arXiv subjects

Anders Johansen

Publications and source records attributed to Anders Johansen.

At least 37 records · Page 2Linked to original sources

arXiv2025

The influence of dust growth on the observational properties of circumplanetary discs

Dust growth is often indirectly inferred observationally in star-forming environments, theoretically predicted to produce mm-sized particles in circumstellar discs, and also presumably witnessed by the predecessors of the terrestrial meteoritic record. For those reasons it is believed that young gas giants under formation in protoplanetary discs with putative circumplanetary discs (CPDs) surrounding them, such as PDS 70c, should be containing mm-sized particles. We model the spectra of a set of CPDs, which we obtained from radiation hydrodynamic simulations at varying Rosseland opacities kappa_R. The kappa_R from the hydrodynamic simulations are matched with consistent opacity sets of ISM-like composition, but grown to larger sizes. Our high kappa_R hydro data nominally corresponds to 10 mum-sized particles, and our low kappa_R-cases correspond to mm-sized particles. We investigate the resulting broad spectral features at first while keeping the overall optical depth in the planetary envelope constant. Dust growth to size distributions dominated by millimeter particles generally results in broad, featureless spectra with black-body like slopes in the far-infrared, while size distributions dominated by small dust develop steeper slopes in the far-infrared and maintain some features stemming from individual minerals. We find that significant dust growth from microns to millimeters can explain the broad features of the PDS 70c data, when upscaling the dust masses from our simulations by x100. Furthermore our results indicate that the spectral range of 30-500 mum is an ideal hunting ground for broadband features arising from the CPD, but that longer wavelengths observed with ALMA can also be used for massive circumplanetary discs

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arXiv2025

The coexistence of the streaming instability and the vertical shear instability in protoplanetary disks: Scale-dependence of dust diffusion

The vertical shear instability and the streaming instability are two robust sources of turbulence in protoplanetary disks. The former has been found to induce anisotropic turbulence that is stronger in the vertical than in the radial dimension and to be overall stronger compared to the largely isotropic turbulence caused by the streaming instability. In this study, we shed light on the dust diffusion by the vertical shear instability and the streaming instability separately and together, and in particular on the direction- and scale-dependence of the diffusion. To this end, we employ two-dimensional global models of the two instabilities either in isolation or in combination. The vertical shear instability in isolation diffuses dust more strongly in the vertical direction than the streaming instability in isolation, resulting in a wave-shaped dust layer in our two-dimensional simulations. Compared with this large-scale diffusion, though, our study highlights that the vertical shear instability causes substantially weaker or even negligible small-scale diffusion. We validate this result using previously published three-dimensional simulations. In particular when simulating centimetre-sized dust, the undulating dust layer becomes internally razor-thin. In contrast, the diffusion owing to the streaming instability exhibits only a marginal scale-dependence, with the dust layer possessing a Gaussian shape. In models including both instabilities, the undulating mid-plane layer is broadened to a width set by the intrinsic diffusion level caused by the streaming instability.

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arXiv2025

The evolution of the flux-size relationship in protoplanetary discs by viscous evolution and radial pebble drift

In this paper we study the evolution of radiative fluxes, flux radii and observable dust masses in protoplanetary discs, in order to understand how these depend on the angular momentum budget and on the assumed heat sources. We use a model that includes the formation and viscous evolution of protoplanetary gas discs, together with the growth and radial drift of the dust component. We find that we are best able to match the observed fluxes and radii of class 0/I discs when we assume (i) an initial total angular momentum budget corresponding to a centrifugal radius of 40 au around solar-like stars, and (ii) inefficient viscous heating. Fluxes and radii of class II discs appear consistent with disc models with angular momentum budgets equivalent to centrifugal radii of both 40 au or 10 au for solar like stars, and with models where viscous heating occurs at either full efficiency or at reduced efficiency. During the first 0.5 Myr of their evolution discs are generally optically thick at a wavelength of 1.3 mm. However, after this discs are optically thin at mm-wavelengths, supporting standard means of dust mass estimates. Using a disc population synthesis model, we then show that the evolution of the cumulative evolution of the observable dust masses agrees well with that observed in young star forming clusters of different ages.

