Modelling cosmic masers in C-type shock waves -- the coexistence of
  Class I CH3OH and 1720 MHz OH masers
  The collisional pumping of CH3OH and OH masers in non-dissociative C-type
shock waves is studied. The chemical processes responsible for the evolution of
molecule abundances in the shock wave are considered in detail. The large
velocity gradient approximation is used to model radiative transfer in
molecular lines. We present calculations of the optical depth in maser
transitions of CH3OH and OH for a grid of C-type shock models that vary in
cosmic ray ionization rate, gas density and shock speed. We show that pre-shock
gas densities $n_{H,tot} = 2 \times 10^4-2 \times 10^5$ cm$^{-3}$ are optimal
for pumping of methanol maser transitions. A complete collisional dissociation
of methanol at the shock front takes place for shock speeds $u_{s} \gtrsim 25$
km s$^{-1}$. At high pre-shock gas density $n_{H,tot} = 2 \times 10^{6}$
cm$^{-3}$, the collisional dissociation of methanol takes place at shock speeds
just above the threshold speed $u_{s} \approx 15-17.5$ km s$^{-1}$
corresponding to sputtering of icy mantles of dust grains. We show that the
methanol maser transition E $4_{-1} \to 3_0$ at 36.2 GHz has the optical depth
higher than that of the transition A$^+$ $7_0 \to 6_1$ at 44.1 GHz at high
cosmic ray ionization rate $\zeta_{H_2} \gtrsim 10^{-15}$ s$^{-1}$ and
pre-shock gas density $n_{H,tot} = 2 \times 10^4$ cm$^{-3}$. These results can
be applied to the interpretation of observational data on methanol masers near
supernova remnants and in molecular clouds of the Central Molecular Zone. At
the same time, a necessary condition for the operation of 1720 MHz OH masers is
a high ionization rate of molecular gas, $\zeta_{H_2} \gtrsim 10^{-15}$
s$^{-1}$. We find that physical conditions conducive to the operation of both
hydroxyl and methanol masers are cosmic ray ionization rate $\zeta_{H_2}
\approx 10^{-15} - 3 \times 10^{-15}$ s$^{-1}$, and a narrow range of shock
speeds.
