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Simon L. Grimm

Publications and source records attributed to Simon L. Grimm.

At least 19 recordsLinked to original sources

Coupling dynamical accretion and chemical differentiation: A unified framework for the diversity of Earth and Mars

The physical and geochemical differences between Earth and Mars provide fundamental constraints on terrestrial planet formation, yet a self-consistent framework linking dynamical and chemical aspects remains elusive. Here we present an integrated modeling framework that couples high-resolution N-body simulations with impact-driven metal-silicate equilibration to track the dynamical accretion history and chemical differentiation for Earth and Mars. Using a narrow ring planetesimal accretion scenario, we show that Earth and Mars analogs naturally sample systematically different solid reservoirs within the protoplanetary disk. Earth analogs preferentially accrete reduced material around the planetesimal ring center, whereas Mars analogs acquire a larger fraction of oxidized material exterior to the ring. This leads to diverse bulk redox states, with composition further modified by impact-dependent pressure-temperature equilibration conditions during core formation. As a result, Earth analogs experience deeper equilibration and more efficient transfer of iron into the core, producing mantles with low iron oxide contents and larger core mass fractions. In contrast, Mars analogs equilibrate at shallower conditions, retain more iron in their mantles, and develop smaller cores. Our results demonstrate that the dynamical and geochemical differences between Earth and Mars emerge from the coupled effects of accretion pathways, the disk's radial redox structure, and impact-controlled differentiation rather than from any single process. Our unified framework physically explains the geochemical diversity of terrestrial planets and offers a potential pathway to interpret compositions of rocky planets in exoplanetary systems.

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Terrestrial planet formation in the era of GPU computing

In this chapter, we summarize the underlying numerical methods needed for efficient $N$-body integration of planetary systems. We discuss how symplectic integrators have been developed to tackle the complementary problems of long-term orbital integration and short-term collisional interactions. The public code GENGA, a parallel GPU/CPU planet formation and orbital dynamics simulation code, was developed to unify these methods and take full advantage of the newest available computing hardware. We present state-of-the-art N-body simulations performed with GENGA in a comparative study regarding the basic properties that emerge during the late stages of the terrestrial planet formation process. We show that in modern N-body simulations the commonly used acceleration factor f, used to speed up the collisional growth of planets in simulations, should be avoided since it can lead to distorted chemical composition of the planets. We make a detailed comparison of low to high-resolution simulations, showing that the formation time scale depends on the size of the initial planetesimals. These simulations also show that terrestrial planets can form resonant chains without the need of orbital migration due to gas effects.

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Coupled Thermal-Chemical Evolution Models of Sub-Neptunes Reveal Atmospheric Signatures of Their Formation Location

The observed masses and radii of sub-Neptunes are typically explained by the gas dwarf and the water world scenarios. While their evolutionary history on a population level has been proposed as a method to distinguish between these compositions, previous evolutionary models, neglected the crucial role of atmosphere-interior chemical interaction. We present a novel evolution framework for sub-Neptunes that combines the thermal evolution with the chemical coupling of the atmosphere and interior. Using this model, we examine how planets formed inside and outside the water-ice line can be observationally distinguished, with an emphasis on their atmospheric properties. Young sub-Neptunes store the majority of their volatile budget in the interior, regardless of formation location. Nevertheless, the atmospheric metallicity is a factor 4 higher for the planet formed outside the water-ice line. During cooling, hydrogen and oxygen exsolve from the interior, increasing the atmospheric mass fraction and counteracting the thermal contraction. Consequently, radius evolution alone cannot distinguish between the two formation scenarios. Instead, the primary discriminators are the abundance of carbon-bearing species and the resulting atmospheric C/O ratio. For sub-Neptunes formed beyond the water-ice line, nearly all carbon resides in the gaseous phase. We find that high molar fractions of CH$_4$ ($>10^{-2}$) and H$_2$O ($> 5\times10^{-2}$), and a high C/O ratio $(> 5\times10^{-1})$ are indicative of formation outside the water-ice line. In contrast, sub-Neptunes formed inside the water-ice line exhibit strongly suppressed CH$_4$ abundances, yielding C/O ratios ranging from $10^{-7}$ to $10^{-1}$.

