Catching the Birth of a Dark Molecular Cloud for the First Time

The formation of the H₂ molecules is a key process in converting atoms into molecules in the interstellar medium and is the critical step in the formation of stars. Spitzer (1946) suggested that H₂ formation occurs on dust grains, rather than in the gas phase, because the collision frequency is too low to provide sufficient three-body collisions in molecular clouds (Kaiser 2002). A widely accepted description of an efficient H i–H₂ transformation process in clouds is provided by Hollenbach & Salpeter (1971). Efficient H₂ formation can persist to high temperatures because chemisorbed atoms can stay on the grain surface while maintaining quantum mobility. Such configuration is conducive to hydrogen recombination (H₂ formation) until the dust grain surface temperature reaches ∼500 K (Cazaux & Tielens 2004). Laboratory experiments demonstrated that H₂ formation could also occur on carbon surfaces with a high recombination efficiency over a broad range of temperature (Vidali et al. 2005). The theoretical work in Cazaux et al. (2005) explained the high efficiency under low temperatures in both quiescent diffuse and dense clouds in terms of physisorption forces and thermally activated diffusion. Since the timescale of star formation is tightly constrained by the timescale of molecular gas formation, it is crucial to have a self-consistent understanding of the global star formation efficiency and star formation rate in galaxies. The timescale of star formation is controversial. The canonical model (Shu 1977) favored it to be around 10 Myr, while Bergin et al. (2004) and Elmegreen (2000), hypothesized that star formation occurs on a turbulent crossing scale that corresponds to about only 1 Myr on parsec scales (Glover & Mac Low 2007).

Direct measurement of H₂ formation is difficult because H i is hard to isolate in the Galaxy and H₂ lacks a permanent dipole moment, making it rare to have both measurements of H i and H₂ gas for the same regions of the Galaxy. Key physical parameters need largely to be assumed in calculating cloud formation. Molecular hydrogen can be observed through absorption if it is against a good X-ray and/or ultraviolet background source (e.g., Sembach et al. 2001). Since H₂ itself does not emit at the temperature of molecular clouds, these regions are generally traced emission from the lower rotational transitions of CO. However, subthermal excitation in diffuse gas and depletion in dense gas make CO unsatisfactory to trace H₂ (Kramer et al. 1999). It is also difficult to probe the cloud formation timescale through astrochemistry based on molecular species other than H₂ and H i, such as N₂H⁺ and deuterated species (Caselli et al. 2002), because these tracers comprise only a tiny fraction of cloud mass. The foremost chemical reaction in molecular formation is the formation of molecular hydrogen. It is thus paramount for us to obtain direct measurement of the H₂ formation timescale in order to better understand cloud formation timescale, the star formation efficiency and the star formation rate.

We have developed an observational method called H i Narrow Self-Absorption (H iNSA; Li & Goldsmith 2003; Goldsmith & Li 2005), which is capable of measuring atomic hydrogen abundance in dense clouds. Similar to the well-known H i Self-Absorption (H iSA (Heeschen 1955)) phenomenon in the cold neutral medium (CNM), H iNSA differs in a significant aspect, namely, the thermalization of H i at low temperatures through collisions with H₂. Due to efficient cooling by molecular emission lines, especially the rotational transitions of CO, molecular clouds claim most of the lowest temperatures found in the Milky Way except for a few rare cases, such as those discussed by Knee & Brunt (2001) and Peek et al. (2011b). In contrast, lacking molecular cooling, H iSA is likely a result of temperature fluctuations in the CNM (Gibson et al. 2000). Systematic surveys have shown that H iNSA is associated with molecular clouds (Krčo & Goldsmith 2010), and thus provides a direct measurement of cold H i in dark clouds.

The left image in Figure 2 gives a schematic diagram of the transition from CNM to dense molecular gas. In the warm ionized medium and H ii regions, hydrogen is largely in the form of H⁺. For higher densities and lower UV intensities, H⁺ combines with electrons through radiative recombination and forms H i. With increasing H i volume density, hydrogen atoms start to form molecular hydrogen on the surface of dust grains. In diffuse molecular clouds, even when most of the H is in the molecular form, gas-phase carbon can still be mainly C⁺. After combining with H₂ through radiative association, C⁺ becomes ${{\mathrm{CH}}_{2}}^{+}$; ${{\mathrm{CH}}_{2}}^{+}$ reacts rapidly with electrons to form CH; then CH reacts with O to produce CO. C⁺ can also react with electrons to form C i through dielectronic recombination. C i, along with OH, lead to the formation of CO through neutral–neutral reactions in colder (10 K < T < 100 K) dark clouds (Woodall et al. 2007). Other molecules form following CO in dense cores. In particular, N₂H⁺, NH₃, and cations like H₂D⁺ become significant and have been used to study the cloud core formation timescale (Brünken et al. 2014).

