Context. Stars form in the dense interiors of molecular clouds. The dynamics and physical properties of the atomic interstellar medium (ISM) set the conditions under which molecular clouds and eventually stars form. It is, therefore, critical to investigate the relationship between the atomic and molecular gas phase to understand the global star formation process. Aims. Using the high angular resolution data from The H I/OH/Recombination (THOR) line survey of the Milky Way, we aim to constrain the kinematic and physical properties of the cold atomic hydrogen gas phase toward the inner Galactic plane. Methods. H I self-absorption (HISA) has proven to be a viable method to detect cold atomic hydrogen clouds in the Galactic plane. With the help of a newly developed self-absorption extraction routine (astroSABER), we built upon previous case studies to identify H I self-absorption toward a sample of giant molecular filaments (GMFs). Results. We find the cold atomic gas to be spatially correlated with the molecular gas on a global scale. The column densities of the cold atomic gas traced by HISA are usually on the order of 1020 cm−2 whereas those of molecular hydrogen traced by 13CO are at least an order of magnitude higher. The HISA column densities are attributed to a cold gas component that accounts for a fraction of ~5% of the total atomic gas budget within the clouds. The HISA column density distributions show pronounced log-normal shapes that are broader than those traced by H I emission. The cold atomic gas is found to be moderately supersonic with Mach numbers of approximately a few. In contrast, highly supersonic dynamics drive the molecular gas within most filaments. Conclusions. While H I self-absorption is likely to trace just a small fraction of the total cold neutral medium within a cloud, probing the cold atomic ISM by the means of self-absorption significantly improves our understanding of the dynamical and physical interaction between the atomic and molecular gas phase during cloud formation.
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