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Water-rich sub-Neptunes and rocky super Earths around different Stars: Radii shaped by Volatile Partitioning, Formation, and Evolution

The nature of sub-Neptunes remains unknown due to degeneracies in interior structure solutions. However, a statistical set of small planets with measured masses and radii can be used to test the planet formation theory prediction of large water reservoirs on sub-Neptunes. Here, we investigate whether water is included in photoevaporative mass loss and how much can partition into the rocky and metallic interior. We couple the result of a planetary formation model to evolution models which assume perfect mixing of water with H/He in the envelope or a layered structure. For the mixed envelopes, we also include fractionation during photoevaporative mass-loss. Further, the effect of equilibrium dissolution of water into an assumed magma ocean and into the metallic core is studied for the first time in coupled formation-evolution models. Out of the four tested scenarios, the mass-radius relation of exoplanets is relatively well matched by all scenarios except the one with layered H/He above water. The agreement depends on mass, with better consistency for the model without dissolution below 3 Earth masses and hints of the opposite at higher masses. In contrast to the significant effect of water dissolution, fractionation is not found to alter the properties of the planets for our initial conditions due to initially massive envelopes on all planets. For all scenarios, we quantify the radius valley location and scaling with stellar mass and conclude that water-rich sub-Neptunes mass-radius relations are broadly consistent with observations. Statistical surveys in mass and radius are required for distinction of the scenarios. The dissolution of different volatiles into the planetary interior and solidification of the magma ocean are natural next steps toward a comprehensive treatment of atmosphere-interior interaction in planet evolution models. (abridged)

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Sub-Neptunes Are Drier Than They Seem: Rethinking the Origins of Water-Rich Worlds

Recent claims of biosignature gases in sub-Neptune atmospheres have renewed interest in water-rich sub-Neptunes with surface oceans, often referred to as Hycean planets. These planets are hypothesized to form beyond the snow line, accreting large amounts of H$_2$O (>10 wt%) before migrating inward. However, current interior models often neglect chemical equilibration between primordial atmospheres and molten interiors. Here, we compute global chemical equilibrium states for a synthetic population of sub-Neptunes with magma oceans. Although many initially accrete 5-30 wt% water, interior-atmosphere interactions destroy most of it, reducing final H$_2$O mass fractions to below 1.5 wt%. As a result, none meet the threshold for Hycean planets. Despite that, we find H$_2$O-dominated atmospheres exclusively on planets that accreted the least ice. These planets form inside the snow line, are depleted in carbon and hydrogen, and develop small envelopes with envelope mass fractions below 1%, dominated by endogenic water. In contrast, planets formed beyond the snow line accrete more volatiles, but their water is largely converted to H$_2$ gas or sequestered into the interior, resulting in low atmospheric H$_2$O mass fractions. Most H$_2$O-rich envelopes are also fully miscible with H$_2$, making a separate water layer unlikely. Our results topple the conventional link between ice accretion and water-rich atmospheres, showing instead that H$_2$O-dominated envelopes emerge through chemical equilibration in hydrogen-poor planets formed inside the snow line.

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Atmospheric C/O Ratios of Sub-Neptunes with Magma Oceans: Homemade rather than Inherited

