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 ∼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, CH 3 OH, and H 2 O, 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 CH 3 OH) and olivine cores by collisions with H 2 , He, C, O, Si, Fe, and CO, we follow the evolution of the abundances of silicon, CH 3 OH, and H 2 O ejected from grains along the evolution of the shock. Results. The evolution of the abundances of the sputtered silicon, CH 3 OH, and H 2 O 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 kms -1 ) by CO compared to other models. The sputtering by CO can generate SiO abundances of ∼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, CH 3 OH, and H 2 O observed in this outflow, suggesting that this enhancement may be due to the propagation of two shocks with U s = 30 km s -1 and U s = 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, CH 3 OH, H 2 O, or NH 3 in very young molecular outflows.