The impact of stellar winds and tidal locking effects on the habitability of Earth-like exoplanets around M-dwarf stars

We present an assessment of the effects of stellar wind magnetic and mechanical components on the habitability of Earth-like exoplanets orbiting the inner and outer radii of the habitable zone (HZ) of M dwarfs. We consider stars with masses in the range of $0.09 - 0.75 M_⊙$ and planets with a surface dipolar magnetic field of 0.5 G. We estimated the size of the magnetospheres of such exoplanets using the pressure balance equation including the contribution of magnetic and ram pressures from stellar winds. We explored different scenarios, including fast and slow stellar winds, to assess the relevance of kinetic contribution. Furthermore, the effect of tidal locking and potential deviations from the Parker spiral, typically used to describe the interplanetary magnetic field, were analyzed. We show that for low-mass stars (M < 0.15 M_⊙), the ram pressure exerted by stellar winds affects the size of the magnetosphere more than the stellar wind magnetic pressure. Interestingly, when the ram pressure is not much stronger than the magnetic pressure, typically for higher-mass stars, the inclusion of ram pressure can be beneficial to the magnetosphere due to the magnetopause currents. A magnetosphere with the size of that of modern Earth is difficult to achieve with the current assumptions. However, an early-Earth magnetosphere is achieved by roughly half of our hypothetical planets orbiting the outer radius of the HZ in most of the considered cases. We find that deviations from the Parker spiral can affect the results significantly, reducing the magnetosphere by $56%$ in extreme cases. Most of the hypothetical planets are most likely (or might be) tidally locked, with the notable exception of those orbiting the outer HZ of GJ 846 and V1005 Ori.