Interaction of H$_2$S with H atoms on grain surfaces under molecular cloud conditions

Hydrogen sulfide (H$_2$S) is thought to be efficiently formed on grain surfaces through the successive hydrogenation of S atoms. Its non-detection so far in astronomical observations of icy dust mantles thus indicates that effective destruction pathways must play a significant role in its interstellar abundance. While chemical desorption has been shown to remove H$_2$S very efficiently from the ice, in line with H$_2$S gas-phase detections, possible solid-state chemistry triggered by the related HS radical have been largely disregarded so far -- despite it being an essential intermediate in the H$_2$S + H reaction scheme. We aim to thoroughly investigate the fate of H$_2$S upon H-atom impact under molecular cloud conditions, providing a comprehensive analysis combined with detailed quantification of both the chemical desorption and ice chemistry that ensues. Experiments are performed in an ultrahigh vacuum chamber at temperatures between 10--16 K. The changes in the solid phase during H-atom bombardment are monitored in situ by means of reflection absorption infrared spectroscopy (RAIRS), and desorbed species are measured with a quadrupole mass spectrometer (QMS). We confirm the formation of H$_2$S$_2$ via reactions involving H$_2$S + H, and quantify its formation cross section under the employed experimental conditions. Additionally, we directly assess the chemical desorption of H$_2$S by measuring the gas-phase desorption signals with the QMS, providing unambiguous desorption cross sections. Chemical desorption of H$_2$S$_2$ was not observed. The relative decrease of H$_2$S ices by chemical desorption changes from ~85% to ~74% between temperatures of 10 and 16 K, while the decrease as the result of H$_2$S$_2$ formation is enhanced from ~5% to ~26%, suggesting an increasingly relevant sulfur chemistry induced by HS radicals at warmer environments. The astronomical implications are further discussed.