  Methanol is formed via surface reactions on icy dust grains. Methanol is also
detected in the gas-phase at temperatures below its thermal desorption
temperature and at levels higher than can be explained by pure gas-phase
chemistry. The process that controls the transition from solid state to
gas-phase methanol in cold environments is not understood. The goal of this
work is to investigate whether thermal CO desorption provides an indirect
pathway for methanol to co-desorb at low temperatures. Mixed
CH$_{3}$OH:CO/CH$_{4}$ ices were heated under UHV (ultra-high vacuum)
conditions and ice contents are traced using RAIRS (reflection absorption IR
spectroscopy), while desorbing species were detected mass spectrometrically. An
updated gas-grain chemical network was used to test the impact of the results
of these experiments. The physical model used is applicable for TW Hya, a
protoplanetary disk in which cold gas-phase methanol has recently been
detected. Methanol release together with thermal CO desorption is found to be
an ineffective process in the experiments, resulting in an upper limit of
$\leq$ 7.3 $\times$ 10$^{-7}$ CH3OH molecules per CO molecule over all ice
mixtures considered. Chemical modelling based on the upper limits shows that
co-desorption rates as low as 10$^{-6}$ CH$_{3}$OH molecules per CO molecule
are high enough to release substantial amounts of methanol to the gas-phase at
and around the location of the CO thermal desorption front in a protoplanetary
disk. The impact of thermal co-desorption of CH3OH with CO as a grain-gas
bridge mechanism is compared with that of UV induced photodesorption and
chemisorption.
