  We investigate the impact on convective numerical simulations of
thermo-compositional diabatic processes. We focus our study on simulations with
a stabilizing temperature gradient and a destabilizing mean-molecular weight
gradient. We aim to establish the possibility for a reduced
temperature-gradient in such setups. A suite of 3D simulations were conducted
using a numerical hydrodynamic code. We used as a simplified test case, a
sample region of the secondary atmosphere of a hot rocky exoplanet within which
the chemical transition CO+O $\leftrightarrow$ CO$_{2}$ could occur. Newtonian
cooling and a chemical source term was used to maintain a negative mean
molecular weight gradient. Our results demonstrate that this setup can reduce
the temperature gradient, a result which does not converge away with resolution
or over time. We also show that the presence of the reduced temperature
gradient is a function of the forcing timescales. The above transition leads to
a bifurcation of the temperature profile when the chemical forcing is fast,
reminiscent of the bifurcation seen in the boiling crisis for steam/liquid
convection. With the reduced temperature gradient in these idealized setups,
there exists the possibility for an analogy of the reddening (currently
observed in the spectra of brown dwarfs) in the spectra of rocky exoplanet
atmospheres. Detailed 1D modelling is needed, in order to characterize the
equilibrium thermal and compositional gradients, the timescales, and the impact
of a realistic equation of state, in order to assess if the regime identified
here will develop in realistic situations. This possibility cannot, however, be
excluded a priori. This prediction is new for terrestrial atmospheres and
represents strong motivation for the use of diabatic models when analysing
atmospheric spectra of rocky exoplanets that will be observed with e.g. the
James Webb Space Telescope.