Recently, the James Webb Space Telescope has enabled detailed spectroscopic characterization of sub-Neptune atmospheres. With detections of carbon- and oxygen-bearing species such as CO, CO$_2$, CH$_4$, and H$_2$O, a central question is whether the atmospheric C/O ratio, commonly used to trace formation location in giant planets, can serve a similar diagnostic role for sub-Neptunes. We use the global chemical equilibrium framework of Schlichting & Young (2022) to quantify how magma ocean-atmosphere interactions affect the atmospheric C/O ratio. We find that the resulting C/O ratios range from several orders of magnitude below solar to a few times solar. The atmospheric C/O ratio in sub-Neptunes is therefore not inherited from the protoplanetary disk, but instead emerges from chemical equilibrium between the atmosphere and the underlying magma ocean. Planetary mass, atmospheric mass fraction, and thermal state all strongly influence the atmospheric C/O ratio. In addition, carbon partitioning into the metal phase typically reduces the atmospheric C/O ratio substantially, particularly for atmospheric mass fractions less than a few percent. Finally, we couple the deep equilibrium compositions to 1D atmospheric models that self-consistently solve for the pressure-temperature structure and chemical composition, including photochemistry. We find that the C/O ratio varies with altitude under low vertical mixing conditions (K$_\text{zz}=10^4$ cm$^2$s$^{-1}$), but remains constant under strong mixing (K$_\text{zz}=10^7$ cm$^2$s$^{-1}$). Our results imply that observed C/O ratios of sub-Neptunes can be used to probe their interiors. Specifically, C/O ratios much lower than host star values would imply an underlying magma ocean with iron metal having sequestered significant amounts of carbon.

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Impact of oxygen fugacity on atmospheric structure and emission spectra of ultra hot rocky exoplanets

Atmospheres above lava-ocean planets (LOPs) hold clues as to the properties of their interiors, owing to the expectation that the two reservoirs are in chemical equilibrium. Here we consider `mineral' atmospheres produced in equilibrium with silicate liquids. We treat oxygen fugacity ($f$O$_2$) as an independent variable, together with temperature ($T$) and composition ($X$), to compute equilibrium partial pressures ($p$) of stable gas species at the liquid-gas interface. Above this boundary, the atmospheric speciation and the pressure-temperature structure are computed self-consistently to yield emission spectra. We explore a wide array of plausible compositions, oxygen fugacities (between 6 log$_{10}$ units below- and above the iron-wüstite buffer, IW) and irradiation temperatures (2000, 2500, 3000 and 3500 K) relevant to LOPs. We find that SiO(g), Fe(g) and Mg(g) are the major species below $\sim$IW, ceding to O$_2$(g) and O(g) in more oxidised atmospheres. The transition between the two regimes demarcates a minimum in total pressure ($P$). Because $p$ scales linearly with $X$, emission spectra are only modest functions of composition. By contrast, $f$O$_2$ can vary over orders of magnitude, thus causing commensurate changes in $p$. Reducing atmospheres show intense SiO emission, creating a temperature inversion in the upper atmosphere. Conversely, oxidised atmospheres have lower $p$SiO and lack thermal inversions, with resulting emission spectra that mimic that of a black body. Consequently, the intensity of SiO emission relative to the background, generated by MgO(g), can be used to quantify the $f$O$_2$ of the atmosphere. Depending on the emission spectroscopy metric of the target, deriving the $f$O$_2$ of known nearby LOPs is possible with a few secondary occultations observed by JWST.

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Time-resolved transmission spectroscopy of the ultra-hot Jupiter WASP-189 b

