The evidence for abundant liquid water on early Mars despite the faint young Sun is a long-standing problem in planetary research .
Here we present new ab initio spectroscopic and line-by-line climate calculations of the warming potential of reduced atmospheres on early Mars .
We show that the strength of both \ce CO2- \ce H2 and \ce CO2- \ce CH4 collision-induced absorption ( CIA ) has previously been significantly underestimated .
Contrary to previous expectations , methane could have acted as a powerful greenhouse gas on early Mars due to \ce CO2- \ce CH4 CIA in the critical 250-500 cm ^ { -1 } spectral window region .
In atmospheres of 0.5 bar \ce CO2 or more , percent levels of \ce H2 or \ce CH4 raise annual mean surface temperatures by tens of degrees , with temperatures reaching 273 K for pressures of 1.25-2 bar and 2-10 % of \ce H2 and \ce CH4 .
Methane and hydrogen produced following aqueous alteration of Mars ’ crust could have combined with volcanically outgassed \ce CO2 to form transient atmospheres of this composition 4.5-3.5 Ga. Our results also suggest that inhabited exoplanets could retain surface liquid water at significant distances from their host stars .