COLD AND WARM ATOMIC GAS AROUND THE PERSEUS MOLECULAR CLOUD. I. BASIC PROPERTIES

Most of the molecular gas in galaxies is assembled into giant molecular clouds (GMCs) with masses of 10⁴–10⁷ M_☉ (Fukui & Kawamura 2010). Stars appear intimately associated with the dense regions of these GMCs (Lada et al. 2010), and recent observations suggest that the depletion timescale of molecular gas by star formation does not vary greatly across a wide range of galaxy environments (Schruba et al. 2011; Shetty et al. 2014). This strongly suggests that the ability to form molecular gas in the first place holds the key to understanding the evolutionary tracks of galaxies.

Atomic hydrogen has been considered for decades as the main formation reservoir of GMCs (Shu 1973; Blitz et al. 2007; Kim & Ostriker 2006; Audit & Hennebelle 2005; Heitsch et al. 2005; Clark et al. 2012). Although how exactly GMCs form out of the diffuse atomic medium is still not understood, the H i envelopes frequently observed around GMCs are likely to represent the material left over from the formation epoch and/or a product of photodissociation of molecular gas. In either case, these envelopes play a very important role in the GMC evolution and could explain long-standing questions such as the origin of the internal turbulent energy in GMCs. Theoretical models considering the ongoing accretion of atomic material from the envelope onto GMCs are able to reproduce the level of observed turbulence as well as the total GMC mass (Chieze & Pineau Des Forets 1989; Hennebelle & Inutsuka 2006; Goldbaum et al. 2011). In addition, it has been suggested that the GMC history is highly dependent on the initial surface density of the H i envelope. As shown by Goldbaum et al. (2011), only a factor of two increase of the H i surface density of the envelope from 8 to 16 M_☉ pc⁻² is enough to decide whether or not a GMC mass will reach ∼10⁶ M_☉ over a typical lifetime of 10–20 Myr.

While the H i envelopes around molecular clouds have been largely observationally studied via H i emission (Wannier et al. 1983, 1991; Andersson & Wannier 1993; Fukui et al. 2009), traditionally, H i has not been considered very important for understanding molecule and star formation. For example, many GMC studies trying to estimate the H₂ distribution from dust emission have neglected to account for H i as it was assumed that GMCs are highly dominated by molecular gas (e.g., Pineda et al. 2008). In addition, a strong correlation between the star formation rate and the H₂ surface density in galaxies has been considered as an evidence that only H₂ is directly related to star formation. However, recent extragalactic studies showed that globally across galaxies at kiloparsec scales, as well as in resolved studies at sub-kiloparsec scales, the H i surface density Σ_H i≲ 10 M_☉ pc⁻² (Wong & Blitz 2002; Blitz & Rosolowsky 2004; Bigiel et al. 2008; Schruba et al. 2011), re-opening interest in the role of H i shielding in molecule formation.

To investigate the formation of H₂ from a theoretical point of view and building up on several earlier studies (Spitzer & Jenkins 1975; Elmegreen 1993), Krumholz et al. (2009, KMT09) considered the structure of a photodissociation region in a spherical cloud that is embedded in a uniform and isotropic radiation field. Their model is based on the balance between H₂ formation on dust grains and photodissociation by Lyman–Werner photons and provides an analytic function for the H₂ fraction as a function of the gas surface density. Their most important prediction is that a certain amount of the H i surface density, Σ_H i, is required for shielding of H₂ against photodissociation. Once this minimum Σ_H i is achieved, additional H i is fully converted into H₂ and therefore Σ_H i saturates while Σ_H2 linearly increases. At solar metallicity, KMT09 predict Σ_H i ∼ 10 M_☉ pc⁻² as the minimum Σ_H i required for H₂ formation, this is equivalent to the H i column density of 1.2 × 10²¹ cm⁻².

