Vertical volatile transport in cometary near-surface layers

Introduction

Cometary activity is driven by sublimation of volatile ices in near-surface layers. Gas produced below the surface builds up pressure, diffuses through porous material, and may contribute to lifting dust or pebbles from the surface. The efficiency of this process depends on the microscopic structure, such as pebble size, porosity, and arrangement, which control the diffusion coefficient and gas pressure gradient.

Thermophysical models commonly treat sublimation, heat transport, and gas diffusion in a vertically stratified medium. However, the fate of molecules produced at a sublimation front is often simplified. Molecules diffusing downward into colder layers can re-condense and transport both mass and energy into the interior. This may alter ice distribution, porosity, permeability, thermal conductivity, and mechanical strength. We study this vertical volatile transport on the microscopic scale using a Direct Simulation Monte Carlo (DSMC) model.

• Methods

We use the PI-DSMC code, previously tested for molecular gas diffusion through granular samples (Güttler et al., 2023). The cometary surface is represented by a packing of spherical pebbles with 2.5 mm radius. The sample consists of a desiccated, dry upper layer and an ice-containing lower region.

For each sphere, we prescribe a constant temperature based on a simplified vertical temperature profile from Gundlach et al. (2020). Water molecules are produced from icy spheres according to the Hertz-Knudsen sublimation rate and are adsorbed upon collision with cold icy spheres. By tracking adsorption and desorption events, we determine local and depth-dependent mass-transfer rates.

The model is quasi-static: temperature profile and ice distribution are prescribed and not updated. This isolates the microscopic gas-transport process and provides descriptions for future self-consistent thermophysical models.

Results

For a reference case with a 30 mm dry surface layer (corresponding to six pebble diameters), the DSMC simulation produces a pressure profile consistent with the local sublimation pressure in the icy region and a diffusive pressure decrease through the dry layer towards the surface. Adsorption and desorption bookkeeping shows that net mass loss is concentrated close to the dust-ice interface, while colder layers below gain mass by re-condensation.

Only about 4 percent of the sublimated water molecules escape into space in this reference case. The remaining 96 percent are transported downward and refreeze below the sublimation front. Thus, sublimation at the ice interface can efficiently redistribute ice into deeper layers rather than simply remove it from the comet.

To interpret the DSMC results, we apply a random-walk toy model. A molecule starts at the dust-ice interface and performs a three-dimensional random walk with a step length equal to the mean path length. It escapes only if it reaches the surface without ever moving below its starting depth; otherwise it refreezes. This model is able to reproduce the 4 percent escape probability in the reference case.

The height of the desiccated layer was varied and the escape probability (see figure) shows a strong decrease with dry-layer thickness. The very simple random walk is able to qualitatively reproduce the data surprisingly well; small but systematic differences are to be expected due to its simplicity. Both sets are best reproduced with a 2-parameter power law fit. The widely used “efficiency function” of Gundlach et al. (2020, Eq. A8; orange curve) shows a reasonable match, when the single free parameter, the half-transmission thickness, is applied in the order 3/4 times the mean path (Macher et al., 2024; Eqs. 24 & 32).

Figure 1: Fraction of escaping water molecules as a function of the depth of the dust-ice interface, normalized by the mean path length.

Implications and Outlook

Our results show that diffusion through granular cometary material can strongly reduce the fraction of sublimated water molecules escaping into space. Instead, most molecules re-condense below the sublimation front, causing downward transport of ice and latent heat. The accumulation of ice below the sublimation front may reduce pore space, modify the diffusion coefficient, and form a less permeable layer. This could affect the release of more volatile species from greater depths and may be relevant for delayed, localized, or episodic cometary activity. In future work, we will study how deposited ice changes the pore geometry, for example through sinter-like necks between pebbles, and how this affects gas diffusion.

References

Gundlach, B. et al., 2020. MNRAS 493:4690.
Güttler, C. et al., 2023. MNRAS 524:6114.
Macher, W. et al., 2024. Journal of Engineering Mathematics 144:2.