# Vertical Tracer Mixing in Hot Jupiter Atmospheres

## TL;DR

This paper develops an analytic and numerical framework to understand how vertical tracer mixing in hot Jupiter atmospheres depends on planetary parameters, revealing key transitions in circulation patterns and providing formulas for modeling chemical processes.

## Contribution

It introduces a combined analytic and numerical approach to predict vertical velocities and mixing rates in hot Jupiter atmospheres, highlighting the impact of planetary parameters on tracer transport.

## Key findings

- Vertical mixing rate increases with temperature, decreasing drag, and longer chemical loss timescales.
- Transition from superrotating jet to day-to-night flow significantly alters vertical velocity and tracer distribution.
- Analytic solutions for eddy diffusivity $K_{zz}$ are provided for use in atmospheric chemistry models.

## Abstract

Aerosols appear to be ubiquitous in close-in gas giant atmospheres, and disequilibrium chemistry likely impacts the emergent spectra of these planets. Lofted aerosols and disequilibrium chemistry are caused by vigorous vertical transport in these heavily irradiated atmospheres. Here we numerically and analytically investigate how vertical transport should change over the parameter space of spin-synchronized gas giants. In order to understand how tracer transport depends on planetary parameters, we develop an analytic theory to predict vertical velocities and mixing rates ($K_\mathrm{zz}$) and compare the results to our numerical experiments. We find that both our theory and numerical simulations predict that, if the vertical mixing rate is described by an eddy diffusivity, then this eddy diffusivity $K_\mathrm{zz}$ should increase with increasing equilibrium temperature, decreasing frictional drag strength, and increasing chemical loss timescales. We find that the transition in our numerical simulations between circulation dominated by a superrotating jet and that with solely day-to-night flow causes a marked change in the vertical velocity structure and tracer distribution. The mixing ratio of passive tracers is greatest for intermediate drag strengths that corresponds to this transition between a superrotating jet with columnar vertical velocity structure and day-to-night flow with upwelling on the dayside and downwelling on the nightside. Lastly, we present analytic solutions for $K_\mathrm{zz}$ as a function of planetary effective temperature, chemical loss timescales, and other parameters, for use as input to one-dimensional chemistry models of spin-synchronized gas giant atmospheres.