© ESO, 2016

1. Introduction

The interstellar medium (ISM) is one of the fundamental baryon components of galaxies. The ISM hosts star formation. Determining the composition of the ISM will improve understanding of the lifecycle of ISM and the evolution of galaxies.

The 21-cm hyperfine line of atomic hydrogen has been used to trace the neutral medium. The linear relation between Hi column density and visual extinction, N(Hi) /A_V = 1.9 × 10²¹ cm^-2 mag^-1 (Bohlin et al. 1978), is valid for A_V< 4.7 mag. Molecular hydrogen, H₂, the main component of ISM, lacks a permanent dipole moment and does not have rotational radio transitions in cold ISM. CO and its isotopologues have been used as the main tracers of dense, well-shielded H₂ gas. At Galactic scales, H₂ column density is derived through multiplying integrated CO intensity W(CO) by an X_CO factor of 2 × 10²⁰ cm^-2(K km s^-1)^-1 with ± 30% uncertainty in the Milky Way disk (Bolatto et al. 2013). Though mean values of X_CO are similar for CO-detected molecular gas in diffuse and dense environments (Liszt et al. 2010), the volume density of CO-detected molecular gas is an order of magnitude greater than typical values of diffuse atomic gas shown in Heiles & Troland (2003).

The transition from diffuse atomic hydrogen to dense CO molecular gas is not well understood. Dust is assumed to be mixed well with gas. Infrared emission of dust has been used as a tracer of total hydrogen column density. Results from the all-sky infrared survey by the Infrared Astronomical Satellite (IRAS), the Cosmic Background Explorer (COBE), and the Planck satellite revealed excess of dust emission, implying additional gas that cannot be accounted by Hi and CO alone (Reach et al. 1994, 1998; Hauser et al. 1998; Planck Collaboration XIX 2011). Furthermore, the gamma-ray observations from COS-B (Bloemen et al. 1986) and the Energetic Gamma-Ray Experiment Telescope (EGRET; Strong & Mattox 1996; Grenier et al. 2005) also implied an extra gas component with a mass comparable to that in gas traced by N(Hi)+2X_CO*W(CO) in the Milky Way. This excess component of ISM, which cannot be fully traced by the usual Hi 21-cm or CO 2.6-mm transition, is termed dark gas.

The mainstream view considers dark gas to be unobserved molecular gas due to lack of corresponding CO emission. Most of the direct detections of molecular gas were made with CO emission. There are, however, examples of interstellar molecules detected toward lines of sight without corresponding CO emissions (Wannier et al. 1993; Magnani & Onello 1995; Allen et al. 2015). If the nondetection of CO is taken as a sign of missing molecular gas, the fraction of dark gas varies from 12% to 100% for individual components in Liszt & Pety (2012). The existence of unresolved molecular gas by CO is also supported by photodissociation region (PDR) model (e.g., van Dishoeck & Black 1988). H₂ can exist outside the CO region in an illuminated cloud because the self-shielding threshold of H₂ is smaller than that of CO. The gas in the transition layer between the outer H₂ region and the CO region is CO-dark molecular gas (DMG).

The DMG can be associated with Hi self-absorption (HISA), which is caused by a foreground Hi cloud that is colder than Hi background at the same radial velocity (e.g., Knapp 1974). The Canadian Galactic Plane Survey (CGPS; Gibson et al. 2000; Taylor et al. 2003) and the Southern Galactic Plane Survey (SGPS; McClure-Griffiths et al. 2005) revealed that HISA is correlated with molecular emission in space and velocity (Gibson et al. 2005; Kavars et al. 2005) although HINSA without H₂ can exist (Knee & Brunt 2001). It is now accepted fully that large portion of cold neutral medium (CNM) is colder (Heiles & Troland 2003) than the predictions of the three-phase ISM model (McKee & Ostriker 1977). When HINSA does contain H₂, it is dubbed Hi narrow self-absorption (HINSA; Li & Goldsmith 2003). In normal molecular clouds, HINSA can be easily identified through its correlation with ¹³CO. Without the emission of CO as a clear comparison mark, distinguishing between HISA and HINSA relies on the empirical threshold of δV ~ 1.5 km s^-1, which seems to be applicable in most diffuse regions, but can be subjective. We henceforth adopt the term HINSA because of our focus on DMG.

The total H₂ column density can be measured directly through ultraviolet (UV) absorption of H₂ toward stars. Observations taken by the Copernicus satellite (Savage et al. 1977) and the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite (Rachford et al. 2002, 2009) revealed a weak inverse correlation between rotational temperature and reddening, as well as increasing correlation between molecular fraction and reddening. These kinds of observations are limited to strong UV background stars with low extinction (<3 mag), and cannot resolve a Galactic cloud due to coarse spectral resolution (>10 km s^-1) at UV bands (Snow & McCall 2006). The C⁺-158 μm emission, a fine structure transition →, can be used as a probe of molecular gas in PDR. Based on C⁺ spectra obtained from a Herschel open time key program, Galactic Observations of Terahertz C+ (GOT C+), Langer et al. (2014, hereafter L14) found that DMG mass fraction varies from ~75% in diffuse molecular clouds without corresponding CO emission to ~20% for dense molecular clouds with CO emission.

There are two critical challenges in quantifying the DMG environment: the determination of the kinetic temperature, T_k, and the determination of the column and volume densities of Hi and H₂. Analysis of dust emission and extinction can aid in meeting these challenges. When looking into the Galactic plane, however, analysis of dust is muddied by source confusion. In previous studies, Kavars et al. (2005) attempted to constrain T_k and volume density n based on an analysis of Hi absorption. Because of the lack of an effective tracer of total hydrogen gas, these authors had to rely on the Galactic thermal pressure distribution in Wolfire et al. (2003) to estimate the molecular fraction. The study L14 introduced C⁺ emission as an effective tracer of total hydrogen gas. The study L14 assumed an overall temperature of 70 K and Galactic thermal pressure distribution to calculate total volume density. They analyzed C⁺ excitation to determine molecular abundance. Because C⁺ emission is sensitive to kinetic temperature and volume density, the lack of direct measurements of excitation temperature and volume density in L14 introduced uncertainties, especially for single clouds at low Galactic latitudes. Moreover, L14 obtained Hi intensity by integrating velocity width defined by the C⁺ (or ¹³CO) line. This overestimated Hi column density as widespread background Hi emission is included. Additionally, the optically thin assumption for the 21-cm line adopted in L14 results in an uncertainty of 20% for optical depth between 0.5 and 1 as discussed in their paper. Considering the caveats above, it is of great importance to inspect the effects of kinetic temperature, volume density, and Hi optical depth.

