  Chemical models predict that in cold cores gas-phase methanol is expected to
be abundant at the outer edge of the CO depletion zone, where CO is actively
adsorbed. CO adsorption correlates with volume density in cold cores, and, in
nearby molecular clouds, the catastrophic CO freeze-out happens at volume
densities above 10$^4$ cm$^{-3}$. The methanol production rate is maximized
there and its freeze-out rate does not overcome its production rate, while the
molecules are shielded from UV destruction by gas and dust. Thus, in cold
cores, methanol abundance should generally correlate with visual extinction
that depends both on volume and column density. In this work, we test the most
basic model prediction that maximum methanol abundance is associated with a
local $A_V\simeq$4 mag in dense cores and constrain the model parameters with
the observational data. With the IRAM 30 m antenna, we mapped the CH$_3$OH
(2-1) and (3-2) transitions toward seven dense cores in the L1495 filament in
Taurus to measure the methanol abundance. We use the Herschel/SPIRE maps to
estimate visual extinction, and the C$^{18}$O(2-1) maps from Tafalla & Hacar
(2015) to estimate CO depletion. We explored the observed and modeled
correlations between the methanol abundances, CO depletion, and visual
extinction varying the key model parameters. The modeling results show that
hydrogen surface diffusion via tunneling is crucial to reproduce the observed
methanol abundances, and the needed reactive desorption efficiency matches the
one deduced from laboratory experiments.
