  The habitability of a planet depends on various factors, such as delivery of
water during the formation, the co-evolution of the interior and the
atmosphere, as well as the stellar irradiation which changes in time. Since an
unknown number of rocky exoplanets may operate in a one-plate convective
regime, i.e., without plate tectonics, we aim at understanding under which
conditions planets in such a stagnant-lid regime may support habitable surface
conditions. Understanding the interaction of the planetary interior and
outgassing of volatiles with the atmosphere in combination with the evolution
of the host star is crucial to determine the potential habitability. M-dwarf
stars in particular possess a high-luminosity pre-main sequence phase which
endangers the habitability of planets around them via water loss. We therefore
explore the potential of secondary outgassing from the planetary interior to
rebuild a water reservoir allowing for habitability at a later stage. We
compute the boundaries of the habitable zone around M, K, G, and F-dwarf stars
using a 1D cloud-free radiative-convective climate model accounting for the
outgassing history of CO2 and H2O from an interior evolution and outgassing
model for different interior compositions and stellar luminosity evolutions.
The outer edge of the habitable zone strongly depends on the amount of CO2
outgassed from the interior, while the inner edge is mainly determined via the
stellar irradiation, as soon as a sufficiently large water reservoir has been
outgassed. A build-up of a secondary water reservoir for planets around M-dwarf
stars is possible even after severe water loss during the high luminosity
pre-main sequence phase as long as some water has been retained within the
mantle. Earth-like stagnant-lid planets allow for habitable surface conditions
within a continuous habitable zone that is dependent on interior composition.