Isolated, cold dark clouds are the ideal laboratory for studying H₂ formation in the Milky Way. In a previous study, B227, CB45, and L1574, were identified as isolated dark clouds, and coincidently aligned in a linear configuration from north to south spanning about two degrees (Martin & Barrett 1978). There are no nearby UV sources such as massive stars or H ii regions.

In this paper, we present a combined analysis of H iNSA, CO emission, dust emission, and extinction for a rare, isolated dark cloud, currently undergoing H₂ formation. The [H i]/[H₂] abundance varies from 2% to 0.2%, within one region and the formation timescale was derived as ∼6 Myr, which is consistent with both an analytical model and a numerical chemistry model.

To reconstruct the chemical state and the evolutionary history of isolated dark clouds, we mapped H i, ¹³CO J = 1–0 emission, and dust continuum emission in B227, CB45, and L1574, which were identified as H iNSA sources by Goldsmith & Li (2005). In 2012 May and November, the sources were observed in the 1420 MHz transition of H i using the Arecibo L-band Feed Array (ALFA) on the 305 m radio telescope. We implemented the observations in the "total power" mode because of a clear "off" position that was difficult to find in the Galaxy. The nominal system temperature of 30 K has contributions from the system temperature and the H i emission. In addition, the temperature of the H i emission from standard CNM is around 70 K (Heiles & Troland 2003). Hence, we consider an equivalent system temperature of 100 K for evaluating the observing sensitivity. To accomplish the mapping for the sources that extend 1° × 2°, the"leap frog" drift scan was adopted (Minchin et al. 2007). Spectra were recorded by GALSPECT, the Galactic ALFA spectrometer. The resolution is 0.18 km s⁻¹ per channel with 7,679 channels. Using the Spectral and Photometric Imaging REceiver (SPIRE) on board the Herschel Space Observatory, the sources (B227, L1574, and CB45) were observed at 250, 350, and 500 μm on 2011 September 11 within a Herschel Open Time (OT) 1 Program (OT1_dli_2). In the fast mapping mode having a nominal scan speed of 30'' s⁻¹, two 9' legs were used at each band for mapping each of the sources covered by the scanned area of 30' × 30'. ¹³CO data were taken with the Five College Radio Astronomy Observatory (FCRAO) and adapted from Goldsmith & Li (2005).

Our SPIRE data were processed by using the software package HIPE.¹¹ The original image at each band was produced based on a zero-median brightness. To calibrate the offsets between bands, the zeroPointCorrection subroutine was used, which implements a cross-calibration with the Planck HFI-545 and HFI-857 images and a color correction HFI to SPIRE wavebands assuming a gray body function with fixed beta. We used the subroutine Baseline Removal and Destriper to remove the baseline with correcting the relative gain of the bolometer. Photometer Map Merging was then used to merge the images of the bands. The Arecibo H i data were processed following the procedure of the GALFA-H i Standard Reduction (Peek et al. 2011a). It is designed for the ALFA in order to take the time-ordered data that come out of GALSPECT, over a single region and turn it into a calibrated, gridded spectral (PPV) data cube. The resulting data also showed stripes along the scan direction, we destriped the data by running the procedure to use the places of the data cross each other to self-calibrate the gains of each beam. We obtained Two Micron All Sky Survey (2MASS) extinction data based on the J, H, and K_s bands of the 2MASS data. ¹³CO data were taken with FCRAO and adapted from Goldsmith & Li (2005). We regrided the pixel onto a 1' grid in order to match the H i data.

Our new continuous, Nyquist-sampled H i map complemented by ¹³CO and dust images enables us to identify a striking H iNSA ring and directly measure the variation of H i abundance in these transition clouds (Figure 1).

