  Methanol is a common component of interstellar and circumstellar ice mantles
and is often used as an evolution indicator in star-forming regions. The
observations of gas-phase methanol in the interiors of dense molecular clouds
at temperatures as low as 10 K suggests that a non-thermal ice desorption must
be active. Ice photodesorption was proposed to explain the abundances of
gas-phase molecules toward the coldest regions. Laboratory experiments were
performed to investigate the potential photodesorption of methanol toward the
coldest regions. Solid methanol was deposited at 8 K and UV-irradiated at
various temperatures starting from 8 K. The irradiation of the ice was
monitored by means of infrared spectroscopy and the molecules in the gas phase
were detected using quadrupole mass spectroscopy. Fully deuterated methanol was
used for confirmation of the results. The photodesorption of methanol to the
gas phase was not observed in the mass spectra at different irradiation
temperatures. We estimate an upper limit of 3x10e-5 molecules per incident
photon. On the other hand, photon-induced desorption of the main photoproducts
was clearly observed. The negligible photodesorption of methanol could be
explained by the ability of UV-photons in the 114 - 180 nm (10.87 - 6.88 eV)
range to dissociate this molecule efficiently. Therefore, the presence of
gas-phase methanol in the absence of thermal desorption remains unexplained. On
the other hand, we find CH_4 to desorb from irradiated methanol ice, which was
not found to desorb in the pure CH_4 ice irradiation experiments.