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arXiv2024

UV-processing of icy pebbles in the outer parts of VSI-turbulent disks

Icy dust particles emerge in star-forming clouds and are subsequently incorporated in protoplanetary disks, where they coagulate into larger pebbles up to mm in size. In the disk midplane, ices are shielded from UV radiation, but moderate levels of disk turbulence can lift small particles to the disk surface, where they can be altered, or destroyed. Nevertheless, studies of comets and meteorites generally find that ices at least partly retained their interstellar medium (ISM) composition before being accreted onto these minor bodies. Here we model this process through hydrodynamical simulations with VSI-driven turbulence in the outer protoplanetary disk. We use the PLUTO code in a 2.5 D global accretion setup and include Lagrangian dust particles of 0.1 and 1 mm sizes. In a post-processing step, we use the RADMC3D code to generate the local UV radiation field to assess the level of ice processing of pebbles. We find that a small fraction ($\sim$17$\%$) of 100 $μ$m size particles are frequently lifted up to $Z/R=0.2$ which can result in the loss of their pristine composition as their residence time in this layer allows for effective CO and water photodissociation. The larger 1 mm size particles remain UV-shielded in the disk midplane throughout the dynamical evolution of the disk. Our results indicate that the assembly of icy bodies via the accretion of drifting mm-size icy pebbles can explain the presence of pristine ice from the ISM, even in VSI-turbulent disks. Nevertheless, particles $\leq$ 100 $μ$m experience efficient UV processing and may mix with unaltered icy pebbles, resulting in a less ISM-like composition in the midplane.

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arXiv2024

Comment on "Did the terrestrial planets of the Solar System form by pebble accretion?"

Morbidelli, Kleine & Nimmo (2024) (MKN) recently published a critical analysis on whether the terrestrial planets in the Solar System formed by rapid pebble accretion or by the classical route of multiple giant impacts between planetary embryos after the dissipation of the protoplanetary disc. They arrive at the conclusion that the terrestrial planets did not form by pebble accretion. Although we welcome debate on this topic, we want to emphasize here several points that we disagree on. We will not address in detail every claim made in MKN, but rather stick to four main points. Our conclusion is that pebble accretion remains a viable mechanism to drive significant growth of protoplanets in the protoplanetary disc, with as much as 70% of Earth formed by pebble accretion. This rapid growth phase must nevertheless have been followed by an extended period of collisional growth after the end of the protoplanetary disc phase, likely culminating with the moon-forming giant impact. We emphasize here an important recent result from Olson & Sharp (2023), namely that significant growth by pebble accretion can be reconciled with the Hf-W decay system even for a canonical moon-forming giant impact with a Mars-mass protoplanet and a low equilibration efficiency - a more massive impactor, as proposed in Johansen et al. (2023), is not necessary. Given that terrestrial planet formation naturally involves both pebble accretion and a combination of small and large impactors, this challenges the very notion of making an either/or distinction between the classical collision model and the pebble accretion model.

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arXiv2024

Large Interferometer For Exoplanets (LIFE). XIV. Finding terrestrial protoplanets in the galactic neighborhood

The increased brightness temperature of young rocky protoplanets during their magma ocean epoch makes them potentially amenable to atmospheric characterization to distances from the solar system far greater than thermally equilibrated terrestrial exoplanets, offering observational opportunities for unique insights into the origin of secondary atmospheres and the near surface conditions of prebiotic environments. The Large Interferometer For Exoplanets (LIFE) mission will employ a space-based mid-infrared nulling interferometer to directly measure the thermal emission of terrestrial exoplanets. Here, we seek to assess the capabilities of various instrumental design choices of the LIFE mission concept for the detection of cooling protoplanets with transient high-temperature magma ocean atmospheres, in young stellar associations in particular. Using the LIFE mission instrument simulator (LIFEsim) we assess how specific instrumental parameters and design choices, such as wavelength coverage, aperture diameter, and photon throughput, facilitate or disadvantage the detection of protoplanets. We focus on the observational sensitivities of distance to the observed planetary system, protoplanet brightness temperature using a blackbody assumption, and orbital distance of the potential protoplanets around both G- and M-dwarf stars. Our simulations suggest that LIFE will be able to detect (S/N $\geq$ 7) hot protoplanets in young stellar associations up to distances of $\approx$100 pc from the solar system for reasonable integration times (up to $\sim$hours). Detection of an Earth-sized protoplanet orbiting a solar-sized host star at 1 AU requires less than 30 minutes of integration time. M-dwarfs generally need shorter integration times. The contribution from wavelength regions $<$6 $μ$m is important for decreasing the detection threshold and discriminating emission temperatures.