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3.1. Dust Temperature and Column Density

For each image pixel, an SED was extracted and fitted with a single-temperature modified blackbody of the form

$$\begin{eqnarray}&&{S}_{\nu }={\rm{\Omega }}{B}_{\nu }(\nu ,\,{T}_{{\rm{d}}}){\kappa }_{\nu }\mu {m}_{{\rm{H}}}{N}_{{{\rm{H}}}_{2}},\end{eqnarray} \tag{ 1 }$$

where Ω is the solid angle of the emitting element, B_ν is the blackbody emission from the dust at temperature T_d, κ_ν is the dust mass absorption coefficient, μ = 2.33 is the particle mass per hydrogen molecule, m_H is the mass of hydrogen atom, and ${N}_{{{\rm{H}}}_{2}}$ is the column density of hydrogen molecules, and we assumed the gas-to-dust ratio is 100. In Equation (1),

$$\begin{eqnarray}&&{B}_{\nu }(\nu ,\,{T}_{{\rm{d}}})=\displaystyle \frac{2h{\nu }^{3}}{{c}^{2}}\displaystyle \frac{1}{{e}^{(h\nu /{{kT}}_{{\rm{d}}})}-1}\end{eqnarray} \tag{ 2 }$$

is the Planck function and

$$\begin{eqnarray}&&{\kappa }_{\nu }={\kappa }_{230}{\left(\displaystyle \frac{\nu }{230\mathrm{GHz}}\right)}^{\beta },\end{eqnarray} \tag{ 3 }$$

(where κ₂₃₀ = 0.009 cm² g⁻¹) is the emissivity of the dust grains at 230 GHz.

We used 2MASS extinction data to eliminate the column density of hydrogen atoms as a parameter for fitting the dust temperature T_d and emissivity spectral index β. The hydrogen column density N_H can be estimated from the optical extinction (Güver & Özel 2009),

$$\begin{eqnarray}&&\displaystyle \frac{{N}_{{\rm{H}}}}{{\mathrm{cm}}^{-2}}=2.2\times {10}^{21}\left(\displaystyle \frac{{A}_{{\rm{v}}}}{\mathrm{mag}}\right).\end{eqnarray} \tag{ 4 }$$

As the atomic hydrogen fractional abundance is small, we take ${N}_{{\rm{H}}{\rm{I}}}=0$ and obtain

$$\begin{eqnarray}&&{N}_{{\rm{H}}}=2{N}_{{{\rm{H}}}_{2}}.\end{eqnarray} \tag{ 5 }$$

The column density of hydrogen molecules ${N}_{{{\rm{H}}}_{2}}$ is related to visual extinction A_v,

$$\begin{eqnarray}&&\displaystyle \frac{{N}_{{{\rm{H}}}_{2}}}{{\mathrm{cm}}^{-2}}=1.1\times {10}^{21}\left(\displaystyle \frac{{A}_{{\rm{v}}}}{\mathrm{mag}}\right).\end{eqnarray} \tag{ 6 }$$

Combined Herschel SPIRE 250, 350 and 500 μm data with 2MASS extinction data, the dust temperature T_d, column density of hydrogen molecules ${N}_{{{\rm{H}}}_{2}}$ and emissivity spectral index β can be fitted simultaneously by using Equation (1).

3.2. Column Density of Cold Hi

The new Arecibo H i images provide us with the overall H iNSA distribution in these sources. In order to extract the absorption component, we subtracted a relatively uniform background by averaging the H i emission values from surrounding points of the clouds, which has been done in a fashion similar to that described by Knee & Brunt (2001). The method for solving for the optical depth of the absorbing gas is described from Equation (12) in Li & Goldsmith (2003),

$$\begin{eqnarray}&&{\tau }_{0}=\mathrm{ln}\left[\displaystyle \frac{{{pT}}_{{\rm{H}}{\rm{I}}}+({T}_{{\rm{c}}}-{T}_{{\rm{x}}})(1-{\tau }_{{\rm{f}}})}{{{pT}}_{{\rm{H}}{\rm{I}}}+({T}_{{\rm{c}}}-{T}_{{\rm{x}}})(1-{\tau }_{{\rm{f}}})-{T}_{\mathrm{ab}}}\right],\end{eqnarray} \tag{ 7 }$$

where τ₀ is the peak optical depth of the absorption feature at the centroid velocity, ${\tau }_{{\rm{f}}}$ is the foreground H i optical depth, taken to be 0.1, which is the typical value of the foreground H i and only results in 0.4% uncertainty of optical depth of H i. T_{H i} is the quantity obtained from the spectrum by fitting a polynomial to the portion of the spectrum without the absorption, T_c is continuum temperature, taken to be 3.5 K, including the cosmic background and Galactic continuum emission. T_x is the excitation temperature of H i in the dark cloud, which could be replaced by the dust temperature, T_ab is the absorption temperature, which is referred to as the depth of absorption line, p is the ratio of background H i optical depth τ_b to optical depth of the uniformed Galactic atomic gas τ_h (τ_b = pτ_h), τ_h is the total of the foreground H i optical depth and the background H i optical depth (τ_h = τ_f + τ_b), and p can be calculated from a model of the local H i distribution and is generally in the range of 0.8–0.9.

