As Earth and Mars grew in the young solar system, heat stripped some elements from the material falling onto their surfaces, leaving behind a chemical record of how the planets were assembled. A new modeling study argues that record is consistent with both worlds having grown through a mixture of pebble accretion and collisions between larger planetary building blocks, rather than through a single growth process.
Earth and Mars are both depleted in moderately volatile lithophile elements, or elements that are relatively easy to vaporize but tend to remain in a planet’s rocky mantle rather than entering its core. The depletion follows the elements’ volatility, with the less easily vaporized rock-forming elements generally remaining more abundant than elements that evaporate at lower temperatures.
That pattern has several possible explanations. Material could have condensed incompletely in a hot early solar nebula. Early planetesimals could have been heated and partially evaporated by radioactive decay or collisions. Or growing protoplanets could have lost volatile material during giant impacts.
The new study examines another part of that picture: what happens to volatile elements when small, pebble-sized solids fall into the atmosphere surrounding a growing rocky planet.
The researchers modeled the thermal processing of those pebbles and combined it with the contribution expected from larger, early-formed planetesimals. They then compared the resulting compositions with measurements of bulk silicate Earth and bulk silicate Mars.
The aim was not to choose between pebble accretion and collisional growth as competing explanations. Instead, the researchers tested whether the observed elemental depletion could be used to determine how much each process contributed to the two planets.
Pebbles do not simply fall intact onto a growing planet
The model follows a protoplanet as it grows through pebble accretion. At first, the surrounding gas envelope is relatively cool, but as the protoplanet grows and accretes material, its envelope becomes hot enough for progressively less refractory elements to sublimate from incoming pebbles.
The calculations used pressure-dependent sublimation temperatures for a set of lithophile elements spanning a broad range of volatility. The modeled elements included Al, Ti, Ca, Cr, Mg, Si, Li, Mn, Na, K, F, Zn and In.
The thermal structure of the envelope produces an important separation between moderately volatile and more refractory elements. Moderately volatile elements such as Li and Mn are expected to sublimate before incoming pebbles reach the deepest, hottest region. The model assumes that these vaporized elements can be carried back into the surrounding protoplanetary disk by the envelope’s recycling flow.
More refractory elements, including Mg and Si, behave differently in the model. Once an inner radiative zone forms, refractory material that sublimates deeper in the envelope is protected from being efficiently carried away.
That distinction produces a sharp transition in the modeled volatile-depletion pattern. The researchers adopted about 1,400 kelvin as a characteristic temperature separating moderately volatile elements that can be lost from more refractory material that is retained.
The study cautions, however, that this treatment does not fully capture an earlier stage of growth in which moderately refractory elements such as Mg, Si and Cr could potentially experience some sublimative loss before the protective radiative zone develops.
Three-dimensional simulations tested whether vapor can escape
The volatile-loss model was also tested with three-dimensional hydrodynamical simulations of a convective protoplanetary envelope.
The simulations used the Athena++ code and represented vapor released from pebbles as passive tracer particles carried by the gas. Particles that crossed a specified recycling boundary were removed to represent material escaping back into the protoplanetary disk.
With the recycling boundary placed at twice the Bondi radius, about 30% of the tracer material remained in the envelope after one year and no more than about 3% remained after five years. The simulations gave a diffusion timescale of roughly one year.
The authors also tested a recycling boundary closer to the Bondi radius, which they describe as more realistic based on previous simulations. Under that assumption, the diffusion timescale falls to roughly 0.1 to 1 year.
The simulations therefore support rapid removal of volatile material from the outer convective envelope. The study also notes that the same efficient escape applies to material that recondenses into grains small enough to remain coupled to the gas. Even under an extreme assumption in which vapor recondenses onto larger, sedimenting particles, the authors argue that repeated sublimation and recondensation would favor eventual transfer to much smaller grains that can be carried outward.
Earth’s composition points to a pebble-grown core of the planet
For Earth, the researchers modeled three main components.
The first was a proto-Earth that grew through pebble accretion. The second was a giant impactor that also grew through pebble accretion. The third was a population of early-formed planetesimals with a volatile-depletion pattern modeled on material from Vesta.
The Vesta-like component was important because meteorites from Vesta show strong depletion of elements with sublimation temperatures below about 1,200 kelvin. The researchers used that composition as a representative model for early planetesimals that had already lost some volatile elements before being incorporated into Earth.
They fitted these components to 13 lithophile elements using both reduced-chi-squared minimization and Bayesian inference.
The reference three-component model produced a reduced chi-squared value of 3.3. Its inferred mass fractions were 64% for the pebble-grown proto-Earth, 14% for Vesta-like planetesimals and 22% for the pebble-grown impactor, with the uncertainties reported by the Bayesian analysis.