To improve constraints on physical properties of DMG, we adopted here the HINSA method in Li & Goldsmith (2003) to obtain an independent measure of T_ex(Hi), N(Hi), and n(Hi) = N(Hi) /L_Hi, where L_Hi is the linear dimension of HINSA cloud. H₂ volume density, n(H₂), and H₂ column density, N(H₂), can be related as n(H₂) = N(H₂) /L_H2, where L_H2 is the linear dimension of H₂ region of the HINSA cloud. According to the PDR model T6 (model parameters are proton density of 10³ cm^-3, temperature of 15 K, UV intensity of 1, and total visual extinction of 5.1 mag) in van Dishoeck & Black (1988), the outer layer with pure Hi (L_Hi− L_H2~ 0.03 pc) is relatively thin compared to the cloud with A_V = 1 mag (~0.9 pc). N(H₂) and n(H₂) can then be determined through C⁺ excitation analysis after adopting the ratio L_H2/L_Hi = 1. The uncertainty caused by the value of L_H2/L_Hi is discussed in detail in Sect. 4.3.

This paper is organized as follows. In Sect. 2, we describe our observations and data. In Sect. 3, we present our procedure to identify DMG clouds. In Sect. 4, we present derived spatial distribution, Hi excitation temperatures, column and volume densities of Hi and H₂ of identified DMG clouds from Hi and C⁺ analysis. In Sect. 5, we present derived DMG cloud properties. The discussion and summary are presented in Sects. 6 and 7, respectively.

Fig. 1 C+, Hi, and CO spectra toward G132.5-1.0, G337.0+0.5, G207.2-1.0, and G352.6+0.5. They are shown in top, middle, and bottom panel of each plot, respectively. In the top panel, the red solid line represents the gauss fit of the C+ emission profile of DMG component. In the middle panel, Hi On and OFF profile are derived from ON and around each sightline, respectively. The green solid line represents the residual profile derived from OFF-ON. The red solid line represents the gauss fit of the OFF-ON profile around the velocity of the DMG component. In the middle panel toward G207.2-1.0, THi and Tab in Eq. (2) are labeled.

2. Data

2.1. C⁺

The Herschel open time key program, GOT C+ observed C⁺-158 μm line toward 452 lines of sight toward the Galactic plane (e.g., Langer et al. 2010). Most of the lines of sight are within 1 degree of the Galactic plane in latitude except for a small fraction of lines of sight in the outer Galaxy that are within 2 degrees. Longitude distribution of all lines of sight can be found in Fig. 1 of L14. We obtained public C⁺ data from Herschel Science Archive (HSA) with the kind aid of J. Pineda. The angular resolution of the C⁺ observations is 12′′. The data have already been smoothed to a channel width of 0.8 km s^-1 with an average root mean square (rms) of 0.1 K. A detailed description of the GOT C+ program and the data can be found in Pineda et al. (2013) and L14.

Fig. 2 Hi spectrum and Hi channel map around absorption velocity toward G352.6+0.5 and G337.0+0.0, respectively. The dashed line on top of two Hi spectra profiles represents the central velocity of the absorption line. Red crosses below two channel maps represent positions toward G352.6+0.5 or G337.0+0.0. HINSA with real Hi absorption of foreground cold Hi cloud around ~−8.7 km s-1 is clearly seen toward G352.6+0.5. Non-HINSA with pseudo-absorption caused by relatively high brightness temperatures in neighbor velocity channels around ~−21.9 km s-1 is shown toward G337.0+0.0.

2.2. HI

The Hi data used here were taken from international Hi Galactic plane surveys. The Southern Galactic Plane Survey (SGPS; McClure-Griffiths et al. 2005) covers Galactic longitudes 253°≤ l ≤ 358° and 5°≤ l ≤ 20° with latitudes | b | ≤ 1.5°. The SGPS data have an angular resolution of 2′ and a rms of 1.6 K per 0.8 km s^-1. The VLA Galactic Plane Survey (VGPS; Stil et al. 2006) covers Galactic longitudes 18°≤ l ≤ 67° and latitudes | b | ≤ 1.3° to 2.3°. The VGPS image data have an angular resolution of 1′ and a rms of 2 K per 0.82 km s^-1. The Canadian Galactic Plane Survey (CGPS; Taylor et al. 2003) covers Galactic longitudes 63°≤ l ≤ 175° and latitude −3.6°≤ b ≤ 5.6°. The CGPS data have an angular resolution of 1′ and a rms of 2 K per 0.82 km s^-1. The Galactic Arecibo L-band Feed Array Hi (GALFA-Hi; Peek et al. 2011) survey covers −1.3°≤ δ ≤ 38.0°, about 32% of the sky. For Galactic longitudes 180°≤ l ≤ 212°, we extracted Hi spectra from GALFA-Hi data with an angular resolution of 3.4′ and a rms of 80 mK per 1 km s^-1.

2.3. CO

For lines of sight of GOT C+ in the Galactic longitude −175.5°≤ l ≤ 56.8°, J = 1→ 0 transitions of ¹²CO, ¹³CO, and C¹⁸O were observed with the ATNF Mopra Telescope (see Pineda et al. 2013 and L14 for details). The Mopra data have an angular resolution of 33′′. Two channels of CO spectrum were smoothed into one to derive a comparable velocity resolution to that of Hi spectra. The typical rms values are 0.44 K for ¹²CO per 0.7 km s^-1, 0.18 K for ¹³CO per 0.74 km s^-1, and 0.21 K for C¹⁸O per 0.73 km s^-1.

For those GOT C+ sightlines (56.8°<l< 184.5°) that are out of the Mopra sky coverage, we obtained J = 1 → 0 transitions of ¹²CO, ¹³CO, C¹⁸O with the Delingha 13.7 m telescope. Full width at half power of Delingha telescope is about 60′′. The observations were made between May 9 and 14 2014, using the configuration of 1 GHz bandwidth and 61 kHz channel resolution (velocity resolution of ~0.16 km s^-1). The data were reduced with GILDAS/CLASS¹ data analysis software and were smoothed to ~0.8 km s^-1 to be consistent with velocity resolution of Hi spectra. The derived rms values are 0.16 K for ¹²CO per 0.79 km s^-1 and 0.09 K for both ¹³CO and C¹⁸O per 0.83 km s^-1.

2.4. Radio continuum

To calculate excitation temperature from the HINSA features, background continuum temperature T_c is needed. The Milky Way background continuum temperature is estimated to be ~0.8 K in the L band (e.g., Winnberg et al. 1980). Total T_c containing contribution from the cosmic microwave background (2.7 K; Fixsen 2009) and the Milky Way is estimated to be 3.5 K, but T_c of 3.5 K is only valid for lines of sight toward high Galactic latitudes and T_c in the Galactic plane is seriously affected by continuum sources, e.g., H II regions. We adopted 1.4 GHz continuum data from the Continuum Hi Parkes All-Sky Survey (CHIPASS; Calabretta et al. 2014) with an angular resolution of 14.4′ and a sensitivity of 40 mK to derive T_c. The CHIPASS covers the sky south of declination +25° that corresponds to −180°<l< 68° in the Galactic plane. In 68°<l< 175°, continuum data from CGPS with a rms of ~0.3 mJy beam^-1 at 1420 MHz were utilized.

