Spatial distribution of small hydrocarbons in the neighborhood of the Ultra Compact HII region Monoceros R2

We study the chemistry of small hydrocarbons in the photon-dominated regions (PDRs) associated with the ultra-compact HII region Mon R2. Our goal is to determine the variations of the abundance of small hydrocarbons in a high-UV irradiated PDR and investigate their chemistry. We present an observational study of CH, CCH and c-C$_3$H$_2$ in Mon R2 combining data obtained with the IRAM 30m telescope and Herschel. We determine the column densities of these species, and compare their spatial distributions with that of polycyclic aromatic hydrocarbon (PAH). We compare the observational results with different chemical models to explore the relative importance of gas-phase, grain-surface and time-dependent chemistry in these environments. The emission of the small hydrocarbons show different patterns. The CCH emission is extended while CH and c-C$_3$H$_2$ are concentrated towards the more illuminated layers of the PDR. The ratio of the column densities of c-C$_3$H$_2$ and CCH shows spatial variations up to a factor of a few, increasing from $N(c-C$_3$H$_2$)/N(CCH)\approx0.004$ in the envelope to a maximum of $\sim0.015-0.029$ towards the 8$\mu$m emission peak. Comparing these results with other galactic PDRs, we find that the abundance of CCH is quite constant over a wide range of G$_0$, whereas the abundance of c-C$_3$H$_2$ is higher in low-UV PDRs. In Mon R2, the gas-phase steady-state chemistry can account relatively well for the abundances of CH and CCH in the most exposed layers of the PDR, but falls short by a factor of 10 to reproduce c-C$_3$H$_2$. In the molecular envelope, time-dependent effects and grain surface chemistry play a dominant role in determining the hydrocarbons abundances. Our study shows that CCH and c-C$_3$H$_2$ present a complex chemistry in which UV photons, grain-surface chemistry and time dependent effects contribute to determine their abundances.