Puffy Venuses: the Mass - Radius Impact of Carbon-Rich Atmospheres on Magma Ocean Exoplanets

The recent advancements in exoplanet observations enable the potential detection of exo-Venuses, rocky planets with carbon-rich atmospheres. How extended these atmospheres can be, given high carbon abundances, is not well understood. To answer this, we present a model for a theoretical class of exoplanets - puffy Venuses - characterized by thick, carbon-dominated atmospheres in equilibrium with global magma oceans (MOs). Our model accounts for carbon and hydrogen partition between the atmosphere and the MO, as well as an atmosphere in C-H-O equilibrium chemistry. Our radiative-convective atmosphere treatment generalizes the irradiation pattern proposed for hot steam atmospheres by Selsis et al. (2023) and introduces a deep radiative zone below the troposphere. This is an upgrade from the traditional adiabatic troposphere + isothermal stratosphere approach. We find that radius inflation by puffy Venus atmospheres is significant on small and irradiated planets. We identify TOI-561 b as an especially promising puffy Venus candidate, whose large radius could be attributed to a thick C-rich atmosphere. The deep radiative zone lowers MO surface temperatures, but our model can still explain the low bulk density of TOI-561 b. We compare the effects of different opacity parameterizations on the atmospheric profile. We also probe the radius inflation effects of varying bulk C abundances, mantle redox states, and atmospheric chemistry scenarios. Puffy Venuses may constitute a testable alternative interpretation for the interior structure of low-mass exoplanets.