To investigate the role of H i shielding on sub-parsec scales in Lee et al. (2012) we mapped the transition from H i to H₂ across the Perseus molecular cloud.⁵ The H i data in this study were from the Galactic Arecibo L-band Feed Array Survey in H i (GALFA-H i; Peek et al. 2011; Stanimirović et al. 2006) and the H i column density was estimated under the optically thin assumption. To estimate the H₂ image, the 60 and 100 μm data from the Improved Reprocessing of the IRAS Survey (Miville-Deschênes & Lagache 2005) were used. We derived T_dust from the I₆₀/I₁₀₀ ratio, and then converted τ₁₀₀ to A_V by finding a proportionality constant between our derived A_V and the A_V image derived from optical extinction (provided by the COMPLETE survey; Ridge et al. 2006). Finally, the H₂ column density was calculated as N(H₂) = (A_V/DGR − N(H i))/2; the dust-to-gas ratio, DGR = 1.1 × 10⁻²¹ mag cm², was measured locally around Perseus.

The key result from Lee et al. (2012) is the detection of an almost constant Σ_H i of 6–8 M_☉ pc⁻² for several dark and star-forming regions in Perseus. This is in agreement with KMT09's prediction for the saturation of Σ_H i. In addition, Lee et al. showed that H₂ extends up to 20 pc from core centers and that the H i envelope is very extended (>20 pc). The H i halo of Perseus was previously studied by Andersson & Wannier (1993), who focused on dark region B5. Using radiative transfer modeling, they found that the H i halo is about 5 × 8 pc in size.

While the observed flattening of Σ_H i can be attributed to the conversion of H i into H₂ as in KMT09, an alternative possibility is that Σ_H i is simply underestimated due to the presence of high optical depth H i that is not fully measured in emission line observations. The high optical depth H i can be measured from self-absorption features, caused by the background Galactic H i emission being absorbed by the cooler foreground H i (Knapp 1974; Goodman & Heiles 1994; Li & Goldsmith 2003). Many narrow self-absorption features have been considered as kinematically associated with CO and have inferred temperature of less than 40 K and the atomic hydrogen column density fraction of only 0.0016 relative to H₂. If H i is a dissociation product of H₂, these measurements suggest a cloud age of 3–30 Myr (Goldsmith & Li 2005). While self-absorption can provide spatial information about the cold H i, e.g., Gibson et al. (2000), it always requires complicated line modeling and is limited by the ability to clearly distinguish self-absorption features from temperature fluctuations and/or multiple individual line-of-sight components.

The main aim of this study is to investigate the effect of high optical depth on the H i surface density saturation observed in Lee et al. (2012). We use the most direct way to estimate the "true" H i column density by measuring H i absorption against radio continuum sources located behind Perseus. We use these observations to investigate properties of the cold and warm H i around Perseus (Paper I), as well as to derive the ratio of the true H i column density to the H i column density derived under the optically thin assumption (Paper II).

The structure of this study is organized in the following way. In this paper (Paper I), we focus on the properties of cold gas around Perseus. Our observing and data processing strategies are explained in Section 2 and in Section 3, we summarize the methodology used to estimate spin temperature and column density of the cold neutral medium (CNM) and the warm neutral medium (WNM). In Section 4, we investigate the basic physical properties of atomic gas in the Perseus H i envelope and in Section 5, we compare H i absorption and carbon monoxide (CO) emission spectra. We summarize our results in Section 6. In Paper II, we estimate the correction for high optical depth using our H i absorption measurements, apply this correction, and re-visit the question of H i saturation in Perseus.

2.1. H i Absorption Observations

We selected 27 radio continuum sources from the NVSS survey (Condon et al. 1998), located over an area of roughly 500 deg² centered on Perseus with flux densities at 1.4 GHz greater than 0.8 Jy. Figure 1 shows the source positions overlaid on the H₂ surface density image of Perseus from Lee et al. (2012). Source information (right ascension (R.A.), declination (decl.), flux density at 21 cm, and the diffuse background radio continuum emission) is given in Table 1.

