We show that collision-induced absorption allows molecular hydrogen to act as an incondensible greenhouse gas, and that bars or tens of bars of primordial H2-He mixtures can maintain surface temperatures above the freezing point of water well beyond the "classical" habitable zone defined for CO2 greenhouse atmospheres. Using a 1-D radiative-convective model we find that 40 bars of pure H2 on a 3 Earth-mass planet can maintain a surface temperature of 280K out to 1.5AU from an early-type M dwarf star and 10 AU from a G-type star. Neglecting the effects of clouds and of gaseous absorbers besides H2, the flux at the surface would be sufficient for photosynthesis by cyanobacteria (in the G star case) or anoxygenic phototrophs (in the M star case). We argue that primordial atmospheres of one to several hundred bars of H2-He are possible, and use a model of hydrogen escape to show that such atmospheres are likely to persist further than 1.5 AU from M stars, and 2 AU from G stars, assuming these planets have protecting magnetic fields. We predict that the microlensing planet OGLE-05-390L could have retained a H2-He atmosphere and be habitable at ~2.6 AU from its host M star.Comment: Accepted to Astrophysical Journal Letter
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