Sulphur-bearing molecules in AGB stars I: The occurrence of hydrogen sulfide

Through a survey of (sub-)millimetre emission lines of various sulphur-bearing molecules, we aim to determine which molecules are the primary carriers of sulphur in different types of AGB stars. In this paper, the first in a series, we investigate the occurrence of H$_2$S in AGB circumstellar envelopes and determine its abundance, where possible. We have surveyed 20 AGB stars with a range of mass-loss rates and of different chemical types using the APEX telescope to search for rotational transition lines of five key sulphur-bearing molecules: CS, SiS, SO, SO$_2$ and H$_2$S. Here we present our results for H$_2$S, including detections, non-detections and detailed radiative transfer modelling of the detected lines. We compare results based on different descriptions of the molecular excitation of H$_2$S and different abundance distributions, including those derived from chemical modelling results. We detected H$_2$S towards five AGB stars, all of which have high mass-loss rates of $\dot{M}\geq 5\times 10^{-6}M_\odot$ yr$^{-1}$ and are oxygen-rich. H$_2$S was not detected towards the carbon or S-type stars that fall in a similar mass-loss range. For the stars in our sample with detections, we find peak o-H$_2$S abundances relative to H$_2$ between $4\times 10^{-7}$ and $2.5\times 10^{-5}$. Overall, we conclude that H$_2$S can play a significant role in oxygen-rich AGB stars with higher mass-loss rates, but is unlikely to play a key role in stars of other chemical types or the lower mass-loss rate oxygen-rich stars. For two sources, V1300 Aql and GX Mon, H$_2$S is most likely the dominant sulphur-bearing molecule in the circumstellar envelope.