Tracking CHNOS during the first stages of planet formation

Summary

The local elemental abundances of Carbon, Hydrogen, Nitrogen, Oxygen and Sulfur (CHNOS) in icy dust grains in planet-forming disks are crucial to understand the initial volatile budgets of planetesimals and, by extension, planets. The evolution of the ice composition of local dust, however, is affected by disk processes such as dust settling, radial drift, turbulent stirring, collisional growth and fragmentation of dust grains, and the formation and evaporation of ice. Altogether the processes which affect the evolution of the ice composition of local dust can be coupled and non-local. 
We develop a model where we track the effects of these processes on a single tracer dust grain. We use our model to constrain the disk regions where dynamical, collisional and ice processing are fully coupled. In addition, we predict the resulting evolutionary trajectories of individual dust grains. These individual dust grain histories can subsequently be used to make inferences about the ice composition of local dust. We find that the locations of regions where disk processes are fully coupled depend on both the chemical species considered and the grain size. In addition, the evolutionary trajectories of initially fully identical dust grains can diverge significantly, both spatially and in terms of composition. Since different grain sizes are connect via collisional growth and fragmentation, our results imply that there is no region where the disk processes considered fully decouple. Therefore, our model highlights the importance a statistical analysis of many individual dust grains to predict the volatile CHNOS present on local dust and, by extension, available for planetesimal formation.

Background
CHNOS play a crucial role in the evolution and chemical habitability of rocky planets [1]. For example, CHNOS-bearing volatile molecules such as H₂O, CO₂, CH₄ or N₂ play a key role in the surface conditions and habitability via their abundance in the planet atmosphere [2]. In addition, the abundance of CHNOS in the planetary interior has profound effects on processes such as core formation [3] and volcanic outgassing [4].
In order to understand the evolution of a planet, the amount of CHNOS a planet accumulates during its formation needs to be constrained. The first stage of planet formation involves the growth of micron-sized dust grains into millimeter- to centimeter-sized aggregates through collisions [5]. Planetesimals can subsequently form either as a product of continuous coagulation with efficient sticking or through gravitational collapse triggered by e.g. the streaming instability [6].
In the colder regions of the disk, a considerable fraction of the solid-phase CHNOS mass budget exists as ices associated with volatile molecular species such as H₂O, CO, CO₂, CH₄, NH₃, H₂S and SO₂ [1]. The amount of volatile CHNOS present on a dust grain is thus set by a balance of molecule adsorption and desorption. However, the adsorption and desorption rates strongly depend on the local temperature, radiation field and composition of the gas phase [7]. Moreover, as dust grains grow into larger aggregates through collisions, dynamical processes such as vertical settling, radial drift and turbulent diffusion result in significant displacement of dust throughout the disk [8]. This dynamical transport exposes individual dust grains to a wide range of local conditions, which could have profound consequences on the ice composition. 
Although numerous models have been developed to describe one or several aspects of the interplay between local dust ice composition and non-local disk processes, a fully coupled, systematic approach which can be used to describe any set of volatile molecule is not available to date [9,10,11].

Methods, results and outlook
We develop a stochastic model where inferences about the ice composition of the local dust population can be made by tracking the behavior of individual small tracer particles called “monomers” embedded in a larger “home aggregate” (Figure 1). The size of the home aggregate may change over time due to collisions with other dust particles, while we trace the amount and composition of ice on the monomer. The monomer and home aggregate are allowed to interact with the background disk environment, which is informed from a thermo-chemical disk model (ProDiMo) [12].
We use our model to explore the importance of the interplay between turbulent diffusion, vertical settling, radial drift and collisions for the ice properties of individual monomers. Figure 2 depicts an example of a monomer whose CO and CH₄ ice is lost due to thermal desorption, which is in turn a consequence of the home aggregate drifting into a warmer disk region.
As a next step, we are quantifying the effect of these non-local disk processes on the ice composition of local dust populations by studying the statistical behaviour of a large group of monomers. Specifically, we aim to predict the ice composition of dust present in the midplane in order to derive implications for the volatile CHNOS abundance of the first generation of planetesimals.    

Figure 1: A monomer of radius s_m is embedded inside a home aggregate of effective radius s_a at some monomer depth z_m. Depending on the monomer depth, the monomer is exposed, which allows the interaction with impinging gas phase molecules (adsorption) and UV photons (photodesorption).

Figure 2: Example evolutionary trajectory of a monomer released from r=50 AU and z=0 AU inside a porous home aggregate with filling factor φ=10^-3. The quantities depicted from left to right are the radial and vertical position (r and z, respectively), the monomer depth z_m, and ice composition.

[1] Krijt et al. 2022, arXiv 2203.10056 [2] Kasting et al. 1993, Icarus 101, p.108-128 [3] Wood et al. 2014, Geochimica et Cosmochimica Acta 145, p.248-267 [4] Van Hoolst et al. Advances in Physics: X, 4 [5] Dominik & Tielens 1997, The Astrophysical Journal 480, p.647-673 [6] Johansen et al. 2014, Protostars and Planets VI, p.547 [7] Cuppen et al. 2017, Space Science Reviews 2012, p.1-58 [8] Armitage 2010, Astrophysics of Planet Formation [9] Krijt et al. 2020, The Astrophysicsl Journal 899, p.134 [10] Bergner & Ciesla 2021, The Astrophysical Journal 919, p.45 [11] Van Clepper et al. 2022, arXiv 2202.00524 [12] Woitke et al. 2009, Astronomy & Astrophysics 501, p.383-406