Beyond monoculture: Polydisperse moment methods for sub-stellar atmosphere cloud microphysics

II. A three-moment gamma distribution formulation for GCM applications

¹ Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland
² Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka-shi, Tokyo, Japan

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 16 July 2025
Accepted: 3 November 2025

Abstract

Context. Understanding how the shape of cloud particle size distributions affects the atmospheric properties of sub-stellar atmospheres is a key area to explore, particularly in the JWST era of broad wavelength coverage, where observations are sensitive to particle size distributions. It is therefore important to elucidate how underlying cloud microphysical processes influence the size distribution, in order to better understand how clouds affect observed atmospheric properties.

Aims. In this follow-up paper, we aimed to extend our sub-stellar atmosphere microphysical cloud formation framework to include effects of assuming a polydisperse gamma particle size distribution, requiring a three-moment solution set of equations.

Methods. We developed a three-moment framework for sub-stellar mineral cloud particle microphysical nucleation, condensation, evaporation, and collisional growth assuming a gamma distribution. As in our previous work, we demonstrated the effects of polydispersity using a simple 1D Y-dwarf KCl cloud formation scenario, and compared the results with the monodisperse case.

Results. Our three-moment scheme provides a generalised framework applicable to any size distribution with a defined moment generation expression. In our test case, we showed that the gamma distribution evolves with altitude, initially broad at the cloud base and narrowing at lower pressures. We found that differences between the gamma and monodisperse cloud structures can be significant, depending on the surface gravity of the atmosphere.

Conclusions. We presented a self-consistent framework for including the effects of polydispersity for sub-stellar microphysical cloud studies using the moment method.