Accurate sub-millimetre rest-frequencies for HOCO$^+$ and DOCO$^+$ ions

Abstract

HOCO$^+$ is a polar molecule that represents a useful proxy for its parent molecule CO$_2$, which is not directly observable in the cold interstellar medium. This cation has been detected towards several lines of sight, including massive star forming regions, protostars, and cold cores. Despite the obvious astrochemical relevance, protonated CO$_2$ and its deuterated variant, DOCO$^+$, still lack an accurate spectroscopic characterisation. The aim of this work is to extend the study of the ground-state pure rotational spectra of HOCO$^+$ and DOCO$^+$ well into the sub-millimetre region. Ground-state transitions have been recorded in the laboratory using a frequency-modulation absorption spectrometer equipped with a free-space glow-discharge cell. The ions were produced in a low-density, magnetically-confined plasma generated in a suitable gas mixture. The ground-state spectra of HOCO$^+$ and DOCO$^+$ have been investigated in the 213-967 GHz frequency range, with the detection of 94 new rotational transitions. Additionally, 46 line positions taken from the literature have been accurately remeasured. The newly-measured lines have significantly enlarged the available data sets for HOCO$^+$ and DOCO$^+$, thus enabling the determination of highly accurate rotational and centrifugal distortion parameters. Our analysis showed that all HOCO$^+$ lines with Ka $\geq$ 3 are perturbed by a ro-vibrational interaction that couples the ground state with the v$_ 5$ = 1 vibrationally-excited state. This resonance has been explicitly treated in the analysis in order to obtain molecular constants with clear physical meaning. The improved sets of spectroscopic parameters provide enhanced lists of very accurate, sub-millimetre rest-frequencies of HOCO$^+$ and DOCO$^+$ for astrophysical applications. These new data challenges a recent tentative identification of DOCO$^+$ toward a pre-stellar core.