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Table 1. Source List

Source	R.A. (J2000)	Decl. (J2000)	Tsrc	Tsky
	(h m s)	(° ' '')	(Jy)	(K)
NV0157+28	01:57:12.85	28:51:38.49	1.4	2.782
4C+29.05	02:01:35.91	29:33:44.18	1.2	2.785
4C+27.07	02:17:01.89	28:04:59.12	1.0	2.785
5C06.237	02:20:48.06	32:41:06.64	0.9	2.787
B20218+35	02:21:05.48	35:56:13.91	1.7	2.790
3C067	02:24:12.31	27:50:11.69	3.0	2.786
4C+34.07	02:26:10.34	34:21:30.45	2.9	2.791
NV0232+34	02:32:28.72	34:24:06.08	2.6	2.791
3C068.2	02:34:23.87	31:34:17.62	1.0	2.787
4C+28.06	02:35:35.41	29:08:57.73	1.3	2.788
4C+28.07	02:37:52.42	28:48:09.16	2.2	2.790
4C+34.09	03:01:42.38	35:12:20.84	1.9	2.794
4C+30.04	03:11:35.19	30:43:20.62	1.0	2.792
B20326+27	03:29:57.69	27:56:15.64	1.3	2.787
4C+32.14	03:36:30.12	32:18:29.47	2.7	2.793
3C092	03:40:08.55	32:09:02.32	1.6	2.791
3C093.1	03:48:46.93	33:53:15.41	2.4	2.795
4C+26.12	03:52:04.36	26:24:18.11	1.4	2.783
B20400+25	04:03:05.61	26:00:01.61	0.9	2.785
3C108	04:12:43.69	23:05:05.53	1.5	2.788
B20411+34	04:14:37.28	34:18:51.31	1.9	2.793
4C+25.14	04:20:49.30	25:26:27.63	1.0	2.785
4C+33.10	04:47:08.90	33:27:46.85	1.2	2.799
3C131	04:53:23.35	31:29:25.36	2.9	2.801
3C132	04:56:43.08	22:49:22.27	3.4	2.795
4C+27.14	04:59:56.10	27:06:02.19	0.9	2.796
3C133	05:02:58.51	25:16:25.16	5.8	2.796

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The observations were conducted with the Arecibo telescope.⁶ Using the L-wide receiver, we simultaneously recorded spectra centered at 1420 MHz and the two OH main lines (1665 and 1667 MHz), achieving a velocity resolution of 0.16 km s⁻¹. We sampled simultaneously two linearly polarized channels performing both auto- and cross-correlations with the Arecibo's three-level "interim" digital correlator. The Arecibo telescope has an angular resolution of 35 at these frequencies. As shown by Heiles & Troland (2003a) in their Millennium H i survey, Arecibo can accurately measure H i absorption lines for strong sources (flux density larger than ∼1 Jy).

The observing procedure used was the same as in Heiles & Troland (2003a) and Stanimirović & Heiles (2005). This technique employs a 17 point observing pattern including 16 off-source measurements and 1 on-source measurement. The pattern was designed to measure the first and second derivatives of the 21 cm intensity fluctuations on the sky and also to fine-tune for the instrumental effects involving the system gain. The auto-correlation data were used to derive the "expected" H i emission profile (T_exp), which is the profile that would be observed at the source position if the continuum sources were absent, the optical depth profile (τ), and their uncertainties. With 17 measurements, the off-source spectra are expressed in a Taylor series expansion of the expected profile and a small contribution from the source intensity attenuated by the optical depth. A least-squares fitting technique is then used to estimate the optical depth profile, the expected profile and its spatial derivatives, and the off-source gain simultaneously (Heiles & Troland 2003a). However, our updated data reduction software takes a slightly simpler approach by not including the fine-tuning of gain variations under the assumption that the on-axis telescope gain and the beam properties vary spatially and a detailed knowledge of these variations is required to estimate properly off-axis gains. Therefore, we just derive the optical depth profile, the expected profile and its spatial derivatives for each of 16 off positions. These are used to derive the uncertainty spectra for both the expected emission and optical depth spectra.

