Detection of the HC$_3$NH$^+$ and HCNH$^+$ ions in the L1544 pre-stellar core
The L1544 pre-stellar core was observed as part of the ASAI (Astrochemical Surveys At IRAM) Large Program. We report the first detection in a pre-stellar core of the HCNH$^+$ and HC$_3$NH$^+$ ions. The high spectral resolution of the observations allows to resolve the hyperfine structure of HCNH$^+$. Local thermodynamic equilibrium analysis leads to derive a column density equal to (2.0$\pm$0.2)$\times$10$^{13}$cm$^{-2}$ for HCNH$^+$ and (1.5$\pm$0.5)$\times$10$^{11}$cm$^{-2}$ for HC$_3$NH$^+$. We also present non-LTE analysis of five transitions of HC$_3$N, three transitions of H$^{13}$CN and one transition of HN$^{13}$C, all of them linked to the chemistry of HCNH$^+$ and HC$_3$NH$^+$. We computed for HC$_3$N, HCN, and HNC a column density of (2.0$\pm$0.4)$\times$10$^{13}$cm$^{-2}$, (3.6$\pm$0.9)$\times10^{14}$cm$^{-2}$, and (3.0$\pm$1.0)$\times$10$^{14}$cm$^{-2}$, respectively. We used the gas-grain chemical code Nautilus to predict the abundances all these species across the pre-stellar core. Comparison of the observations with the model predictions suggests that the emission from HCNH$^+$ and HC$_3$NH$^+$ originates in the external layer where non-thermal desorption of other species was previously observed. The observed abundance of both ionic species ([HCNH$^+$]$\,\simeq3\times10^{-10}$ and [HC$_3$NH$^+$]$\,\simeq[1.5-3.0]\times10^{-12}$, with respect to H$_2$) cannot be reproduced at the same time by the chemical modelling, within the error bars of the observations only. We discuss the possible reasons for the discrepancy and suggest that the current chemical models are not fully accurate or complete. However, the modelled abundances are within a factor of three consistent with the observations, considering a late stage of the evolution of the pre-stellar core, compatible with previous observations.