An Atmospheric Structure Equation for Grain Growth

TL;DR

This paper introduces a method to model grain growth and opacity evolution in protoplanetary atmospheres, accounting for factors like planetesimal deposition and grain porosity, revealing efficient coagulation and reduced opacities.

Contribution

The paper presents a novel approach to include grain size evolution and opacity changes in atmosphere models, considering mass deposition and porosity effects.

Findings

Grain coagulation is highly efficient in protoplanetary atmospheres.

Opacity drops below ISM values, affecting temperature and density profiles.

Planetesimal deposition has minimal impact on grain coagulation outcomes.

Abstract

We present a method to include the evolution of the grain size and grain opacity $\kappa_\mathrm{gr}$ in the equations describing the structure of protoplanetary atmospheres. The key assumption of this method is that a single grain size dominates the grain size distribution at any height $r$. In addition to following grain growth, the method accounts for mass deposition by planetesimals and grain porosity. We illustrate this method by computation of a simplified atmosphere structure model. In agreement with previous works, grain coagulation is seen to be very efficient. The opacity drops to values much below the often-used `ISM-opacities' ($\sim$$1\ \mathrm{cm^2\ g}^{-1}$) and the atmosphere structure profiles for temperature and density resemble that of the grain-free case. Deposition of planetesimals in the radiative part of the atmosphere hardly influences this outcome as the added surface is quickly coagulated away. We observe a modest dependence on the internal structure (porosity), but show that filling factors cannot become too large because of compression by gas drag.