Aims. We investigate the impact of CO2 on the distribution of water on TRAPPIST-1 e, f, and g during the magma ocean stage. These potentially habitable rocky planets are currently the most accessible for astronomical observations. A constraint on the volatile budget during the magma ocean stage is a key link to planet formation and also to judging their habitability. Methods. We expanded the MagmOc module of the VPLanet environment to perform simulations with 1-100 terrestrial oceans (TOs) of H2O with and without CO2 and for albedos 0 and 0.75. The CO2 mass was scaled with initial H2O by a constant factor between 0.1 and 1. Results. The magma ocean state of rocky planets begins with a CO2-dominated atmosphere but can evolve into a H2O dominated state, depending on initial conditions. For less than 10 TO initial H2O, the atmosphere tends to desiccate and the evolution can end with a CO2 dominated atmosphere. Otherwise, the final state is a thick (>1000 bar) H2O-CO2 atmosphere. Complete atmosphere desiccation with less than 10 TO initial H2O can be significantly delayed for TRAPPIST-1 e and f, when H2O has to diffuse through a CO2 atmosphere to reach the upper atmosphere, where photolysis due to extreme ultra violet irradiation occurs. As a consequence of CO2 diffusion-limited water loss, the time of mantle solidification for TRAPPIST-1 e, f, and g can be significantly extended compared to a pure H2O evolution by up to 40 Myrs for an albedo of 0.75 and by up to 200 Mys for an albedo of 0. The addition of CO2 further results in a higher water content in the melt during the magma ocean stage. Thus, more water can be sequestered in the solid mantle. However, only up to 6% of the initial water mass can be stored in the mantle at the end of the magma ocean stage. Our compositional model adjusted for the measured metallicity of TRAPPIST-1 yields for the dry inner planets (b, c, d) an iron fraction of 27 wt%. For TRAPPIST-1 e, this iron fraction would be compatible with a (partially) desiccated evolution scenario and a CO2 atmosphere with surface pressures of a few 100 bar. Conclusions. A comparative study between TRAPPIST-1 e and the inner planets may yield the most insights about formation and evolution scenarios by confronting, respectively, a scenario with a desiccated evolution due to volatile-poor formation and a volatile-rich scenario with extended atmospheric erosion.
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