Ultra-hot Jupiters are tidally locked with their host stars dividing their atmospheres into a hot dayside and a colder nightside. As the planet moves through transit, different regions of the atmosphere rotate into view revealing different chemical regimes. High-resolution spectrographs can observe asymmetries and velocity shifts, and offer the possibility for time-resolved spectroscopy. In this study, we search for other atoms and molecules in the planet`s transmission spectrum and investigate asymmetric signals. We analyse and combine eight transits of the ultra-hot Jupiter WASP-189 b taken with the HARPS, HARPS-N, ESPRESSO and MAROON-X high-resolution spectrographs. Using the cross-correlation technique, we search for neutral and ionised atoms, and oxides and compare the obtained signals to model predictions. We report significant detections for H, Na, Mg, Ca, Ca+, Ti, Ti+, TiO, V, Cr, Mn, Fe, Fe+, Ni, Sr, Sr+, and Ba+. Of these, Sr, Sr+, and Ba+ are detected for the first time in the transmission spectrum of WASP-189 b. In addition, we robustly confirm the detection of titanium oxide based on observations with HARPS and HARPS-N using the follow-up observations performed with MAROON-X and ESPRESSO. By fitting the orbital traces of the detected species by means of time-resolved spectroscopy using a Bayesian framework, we infer posterior distributions for orbital parameters as well as lineshapes. Our results indicate that different species must originate from different regions of the atmosphere to be able to explain the observed time dependence of the signals. Throughout the course of the transit, most signal strengths are expected to increase due to the larger atmospheric scale height at the hotter trailing terminator. For some species, however, the signals are instead observed to weaken due to ionisation for atoms and their ions, or the dissociation of molecules on the dayside.

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The Mantis Network I: A standard grid of templates and masks for cross-correlation analyses of ultra-hot Jupiter transmission spectra

The atmospheres of ultra-hot Jupiters are highly interesting and unique chemical laboratories. Due to the very high atmospheric temperatures, their chemical composition is dominated by atoms and ions instead of molecules, and the formation of aerosols on their day-sides is unlikely. Thus, for these planets detailed chemical characterisations via the direct detection of elements through high-resolution day-side and transit spectroscopy are possible. This in principle allows the element abundances of these objects to be directly inferred, which may provide crucial constraints on their formation process and evolution history. In the recent past, several chemical species, mostly in the form of atoms and ions, have already been detected using high-resolution spectroscopy in combination with the cross-correlation technique. As part of the Mantis network, we provide a grid of standard templates in this study, designed to be used together with the cross-correlation method. This allows for the straightforward detection of chemical species in the atmospheres of hot extrasolar planets. In total, we calculate high-resolution templates for more than 140 different species across several atmospheric temperatures. In addition to the high-resolution templates, we also provide line masks that just include the position of line peaks and their absorption depths relative to the spectral continuum. A separate version of these line masks also takes potential blending effects with lines of other species into account. All templates and line masks are publicly available on the CDS data server.

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GENGA II: GPU planetary N-body simulations with non-Newtonian forces and high number of particles

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.

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3D radiative-transfer for exoplanet atmospheres. gCMCRT: a GPU accelerated MCRT code

Radiative-transfer (RT) is a key component for investigating atmospheres of planetary bodies. With the 3D nature of exoplanet atmospheres being important in giving rise to their observable properties, accurate and fast 3D methods are required to be developed to meet future multi-dimensional and temporal data sets. We develop an open source GPU RT code, gCMCRT, a Monte Carlo RT forward model for general use in planetary atmosphere RT problems. We aim to automate the post-processing pipeline, starting from direct global circulation model (GCM) output to synthetic spectra. We develop albedo, emission and transmission spectra modes for 3D and 1D input structures. We include capability to use correlated-k and high-resolution opacity tables, the latter of which can be Doppler shifted inside the model. We post-process results from several GCM groups including ExoRad, SPARC/MITgcm THOR, UK Met Office UM, Exo-FMS and the Rauscher model. Users can therefore take advantage of desktop and HPC GPU computing solutions. gCMCRT is well suited for post-processing large GCM model grids produced by members of the community and for high-resolution 3D investigations.

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The THOR+HELIOS general circulation model: multi-wavelength radiative transfer with accurate scattering by clouds/hazes