The corresponding Bayesian evidence was ln Z = 6.09 ± 0.05.
An important result is that the model does not require the Vesta-like planetesimal component to make up a large fraction of Earth. The combined pebble-grown proto-Earth and impactor account for more than 75% of the inferred mass in the reference scenario, while the Vesta-like material contributes up to about 25%.
The data also allow a simpler model containing only the pebble-grown proto-Earth and impactor. Its Bayesian evidence is statistically comparable to the reference three-component model, with Δln Z = 0.07 ± 0.06 relative to the three-component reference.
But the addition of Vesta-like material improves the fit to particular parts of the elemental pattern. The authors specifically point to lithium, whose abundance is elevated in Earth relative to the two-component pebble-grown model.
Alternative sources of Earth’s volatile depletion were tested
The researchers tested whether Earth could instead have received a larger contribution from volatile-rich, CI-like planetesimals.
A model containing only CI-like planetesimals and a Vesta-like planetesimal component performed poorly, with Δln Z = −11.31 ± 0.07 relative to the reference. Adding one or both pebble-grown components improved the result, but those models remained substantially disfavored relative to the reference model.
The inferred contribution of a CI-like planetesimal population was no more than about 10% of Earth’s mass within the reported 1-sigma uncertainty in those tests.
The researchers also varied the number of giant impactors. A model with two impactors was not strongly distinguished from the reference model by Bayesian evidence. In that case, the secondary impactor had an inferred mass of 0.04 +0.08/−0.03 Earth masses and the posterior distribution favored the lower end of that range.
A three-impactor model was disfavored, with Δln Z = −1.77 ± 0.07. The inferred mass of a possible third impactor was only 0.01 +0.02/−0.01 Earth masses.
For the favored one-impact and two-impact scenarios, the inferred impactor contribution spans a broad range. The paper reports 8% to 43% of an Earth mass within 1-sigma uncertainty.
The researchers also asked whether the pebbles arriving at Earth might already have been depleted in volatile elements before they entered the protoplanet’s atmosphere. They modeled several degrees of pre-depletion relative to H chondrites.
Increasing the assumed pre-depletion made the reduced chi-squared value worse. The Bayesian evidence, however, did not decisively rule out pre-depleted pebbles, with the difference in logarithmic evidence remaining at roughly |Δln Z| ≲ 1 for the tested cases.
The authors therefore do not exclude a contribution from pre-depleted pebbles, particularly during the later growth of proto-Earth beyond about 0.15 Earth masses, when the model indicates that moderately volatile elements would already be lost during accretion.
Mars carries a different balance of ingredients
Mars produced a different inferred mixture.
The reference Mars model combines a pebble-grown Mars component with Vesta-like planetesimals. The Bayesian analysis gives 27 ± 5% of Mars’s mass from pebble accretion and 73 ± 5% from the Vesta-like planetesimal population.
The model has a reduced chi-squared value of 1.2 and a Bayesian evidence of ln Z = 4.23 ± 0.05.
The contrast with Earth is therefore substantial within the models tested. Earth is reproduced primarily by pebble-grown components, supplemented by a smaller amount of Vesta-like material. Mars is reproduced primarily by early-formed planetesimals, with a smaller but still significant pebble-grown component.
The researchers again tested a CI-like planetesimal population. A model consisting of CI-like and Vesta-like planetesimals was strongly disfavored, with Δln Z = −4.11 ± 0.06. Adding the pebble-grown component improved the fit, but the resulting model remained substantially disfavored because of its additional complexity.
The inferred CI-like contribution remained below 10% of Mars’s mass, at 0.03 +0.04/−0.02 Mars masses.
Pre-depleted pebbles could increase the inferred pebble contribution to Mars by about 10%, but the resulting models produced poorer fits to Mars’s volatile-depletion pattern.
Mars may contain an unidentified volatile-depleted component
The researchers then relaxed an important assumption: that all of Mars’s early planetesimals had exactly the volatile-depletion pattern observed in Vesta.
They allowed the temperature at which the planetesimal depletion curve turns over to vary. A reduced-chi-squared search identified a region with relatively good fits when the inflection temperature was roughly 1,100 to 1,400 kelvin and the planetesimal contribution was about 60% to 80%.
A Bayesian analysis gave one alternative solution with an inflection temperature of 1,363 +43/−52 kelvin and a planetesimal fraction of 68 ± 5%.
That result would correspond to a population of planetesimals more depleted in moderately volatile elements than Vesta. The study does not identify such a population as an observed type of meteorite parent body. Instead, it treats it as a hypothetical possibility.
The researchers also allowed both the inflection temperature and the steepness of the depletion curve to vary. Over the tested range, the highest-evidence solution had an inflection temperature of 1,273 +70/−65 kelvin and a steepness parameter of 227 +78/−75 kelvin.
