent updates and improvements of the graphical processing unit (GPU)
N
-body code GENGA. Modern state-of-the-art simulations of planet formation require the use of a very high ...number of particles to accurately resolve planetary growth and to quantify the effect of dynamical friction. At present the practical upper limit is in the range of 30,000–60,000 fully interactive particles; possibly a little more on the latest GPU devices. While the original hybrid symplectic integration method has difficulties to scale up to these numbers, we have improved the integration method by (i) introducing higher level changeover functions and (ii) code improvements to better use the most recent GPU hardware efficiently for such large simulations. We added treatments of non-Newtonian forces such as general relativity, tidal interaction, rotational deformation, the Yarkovsky effect, and Poynting–Robertson drag, as well as a new model to treat virtual collisions of small bodies in the solar system. We added new tools to GENGA, such as semi-active test particles that feel more massive bodies but not each other, a more accurate collision handling and a real-time openGL visualization. We present example simulations, including a 1.5 billion year terrestrial planet formation simulation that initially started with 65,536 particles, a 3.5 billion year simulation without gas giants starting with 32,768 particles, the evolution of asteroid fragments in the solar system, and the planetesimal accretion of a growing Jupiter simulation. GENGA runs on modern NVIDIA and AMD GPUs.
We present results from a suite of
N-body simulations that follow the formation and accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially ...place 2000 equal size planetesimals between 0.5 and 4.0 AU and the collisional growth is followed until the completion of planetary accretion (>100
Myr). A total of 64 simulations were carried out to explore sensitivity to the key parameters and initial conditions. All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk–planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We vary the initial total mass and spatial distribution of the planetesimals, the time scale of dissipation of nebular gas (which dissipates uniformly in space and exponentially in time), and orbits of Jupiter and Saturn. We end up with 1–5 planets in the terrestrial region. In order to maintain sufficient mass in this region in the presence of Type I migration, the time scale of gas dissipation needs to be 1–2
Myr. The final configurations and collisional histories strongly depend on the orbital eccentricity of Jupiter. If today’s eccentricity of Jupiter is used, then most of bodies in the asteroidal region are swept up within the terrestrial region owing to the inward migration of the secular resonance, and giant impacts between protoplanets occur most commonly around 10
Myr. If the orbital eccentricity of Jupiter is close to zero, as suggested in the Nice model, the effect of the secular resonance is negligible and a large amount of mass stays for a long period of time in the asteroidal region. With a circular orbit for Jupiter, giant impacts usually occur around 100
Myr, consistent with the accretion time scale indicated from isotope records. However, we inevitably have an Earth size planet at around 2 AU in this case. It is very difficult to obtain spatially concentrated terrestrial planets together with very late giant impacts, as long as we include all the above effects of gas and assume initial disks similar to the minimum mass solar nebular.
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