The column density of H i is given by

$$\begin{eqnarray}&&\displaystyle \frac{{N}_{{\rm{H}}{\rm{I}}\mathrm{NSA}}}{{\mathrm{cm}}^{-2}}=1.95\times {10}^{18}{\tau }_{0}\displaystyle \frac{{\rm{\Delta }}V}{\mathrm{km}\,{{\rm{s}}}^{-1}}\displaystyle \frac{{T}_{{\rm{k}}}}{{\rm{K}}},\end{eqnarray} \tag{ 8 }$$

where ΔV is the FWHM of the absorption line from a Gaussian fit, and T_k is the kinetic temperature. We used the dust temperature T_d derived from Herschel SPIRE maps as T_k, which should be well coupled in such clouds (Goldsmith & Li 2005). The column density of cold H i had been obtained based on H iNSA analysis.

Since the true total column density measurement will be affected by the optically thin approximation, several approaches have been employed to evaluate this potential problem. Lee et al. (2015) used two different methods to estimate the correction factor f for high optical depth and found that they are consistent, which is likely due to the relatively low optical depth and insignificant contribution from the diffuse radio continuum emission. As the clouds we study are located in the outer region of the Galaxy and the optical depths are small (Kolpak et al. 2002), the correction for the optical depth should not affect the H i column density significantly. The overall uncertainty is approximately 50%.

Since we cannot obtain the T_k, we present the upper and lower limit H i column density and H i abundance by using temperature of 10 and 30 K. The upper and lower limits for the H i column density for the three clouds are 7.50 × 10¹⁹ cm⁻² and 2.31 × 10¹⁸ cm⁻² respectively. The upper and lower limits for the H i abundance are 0.09 and 0.001 respectively.

3.3.  ${}^{13}{CO}$ Column Density

The central frequency of the ¹³CO J = 1–0 line ν is 110.2 GHz.

The column density of ¹³CO in the upper level (J = 1) can be expressed as

$$\begin{eqnarray}&&{N}_{{\rm{u}},{}^{13}\mathrm{CO}}=\displaystyle \frac{8\pi k{\nu }^{2}}{{{hc}}^{3}{A}_{\mathrm{ul}}}\int {T}_{{\rm{b}}}{dv},\end{eqnarray} \tag{ 9 }$$

where k is Boltzmann's constant, h is Planck's constant, c is the speed of light, A_ul is the spontaneous decay rate from the upper level to the lower level, and T_b is the brightness temperature. We obtain

$$\begin{eqnarray}&&\left(\displaystyle \frac{{N}_{{\rm{u}},{}^{13}\mathrm{CO}}}{{\mathrm{cm}}^{-2}}\right)=3.7\times {10}^{14}\int \left(\displaystyle \frac{{T}_{{\rm{b}}}}{{\rm{K}}}\right)d\left(\displaystyle \frac{v}{\mathrm{km}\,{{\rm{s}}}^{-1}}\right).\end{eqnarray} \tag{ 10 }$$

The total ¹³CO column density N_tot is related to the upper level column density N_u through

$$\begin{eqnarray}&&{N}_{\mathrm{tot},{}^{13}\mathrm{CO}}={f}_{{\rm{u}}}{f}_{\tau }{f}_{{\rm{b}}}{N}_{{\rm{u}},{}^{13}\mathrm{CO}},\end{eqnarray} \tag{ 11 }$$

where the level correction factor f_u can be calculated analytically under the assumption of local thermal equilibrium (LTE) as

$$\begin{eqnarray}&&{f}_{{\rm{u}}}=\displaystyle \frac{Q({T}_{\mathrm{ex}})}{{g}_{{\rm{u}}}\exp \left(-\tfrac{h\nu }{{{kT}}_{\mathrm{ex}}}\right)},\end{eqnarray} \tag{ 12 }$$

