Evolution of the habitable zone of low-mass stars Detailed stellar models and analytical relationships for different masses and chemical compositions

Context. The habitability of an exoplanet is assessed by determining the times at which its orbit lies in the circumstellar habitable zone (HZ). This zone evolves with time following the stellar luminosity variation, which means that the time spent in the HZ depends on the evolution of the host star. Aims. We study the temporal evolution of the HZ of low-mass stars - only due to stellar evolution - and evaluate the related uncertainties. These uncertainties are then compared with those due to the adoption of different climate models. Methods. We computed stellar evolutionary tracks from the pre-main sequence phase to the helium flash at the red-giant branch tip for stars with masses in the range [0.70-1.10] M-circle dot, metallicity Z in the range [0.005-0.04], and various initial helium contents. By adopting a reference scenario for the HZ computations, we evaluated several characteristics of the HZ, such as the distance from the host star at which the habitability is longest, the duration of this habitability, the width of the zone for which the habitability lasts one half of the maximum, and the boundaries of the continuously habitable zone (CHZ) for which the habitability lasts at least 4 Gyr. We developed analytical models, accurate to the percent level or lower, which allowed to obtain these characteristics in dependence on the mass and the chemical composition of the host star. Results. The metallicity of the host star plays a relevant role in determining the HZ. The importance of the initial helium content is evaluated here for the first time; it accounts for a variation of the CHZ boundaries as large as 30% and 10% in the inner and outer border. The computed analytical models allow the first systematic study of the variability of the CHZ boundaries that is caused by the uncertainty in the estimated values of mass and metallicity of the host star. An uncertainty range of about 30% in the inner boundary and 15% in the outer one were found. We also verified that these uncertainties are larger than that due to relying on recently revised climatic models, which leads to a CHZ boundary shift within +/- 5% with respect to those of our reference scenario. We made an on-line tool available that provides both HZ characteristics and interpolated stellar tracks.