2025A&A...699A.354S

In recent decades, significant attention has been dedicated to analytical and observational studies of the atomic hydrogen (H I) to molecular hydrogen (H₂) transition in the interstellar medium. We focussed on the Draco diffuse cloud to gain deeper insights into the physical properties of the transition from H I to H₂. We employed the total hydrogen column density probability distribution function (N-PDF) derived from Herschel dust observations and the N_HI-PDF obtained from H I data collected by the Effelsberg H I survey. The N-PDF of the Draco cloud exhibits a double-log-normal distribution, whereas the N_HI-PDF follows a single log-normal distribution. The H I-to-H₂ transition is identified as the point where the two log-normal components of the dust N-PDF contribute equally; it occurs at A_V ∼ 0.33 (N ∼ 6.2 × 10²⁰ cm^–2). The low-column-density segment of the dust N-PDF corresponds to the cold neutral medium, which is characterized by a temperature of around 100 K. The higher-column-density part is predominantly associated with H₂. The shape of the Draco N-PDF is qualitatively reproduced by numerical simulations. In the absence of substantial stellar feedback, such as radiation or stellar winds, turbulence exerts a significant influence on the thermal stability of the gas and can regulate the condensation of gas into denser regions and its subsequent evaporation. Recent observations of the ionized carbon line at 158 μm in Draco support this scenario. Using the KOSMA-tau photodissociation model, we estimate a gas density of n ∼50 cm^–3 and a temperature of ∼100 K at the location of the H I-to-H₂ transition. Both the molecular and atomic gas components are characterized by supersonic turbulence and strong mixing, suggesting that simplified steady-state chemical models are not applicable under these conditions.