We have experimented with using the first-order Taylor expansion instead of the second order. For all sources, we find that the difference between optical depth profiles derived used the two expansions is within 1σ uncertainty. While the second-order expansion is clearly more accurate (has smaller systematic errors), the derived T_exp(v) and τ(v) are noiser than when using the first-order expansion. The increased noise comes from fitting a larger number of unknown parameters and also from a large covariance between the second derivatives of the expected profile, T_exp(v), and τ(v). We tolerate the slightly higher noise for better accuracy of derived profiles and therefore use the second-order Taylor expansion for all sources.

Following the data reduction, for all sources, we obtained an H i absorption spectrum (e^−τ(v)), an H i (expected) emission spectrum (T_exp(v)), and their uncertainty profiles. A main beam efficiency of η = 0.85 (based on calibration measurements at Arecibo; P. Perillat et al.⁷) was used to convert T_exp(v) from the antenna temperature units to the brightness temperature scale. With an integration time on average of about 1 hr, we achieved an rms noise level in optical depth of ∼1 × 10⁻³ per 1 km s⁻¹ velocity channel.

Inspection of derived profiles revealed that several sources have small positive spectral features in their optical depth profiles at a level slightly higher than the 1σ uncertainty and highly localized in velocity. This effect is a result of high spatial derivatives of the H i emission (due to the presence of significant small-scale structure) and suggests that even the second-order Taylor expansion is not a good representation of the measured off positions in several cases. These sources are: 4C+27.14 and 4C+33.10. In addition, 4C+33.10 has very broad both absorption and emission profiles with many velocity components and its component fitting is more difficult and ambiguous than for other sources. However, in order to use as many sources as possible and considering that small artifacts are very localized in velocity, we include these three sources in our analysis (but make sure that artifacts are not fitted as real features). One source that we exclude from analysis is 4C+32.14 which has a highly saturated absorption profile and therefore all fitted parameters are highly uncertain for this source.

2.1.1. Comparison with HT03

Several of our sources were observed previously by (Heiles & Troland 2003b, from now on HT03): 3C+93.1, 3C131, 3C132, and 3C133. In terms of optical depth spectra, our results for 3C+93.1, 3C132, and 3C133 agree extremely well with HT03, within 3%. In the case of 3C131 we find a slightly larger difference but this is still within the 3σ uncertainty. In case of expected profiles expressed in terms of antenna temperature, we find excellent agreement with HT03 for all sources. We do correct our expected profiles for the beam efficiency and work with brightness temperature profiles in this paper.

2.2. H i Emission Data from the GALFA-H i Survey

2.3. Stray Radiation Consideration for H i Emission

2.4. Additional Data Sets

To analyze H i absorption spectra, we performed a decomposition into individual velocity components by employing the technique of Heiles & Troland (2003a). This allows us to estimate spin temperature and the H i column density for individual CNM components. This technique assumes that the CNM contributes to both H i absorption and emission spectra, while the WNM contributes only to the H i emission spectrum. The technique is based on the Gaussian decomposition of both absorption and emission spectra, and it takes into account the fact that a certain fraction of the WNM gas may be located in front of the CNM clouds, resulting in a portion of the WNM being absorbed by the CNM. All possible permutations of the CNM components along the line of sight have been taken into account when searching for the best fit. Pros and cons regarding the use of Gaussian functions to represent the CNM absorption profiles have been discussed in Heiles & Troland (2003a).

We first fit τ(v) with a set of N Gaussian functions using a least-squares technique:

$$\begin{equation} \tau (v) = \sum _{0}^{N-1} \tau _{0,n} e^{-[ (v-v_{0,n})/\delta v_{n} ]^2}, \end{equation} \tag{ 1 }$$

where τ_{0, n} is the peak optical depth, v_{0, n} is the central velocity, and δv_n is the 1/e width of component n. N is the minimum number of components necessary to make the residuals of the fit smaller or comparable to the estimated noise level of τ(v).

