Molecular ions in the O-rich evolved star OH231.8+4.2: HCO$^+$,H$^{13}$CO$^+$ and first detection of SO$^+$, N$_2$H$^+$, and H$_3$O$^+$
OH 231.8+4.2, a bipolar outflow around a Mira-type variable star, displays a unique molecular richness amongst circumstellar envelopes (CSEs) around O-rich AGB and post-AGB stars. We report line observations of the HCO+ and H13CO+ molecular ions and the first detection of SO+, N2H+, and (tentatively) H3O+ in this source. SO+ and H3O+ have not been detected before in CSEs around evolved stars. These data have been obtained as part of a full mm-wave and far-IR spectral line survey carried out with the IRAM 30 m radio telescope and with Herschel/HIFI. Except for H3O+, all the molecular ions detected in this work display emission lines with broad profiles (FWHM 50-90 km/s), which indicates that these ions are abundant in the fast bipolar outflow of OH 231.8. The narrow profile (FWHM 14 km/s) and high critical densities (>1e6cm-3 ) of the H3O+ transitions observed are consistent with this ion arising from denser, inner (and presumably warmer) layers of the fossil remnant of the slow AGB CSE at the core of the nebula. From rotational diagram analysis, we deduce excitation temperatures of Tex 10-20 K for all ions except for H3O+, which is most consistent with Tex 100 K. Although uncertain, the higher excitation temperature suspected for H3O+ is similar to that recently found for H2O and a few other molecules, which selectively trace a previously unidentified, warm nebular component.The column densities of the molecular ions reported here are in the range Ntot [1-8]x1e13 cm-2, leading to beam-averaged fractional abundances relative to H2 of X(HCO+) 1e-8, X(H13CO+) 2e-9, X(SO+) 4e-9, X(N2H+) 2e-9, and X(H3O+) 7e-9 cm-2. We have performed chemical kinetics models to investigate the formation of these ions in OH 231.8 as the result of standard gas phase reactions initiated by cosmic-ray and UV-photon ionization. (abridged).