General circulation models (GCMs) provide context for interpreting multi-wavelength, multi-phase data of the atmospheres of tidally locked exoplanets. In the current study, the non-hydrostatic THOR GCM is coupled with the HELIOS radiative transfer solver for the first time, supported by an equilibrium chemistry solver (FastChem), opacity calculator (HELIOS-K) and Mie scattering code (LX-MIE). To accurately treat the scattering of radiation by medium-sized to large aerosols/condensates, improved two-stream radiative transfer is implemented within a GCM for the first time. Multiple scattering is implemented using a Thomas algorithm formulation of the two-stream flux solutions, which decreases the computational time by about 2 orders of magnitude compared to the iterative method used in past versions of HELIOS. As a case study, we present four GCMs of the hot Jupiter WASP-43b, where we compare the temperature, velocity, entropy, and streamfunction, as well as the synthetic spectra and phase curves, of runs using regular versus improved two-stream radiative transfer and isothermal versus non-isothermal layers. While the global climate is qualitatively robust, the synthetic spectra and phase curves are sensitive to these details. A THOR+HELIOS WASP-43b GCM (horizontal resolution of about 4 degrees on the sphere and with 40 radial points) with multi-wavelength radiative transfer (30 k-table bins) running for 3000 Earth days (864,000 time steps) takes about 19-26 days to complete depending on the type of GPU.

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An upper limit on late accretion and water delivery in the Trappist-1 exoplanet system

The Trappist-1 system contains seven roughly Earth-sized planets locked in a multi-resonant orbital configuration, which has enabled precise measurements of the planets' masses and constrained their compositions. Here we use the system's fragile orbital structure to place robust upper limits on the planets' bombardment histories. We use N-body simulations to show how perturbations from additional objects can break the multi-resonant configuration by either triggering dynamical instability or simply removing the planets from resonance. The planets cannot have interacted with more than ${\sim 5\%}$ of an Earth mass (${M_\oplus}$) in planetesimals -- or a single rogue planet more massive than Earth's Moon -- without disrupting their resonant orbital structure. This implies an upper limit of ${10^{-4}}$ to ${10^{-2} M_\oplus}$ of late accretion on each planet since the dispersal of the system's gaseous disk. This is comparable to or less than the late accretion on Earth after the Moon-forming impact, and demonstrates that the Trappist-1 planets' growth was complete in just a few million years, roughly an order of magnitude faster than Earth's. Our results imply that any large water reservoirs on the Trappist-1 planets must have been incorporated during their formation in the gaseous disk.

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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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Simulating gas giant exoplanet atmospheres with Exo-FMS: Comparing semi-grey, picket fence and correlated-k radiative-transfer schemes

Radiative-transfer (RT) is a fundamental part of modelling exoplanet atmospheres with general circulation models (GCMs). An accurate RT scheme is required for estimates of the atmospheric energy transport and for gaining physical insight from model spectra. We implement three RT schemes for Exo-FMS: semi-grey, non-grey `picket fence', and real gas with correlated-k. We benchmark the Exo-FMS GCM using these RT schemes to hot Jupiter simulation results from the literature. We perform a HD 209458b-like simulation with the three schemes and compare their results. These simulations are then post-processed to compare their observable differences. The semi-grey scheme results show qualitative agreement with previous studies in line with variations seen between GCM models. The real gas model reproduces well the temperature and dynamical structures from other studies. After post-processing our non-grey picket fence scheme compares very favourably with the real gas model, producing similar transmission spectra, emission spectra and phase curve behaviours. Exo-FMS is able to reliably reproduce the essential features of contemporary GCM models in the hot gas giant regime. Our results suggest the picket fence approach offers a simple way to improve upon RT realism beyond semi-grey schemes.

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An N-body population synthesis framework for the formation of moons around Jupiter-like planets

