Physical properties of CO-dark molecular gas traced by C+^+

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. We identified 36 DMG clouds with C$^+$ emission (data from Galactic Observations of Terahertz C+ (GOT C+) project) and HINSA features. Based on uncertainty analysis, optical depth of HI $\tau\rm_{HI}$ of 1 is a reasonable value for most clouds. With the assumption of $\tau\rm_{HI}=1$, 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 $6.2\times10^1$ cm$^{-3}$ to $1.2\times 10^3$ cm$^{-3}$ with a median value of $2.3\times 10^2$ cm$^{-3}$. The fraction of DMG column density in the cloud ($f\rm_{DMG}$) decreases with increasing excitation temperature following an empirical relation $f\rm_{DMG}=-2.1\times 10^{-3}T_(ex,\tau_{HI}=1)$+1.0. The relation between $f\rm_{DMG}$ and total hydrogen column density $N_H$ is given by $f\rm_{DMG}$=$1.0-3.7\times 10^{20}/N_H$. The values of $f\rm_{DMG}$ in the clouds of low extinction group ($A\rm_V \le 2.7$ 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 ($A\rm_V > 2.7$ mag). Compared to clouds in the low extinction group ($A\rm_V \le 2.7$ mag), clouds in the high extinction group ($A\rm_V > 2.7$ mag) have comparable volume densities but excitation temperatures that are 1.5 times lower. Moreover, CO abundances in clouds of the high extinction group ($A\rm_V > 2.7$ mag) are $6.6\times 10^2$ times smaller than the canonical value in the Milky Way. #[Full version of abstract is shown in the text.]#Comment: Accepted for publishing in Astronomy & Astrophysics. 13 pages, 8 figure

Dust-Gas Scaling Relations and OH Abundance in the Galactic ISM

Observations of interstellar dust are often used as a proxy for total gas column density $N_\mathrm{H}$. By comparing $\textit{Planck}$ thermal dust data (Release 1.2) and new dust reddening maps from Pan-STARRS 1 and 2MASS (Green et al. 2018), with accurate (opacity-corrected) HI column densities and newly-published OH data from the Arecibo Millennium survey and 21-SPONGE, we confirm linear correlations between dust optical depth $\tau_{353}$, reddening $E(B{-}V)$ and the total proton column density $N_\mathrm{H}$ in the range (1$-$30)$\times$10$^{20}$cm$^{-2}$, along sightlines with no molecular gas detections in emission. We derive an $N_\mathrm{H}$/$E(B{-}V)$ ratio of (9.4$\pm$1.6)$\times$10$^{21}$cm$^{-2}$mag$^{-1}$ for purely atomic sightlines at $|b|$$>$5$^{\circ}$, which is 60$\%$ higher than the canonical value of Bohlin et al. (1978). We report a $\sim$40$\%$ increase in opacity $\sigma_{353}$=$\tau_{353}$/$N_\mathrm{H}$, when moving from the low column density ($N_\mathrm{H}$$<$5$\times$10$^{20}$cm$^{-2}$) to moderate column density ($N_\mathrm{H}$$>$5$\times$10$^{20}$cm$^{-2}$) regime, and suggest that this rise is due to the evolution of dust grains in the atomic ISM. Failure to account for HI opacity can cause an additional apparent rise in $\sigma_{353}$, of the order of a further $\sim$20$\%$. We estimate molecular hydrogen column densities $N_{\mathrm{H}_{2}}$ from our derived linear relations, and hence derive the OH/H$_2$ abundance ratio of $X_\mathrm{OH}$$\sim$1$\times$10$^{-7}$ for all molecular sightlines. Our results show no evidence of systematic trends in OH abundance with $N_{\mathrm{H}_{2}}$ in the range $N_{\mathrm{H}_{2}}$$\sim$(0.1$-$10)$\times$10$^{21}$cm$^{-2}$. This suggests that OH may be used as a reliable proxy for H$_2$ in this range, which includes sightlines with both CO-dark and CO-bright gas.Comment: The revised manuscript is accepted for publication in The Astrophysical Journa

