  The existence of liquid water within an oxidized environment on early Mars
has been inferred by the Mn-rich rocks found during recent explorations on
Mars. The oxidized atmosphere implied by the Mn-rich rocks would basically be
comprised of CO$_2$ and H$_2$O without any reduced greenhouse gases such as
H$_2$ and CH$_4$. So far, however, it has been thought that early Mars could
not have been warm enough to sustain water in liquid form without the presence
of reduced greenhouse gases. Here, we propose that H$_2$O$_2$ could have been
the gas responsible for warming the surface of the oxidized early Mars. Our
one-dimensional atmospheric model shows that only 1 ppm of H$_2$O$_2$ is enough
to warm the planetary surface because of its strong absorption at far-infrared
wavelengths, in which the surface temperature could have reached over 273~K for
a CO$_2$ atmosphere with a pressure of 3~bar. A wet and oxidized atmosphere is
expected to maintain sufficient quantities of H$_2$O$_2$ gas in its upper
atmosphere due to its rapid photochemical production in slow condensation
conditions. Our results demonstrate that a warm and wet environment could have
been maintained on an oxidized early Mars, thereby suggesting that there may be
connections between its ancient atmospheric redox state and possible aqueous
environment.