3. Procedures for HINSA identification and Gaussian fitting

As shown in Fig. 1, the relations between Hi, C⁺, and CO are complicated. For example, the cloud at V_lsr−52 km s^-1 for G337.0+0.5 has Hi, ¹²CO, and C⁺ emission. In contrast, the cloud at −44 km s^-1 for G337.0+0.5 has only Hi and ¹²CO, but no C⁺ emission. Our focus in this study is DMG clouds that have C⁺ emission with corresponding HINSA features, but without CO emission.

The first step is to identify DMG-HINSA candidates showing C⁺ emission and Hi depressions but no obvious CO emission. We found 377 such candidates toward 243 sightlines out of a total of 452 in the GOT C+ program by eye. The candidates were further filtered by the following procedures:

• 1.

  Depression features are common in GalacticHi spectra. They can be caused by temperaturefluctuations, gap effects between multiple emission lines,absorption toward continuum sources, or cooling throughcollision with H₂ (HINSA) as described inSect. 1. We checked Hi channelmap around the depression velocity to ascertain whether aHi depression feature is HINSA. A HINSAcloud should appear as a colder region than its surroundings inthe Hi channel map at its absorption velocity.Moreover, the colder region should be visible in maps of adjacentvelocity channels (≥ 2). Checking the channel map is necessary because non-HINSA features, with an obvious Hi spectral depression feature, are common. Examples of HINSA and non-HINSA features are shown in Fig. 2. We rejected more than half of Hi depression features as fake HINSA features after this inspection.

• 2.

  After visual inspection, we employed a quantitative inspection of the absorption to weed out confusion originating from temperature fluctuations. The Hi spectrum toward the GOT C+ sightline was labeled the ON spectrum. Background Hi emission arising from behind the foreground absorption cloud was derived through averaging spectra of nearby positions around the absorption cloud and was labeled the OFF spectrum. The nearby positions were selected from regions with HI emission contiguous with the ON position and at about 5 arcmin from the cloud boundary. An absorption signal in the ON spectrum is seen as an emission feature in the OFF-ON spectrum. The component in the residual OFF-ON spectrum is contributed by foreground cold HI cloud. (e.g., around −50 km s^-1 toward G132.5-1.0 of Fig. 1). Hi ON spectra in velocity ranges where Galactic Hi emissions are absent (e.g., V ≥ 60 km s^-1 or V ≤−20 km s^-1 in the Hi spectrum of G207.2-1.0) were chosen to calculate 1σ rms. Hi OFF-ON signals with signal-to-noise (S/N) greater than 3.0 were identified as absorption lines.

• 3.

  The rms values in different C⁺ spectra vary owing to different integration time. Spectral ranges without obvious signals were chosen to calculate 1σ rms. The typical 1σ rms of C⁺ is listed in Table 1. The rms values of different C⁺ spectra vary by as much as a factor of 1.5. Those C⁺ signals with S/N greater than 2.5 were identified as C⁺ emission lines, considering the generally weaker C⁺ emission for clouds without CO emission.

Most spectra are complicated and are far from isolated Gaussian components. Decomposition is necessary. The outcome of the fitting is sensitive to initial inputs, especially the number of Gaussian components and the central velocities of individual components. We developed an IDL code to do Gaussian decomposition. In the code, the number of Gaussian components was automatically determined by the method presented in Lindner et al. (2015). The key is the solution of derivatives of the spectra. A regularization method is introduced. It is difficult to define a suitable regularization parameter, which controls the smoothness of the derivations of the spectra. We chose a coarse regularization parameter that may introduce extraneous components. A visual check of all components was performed to remove obviously unreliable components. The estimated parameters of Gaussian components were input as initial conditions into the Gaussian fitting procedure gfit.pro, which was adopted from the Millennium Arecibo 21 cm absorption-line survey (Heiles & Troland 2003), to give final fitting parameters of decomposed Hi and C⁺ components.

We first fitted Gaussians to the Hi OFF-ON spectra around HINSA velocity because the HINSA components are easily recognized. In most cases, Hi OFF-ON spectra can be fitted with only one Gaussian component. In other cases, two components were used, and no case of three components was needed. The derived Hi parameters were used as initial conditions for C⁺ emission fitting. Examples of Gaussian decomposition for Hi and C⁺ spectra are shown in Fig. 1.

The derived components were further filtered based on line widths. We required that an emission line should have at least two channels, corresponding to 1.6 km s^-1 in C⁺ and Hi spectra.

A final check was necessary to determine whether the observed Hi gas can produce the observed C⁺ emission alone; details are in Sect. 4.3. Finally, we ended up with 36 DMG clouds with relatively clearly visible HINSA features and Gaussian components.

4. Derivation of cloud parameters

4.1. Galactic spatial distribution

Kinematic distance was derived based on the Milky Way rotation curve (Brand & Blitz 1993). The galactocentric radius, R, for a cloud with Galactic longitude, l, latitude, b, and radial velocity along line of sight, V_los, is given by (1)where V_R is orbital velocity at R. V_⊙ = 220 km s^-1 is local standard of rest (LSR) orbital velocity of the Sun at R_⊙ of 8.5 kpc as recommended by International Astronomical Union (IAU); V_R/V_⊙ = a₁(R/R_⊙)^a₂ + a₃ with a₁ = 1.00767, a₂ = 0.0394, and a₃ = 0.00712 (Brand & Blitz 1993). Then the distance to the cloud, d, can be expressed as a function of R. In the outer galaxy (R > R_⊙), the solution is unique, . In the inner Galaxy (R<R_⊙), there exists kinematic distance ambiguity (KDA) with two simultaneous solutions for a velocity along a line of sight, .

There are three main resolutions of the KDA: (1) Hi absorption against bright pulsars (Koribalski et al. 1995) or against H II regions with well-known distances (Kolpak et al. 2003); (2) judgement of different angular extent of the cloud at the near and far kinematic distances (e.g., Clemens et al. 1988); and (3) the HINSA method. Clouds in the near distance tend to show HINSA features while clouds in the far distance do not because of the lack of absorption background (Roman-Duval et al. 2009; Wienen et al. 2015). A comparison of the optical image with the ¹³CO distribution for GRSMC 45.6+0.3 supports this premise (Jackson et al. 2002).

While solutions 1 and 2 are limited to sources satisfying specific conditions, solution 3 can be applied to more sources. To test the validity of our distance calculation, we compared our calculated kinematic distance with maser trigonometric parallax distances for four sources listed in Table 3 of Roman-Duval et al. (2009). Two kinds of distances are consistent within ≤5%. We took the near distance value for our sources located in the inner Galaxy. The distance thus derived was used to calculate the background Hi fraction p in Eq. (2) in Sect. 4.2.