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arXiv2024

Thousands of planetesimals: Simulating the streaming Instability in very large computational domains

The streaming instability is a mechanism whereby pebble-sized particles in protoplanetary discs spontaneously come together in dense filaments, which collapse gravitationally to form planetesimals upon reaching the Roche density. The extent of the filaments along the orbital direction is nevertheless poorly characterised, due to a focus in the literature on small simulation domains where the behaviour of the streaming instability on large scales cannot be determined. We present here computer simulations of the streaming instability in boxes with side lengths up to 6.4 scale heights in the plane. This is 32 times larger than typically considered simulation domains and nearly a factor 1,000 times the volume. We show that the azimuthal extent of filaments in the non-linear state of the streaming instability is limited to approximately one gas scale height. The streaming instability will therefore not transform the pebble density field into axisymmetric rings; rather the non-linear state of the streaming instability appears as a complex structure of loosely connected filaments. Including the self-gravity of the pebbles, our simulations form up to 4,000 planetesimals. This allows us to probe the high-mass end of the initial mass function of planetesimals with much higher statistical confidence than previously. We find that this end is well-described by a steep exponential tapering. Since the resolution of our simulations is moderate -- a necessary trade-off given the large domains -- the mass distribution is incomplete at the low-mass end. When putting comparatively less weight on the numbers at low masses, at intermediate masses we nevertheless reproduce the power-law shape of the distribution established in previous studies.

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arXiv2024

Self-oxidation of the atmospheres of rocky planets with implications for the origin of life

Rocky planets may acquire a primordial atmosphere by outgassing of volatiles from their magma ocean. The distribution of O between H$_2$O, CO and CO$_2$ in chemical equilibrium subsequently changes significantly with decreasing temperature. We explore here two chemical models: one where CH$_4$ and NH$_3$ are assumed to be irrevocably destroyed by photolysis, and one where these molecules persist. In the first case, we show that CO cannot co-exist with H$_2$O, since CO oxidizes at low temperatures to form CO$_2$ and H$_2$. In both cases, H escapes from the thermosphere within a few ten million years by absorption of stellar XUV radiation. This escape drives an atmospheric self-oxidation process whereby rocky planet atmospheres become dominated by CO$_2$ and H$_2$O, regardless of their initial oxidation state at outgassing. HCN is considered a potential precursor of prebiotic compounds and RNA. Our oxidizing atmospheres are inefficient at producing HCN by lightning. Instead, we demonstrate that lightning-produced NO, which dissolves as nitrate in the oceans, and interplanetary dust particles may be the main sources of fixed nitrogen to emerging biospheres. Our results highlight the need for origin-of-life scenarios where the first metabolism fixes its C from CO$_2$, rather than from HCN and CO.

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arXiv2024

Evolution of gas envelopes and outgassed atmospheres of rocky planets formed via pebble accretion

We present here results of numerical simulations of the formation and early evolution of rocky planets through pebble accretion, with an with an emphasis on hydrogen envelope longevity and the composition of the outgassed atmosphere. We model planets with a range in mass from 0.1 to 5 Earth masses that orbit between 0.7 and 1.7 AU. The composition of the outgassed atmosphere is calculated with the partial pressure of free oxygen fit to geophysical models of magma ocean self-oxidation. XUV radiation powered photoevaporation is considered as the main driver of atmospheric escape. We model planets that remain below the pebble isolation mass and hence accrete tenuous envelopes only. We consider slow, medium or fast initial stellar rotation for the temporal evolution of the XUV flux. The loss of the envelope is a key event that allows the magma ocean to crystallise and outgas its bulk volatiles. The atmospheric composition of the majority of our simulated planets is dominated by CO$_2$. Our planets accrete a total of 11.6 Earth oceans of water, the majority of which enters the core. The hydrospheres of planets lighter than the Earth reach several times the mass of the Earth's modern oceans, while the hydrospheres of planets ranging from 1 to 3.5 Earth masses are comparable to those of our planet. However, planets of 4-5 Earth masses have smaller hydrospheres due to trapping of volatiles in their massive mantles. Overall, our simulations demonstrate that hydrogen envelopes are easily lost from rocky planets and that this envelope loss triggers the most primordial partitioning of volatiles between the solid mantle and the atmosphere.

