  Methane is typically thought to be formed in the solid state on the surface
of cold interstellar icy grain mantles via the successive atomic hydrogenation
of a carbon atom. In the current work we investigate the potential role of
molecular hydrogen in the CH$_4$ reaction network. We make use of an ultra-high
vacuum cryogenic setup combining an atomic carbon atom beam and both atomic
and/or molecular beams of hydrogen and deuterium on a H$_2$O ice. These
experiments lead to the formation of methane isotopologues detected in situ
through reflection absorption infrared spectroscopy. Most notably, CH$_4$ is
formed in an experiment combining C atoms with H$_2$ on amorphous solid water,
albeit slower than in experiments with H atoms present. Furthermore,
CH$_2$D$_2$ is detected in an experiment of C atoms with H$_2$ and D$_2$ on
H$_2$O ice. CD$_4$, however, is only formed when D atoms are present in the
experiment. These findings have been rationalized by means of computational
chemical insights. This leads to the following conclusions: a) the reaction C +
H$_2$ -> CH$_2$ can take place, although not barrierless in the presence of
water, b) the reaction CH + H$_2$ -> CH$_3$ is barrierless, but has not yet
been included in astrochemical models, c) the reactions CH$_2$ + H$_2$ ->
CH$_3$ + H and CH$_3$ + H$_2$ -> CH$_4$ + H can take place only via a tunneling
mechanism and d) molecular hydrogen possibly plays a more important role in the
solid-state formation of methane than assumed so far.
