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A major goal in the search for extraterrestrial life is the detection ofliquid water on the surface of exoplanets. On terrestrial planets, volcanicoutgassing is a significant source of atmospheric and surface water and a majorcontributor to the long-term evolution of the atmosphere. The rate of volcanismdepends on the interior evolution and on numerous feedback processes betweenatmosphere and interior, which continuously shape atmospheric composition,pressure, and temperature. We present the results of a comprehensive 1D modelof the coupled evolution of the interior and atmosphere of rocky exoplanetsthat combines central feedback processes between these two reservoirs. Wecarried out more than \num{280000} simulations over a wide range of mantleredox states and volatile content, planetary masses, interior structures andorbital distances in order to robustly assess the emergence, accumulation andpreservation of surface water on rocky planets. To establish a conservativebaseline of which types of planets can outgas and sustain water on theirsurface, we focus here on stagnant-lid planets. We find that only a narrowrange of the mantle redox state around the iron-w\"ustite buffer allows theformation of atmospheres that lead to long-term habitable conditions. Atoxidizing conditions similar to those of the Earth's mantle, most stagnant-lidplanets end up in a hothouse regime akin to Venus due to strong \ce{CO2}outgassing. At more reducing conditions, the amount of outgassed greenhousegases is often too low to keep surface water from freezing. In addition,Mercury-like planets with large metallic cores are able to sustain habitableconditions at an extended range of orbital distances as a result of lowervolcanic activity.

Redox state and interior structure control on the long-term habitability of stagnant-lid planets