In that model, the hypothetical mixture of volatile-depleted planetesimals contributed 79 +11/−9% of Mars’s mass, leaving 21 +9/−11% for pebble accretion.
Across the Mars models tested, the authors found that the planetesimal contribution remained above about 65%, while the pebble contribution remained at least 10% within 1-sigma uncertainty.
Some of the chemistry remains outside the model
The researchers emphasize several qualifications to the interpretation.
Their Earth model assumes that the giant impact did not itself remove moderately volatile lithophile elements. Impact-driven devolatilization depends on impact speed and the mass of the target, and the authors note that the behavior of material lost during impacts in the gas-rich disk remains poorly understood.
The model also does not precisely describe the temporary period before an inner radiative zone forms, when even moderately refractory elements could potentially be lost from incoming pebbles.
The treatment of chromium, manganese and zinc also requires correction because these elements may have some tendency to partition into the core rather than simply recording volatility. The analysis accounts for those effects and tests the sensitivity of the results to excluding the elements.
Chlorine, bromine and iodine were not included in the quantitative model fits. Their measured abundances in CI chondrites have been revised in one study, but those revisions have been questioned because of limited sampling and disagreement with earlier measurements. The researchers therefore show both sets of estimates but exclude the heavy halogens from their model fitting.
The authors also tested alternative descriptions of the Vesta-like depletion pattern, including an exponential model and a case without fitting the Vesta meteorite data. These tests were part of their effort to determine whether the inferred accretion mixtures depended strongly on the specific mathematical representation of volatile depletion.
The model also constrains sulfur
The study extends the composition analysis beyond the lithophile elements used to infer the accretion histories.
Moderately volatile siderophile elements can behave differently because they may be preserved in the cores of early planetesimals. The researchers focus on sulfur, which is a candidate light element in the cores of both Earth and Mars.
Using an approximate CI-normalized sulfur abundance of about 0.1 to 1 for the iron-meteorite parent bodies represented by the Vesta-like planetesimal component, they estimate protosolar-normalized sulfur abundances of 0.10 to 0.23 for bulk Earth and 0.19 to 0.85 for bulk Mars.
These estimates come from the best solutions of the reference hybrid-accretion models rather than from a direct measurement of sulfur in the planets’ bulk interiors.
The paper also notes that the Vesta-like planetesimals could contain sulfur-rich cores, meaning that volatile depletion measured in the rocky material does not necessarily describe the entire volatile inventory of an early planetesimal.
The same elemental pattern can encode different growth histories
The central result of the modeling is therefore not simply that Earth and Mars are volatile-poor. It is that their particular patterns of volatile depletion can be reproduced by mixtures of different planetary building blocks that experienced different thermal histories.
For Earth, the reference model is dominated by two pebble-grown bodies, a proto-Earth and an impactor, with a smaller contribution from Vesta-like planetesimals. For Mars, the reference model reverses that balance, with most of the mass supplied by Vesta-like planetesimals and about one-quarter supplied by pebble accretion.
The researchers interpret this as evidence for hybrid accretion, in which pebble accretion and collisional assembly both contribute to the growth of terrestrial planets.
They further suggest that Earth’s relatively larger inferred pebble contribution could reflect a higher pebble accretion rate, while Mars’s slower pebble growth may have been related to gravitational stirring of its orbit by other, more massive protoplanets. That proposed explanation is presented as a possibility rather than a demonstrated cause.
The authors note that their Earth model is also compatible with a separate three-component formation model proposed to explain Earth’s relatively low excess of tungsten-182 in its mantle. In that model, about 20% of Earth comes from planetesimals and 80% from two pebble-grown protoplanets. The comparison is presented as consistency between independent lines of modeling rather than as a direct test of the tungsten model.
The study also discusses continuing uncertainty over whether Earth and Mars incorporated material from inner and outer regions of the solar system. Isotopic evidence has been interpreted in different ways, and the authors describe those interpretations as still debated. Their volatile-depletion analysis provides a separate composition-based constraint on possible formation pathways.
The resulting picture is one in which the volatile inventory of a growing rocky planet depends not only on what material it accretes, but also on when and how that material passes through the hot environment around the growing planet. Pebbles can lose moderately volatile elements during accretion, while early-formed planetesimals can carry a different depletion pattern produced before they were incorporated into a larger planet.
The authors finally discuss volatile delivery in the context of rocky planets more generally. In their model, volatile-rich pebbles can contribute before a growing planet becomes hot enough to strip the relevant elements, while impacts and primitive planetesimals can provide additional material later. They suggest that the same type of volatile-loss process may help interpret depleted rocky material observed outside the Solar System, although the paper treats that extension as an implication of the model rather than a direct observation of exoplanet formation.
The study was published in Nature Astronomy.