The above distance estimates have the following caveats: (1) there may exist enough background for a cloud to show HINSA, even at the far distance; for example, such a background can be provided by spiral density waves (Gibson et al. 2000, 2005a). (2) The existence of cloud-to-cloud velocity dispersion of about 3 km s^-1 (Clemens 1985) adds uncertainty to the one-to-one mapping of distance to velocity. Streaming motions of 3 km s^-1 will introduce an uncertainty of <~220 pc for cloud with (l,b) = (45°, 0°) and LSR velocity of 40 km s^-1.

Figure 3 shows the spatial distribution of 36 DMG clouds in the Galactic plane. Four Galactic spiral arms revealed by distributions of star-forming complexes in Russeil (2003) are also drawn. It can be seen that most clouds are located between 311° and 55° in Galactic longitude. The two ends of the longitude range correspond to tangent directions along Scutum-Crux Arm and Sagittarius Arm, respectively. Selection effect may contribute to this. Foreground clouds preferentially exhibit HINSA features when they are backlit by warmer Hi emerging from the Galactic bar and spiral arms.

Fig. 3 Spactial distribution of DMG clouds in the Galactic plane. The positions of the Sun and the Galactic center (GC in the plot) are indicated with red crosses.

4.2. Analysis of HINSA

The excitation temperature of cold Hi absorption cloud can be derived as (Li & Goldsmith 2003) (2)where T_c is the background continuum temperature derived from CHIPASS and CGPS continuum data (Sect. 2.4); p is Hi fraction behind the foreground cold cloud; T_Hi is the reconstructed background Hi brightness temperature without absorption of the foreground cold cloud; and T_ab is the absorption brightness temperature. The temperatures T_Hi and T_ab are shown in the spectra toward G207.2-1.0 in Fig. 1; τ_f, the foreground Hi optical depth, was adopted as 0.1; and τ_Hi is the optical depth of Hi in the cold cloud. Infinite τ_Hi results in an upper limit of excitation temperature, . Kolpak et al. (2002) showed an average optical depth of 1 for clouds in the spatial range between Galactic radius 4 and 8 kpc. As seen from Fig. 3, most of our clouds are located in that spatial range. Thus it is reasonable to assume τ_Hi = 1 for our clouds. The uncertainties of adopting different τ_Hi are discussed further in Sect. 5.1.

Galactic Hi spatial distribution and positions of DMG clouds are necessary for calculating p. The Galaxy was divided into a set of concentric rings, with a galactocentric radius R and radius width ΔR = 1 kpc. The Hi surface density Σ(r) of each concentric ring was assumed to be constant and distributed as Fig. 10 in Nakanishi & Sofue (2003). The maximum galactocentric radius of the Galaxy was chosen as 25 kpc. The spatial information derived in the Sect. 4.1 was applied here. The Hi fraction behind foreground cold cloud , where is the total integrated Hi surface density along a sightline and the is the integrated Hi surface density behind the cloud.

Derived T_ex,(τ_Hi = 1) and are shown in Cols. (4) and (5) of Table 2, respectively. Excitation temperature distributions of DMG are shown in Fig. 4. T_ex,(τ_Hi = 1) ranges from 20 to 92 K, with a median value of 55 K. This median value is comparable to the observed median temperature of 48 K for 143 components of cold neutral medium (Heiles & Troland 2003), which were decomposed from emission/absorption spectra toward 48 continuum sources. Moreover, this median value is consistent with the calculated temperature range of ~50−80 K in the CO-dark H₂ transition zone in (Wolfire et al. 2010). The derived lowest T_ex,(τ_Hi = 1) is 20.3 K for G028.7-1.0.

The uncertainties of T_ex result from p are associated with two aspects. The first is our adoption of the average Hi surface density in each concentric ring is ideal. This is idealized for two reasons. Firstly, and probably more importantly, is the presence of the localized Hi structure, some of which is associated with the very dark gas we are studying; excess Hi associated with this structure can lie in front of or behind the HINSA. Secondly, such a smooth Hi distribution on large scales is idealized because it neglects such things as spiral structure. The second is the distance ambiguity of the cloud, which may cause a twice the uncertainty. For instance, the near and far distance of G025.2+0.0 is 2.4 kpc and 13.0 kpc. The values of p are 0.86 and 0.59, resulting in T_ex of 52.9 K and 28.7 K, respectively. As we discussed in Sect. 4.1, we prefer the near distance due to Hi absorption feature in our sources. Thus the derived Hi excitation temperature is an upper limit because of our adoption of the near distance.

Fig. 4 Histogram of excitation temperature distribution. Blue rectangles represent the distribution of upper limits to the excitation temperature. Rectangles with filled red lines represent the distribution of excitation temperature when optical depth τHi = 1.

With the condition of hν/kT_ex ≪ 1, Hi column density N(Hi) is related to Hi optical depth τ_Hi and excitation temperature T_ex through (3)We derived N(Hi) by adopting T_ex,(τ_Hi = 1) and τ_Hi = 1, where T_ex is excitation temperature of the cloud. The values of N(Hi) are shown in Col. (8) of Table 2, assuming τ_Hi = 1. The median value of N(Hi) is 3.1 ×10²⁰ cm^-2. As seen in Eq. (2), T_ex depends on τ_Hi. The uncertainty in τ_Hi would strongly affect N(Hi) and the DMG fraction as seen in Sect. 5.1.

The HINSA angular scale, Δθ, can be measured from Hi channel maps. Though most HINSA have a complex nonspherical structure, we used a geometric radius to model the HINSA region in Hi channel map. For a cylinder structure, we chose the width as cloud diameter. For some HINSA clouds without a clear boundary, there may exist larger uncertainties. Combining with the calculated distance d in Sect. 4.1, we can determine the spatial scale of cloud L_Hi = Δθ·d. Hi volume density can then be calculated through n(Hi) = N(Hi) /L_Hi. The derived n(Hi) are shown in Col. (6) of Table 2 with a median value of 34 cm^-3, which is consistent with the typical CNM volume density, n(Hi)_CNM ~ 56 cm^-3 (Heiles & Troland 2003).

4.3. Analysis of C⁺

C⁺ is one of the main gaseous forms of carbon elements in the Galactic ISM. It exists in ionized medium, diffuse atomic clouds, and diffuse/translucent molecular gas regions where the phase transition between atomic and molecular gas happens (e.g., Pineda et al. 2013). The C⁺ 158 μm line intensity, a major cooling line of the CNM, is sensitive to physical conditions. This line is an important tool for tracing star formation activity and ISM properties in the Milky Way and galaxies (e.g., Boselli et al. 2002; Stacey et al. 2010).

