Parametrization of C-shocks.: Evolution of the sputtering of grains

Context. The detection of narrow SiO line emission toward the young shocks of the L1448- mm outflow has been interpreted as a signature of the magnetic precursor of C-shocks. In contrast with the low SiO abundances (<= 10(-12)) derived from the ambient gas, the narrow SiO emission in the precursor component at almost ambient velocities reveals enhanced SiO abundances of similar to 10(-11). It has been proposed that this enhancement of the SiO abundance is produced by the sputtering of the grain mantles at the early stages of C-shocks. However, modelling of the sputtering of grains has usually averaged the SiO abundances over the dissipation region of C-shocks, which cannot explain the recent observations. Aims. We model the evolution of the gas-phase abundances of molecules like SiO, CH3OH, and H2O, produced by the sputtering of the grain mantles and cores as the shock propagates through the ambient gas. We consider different initial gas densities and shock velocities. Methods. We propose a parametric model to describe the physical structure of C-shocks as a function of time. Using the known sputtering yields for water mantles ( with other minor constituents like silicon and CH3OH) and olivine cores by collisions with H-2, He, C, O, Si, Fe, and CO, we follow the evolution of the abundances of silicon, CH3OH, and H2O ejected from grains along the evolution of the shock. Results. The evolution of the abundances of the sputtered silicon, CH3OH, and H2O shows that CO seems to be the most efficient sputtering agent in low-velocity shocks. The velocity threshold for the sputtering of silicon from the grain mantles is appreciably reduced ( by 5-10 km s(-1)) by CO compared to other models. The sputtering by CO can generate SiO abundances of similar to 10(-11) at the early stages of low-velocity shocks, consistent with those observed in the magnetic precursor component of L1448- mm. Our model satisfactorily reproduces the progressive enhancement of SiO, CH3OH, and H2O observed in this outflow, suggesting that this enhancement may be due to the propagation of two shocks with v(s) = 30 km s(-1) and vs = 60 km s(-1) coexisting within the same region. Conclusions. Our simple model can be used to estimate the time-dependent evolution of the abundances of molecular shock tracers like SiO, CH3OH, H2O, or NH3 in very young molecular outflows.