where g_u is the statistical weight of the upper level. T_ex is the excitation temperature and Q(T_ex) = kT_ex/B_e is the LTE partition function, where B_e is the rotational constant (Tennyson 2005). The partition function can be expressed as Q(T_ex) ≈ T_ex/2.76 K. The correction factor for opacity f_τ is defined as

$$\begin{eqnarray}&&{f}_{\tau }=\displaystyle \frac{\int {\tau }_{13}{dv}}{\int (1-{e}^{-{\tau }_{13}}){dv}},\end{eqnarray} \tag{ 13 }$$

and the correction for the background f_b can be expressed as

$$\begin{eqnarray}&&{f}_{{\rm{b}}}={\left[1-\displaystyle \frac{{e}^{\tfrac{h\nu }{{{kT}}_{\mathrm{ex}}}}-1}{{e}^{\tfrac{h\nu }{{{kT}}_{\mathrm{bg}}}}-1}\right]}^{-1},\end{eqnarray} \tag{ 14 }$$

where τ₁₃ is the opacity of the ¹³CO transition and T_bg is the background temperature, which is assumed to be 2.7 K. The ¹³CO opacity is estimated under the assumption of being optically thin, for which f_τ = 1. The excitation temperature T_ex can be replaced by the dust temperature T_d. The maximum ¹³CO column densities obtained using this analysis for the three sources B227, L1574, and CB45 are 4.1 × 10¹⁵ cm⁻², 4.9 × 10¹⁵ cm⁻², and 7.3 × 10¹⁵ cm⁻². We then derived the ¹³CO abundance through column densities of dust and ¹³CO with consideration of other chemical effects, like ¹³CO depletion, and all of them are likely not dominant for our case.

Based on the dust data, the central volume densities of the three clouds, B227, L1574, and CB45 are 1600 cm⁻³, 2200 cm⁻³, and 1800 cm⁻³, assuming cloud sizes of 0.8 pc, 1.0 pc, and 1.5 pc respectively. The volume density is much greater than the ¹³CO critical density of 1266 cm⁻³, confirming the validation of the LTE assumption.

3.4. Abundances

4.1.  ${H}_{2}$ Formation Model

H₂ formation occurs on the dust grain with a formation rate (Hollenbach & Salpeter 1971)

$$\begin{eqnarray}&&{R}_{{{\rm{H}}}_{2}}=\displaystyle \frac{1}{2}{S}_{{\rm{H}}{\rm{I}}}{\epsilon }_{{{\rm{H}}}_{2}}{n}_{{\rm{H}}{\rm{I}}}\langle {v}_{{\rm{H}}{\rm{I}}}\rangle {\sigma }_{\mathrm{gr}}{n}_{\mathrm{gr}},\end{eqnarray} \tag{ 15 }$$

where ${R}_{{{\rm{H}}}_{2}}$ has units of cm⁻³ s⁻¹, ${S}_{{\rm{H}}{\rm{I}}}$ is the sticking efficiency, ${\epsilon }_{{{\rm{H}}}_{2}}$ is the recombination efficiency, n_gr (cm⁻³) is the atomic hydrogen density in the gas, $\langle {v}_{{\rm{H}}{\rm{I}}}\rangle \,(\mathrm{cm}\,{{\rm{s}}}^{-1})$ is the mean velocity of atoms, σ_gr (cm²) is the cross section of grains, and n_gr (cm⁻³) is the number density of grains.

The values and derivations of the parameters are taken from Goldsmith & Li (2005). The simplification of the H₂ formation rate can be expressed as

$$\begin{eqnarray}&&{R}_{{{\rm{H}}}_{2}}={k}_{{{\rm{H}}}_{2}}{n}_{\mathrm{gas}}{n}_{{\rm{H}}{\rm{I}}}.\end{eqnarray} \tag{ 16 }$$

We denote the H₂ formation rate coefficient ${k}_{{{\rm{H}}}_{2}}$ as k' = 1.2⁻¹⁷ cm³ s⁻¹ after taking the effect of grain size distribution into account (Goldsmith & Li 2005).

