# Scaling Relations for Terrestrial Exoplanet Atmospheres from Baroclinic Criticality

## TL;DR

This paper develops a scaling theory for the temperature contrast and lapse rate in terrestrial exoplanet atmospheres driven by baroclinic instabilities, validated against GCM simulations, aiding future observational characterization.

## Contribution

It introduces a novel scaling theory linking baroclinic criticality to heat transport in exoplanet atmospheres, validated by GCM comparisons.

## Key findings

- Theoretical predictions agree with GCM results across various parameters.
- Baroclinic instabilities significantly influence heat transport in Earth-like exoplanets.
- Scalings can be tested with future spectroscopic and light curve observations.

## Abstract

The macroturbulent atmospheric circulation of Earth-like planets mediates their equator-to-pole heat transport. For fast-rotating terrestrial planets, baroclinic instabilities in the mid-latitudes lead to turbulent eddies that act to transport heat poleward. In this work, we derive a scaling theory for the equator-to-pole temperature contrast and bulk lapse rate of terrestrial exoplanet atmospheres. This theory is built on the work of Jansen & Ferrari (2013), and determines how unstable the atmosphere is to baroclinic instability (the baroclinic "criticality") through a balance between the baroclinic eddy heat flux and radiative heating/cooling. We compare our scaling theory to General Circulation Model (GCM) simulations and find that the theoretical predictions for equator-to-pole temperature contrast and bulk lapse rate broadly agree with GCM experiments with varying rotation rate and surface pressure throughout the baroclincally unstable regime. Our theoretical results show that baroclinic instabilities are a strong control of heat transport in the atmospheres of Earth-like exoplanets, and our scalings can be used to estimate the equator-to-pole temperature contrast and bulk lapse rate of terrestrial exoplanets. These scalings can be tested by spectroscopic retrievals and full-phase light curves of terrestrial exoplanets with future space telescopes.