Abundance ratios of OH/CO and HCO+/CO as probes of the cosmic ray ionization rate in diffuse clouds

The cosmic-ray ionization rate (CRIR, $\zeta_2$) is one of the key parameters controlling the formation and destruction of various molecules in molecular clouds. However, the current most commonly used CRIR tracers, such as H$_3^+$, OH$^+$, and H$_2$O$^+$, are hard to detect and require the presence of background massive stars for absorption measurements. In this work, we propose an alternative method to infer the CRIR in diffuse clouds using the abundance ratios of OH/CO and HCO$^+$/CO. We have analyzed the response of chemical abundances of CO, OH, and HCO$^+$ on various environmental parameters of the interstellar medium in diffuse clouds and found that their abundances are proportional to $\zeta_2$. Our analytic expressions give an excellent calculation of the abundance of OH for $\zeta_2$ $\leq$10$^{-15}$ s$^{-1}$, which are potentially useful for modelling chemistry in hydrodynamical simulations. The abundances of OH and HCO$^+$ were found to monotonically decrease with increasing density, while the CO abundance shows the opposite trend. With high-sensitivity absorption transitions of both CO (1--0) and (2--1) lines from ALMA, we have derived the H$_2$ number densities ($n_{\rm H_2}$) toward 4 line-of-sights (LOSs); assuming a kinetic temperature of $T_{\rm k}=50\,{\rm K}$, we find a range of (0.14$\pm$0.03--1.2$\pm$0.1)$\times$10$^2$ cm$^{-3}$}. By comparing the observed and modelled HCO$^+$/CO ratios, we find that $\zeta_2$ in our diffuse gas sample is in the { range of $1.0_{-1.0}^{+14.8}$ $\times$10$^{-16}- 2.5_{-2.4}^{+1.4}$ $\times$10$^{-15}$ s$^{-1}$. This is $\sim$2 times higher than the average value measured at higher extinction, supporting an attenuation of CRs as suggested by theoretical models.Comment: 22 pages, 9 figures, accepted by Ap

Dependence of Chemical Abundance on the Cosmic Ray Ionization Rate in IC 348

Ions (e.g., H$_3^+$, H$_2$O$^+$) have been used extensively to quantify the cosmic-ray ionization rate (CRIR) in diffuse sightlines. However, measurements of CRIR in low-to-intermediate density gas environments are rare, especially when background stars are absent. In this work, we combine molecular line observations of CO, OH, CH, and HCO$^+$ in the star-forming cloud IC~348, and chemical models to constrain the value of CRIR and study the response of the chemical abundances distribution. The cloud boundary is found to have an $A_{\rm V}$ of approximately 4 mag. From the interior to the exterior of the cloud, the observed $^{13}$CO line intensities drop by an order of magnitude. The calculated average abundance of $^{12}$CO (assuming $^{12}$C/$^{13}$C = 65) is (1.2$\pm$0.9) $\times$10$^{-4}$, which increases by a factor of 6 from the interior to the outside regions. The average abundance of CH (3.3$\pm$0.7 $\times$ 10$^{-8}$) is in good agreement with previous findings in diffuse and translucent clouds ($A_{\rm V}$ $<$ 5 mag). However, we did not find a decline in CH abundance in regions of high extinction ($A_{\rm V}\simeq$8 mag) as previously reported in Taurus. By comparing the observed molecular abundances and chemical models, we find a decreasing trend of CRIR as $A_{\rm V}$ increases. The inferred CRIR of $\zeta_{cr}$ = (4.7$\pm$1.5) $\times$ 10$^{-16}$ s$^{-1}$ at low $A_{\rm V}$ is consistent with H$^+_3$ measurements toward two nearby massive stars.Comment: 21 pages, 11 figures. Submitted to Ap