The formation rate coefficient k' is related to the grain size, namely the cross-section area of dust grains, which is connected to the thermal balance and the estimate of dust mass. Based on the study of grain size distribution from Mathis et al. (1977), the reasonable upper and lower limits of radii, a_max = 10000 Å and a_min = 25 Å, which enter as (a_maxa_min)^−0.5, are adopted for evaluating the effect of the grain size distribution on the formation rate coefficient. In comparison with the standard grain radius 1700 Å, the formation rate coefficient is increased by a factor of 3.4. Combining the grain size distribution and other factors, the uncertainty of H₂ formation rate coefficient may differ from its nominal value by a factor of 5. Although the nominal value of k' we take has large uncertainty, it is well beyond the goal of this paper to consider the overall context. Therefore, we are utilizing the most common value for the cross-section area of the dust.

The density of gas n_gas can be regarded as total density n₀ as n₀ ∝ n_gas. We derived the volume proton density of the clouds through the dust data. For the volume proton density, we derived the mean values from outer to inner of the cloud by assuming the cloud is spherical. It ranges from 10^2.9 cm⁻³ to 10^3.2 cm⁻³ approximately (Figure 2). The time dependence of the molecular hydrogen can be express as

$$\begin{eqnarray}&&\displaystyle \frac{{{dn}}_{{{\rm{H}}}_{2}}}{{dt}}=k^{\prime} {n}_{{\rm{H}}{\rm{I}}}{n}_{0}-{\zeta }_{{{\rm{H}}}_{2}}{n}_{{{\rm{H}}}_{2}},\end{eqnarray} \tag{ 17 }$$

where ${\zeta }_{{{\rm{H}}}_{2}}$ is the cosmic-ray ionization rate. We defined the fractional abundance of atomic and molecular hydrogen, ${x}_{{\rm{H}}{\rm{I}}}$ and ${x}_{{{\rm{H}}}_{2}}$, as the density of species ${n}_{{\rm{H}}{\rm{I}}}$ and ${n}_{{{\rm{H}}}_{2}}$ divided by the total proton density n₀, then we find

$$\begin{eqnarray}&&\displaystyle \frac{{{dx}}_{{{\rm{H}}}_{2}}}{{dt}}=k^{\prime} {x}_{{\rm{H}}{\rm{I}}}{n}_{0}-{\zeta }_{{{\rm{H}}}_{2}}{x}_{{{\rm{H}}}_{2}}.\end{eqnarray} \tag{ 18 }$$

Substituting ${n}_{0}={n}_{{\rm{H}}{\rm{I}}}+{n}_{{{\rm{H}}}_{2}}$, we can rewrite this as

$$\begin{eqnarray}&&\displaystyle \frac{{{dx}}_{{{\rm{H}}}_{2}}}{{dt}}=k^{\prime} {n}_{0}-(2k^{\prime} {n}_{0}+{\zeta }_{{{\rm{H}}}_{2}}){x}_{{{\rm{H}}}_{2}}.\end{eqnarray} \tag{ 19 }$$

The time dependence of the fractional abundance of molecular hydrogen is then given by

$$\begin{eqnarray}&&{x}_{{{\rm{H}}}_{2}}(t)=\displaystyle \frac{k^{\prime} {n}_{0}}{2k^{\prime} {n}_{0}+{\zeta }_{{{\rm{H}}}_{2}}}\left[1-\exp \left(\displaystyle \frac{-t}{{\tau }_{{\rm{H}}{\rm{I}}\to {{\rm{H}}}_{2}}}\right)\right].\end{eqnarray} \tag{ 20 }$$

The fractional abundance of atomic hydrogen is $1-2{x}_{{{\rm{H}}}_{2}}$ and is given by

$$\begin{eqnarray}&&{x}_{{\rm{H}}{\rm{I}}}(t)=1-\displaystyle \frac{2k^{\prime} {n}_{0}}{2k^{\prime} {n}_{0}+{\zeta }_{{{\rm{H}}}_{2}}}\left[1-\exp \left(\displaystyle \frac{-t}{{\tau }_{{\rm{H}}{\rm{I}}\to {{\rm{H}}}_{2}}}\right)\right].\end{eqnarray} \tag{ 21 }$$

The timescale for H i to H₂ conversion is given by

$$\begin{eqnarray}&&{\tau }_{{\rm{H}}{\rm{I}}\to {{\rm{H}}}_{2}}=\displaystyle \frac{1}{2k^{\prime} {n}_{0}+{\zeta }_{{H}_{2}}}.\end{eqnarray} \tag{ 22 }$$

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We derived the timescales of these isolated dark clouds to be ∼6 Myr using H i abundance, total gas density, and gas temperature obtained according to the time dependence model described in this section (Figure 2). The upper and lower limits of H i abundances are plotted in Figure 2 and the points at upper limits represent the lower ages of the clouds for the fixed volume densities.

