Understanding the temperatures of H₃⁺ and H₂ in diffuse interstellar sightlines

The triatomic hydrogen ion H-3(+) is one of the most important species for the gas phase chemistry of the interstellar medium. Observations of H-3(+) are used to constrain important physical and chemical parameters of interstellar environments. However, the temperatures inferred from the two lowest rotational states of H-3(+) in diffuse lines of sight - typically the only ones observable - appear consistently lower than the temperatures derived from H-2 observations in the same sightlines. All previous attempts at modelling the temperatures of H-3(+) in the diffuse interstellar medium failed to reproduce the observational results. Here we present new studies, comparing an independent master equation for H-3(+) level populations to results from the Meudon PDR code for photon dominated regions. We show that the populations of the lowest rotational states of H-3(+) are strongly affected by the formation reaction and that H-3(+) ions experience incomplete thermalisation before their destruction by free electrons. Furthermore, we find that for quantitative analysis more than two levels of H-3(+) have to be considered and that it is crucial to include radiative transitions as well as collisions with H-2. Our models of typical diffuse interstellar sightlines show very good agreement with observational data, and thus they may finally resolve the perceived temperature difference attributed to these two fundamental species.