Context. With the ever growing number of detected and confirmed exoplanets, the probability of finding a planet that looks like the Earth increases continuously. While it is clear that the presence of a planet in the habitable zone does not imply the planet is habitable, a systematic study of the evolution of the habitable zone is required to account for its dependence on stellar parameters. Aims. In this article, we aim to provide the community with the dependence of the habitable zone upon the stellar mass, metallicity, rotation, and for various prescriptions of the limits of the habitable zone. Methods. We use stellar evolution models computed with the code STAREVOL, which includes the most current physical mechanisms of internal transport of angular momentum and external wind braking, to study the evolution of the habitable zone and the continuously habitable zone limits. Results. The stellar parameters mass and metallicity affect the habitable zone limits most dramatically. Conversely, for a given stellar mass and metallicity, stellar rotation has only a marginal effect on these limits and does not modify the width of the habitable zone. Moreover, and as expected in the main-sequence phase and for a given stellar mass and metallicity, the habitable zone limits remain almost constant, and this confirms the usual assumptions of a relative constancy of these limits during that phase. The evolution of the habitable zone limits is also correlated to the evolution of the stellar activity (through the Rossby number), which depends on the stellar mass considered. While the magnetic activity has negligible consequence in the case of more massive stars, these effects may have a strong impact on the habitability of a planet around M-dwarf stars. Thus, stellar activity cannot be neglected and may have a strong impact on the development of life during the early stage of the continuously habitable zone phase of low-mass stars. Using observed trends of stellar magnetic field strength, we also constrain the planetary magnetic field (at the zero order) required for a sufficient magnetospheric protection during the whole stellar evolution. Conclusions. We explain for the first time the systematic dependence of planet habitability on stellar parameters along the full evolution of low- and intermediate-mass stars. These results can be used as physical inputs for a first order estimation of exoplanetary habitability.
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