Physical properties of CO-dark molecular gas traced by C

Context. Neither Hi nor CO emission can reveal a significant quantity of so-called dark gas in the interstellar medium (ISM). It is considered that CO-dark molecular gas (DMG), the molecular gas with no or weak CO emission, dominates dark gas. Determination of physical properties of DMG is critical for understanding ISM evolution. Previous studies of DMG in the Galactic plane are based on assumptions of excitation temperature and volume density. Independent measurements of temperature and volume density are necessary. Aims. We intend to characterize physical properties of DMG in the Galactic plane based on C+ data from the Herschel open time key program, namely Galactic Observations of Terahertz C+ (GOT C+) and Hi narrow self-absorption (HINSA) data from international Hi 21 cm Galactic plane surveys. Methods. We identified DMG clouds with HINSA features by comparing Hi, C+, and CO spectra. We derived the Hi excitation temperature and Hi column density through spectral analysis of HINSA features. The Hi volume density was determined by utilizing the on-the-sky dimension of the cold foreground Hi cloud under the assumption of axial symmetry. The column and volume density of H2 were derived through excitation analysis of C+ emission. The derived parameters were then compared with a chemical evolutionary model. Results. We identified 36 DMG clouds with HINSA features. Based on uncertainty analysis, optical depth of HiτHi of 1 is a reasonable value for most clouds. With the assumption of τHi = 1, these clouds were characterized by excitation temperatures in a range of 20 K to 92 K with a median value of 55 K and volume densities in the range of 6.2 × 101 cm-3 to 1.2 × 103 cm-3 with a median value of 2.3 × 102 cm-3. The fraction of DMG column density in the cloud (fDMG) decreases with increasing excitation temperature following an empirical relation fDMG =−2.1 × 10-3Tex,(τHi = 1) + 1.0. The relation between fDMG and total hydrogen column density NH is given by fDMG = 1.0−3.7 × 1020/NH. We divided the clouds into a high extinction group and low extinction group with the dividing threshold being total hydrogen column density NH of 5.0 × 1021 cm-2 (AV = 2.7 mag). The values of fDMG in the low extinction group (AV ≤ 2.7 mag) are consistent with the results of the time-dependent, chemical evolutionary model at the age of ~10 Myr. Our empirical relation cannot be explained by the chemical evolutionary model for clouds in the high extinction group (AV > 2.7 mag). Compa