The C⁺ 158 μm line is mainly excited by collisions with electrons, atomic hydrogen, and molecular hydrogen. Collisional rate coefficient (s^-1/cm^-3) with electrons is ~100 times larger than that with atomic and molecular hydrogen because of the advantage of Coulomb focusing (Goldsmith et al. 2012). The C⁺ emission from ionized gas contributes only 4% of the total C⁺ 158 μm flux in the Milky Way (Pineda et al. 2013). Our selected clouds have T_ex less than 100 K and should be cold neutral medium (CNM) without high percentage of ionization. In neutral region, Hi and H₂ dominate collisions with C⁺. C⁺ intensity can be given by (Goldsmith et al. 2012) (4)where χ_H(C⁺) is C⁺ abundance relative to hydrogen; χ_H(C⁺) = 5.51 × 10^-4exp(−R_gal/ 6.2), is valid for spatial range 3 kpc <R_gal< 18 kpc (Wolfire et al. 2003); and χ_H(C⁺) = 1.5 × 10^-4 was adopted outside that range. The parameters n_cr(Hi), n_cr(H₂) are critical densities of Hi and H₂, respectively; n_cr(Hi) = 5.75 × 10⁴/ (16 + 0.35T^0.5 + 48T^-1) cm^-3 and n_cr(H₂) = 2n_cr(Hi) were adopted from Goldsmith et al. (2010); n_Hi and n_H2 are volume densities of Hi and H₂, respectively; ΔE/k, the transition temperature between - of C⁺, is 91.26 K; and T_k is gas kinetic temperature. It is equivalent to T_ex of Hi because Hi 21 cm emission is always in local thermodynamic equilibrium (LTE) in gas with density ≳ 10 cm^-3 due to low Hi critical density (~10^-5 cm^-3).

We estimated n(H₂) = N(H₂)/L_H2, where L_H2 is the diameter of H₂ layer in cloud and L_H2 = L_Hi was adopted as already discussed in Sect. 1. Thus N(H₂) and n(H₂) can be determined from Eq. (4), and the results are shown in Cols. (7) and (9) of Table 2, respectively. The median value of n(H₂) is 2.3 ×10² cm^-3. The median value of N(H₂) is 2.1 ×10²¹ cm^-2 .

Visual extinction is connected with total proton column density through, A_V = 5.35 × 10^-22 [N(Hi) + 2N(H₂)] mag, assuming a standard Galactic interstellar extinction curve of R_V = A_V/E(B − V) = 3.1 (Bohlin et al. 1978). The corresponding visual extinction values toward each source are shown in Col. (11) of Table 2. In Fig. 5, we plot A_V as a function of T_ex. It is clear that A_V has a decreasing trend when T_ex increases.

The ratio between L_H2 and L_Hi is a key relation during the above calculation, but may vary for clouds with different visual extinction and different PDR models. We took another value L_H2/L_Hi = 0.8, which is the possible lower value of PDR with A_V< 0.2 mag, to estimate the uncertainty. With ratios of 1.0 and 0.8, the maximum differences of N(H₂), A_V, and DMG fraction (Sect. 5.1) are 10%, 10%, and 5%, respectively. Thus the value of the ratio L_H2/L_Hi does not affect the physical parameters associated with H₂ too much.

Fig. 5 Relation between visual extinction and excitation temperature. Red rectangles indicate median visual extinctions for excitation temperature bin of 10 K. The physical widths and heights of the rectangles are 10 K and 1 mag, respectively.

5. Inferred DMG cloud properties

5.1. Observed properties of dark gas clouds

Physical properties and spatial distribution of DMG are fundamental quantities that affect our understanding of the transition between diffuse atomic clouds and dense molecular clouds. If extra H₂ not traced by CO is needed to explain the observed C⁺ intensity, the cloud is considered a DMG cloud.

Following Eq. (7) in L14, the mass fraction of DMG in the cloud is defined as, (5)where N(H₂) = N(CO–dark H₂) + N(CO–traced H₂). In this paper, N(CO–traced H₂) is set to 0 due to absence of CO detection for our samples.

The uncertainty of f_DMG comes from two aspects. First, measurement and fitting of the Hi and C⁺ spectra. They were estimated to be less than ~10% for all the sources. The second is the uncertainty of adopting τ_Hi of Hi. As seen in Sect. 4.2, τ_Hi of Hi greatly affects the Hi column density, and thus f_DMG. It is necessary to investigate available parameter space. The parameters are constrained by the following three conditions:

• 1.

  T_ex > 0 K.

• 2.

  N_H2 ≥ 0 cm^-2.

• 3.

  The derived extinction A_V≤A_V(dust), where A_V(dust) is the total Galactic dust extinction along the sightline. We adopted extinction values from all sky dust extinction database (Schlafly & Finkbeiner 2011), in which dust extinction was derived through analyzing colors of stars E(B − V) of Sloan Digital Sky Survey with a reddening ration A_V/E(B − V) = 3.1.

The relations between f_DMG, T_ex, and τ_Hi for 36 sources are shown in Fig. 6. It is worthwhile to note that the upper values of τ_Hi are overestimated and lower values of τ_Hi are underestimated as A_V(dust) is the total value along the sightline of each source. The parameter A_V(dust) contains contributions from CO-traced molecular gas at other velocities besides those with dark gas.

Fig. 6 Relation curves between fDMG, τHi, and Tex. Panel a) shows 3D curves with red lines. Relations between each two parameters are projected with black lines. Panel b) shows relation between fDMG and τHi. The green dashed line represents τHi = 1. The value with τHi = 1 for 33 sources are indicated with red crosses, but for G132.5-1.0, G207.2-1.0, and G347.4+1.0, τHi = 5.4,4.3, and 0.5, respectively. They are shown with red squares. Panel c) shows the relation between fDMG and Tex. Panel d) shows the relation between τHi = 1 and Tex. The meaning of red crosses and blue dashed lines in panels c) and d) are same as in panel b).

According to Eq. (2), higher T_ex is required to produce a fixed absorption strength when τ_Hi increases. This is reflected in Fig. 6d. According to Eq. (3), a bigger τ_Hi produces larger N(Hi).

In Fig. 6b, we present f_DMG versus τ_Hi. When τ_Hi increases, f_DMG decreases to a nonzero minimum value. This can be understood as follows. C⁺ is mainly excited by collisions with Hi and H₂. According to Eq. (4), for a fixed C+ intensity, increasing N(Hi) and T_k (T_k = T_ex was adopted) increases the contribution of Hi collision to C⁺ emission, requiring decreasing contribution from H₂ collision, thus decreasing the H₂ column density and decreasing the H₂ fraction in the cloud. The lower limits of τ_Hi for all sources are less than 1.0 except for G132.5-1.0 and G207.2-1.0, which have a τ_Hi range of (1.7, 9.0) and (2.3, 6.2), respectively. For these two sources, we apply median value τ_Hi = 5.4 and 4.3, respectively. As seen in Figs. 6c and d, this selection does not affect T_ex and f_DMG too much as they are in narrow value ranges, (23.0, 28.2) K and (0.83, 0.98) for G132.5-1.0, (37.7, 39.8) K and (0.86, 0.95) for G207.2-1.0; τ_Hi = 0.5 is applied for G347.4+1.0 due to an upper limit of 0.85. For other 33 sources, we apply τ_Hi = 1.0. Although this selection is arbitrary, we argue that it is reasonable for two reasons. The first reason is that averaged Hi optical depth between the Galactic radius 4 and 8 kpc is around 1.0 (Kolpak et al. 2002). The second reason is that the changes from 0.5 to 1.5 of τ_Hi strongly affect f_DMG value for only three sources. For other sources, the values of f_DMG have a minimum of ≥ 0.6 in this τ_Hi range, implying a weak dependence of τ_Hi in the range of [0.5, 1.5]. Thus we take a τ_Hi range of [0.5, 1.5] to represent the total uncertainty since uncertainties of τ_Hi are much greater than measurement and fitting uncertainties.

