  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.