The moons of giant planets are believed to form in situ in Circumplanetary Discs (CPDs). Here we present an N-body population synthesis framework for satellite formation around a Jupiter-like planet, in which the dust-to-gas ratio, the accretion rate of solids from the Protoplanetary Disc, the number, and the initial positions of protosatellites were randomly chosen from realistic distributions. The disc properties were from 3D radiative simulations sampled in 1D and 2D grids and evolved semi-analytically with time. The N-body satellitesimals accreted mass from the dust component of the disc, interacted gravitationally with each other, experienced close-encounters, both scattering and colliding. With this improved modeling, we found that about $15\%$ of the resulting population is more massive than the Galilean one, and only $8.5\%$ were in resonances. The moons reach Europa's mass most frequently in $10^5$ years. In $10\%$ of the cases, moons are engulfed by the planet, and $1\%$ of the satellite-systems lose at least 1 Earth-mass into the planet, contributing to the giant planet's envelope's heavy element content. In $1\%$ of cases, we found eccentricities and inclinations of moons above 0.1. We examined the differences in outcome between the 1D and 2D disc models and used machine learning (Randomized Dependence Coefficient together with t-SNE) to compare our population with the Galilean system. Detecting our population around known transiting Jupiter-like planets via transits and TTVs would be challenging, but $14\%$ of the moons could be with an instrumental transit sensitivity of $10^{-5}$.

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HELIOS-K 2.0 Opacity Calculator and Open-source Opacity Database for Exoplanetary Atmospheres

Computing and using opacities is a key part of modeling and interpreting data of exoplanetary atmospheres. Since the underlying spectroscopic line lists are constantly expanding and currently include up to ~ 10^10 - 10^11 transition lines, the opacity calculator codes need to become more powerful. Here we present major upgrades to the HELIOS-K GPU-accelerated opacity calculator and describe the necessary steps to process large line lists within a reasonable amount of time. Besides performance improvements, we include more capabilities and present a toolbox for handling different atomic and molecular data sets: from downloading and pre-processing the data to performing the opacity calculations in a user-friendly way. HELIOS-K supports line lists from ExoMol, HITRAN, HITEMP, NIST, Kurucz and VALD3. By matching the resolution of 0.1 cm^-1 and cutting length of 25 cm^-1 used by the ExoCross code for timing performance (251 seconds excluding data read-in time), HELIOS-K can process the ExoMol BT2 water line list in 12.5 seconds. Using a resolution of 0.01 cm^-1, it takes 45 seconds - equivalent to about 10^7 lines per second. As a wavenumber resolution of 0.01 cm^-1 suffices for most exoplanetary atmosphere spectroscopic calculations, we adopt this resolution in calculating opacity functions for several hundred atomic and molecular species, and make them freely available on the open-access DACE database. For the opacity calculations of the database, we use a cutting length of 100 cm^-1 for molecules and no cutting length for atoms. Our opacities are available for downloading from https://dace.unige.ch/opacityDatabase and may be visualized using https://dace.unige.ch/opacity.

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Growing Mars fast: High-resolution GPU simulations of embryo formation

Recent high precision meteoritic data improve constraints on the formation timescale and bulk composition of the terrestrial planets. High resolution N-body simulations allow direct comparison of embryo growth timescale and accretion zones to these constraints. In this paper, we present results of high resolution simulations for embryo formation from a disc of up to 41,000 fully-self gravitating planetesimals with the GPU-based N-body code GENGA. Our results indicate that the growth of embryos are highly dependent on the initial conditions. More massive initial planetesimals, a shorter gas disc decay timescale and initially eccentric Jupiter and Saturn (EJS) all lead to faster growth of embryos. Asteroid belt material can thereby be implanted into the terrestrial planet region via sweeping secular resonances. This could possibly explain the rapid growth of Mars within 10 Myr inferred from its Hf-W chronology. The sweeping secular resonance almost completely clears the asteroid belt and deposits this material in the Mercury-Venus region, altering the composition of embryos there. This could result in embryos in the Mercury-Venus region accreting an unexpectedly high mass fraction from beyond 2 AU. Changing the initial orbits of Jupiter and Saturn to more circular (CJS) or assuming embryos formed in a gas free environment removes the sweeping secular resonance effect and thus greatly decreases material accreted from beyond 2 AU for Mercury-Venus region embryos. We therefore propose that rock samples from Mercury and Venus could aid greatly in deducing the condition and lifetime of the initial protoplanetary gas disc during planetesimal and embryo formation, as well as the initial architecture of the giant planets.

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