Fig. 7 Relation between DMG fraction and excitation temperature. Median values of fDMG per 10 K are shown with red rectangles. The width and height of the rectangles are 10 K and 0.05, respectively. Green solid curve represents best linear fitting for median values.

The relation between f_DMG and T_ex,(τ_Hi = 1) is shown in Fig. 7. The relation between DMG fraction and gas excitation temperature can be described well by an empirical relation, (6)The decreasing trend of f_DMG toward increasing T_{ex,(τHi = 1)} is clear. This result is consistent with that in Fig. 7 of Rachford et al. (2009). With the FUSE telescope, Rachford et al. (2009) derived the total molecular hydrogen N(H₂) and rotational temperature T₀₁ directly through UV absorption of H₂ toward bright stars. These authors found that molecular fraction f = 2N(H₂)/(2N(H₂) + N(Hi)) decreases from ~0.8 at T₀₁ = 45 K to ~0.0 at T₀₁ = 110 K with relatively large scatter. Though the decreasing trend between our result and that in Rachford et al. (2009) is similar, f_DMG is as high as 7.7 × 10^-1 at T_ex = 110 K in Eq. (6), implying a flatter slope compared to that in Rachford et al. (2009). Our results are more physical meaningful because N(Hi) and T₀₁ in Rachford et al. (2009) are averaged values along a line of slight.

Relation between f_DMG and N_H is shown in Fig. 8. It reflects DMG fractions along different extinctions and is investigated in most theoretical papers. The data are fitted with an empirical relation (7)We compared this result with cloud evolutionary model from Lee et al. (1996), who incorporated time-dependent chemistry and shielding of CO and H₂ in photodissociation clouds. Lee et al. (1996) split the cloud into 43 slabs. We adopted Lee’s model through the following procedures. First, we calculated total hydrogen column density N_H and total H₂ column density N(H₂) at 43 slabs. Then CO-traced H₂ was calculated through N(CO-traced H₂) = N(CO)/Z(CO), where Z(CO) is CO abundance relative to molecular hydrogen. We derived the DMG column density through N(DMG) = N(H₂)-N(CO-traced H₂). Finally, the DMG fraction f_DMG = 2N(DMG)/N_H. As already shown in the models of Lee et al. (1996), Z(CO) varies significantly under different environments as shown in the chemical models (e.g., Lee et al. 1996) and in observations toward diffuse gas clouds (Liszt & Pety 2012). We adopted a constant Z(CO) = 3.2 ×10^-4 (Sofia et al. 2004) that is an upper limit in the ISM during the calculation. This leads to an upper DMG fraction from the model.

We adopted model 1 in Lee et al. (1996), in which all hydrogen were originally in atomic phase. The DMG fractions as a function of hydrogen column density in the age of 10⁵, 10⁶, 10⁷, and 10⁸ yr are shown in Fig. 8 with dashed lines. It can be seen that our results are consistent with model results at age of 10⁷ yr when N_H ≲ 5 × 10²¹ cm^-2 (A_V≲ 2.7 mag). When N_H > 5 × 10²¹ cm^-2, f_DMG decreases according to the modeled results of chemical evolution but still increases in our results. This difference persists even we consider data uncertainties. The 36 clouds were thus divided into two groups: a low extinction group with N_H ≲ 5 × 10²¹ cm^-2 and high extinction group with N_H > 5 × 10²¹ cm^-2.

Planck Collaboration XIX (2011) found an apparent excess of dust optical depth τ_dust compared to the simulated between A_V range of [0.37, 2.5] mag. The A_V value of ~0.37 mag and ~2.5 mag correspond to threshold extinction of H₂ self-shielding and threshold extinction of dust shielding for CO, respectively. When A_V > 2.5 mag, the CO abundance increases, resulting in a deceasing DMG fraction as expected from the chemical evolutionary model predictions at the age of 10⁷ yr in Fig. 8. If the CO luminosity is too weak to be observed, this would lead to an increasing curve when A_V > 2.5 mag. Actually, Liszt & Pety (2012) found patchy CO emission in DMG regions with higher CO sensitivity.

In order to estimate CO abundance limits in high extinction group (A_V > 2.7 mag) clouds, we assumed optically thin and LTE of CO. These two assumptions are reasonable owing to no detection of CO and T_ex/5.56 K ≫ 1. ¹²CO column densities were derived through N(¹²CO) = 4.8 × 10^14∫T_bdυ cm^-2. We used a rms of T_b = 0.6 K and velocity resolution of 0.35 km s^-1 in our CO spectra. An upper limit of ¹²CO column density N(CO) = 1.0 × 10¹⁴ cm^-2 implies an upper CO abundance relative to H₂ for A_V > 2.7 mag; is 6.6 × 10² times smaller than the canonical value of 3.2 × 10^-4 in the Milky Way (Sofia et al. 2004).

Our assumption of optically thin emission of CO in low A_V clouds is mostly empirical. This assumption can be quantified as the following. We smoothed the data to RMS of 0.44 K per 0.7 km s^-1. For a cloud with modest opacity at T_ex = 10 K, T_bg = 2.7 K, τ(CO) = 1, the derived antenna temperature (50% main beam efficiency) is 2.1 K, which is way above our RMS threshold.

Thus we conclude that, clouds in high extinction group (A_V > 2.7 mag) are CO poor molecular clouds. The formation of these clouds are discussed in Sect. 6.1.

Fig. 8 Fraction of DMG vs. hydrogen column density NH. Results for 36 sources are shown in open circles. Red solid line shows the best fitting. Dashed lines with different colors represent chemical evolutionary model results from Lee et al. (1996). Vertical dotted red line represents NH = 5 × 1021 cm-2.