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arXiv2024

Fast formation of large ice pebbles after FU Orionis outbursts

During their formation, nascent planetary systems are subject to FU Orionis outbursts that heat a substantial part of the disc. This causes water ice in the affected part of the disc to sublimate as the ice line moves outwards to several to tens of astronomical units. In this paper, we investigate how the subsequent cooling of the disc impacts the particle sizes. We calculate the resulting particle sizes in a disc model with cooling times between 100 and 1,000 years, corresponding to typical FU Orionis outbursts. As the disc cools and the ice line retreats inwards, water vapour forms icy mantles on existing silicate particles. This process is called heterogeneous nucleation. The nucleation rate per surface area of silicate substrate strongly depends on the degree of super-saturation of the water vapour in the gas. Fast cooling results in high super-saturation levels, high nucleation rates, and limited condensation growth because the main ice budget is spent in the nucleation. Slow cooling, on the other hand, leads to rare ice nucleation and efficient growth of ice-nucleated particles by subsequent condensation. We demonstrate that close to the quiescent ice line, pebbles with a size of about centimetres to decimetres form by this process. The largest of these are expected to undergo cracking collisions. However, their Stokes numbers still reach values that are high enough to potentially trigger planetesimal formation by the streaming instability if the background turbulence is weak. Stellar outbursts may thus promote planetesimal formation around the water ice line in protoplanetary discs.

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arXiv2024

How the presence of a giant planet affects the outcome of terrestrial planet formation simulations

The architecture and masses of planetary systems in the habitable zone could be strongly influenced by outer giant planets, if present. We investigate here the impact of outer giants on terrestrial planet formation, under the assumption that the final assembly of the planetary system is set by a giant impact phase. Utilizing a state-of-the-art N-body simulation software, GENGA, we interpret how the late stage of terrestrial planet formation results in diversity within planetary systems. We design two global model setups: in the first we place a gas giant on the outer side of planetesimals and embryos disk, while the other only has planetesimals and embryos but no giant. For the model including the outer giant, we study the effect of different giant initial masses, in the range 1.0-3.0 Jupiter mass, and orbital radii, in the range 2.0-5.8 AU.We also study the influence of different initial positions of planetesimals and embryos on the results. Our N-body simulation time is approximately 50 Myr. The results show that the existence of outer giant will promote the interaction between planetesimals and embryos, making the orbits of the formed terrestrial planets more compact, but placing the giant planet too close to the planetesimals and embryos disk suppresses the formation of massive rocky planets. In addition, under the classical theory, where planetary embryos and planetesimals collide to form terrestrial planets, our results show that the presence of a giant planet actually decreases the gap complexity of the inner planetary system.

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arXiv2024

Vapor equilibrium models of accreting rocky planets demonstrate direct core growth by pebble accretion

The gaseous envelope of an accreting rocky planet becomes hot enough to sublimate silicates and other refractory minerals. For this work, we studied the effect of the resulting envelope enrichment with a heavy vapor species on the composition and temperature of the envelope. For simplification, we used the gas-phase molecule SiO to represent the sublimation of silicate material. We solved the equilibrium structure equations in 1D for planets in the mass range of $0.1$ to $3\,M_\oplus$. The convective stability criterion was extended to take the stabilizing effect of the condensation of SiO clouds into account. We assumed that the envelope is both in hydrostatic equilibrium and in vapor equilibrium with the underlying magma ocean. This means that pebbles do not undergo sublimation in the envelope and therefore survive until they plunge into the magma ocean. We find that the emergence of an inner radiative region, where SiO condensation suppresses convection, increases the pressure and temperature in the inner envelope compared to pure H$_2$/He envelopes once $M_\mathrm{pl} \gtrsim 0.3\,M_\oplus$. For $M_\mathrm{pl}>0.75\,M_\oplus$, the temperature and pressure close to the surface reach the supercritical point of SiO. The amount of SiO stored in the envelope is lower than the total planet mass for low mass planets. However, for $M_\mathrm{pl}>2.0\,M_\oplus$, all accreted pebble material must contribute to maintain the vapor equilibrium in the envelope. Therefore, the non-vapor mass of the planet ceases to increase beyond this threshold. Overall, our vapor equilibrium model of the planetary envelope allows for direct core growth by pebble accretion up to much higher masses than previously thought.

