The role of planetary interior in the long-term evolution of atmospheric CO₂ on Earth-like exoplanets

Context. The long-term carbonate silicate cycle plays an important role in the evolution of Earth's climate and, therefore, may also be an important mechanism in the evolution of the climates of Earth-like exoplanets. However, given the large diversity in the possible interiors for Earth-like exoplanets, the ensuing evolution of the atmospheric CO2 pressure may be widely different. Aims: We assess the role of the thermal evolution of the planetary interior on the long-term carbon cycle of Earth-like exoplanets. In particular, we investigate the effects of radiogenic mantle heating, core size, and planetary mass on the atmospheric partial CO2 pressure, and the ability of a long-term carbon cycle driven by plate tectonics to control the atmospheric CO2 pressure. Methods: We developed a box-model which connects carbon cycling to parametrized mantle convection. Processes considered in the carbon cycle are temperature-dependent continental weathering, seafloor weathering, subduction, and degassing through ridge and arc volcanism. The carbon cycle was coupled to the thermal evolution via the plate speed, which was parametrized in terms of the global Rayleigh number. Results: We find decreasing atmospheric CO2 pressure with time, up to an order of magnitude over the entire main sequence lifetime of a solar-type star. High abundances of radioactive isotopes allow for more efficient mantle degassing, resulting in higher CO2 pressures. Within the spread of abundances found in solar-type stars, atmospheric CO2 pressures at 4.5 Gyr were found to vary from 14 Pa to 134 Pa. We find a decreasing Rayleigh number and plate speed toward planets with larger core mass fractions fc, which leads to reduced degassing and lower atmospheric CO2 pressure. In particular for fc ≳ 0.8, a rapid decrease of these quantities is found. Variations in planet mass have more moderate effects. However, more massive planets may favor the development of more CO2 rich atmospheres due to hotter interiors. Conclusions: The dependence of plate tectonics on mantle cooling has a significant effect on the long-term evolution of the atmospheric CO2 pressure. Carbon cycling mediated by plate tectonics is efficient in regulating planetary climates for a wide range of mantle radioactive isotope abundances, planet masses and core sizes. More efficient carbon cycling on planets with a high mantle abundance of thorium or uranium highlights the importance of mapping the abundances of these elements in host stars of potentially habitable exoplanets. Inefficient carbon recycling on planets with a large core mass fraction (≳0.8) emphasizes the importance of precise mass-radius measurements of Earth-sized exoplanets