SOLIS IV. Hydrocarbons in the OMC-2 FIR 4 region, a probe of energetic particle irradiation of the region

We report new interferometric images of cyclopropenylidene, c-C$_3$H$_2$, towards the young protocluster OMC-2 FIR\,4. The observations were performed at 82 and 85 GHz with the NOrthern Extended Millimeter Array (NOEMA) as part of the project Seeds Of Life In Space (SOLIS). In addition, IRAM-30m data observations were used to investigate the physical structure of OMC-2 FIR\,4. We find that the c-C$_3$H$_2$ gas emits from the same region where previous SOLIS observations showed bright HC$_5$N emission. From a non-LTE analysis of the IRAM-30m data, the c-C$_3$H$_2$ gas has an average temperature of $\sim$40K, a H$_2$ density of $\sim$3$\times$10$^{5}$~cm$^{-3}$, and a c-C$_3$H$_2$ abundance relative to H$_2$ of ($7\pm1$)$\times$10$^{-12}$. In addition, the NOEMA observations provide no sign of significant c-C$_3$H$_2$ excitation temperature gradients across the region (about 3-4 beams), with T$_{ex}$ in the range 8$\pm$3 up to 16$\pm$7K. We thus infer that our observations are inconsistent with a physical interaction of the OMC-2 FIR\,4 envelope with the outflow arising from OMC-2 FIR\,3, as claimed by previous studies. The comparison of the measured c-C$_3$H$_2$ abundance with the predictions from an astrochemical PDR model indicates that OMC-2 FIR\,4 is irradiated by a FUV field $\sim$1000 times larger than the interstellar one, and by a flux of ionising particles $\sim$4000 times larger than the canonical value of $1\times10^{-17}$~s$^{-1}$ from the Galaxy cosmic rays, which is consistent with our previous HC$_5$N observations. This provides an important and independent confirmation of other studies that one or more sources inside the OMC-2 FIR\,4 region emit energetic ($\geq10$~MeV) particles.