5.2. Comparison between clouds in low and high extinction groups

We plotted the total gas volume density n_gas = n_Hi + n_H2 as a function of T_ex for 36 sources in Fig. 9. Typical thermal pressure P_th of 6 × 10³ K cm^-3 in Galactic radius of 5 kpc (Wolfire et al. 2003), P_th of 1.4 × 10⁴ K cm^-3 near the Galactic center (Wolfire et al. 2003), and auxiliary P_th of 4 × 10⁴ K cm^-3 are also shown. Median densities for the low extinction (A_V ≤ 2.7 mag) and high extinction (A_V > 2.7 mag) groups are 212.1 and 231.5 cm^-3, respectively. The median excitation temperatures for the low extinction (A_V ≤ 2.7 mag) and high extinction (A_V > 2.7 mag) groups are 64.8 and 41.9 K, respectively. Densities in these two groups are comparable but excitation temperatures are relatively lower in high extinction (A_V > 2.7 mag) group, resulting lower thermal pressures in this group. We discuss the implication for cloud formation in Sect. 6.1.

Fig. 9 Relation between volume density and excitation temperature. Blue, green, and red lines represent pressure P/k of 6000, 1.4 ×104, 4 ×104 K cm-3, respectively.

6. Discussion

6.1. Assembly of molecular clouds

Molecular clouds can be formed either directly from neutral medium or by assembling pre-existing, cold molecular clumps. The first scenario is commonly accepted (e.g., Hollenbach & McKee 1979). The second scenario is outlined by Pringle et al. (2001), who proposed that clouds formed out of pre-existing, CO-dark, molecular gas. Compared to the first scenario, the second scenario allows for fast cloud formation in a few Myr, which was suggested by observations (Beichman et al. 1986; Lee et al. 1999; Hartmann et al. 2001). The key problem for the second evolutionary scenario is how molecular gas can exist before it is collected together. Pringle et al. (2001) argued that the pre-existing molecular gas should be cold (<10 K) and was shielded from photodissociation by patch dust with A_V of ~0.5 mag (White et al. 1996; Berlind et al. 1997; González et al. 1998; Keel & White 2001). Under A_V of ~0.5 mag, H₂ should exist substantially while CO is in very low abundance. This is because the self-shielding threshold of A_V = 0.02 and 0.5 mag (Wolfire et al. 2010) are widely considered as a condition for maintaining a stable population of abundant H₂ and CO gas, respectively. Listz & Pety (2012) detected strong CO(1−0) emission (4−5 K) in regions with equivalent visual extinction less than 0.5 mag. Two obvious possibilities are 1) the CO gas is transient. Such gas may also have been seen in Goldsmith et al. (2008), who detected a 40% of the total CO mass in Taurus in regions with low to intermediate A_V (mask 0 and 1 in their terminology). 2) Such CO gas lies in a highly clumpy medium with lower apparent averaged extinction when photons travel through lower density interclump medium. When small agglomerations of molecular gas are compressed and heated by shock, e.g., in a spiral arm, they become detectable. This scenario is supported by observations of GMC formation in spiral arms (Dobbs 2008) and simulations of molecular clouds formation (e.g., Clark et al. 2012).

In Sect. 5.1, we showed that clouds in high extinction group (A_V > 2.7 mag) are not consistent with chemical evolutionary model of the first scenario. The upper limit of CO abundance in this group is 6.6 × 10² times smaller than the typical value in the Milky Way. We suggest the CO-poor feature can be explained if clouds in the high extinction group (A_V > 2.7 mag) are formed through coagulation of pre-existing molecular, CO-poor clumps. The clouds should be in the early stage of formation. According to chemical evolutionary model, CO can reach an abundance of 2 × 10^-5 in 10⁵ yr at A_v = 2.7 mag if all hydrogen is locked in H₂ before the cloud formation (Lee et al. 1996). Thus the cloud age may be constrained to be less than 1.0 × 10⁵ yr after cloud assembly.

Moreover, the obvious differences seen in linewidth-scale relation, excitation temperature distribution, and non-thermal/thermal ratio relations for clouds in the low extinction group (A_V ≤ 2.7 mag) and high extinction group (A_V > 2.7 mag) in Sect. 5.2, are possible pieces of evidence to support the cloud formation under the second scenario.

6.2. HI contributes little in explaining dark gas

Dark gas is the gas component that is not detected with either Hi or CO emission but is clearly seen from the excess of A_V compared to N_H (Reach et al. 1994). We focus on DMG, but as pointed out in Planck Collaboration XIX (2011), N(Hi) could be underestimated with the optically thin approximation and an excitation temperature that is too high. Atomic Hi may contribute as much as 50% mass for the excess according to their estimate. Fukui et al. (2015) investigated the Hi optical depth τ_Hi and reanalyzed all sky Planck/IRAS dust data in high galactic latitudes (| b | > 15°). They derived 2−2.5 times higher Hi densities than that with optical thin assumption. They implied that optically thick cold Hi gas may dominate dark gas in the Milky Way.

In this paper, we introduced HINSA as an effective tool to constrain τ_Hi. Though τ_Hi = 1 is applied for 33 clouds, it does not affect the conclusion much that DMG dominated the cloud mass for 0.5 ≤ τ_Hi ≤ 1.5.

Another objection against H₂ dominating dark gas in Fukui et al. (2015) was that, crossing the timescale of ≤ 1 Myr of local clouds is an order of magnitude smaller than H₂ formation timescale 2.6 × 10⁹/n_Hi yr (Hollenbach & Natta 1995; Goldsmith & Li 2005) for typical clouds (n ~ 100 cm^-3). This is not a problem if we adopt the assumption in Sect. 6.1 that molecular clouds are formed by assembling pre-existing molecular gas.

Within our sample of clouds with C+ emission and HI self-absorption, the molecular gas seems to be the dominant component regardless of their individual excitation temperatures, optical depth, and their lack of CO emission. Our conclusion is in line with the direct observational result in the Perseus by Lee et al. (2015).

6.3. Galactic impact

Grenier et al. (2005) indicated that dark gas mass is comparable to that of CO-traced molecular gas in the Milky Way. Our results suggest that H₂ dominates the dark gas. In a previous study, L14 obtained Hi intensity by integrating over a velocity range centered around their V_LSR defined by the C⁺ (or ¹³CO) line. Moreover, they adopted an optically thin assumption and a constant kinematic temperature of 70 K. To compare with L14, we applied these treatments to DMG clouds in this study. Results from these treatments differ from our results by an average factor of for total visual extinction A_V and differ by an average factor of for DMG fraction. The symbol “+” means maximum value of underestimate and “−” means maximum value of overestimate. The actual DMG content detected with previous treatments and method here may differ a little.

The detections in this study are limited for DMG for two reasons. First, DMG clouds without HINSA feature are common in the Milky Way. Second, C⁺ emission in some DMG clouds may be hard to identify.

We estimated quantitatively the detection limits in this study. To be detected under the sensitivities of this study, the excitation temperature should be lower than the background emission temperature. The detection requirement of C⁺ brightness temperature is 0.25 K (2.5σ). As seen in Eq. (4), C⁺ intensity strongly depends on kinetic temperature T_k. To produce a C⁺ intensity of 3.2 × 10^-1 K km s^-1 ( K and FWHM of 1.0 km s^-1), it requires a N(H₂) = 9.0 × 10¹⁹ cm^-2 under T_k = 70.0 K and N(H₂) = 2.2 × 10²¹ cm^-2 under T_k = 20.0 K, assuming n_H2 = 1.0 × 10³ cm^-3. Thus a large fraction of cold, diffuse DMG clouds in the Milky Way may be undetectable as C⁺ emission is under the conditions specified in this paper.

