Sedimentation Efficiency of Condensation Clouds in Substellar Atmospheres

Condensation clouds in substellar atmospheres have been widely inferred from spectra and photometric variability. Up until now, their horizontally averaged vertical distribution and mean particle size have been largely characterized using models, one of which is the eddy diffusion-sedimentation model from Ackerman & Marley (2001) that relies on a sedimentation efficiency parameter, $f_{\rm sed}$, to determine the vertical extent of clouds in the atmosphere. However, the physical processes controlling the vertical structure of clouds in substellar atmospheres are not well understood. In this work, we derive trends in $f_{\rm sed}$ across a large range of eddy diffusivities ($K_{zz}$), gravities, material properties, and cloud formation pathways by fitting cloud distributions calculated by a more detailed cloud microphysics model. We find that $f_{\rm sed}$ is dependent on $K_{zz}$, but not gravity, when $K_{zz}$ is held constant. $f_{\rm sed}$ is most sensitive to the nucleation rate of cloud particles, as determined by material properties like surface energy and molecular weight. High surface energy materials form fewer, larger cloud particles, leading to large $f_{\rm sed}$ ($>$1), and vice versa for materials with low surface energy. For cloud formation via heterogeneous nucleation, $f_{\rm sed}$ is sensitive to the condensation nuclei flux and radius, connecting cloud formation in substellar atmospheres to the objects' formation environments and other atmospheric aerosols. These insights could lead to improved cloud models that help us better understand substellar atmospheres. For example, we demonstrate that $f_{\rm sed}$ could increase with increasing cloud base depth in an atmosphere, shedding light on the nature of the brown dwarf L/T transition.