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arXiv2024

Thermal processing of primordial pebbles in evolving protoplanetary disks

During protoplanetary disk formation, dust grains located in the outer disk retain their pristine icy composition, while solids in the inner stellar-heated disk undergo volatile loss. This process may have left a fossil record in Solar System material showing different nucelosynthetic imprints that have been attributed to different degrees of thermal processing. However, it remains unclear how a large mass fraction of thermally-processed inner-disk pebbles is produced and how these grains are subsequently transported throughout the disk. In this work we numerically investigate the evolution in time of a two-component pebble disk, consisting of pristine pebbles and those that underwent ice sublimation. We find that stellar outbursts exceeding 1000 times the solar luminosity are efficient in thermally altering, through ice sublimation, a large mass fraction of pebbles (around 80%). After the establishment of this initial radial dust composition gradient throughout the disk, the subsequent mixing and inward drift of pristine outer-disk pebbles alter the inner disk bulk composition from processed to more unprocessed in time. Therefore, if processed pebbles without ice mantles have an isotopic composition similar to ureilite meteorites from the inner Solar System, inner-disk minor bodies forming from the early pebble flux (<1Myr) will be isotopically ureilite-like, while later-formed bodies will be increasingly admixed with the signature of the late incoming CI chondrite-like unprocessed pebbles. This appears to be largely consistent with the trend seen between the accretion age of different meteoric classes and their different stable isotope composition anomalies (in $μ$54Cr, $μ$48Ca, $μ$30Si, $μ$58Ni), but further work may be needed to explain the role of isotopically anomalous refractory inclusions and anomaly trends in other elements.

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arXiv2024

Formation of wide-orbit giant planets in protoplanetary disks with a decreasing pebble flux

The presence of distant protoplanets may explain the observed gaps in the dust emission of protoplanetary disks. Here, we derive a novel analytical model to describe the temporal decay of the pebble flux through a protoplanetary disk as the result of radial drift. This has allowed us to investigate the growth and migration of distant protoplanets throughout the lifespan of the disk. We find that Moon-mass protoplanets that formed early on can grow to their pebble isolation mass, between approximately $20$ and $80\,M_{\oplus}$, within less than $1\,\mathrm{Myr,}$ in the $20$ to $80\,\mathrm{AU}$ region around solar-like stars. The subsequent fast migration in the early stages of gas accretion, after pebble accretion ends, transports these giant planets into their final orbits at $<\,$$10\,\mathrm{AU}$. However, our pebble decay model allows us to include a new pathway that may trigger the transition from pebble accretion to gas accretion after the pebble flux has decayed substantially. With this pebble decay pathway, we show that it is also possible to form gas giants beyond $10\,\mathrm{AU}$. The occurrence of these wide-orbit gas giants should be relatively low, since their core must attain sufficient mass to accrete gas before the pebble flux decays, while avoiding excessive migration. Since these gas giants do not reach the pebble isolation mass, their heavy element content is typically less than $10\,M_{\oplus}$. Our results imply that the observed gaps in protoplanetary disks could be caused by distant protoplanets that reached the pebble isolation mass and then migrated, while gas giants in wide orbits, such as PDS 70 b and c, accreted their gas after the decay in the pebble flux.

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arXiv2024

Formation of flattened planetesimals by gravitational collapse of rotating pebble clouds

Planetesimals are believed to form by the gravitational collapse of aerodynamically concentrated clumps of pebbles. Many properties of the objects in the cold classical Kuiper belt -- such as binarity, rotation, and size distribution -- are in agreement with this gravitational collapse model. Further support comes from the pebble-pile structure inferred for comet nuclei. For this study, we simulated the final assembly of a planetesimal from the gravitational collapse of a rotating clump of pebbles. We implemented a numerical method from granular dynamics to follow the collapse that includes the transition from a pebble swarm to solid cells at a high density. We compared the shapes of the simulated planetesimals with the shapes of the lobes of contact binaries and bilobed Solar System objects. We find that the gravitational collapse of slowly rotating pebble clouds naturally explains the formation of flattened ellipsoidal bodies. This result agrees well with the flattened structure of the bilobed planetesimal Arrokoth and the shapes of the components of bilobed comets.