7. Summary

In this paper, we have carried out a study of the DMG properties in the Galactic plane by combining physical properties derived from C⁺ survey of Hershel, international Hi surveys, and CO surveys. The HINSA method was used to determine Hi excitation temperature, which is assumed to be constant in previous works (e.g., Langer et al. 2014). Our conclusions include

• 1.

  Most DMG clouds are distributed between the Sagittarius armand Centaurus arm in the Milky Way. We argue that this is causedby sample selection with HINSA features, which can beproduced only when background temperature is stronger thanexcitation temperature of foreground cloud.

• 2.

  Hi excitation temperatures of DMG clouds vary in a range between 20 and 92 K with a median value of 55 K, which is lower than assumed 70 K in Langer et al. (2014). Gas densities vary from 6.2 × 10¹ to 1.2 × 10³ cm^-3 with a median value of 2.3 × 10² cm^-3.

• 3.

  DMG dominates dark gas in a wide range of Hi optical depth τ_Hi and excitation temperature T_ex.

• 4.

  The Hi optical depth τ_Hi can exist in a wide parameter range without significantly affecting the global relations between DMG fraction, Hi column density, and Hi excitation temperature.

• 5.

  Under the constraint of ¹²CO sensitivity of 0.44 K per 0.7 km s^-1 in this paper, the relation between f_DMG and excitation temperature can be described by a linear function, f_DMG = −2.1 × 10^-3T_ex + 1.0, assuming Hi optical depth of 1.0.

• 6.

  The relation between f_DMG and total hydrogen column density N_H can be described by f_DMG = 1−3.7 × 10²⁰/N_H. When N_H≤ 5.0 × 10²¹ cm^-2, this curve is consistent with the time-dependent chemical evolutionary model at the age of ~10 Myr. The consistency between the data and chemical evolutionary model breaks down when N_H > 5.0 × 10²¹ cm^-2.

• 7.

  We discovered a group of clouds with high extinction (A_V > 2.7 mag), in which an upper CO abundance of 2.1 × 10^-6 relative to H₂ is two orders magnitude smaller than canonical value in the Milky Way. This population of clouds cannot be explained by the chemical evolutionary model. They may be formed through the agglomeration of pre-existing molecular gas in the Milky Way.

It is worthwhile to note that the definition of DMG strongly depends on the sensitivity of CO data. In this paper, this value is 0.44 K per 0.7 km s^-1 for ¹²CO emission. More sensitive data of CO as well as other molecular tracers, e.g., OH, toward these clouds are necessary to constrain CO abundance further and to investigate physical properties of molecular gas in these clouds.

Acknowledgments

This work is supported by Technology under State Key Development Program for Basic Research (973 program) No. 2012CB821802 and National Key Basic Research Program of China (973 Program) 2015CB857100, the China Ministry of Science, and the Guizhou Scientific Collaboration Program (#20130421). We are grateful to the anonymous referee for his/her constructive suggestions, which have greatly improved this paper. The authors would like to thank Pei Zuo for helping Delingha CO observations, John Dickey for discussing Hi self-absorption, Xiaohu Li for discussing chemical evolutionary model. We thank the Pineda team for providing C⁺ and CO data. Part of CO data were observed with the Delingha 13.7 m telescope of the Qinghai Station of Purple Mountain Observatory. We appreciate the help of all the staff members of the observatory during the observations.

References

All Tables

All Figures

Fig. 1 C+, Hi, and CO spectra toward G132.5-1.0, G337.0+0.5, G207.2-1.0, and G352.6+0.5. They are shown in top, middle, and bottom panel of each plot, respectively. In the top panel, the red solid line represents the gauss fit of the C+ emission profile of DMG component. In the middle panel, Hi On and OFF profile are derived from ON and around each sightline, respectively. The green solid line represents the residual profile derived from OFF-ON. The red solid line represents the gauss fit of the OFF-ON profile around the velocity of the DMG component. In the middle panel toward G207.2-1.0, THi and Tab in Eq. (2) are labeled.

In the text

Fig. 2 Hi spectrum and Hi channel map around absorption velocity toward G352.6+0.5 and G337.0+0.0, respectively. The dashed line on top of two Hi spectra profiles represents the central velocity of the absorption line. Red crosses below two channel maps represent positions toward G352.6+0.5 or G337.0+0.0. HINSA with real Hi absorption of foreground cold Hi cloud around ~−8.7 km s-1 is clearly seen toward G352.6+0.5. Non-HINSA with pseudo-absorption caused by relatively high brightness temperatures in neighbor velocity channels around ~−21.9 km s-1 is shown toward G337.0+0.0.

In the text

	Fig. 3 Spactial distribution of DMG clouds in the Galactic plane. The positions of the Sun and the Galactic center (GC in the plot) are indicated with red crosses.
In the text

	Fig. 4 Histogram of excitation temperature distribution. Blue rectangles represent the distribution of upper limits to the excitation temperature. Rectangles with filled red lines represent the distribution of excitation temperature when optical depth τHi = 1.
In the text

	Fig. 5 Relation between visual extinction and excitation temperature. Red rectangles indicate median visual extinctions for excitation temperature bin of 10 K. The physical widths and heights of the rectangles are 10 K and 1 mag, respectively.
In the text

Fig. 6 Relation curves between fDMG, τHi, and Tex. Panel a) shows 3D curves with red lines. Relations between each two parameters are projected with black lines. Panel b) shows relation between fDMG and τHi. The green dashed line represents τHi = 1. The value with τHi = 1 for 33 sources are indicated with red crosses, but for G132.5-1.0, G207.2-1.0, and G347.4+1.0, τHi = 5.4,4.3, and 0.5, respectively. They are shown with red squares. Panel c) shows the relation between fDMG and Tex. Panel d) shows the relation between τHi = 1 and Tex. The meaning of red crosses and blue dashed lines in panels c) and d) are same as in panel b).

In the text

	Fig. 7 Relation between DMG fraction and excitation temperature. Median values of fDMG per 10 K are shown with red rectangles. The width and height of the rectangles are 10 K and 0.05, respectively. Green solid curve represents best linear fitting for median values.
In the text

	Fig. 8 Fraction of DMG vs. hydrogen column density NH. Results for 36 sources are shown in open circles. Red solid line shows the best fitting. Dashed lines with different colors represent chemical evolutionary model results from Lee et al. (1996). Vertical dotted red line represents NH = 5 × 1021 cm-2.
In the text

	Fig. 9 Relation between volume density and excitation temperature. Blue, green, and red lines represent pressure P/k of 6000, 1.4 ×104, 4 ×104 K cm-3, respectively.
In the text