Habitable zone evolution for planets around the different M dwarfs with different initial water contents (see legend) and oxygen fugacities, upper panels (a, b) IW − 1, lower panels (c, d) IW + 0.5 Left panels: HZ evolution for the full outgassed amounts of H₂O and CO₂. Right panels: HZ boundaries assuming that all water outgassed during the pre-main sequence phase of the star has been lost for each initial water concentration. For better visibility the y-axis has been changed to linear scale in the right panels. The locations of Proxima Centauri b and TRAPPIST-1c, d, and e are also shown. The grey box in the left panels indicates the time and distance range shown in the right panels.