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arXiv2023

Forming Giant Planets Around Late-M Dwarfs: Pebble Accretion and Planet-Planet Collision

We propose a pebble-driven core accretion scenario to explain the formation of giant planets around the late-M dwarfs of $M_{\star}{=}0.1{-}0.2 \ M_{\odot}$. In order to explore the optimal disk conditions for giant planet, we perform N-body simulations to investigate the growth and dynamical evolution of both single and multiple protoplanets in the disks with both inner viscously heated and outer stellar irradiated regions. The initial masses of the protoplanets are either assumed to be equal to $0.01 \ M_{\oplus}$ or calculated based on the formula derived from streaming instability simulations. Our findings indicate that massive planets are more likely to form in disks with longer lifetimes, higher solid masses, moderate to high levels of disk turbulence, and larger initial masses of protoplanets. In the single protoplanet growth cases, the highest planet core mass that can be reached is generally lower than the threshold necessary to trigger rapid gas accretion, which impedes the formation of giant planets. Nonetheless, in multi-protoplanet cases, the cores can exceed the pebble isolation mass barrier aided by frequent planet-planet collisions. This consequently speeds up their gas accretion and promotes giant planet formation, making the optimal parameter space to grow giant planets substantially wider. Taken together, our results suggest that even around very low-mass stellar hosts, the giant planets with orbital periods of ${\lesssim}100$ days are still likely to form when lunar-mass protoplanets first emerge from planetesimal accretion and then grow rapidly by a combination of pebble accretion and planet-planet collisions in disks with a high supply of pebble reservoir ${>}50 \ M_{\oplus}$ and turbulent level of $α_{\rm t} {\sim} 10^{-3}{-}10^{-2}$.

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arXiv2023

Planet formation throughout the Milky Way: Planet populations in the context of Galactic chemical evolution

As stellar compositions evolve over time in the Milky Way, so will the resulting planet populations. In order to place planet formation in the context of Galactic chemical evolution, we make use of a large ($N = 5\,325$) stellar sample representing the thin and thick discs, defined chemically, and the halo, and we simulate planet formation by pebble accretion around these stars. We build a chemical model of their protoplanetary discs, taking into account the relevant chemical transitions between vapour and refractory minerals, in order to track the resulting compositions of formed planets. We find that the masses of our synthetic planets increase on average with increasing stellar metallicity [Fe/H] and that giant planets and super-Earths are most common around thin-disc ($α$-poor) stars since these stars have an overall higher budget of solid particles. Giant planets are found to be very rare ($\lesssim$1\%) around thick-disc ($α$-rich) stars and nearly non-existent around halo stars. This indicates that the planet population is more diverse for more metal-rich stars in the thin disc. Water-rich planets are less common around low-metallicity stars since their low metallicity prohibits efficient growth beyond the water ice line. If we allow water to oxidise iron in the protoplanetary disc, this results in decreasing core mass fractions with increasing [Fe/H]. Excluding iron oxidation from our condensation model instead results in higher core mass fractions, in better agreement with the core-mass fraction of Earth, that increase with increasing [Fe/H]. Our work demonstrates how the Galactic chemical evolution and stellar parameters, such as stellar mass and chemical composition, can shape the resulting planet population.

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arXiv2023

Sublimation of refractory minerals in the gas envelopes of accreting rocky planets

Protoplanets growing within the protoplanetary disk by pebble accretion acquire hydrostatic gas envelopes. Due to accretion heating, the temperature in these envelopes can become high enough to sublimate refractory minerals which are the major components of the accreted pebbles. Here we study the sublimation of different mineral species and determine whether sublimation plays a role during the growth by pebble accretion. For each snapshot in the growth process, we calculate the envelope structure and sublimation temperature of a set of mineral species representing different levels of volatility. Sublimation lines are determined using and equilibrium scheme for the chemical reactions responsible for destruction and formation of the relevant minerals. We find that the envelope of the growing planet reaches temperatures high enough to sublimate all considered mineral species when the mass is larger than 0.4 Earth masses. The sublimation lines are located within the gravitionally bound envelope of the planet. We make a detailed analysis of the sublimation of FeS at around 720 K, beyond which the mineral is attacked by H2 to form gaseous H2S and solid Fe. We calculate the sulfur concentration in the planet under the assumption that all sulfur released as H2S is lost from the planet by diffusion back to the protoplanetary disk. Our calculated values are in good agreement with the slightly depleted sulfur abundance of Mars, while the model overpredicts the extensive sulfur depletion of Earth by a factor of approximately 2. We show that a collision with a sulfur-rich body akin to Mars in the moon-forming impact lifts the Earth's sulfur abundance to approximately 10% of the solar value for all impactor masses above 0.05 Earth masses.

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