4.2. Chemical Model

It has been rare to have both H i and H₂ measured for the same regions in the Galaxy. Lee et al. (2015) used the integrated H i emission flux in channels, the range of which was determined by correlation with 2MASS extinction. Such a priori requirements of H i mimicking dust diminish the logical credence of H i emission tracing the atomic component within a molecular cloud. Fukui et al. (2014) found an optically thick H i emission envelope around a molecular cloud. In this work, utilizing H iNSA, we discovered a chemically young molecular cloud undergoing H₂ formation, revealed by a prominent "ring" of self-absorption tracing atomic hydrogen mixed with molecules. We derived the formation timescale to be ∼6 Myr, consistent with both an analytical model and a numerical chemistry model. Our results could further test recent H₂ formation models in different contexts (Sternberg et al. 2014; Bialy et al. 2017).

Our results can also help constrain galaxy evolution simulations. A key recent development is the implementation of the physics of molecular hydrogen and star formation prescription based on the local molecular hydrogen density rather than the total hydrogen density (Zemp et al. 2012). In Gnedin & Kravtsov (2011), only two types of observations were able to calibrate the H₂ formation rate in different environments, UV absorption in diffuse regions and H iNSA in dense clouds. This work further improves the accuracy of the H iNSA measured H₂ formation rate.

Both the timescale and H i abundance distribution of the clouds are inconsistent with fast H₂ formation (Glover & Mac Low 2007), which relies on stochastic processes of localized high volume H i density. Such a fast cloud formation model could produce a significant amount of molecular hydrogen, e.g., for cooling in a short time, but cannot convert the vast majority of the gas into molecular form, which is our key finding here. The fact that more than 99% of the protons have been turned into H₂ requires millions of years and comprehensive global H₂ formation, not just in pockets of locally enhanced condensations. The observed Mach number of the clouds is more than 20, which elevates the inconsistency between our observation and the fast cloud formation model.

The total column densities found in these isolated dark clouds are consistent with commonly used initial conditions for protoplanetary disks. However, the measured H i abundance is one to a few orders of magnitude higher than those assumed in such models (e.g., Walsh et al. 2015). In these models, the H i abundance keeps dropping with time and impacts subsequent chemical reactions. We expect our measured value to affect future consideration of chemical evolution of disks. All the above statements indicate that the parameters of galactic H₂ formation play a crucial role in both galaxy evolution and star formation.

We mapped H i, ¹³CO J = 1–0 emission, and dust continuum emission of isolated dark clouds, B227, CB45, and L1574. The combined analysis of H iNSA, CO emission, dust emission, and extinction enables us to directly measure the variation H i abundance in these transition clouds. The timescale of the clouds had been examined through an analytical model. Our main results are the following.

• 1.  
  We identified a striking "ring" of enhanced H i abundance, which is the first time such a structure has been seen in a molecular cloud. It closely resembles the "onion" shell description of a forming molecular cloud (Figure 1). The displacement between peak abundance positions of H i, CO, and dust indicates the ongoing H₂ formation. Particularly, we find an orderly spatial variation of H i abundance between 2% and 0.2%.
• 2.  
  We derived the H i–H₂ evolutionary timescales for these isolated dark clouds to be ∼6 Myr and further examined the cloud evolution through a time-dependent chemical model.
• 3.  
  Our results could test H₂ formation models, constrain galaxy evolution simulations, and may affect future consideration of chemical evolution of disks, all of which indicate that the parameters of galactic H₂ formation play a crucial role for both galaxy evolution and star formation.

This work is supported by National Key R&D Program of China grant No. 2017YFA0402600, the National Natural Science Foundation of China grant No. 11725313 and No. 11690024, and the International Partnership Program of Chinese Academy of Sciences grant No. 114A11KYSB20160008. The Arecibo Observatory is operated by SRI International under a cooperative agreement with the National Science Foundation (AST-1100968), and in alliance with Ana G. Méndez-Universidad Metropolitana, and the Universities Space Research Association. D.L. acknowledges support from "CAS Interdisciplinary Innovation Team" program. This work was carried out in part by the Jet Propulsion Laboratory, which is operated by NASA through the California Institute of Technology. Z.Y.Z. acknowledges support from ERC in the form of the Advanced Investigator Programme, 321302, COSMICISM.