While the optical depth spectrum predominantly reflects the CNM, both the cold and warm neutral media contribute to the expected H i emission spectrum:

$$\begin{equation} T_{\rm exp}(v)= T_{B,{\rm CNM}}(v) + T_{B,{\rm WNM}}(v). \end{equation} \tag{ 2 }$$

The first term, T_{B, CNM}(v), the H i emission originating from N CNM components is

$$\begin{equation} T_{B,{\rm CNM}}(v) = \sum _{0}^{N-1} T_{s,n}(1-e^{-\tau _{n}(v)}) e^{-\sum _{0}^{M-1} \tau _{m}(v)}, \end{equation} \tag{ 3 }$$

where T_{s, n} is the spin temperature of cloud n, and the subscript m represents each one of the M CNM clouds that lie in front of cloud n.

Next, T_{B, WNM}(v), the H i emission originating from the WNM, is represented with a set of K Gaussian functions. The complicating factor here is that a certain fraction F of the WNM is located in front of the CNM, while a fraction (1 − F) of the WNM is beyond the CNM with its emissions being absorbed by CNM clouds:

$$\begin{equation} T_{B,{\rm WNM}}(v)= \sum _{0}^{K-1} [F_{k} + (1-F_{k})e^{-\tau (v)}] \times T_{0,k}e^{-[(v-v_{0,k})/\delta v_{k}]^2 }, \end{equation} \tag{ 4 }$$

where the subscript k corresponds to each of the WNM components and a fraction F_k of the WNM cloud k lies in front of all CNM components, while a fraction 1 − F_k is being absorbed by the CNM clouds. T_{0, k}, v_{0, k}, and δv_k are the Gaussian parameters of the k-th WNM component, with T_{0, k} being in units of brightness temperature. To fit the corresponding emission spectra, we assume that the center and width of the absorption-selected CNM components are fixed and include a minimum number of additional WNM components to reduce the fit residuals to within the neighborhood of the 1σ uncertainties. We use a certain number of WNM components and fit the T_exp(v) profile simultaneously for the Gaussian parameters of the WNM components and the spin temperature of individual CNM clouds, while assuming a given order of CNM clouds along the line of sight and a given set of F_k values. We try to use the minimum number of WNM components such that the residuals of this fitting process are reasonably close to the 1σ uncertainty for T_exp.

Please note that the expected profile in the left-hand side of Equation (2) has been baseline corrected, which means that we measure T_exp(v) − T_sky, where T_sky contains contributions from the cosmic microwave background (CMB) and the Galactic synchrotron emission. Before doing the radiative transfer calculations we estimate T_sky and add it back to the left-hand side of Equation (2) by assuming 2.725 K for the CMB. To estimate the contribution from the Galactic synchrotron emission we use the Haslam et al. (1982) 408 MHz survey of the Galaxy. The brightness temperature at 408 MHz is converted to 1.4 GHz using the spectral index of −2.7. As the Galactic latitude of observed sources in the vicinity of Perseus is generally >10°, the synchrotron contribution is small and T_sky ranges from 2.78 to 2.80 K in our case (Table 1).

For each source, we vary the order of Gaussian functions along the line of sight (for N CNM components there are N! possible orderings) and perform the T_exp(v) fit. We then choose the ordering of CNM components that gives the smallest residuals in the least-squares fit. Unfortunately, the difference in the fit residuals is often not sufficiently statistically significant to distinguish between different values of F_k. However, F_k has a large effect on the derived spin temperatures. Hence we follow the Heiles & Troland (2003a) suggestion and estimate the final spin temperatures by assigning characteristic values of 0, 0.5, or 1 to each F_k (among the extreme possible values of 0 and 1), and repeating this for all possible combinations of WNM clouds. The final spin temperatures are then derived as a weighted average over all trials.

Out of 26 sources, 23 have well-constrained fits. Three sources, 3C133, 3C131, and 4C+25.14, have more than six individual CNM components in their absorption spectra. The corresponding fit for the spin temperature of these components in the presence of WNM features in emission is therefore more complicated, and the fitting process does not converge. Furthermore, for six sources (3C068.2, 3C133, 4C+25.14, 4C+28.07, 4C+30.04, and B20411+34) the fitted height of one absorption component is too small to be reliably recovered in the corresponding emission spectrum. Thus, the spin temperatures for these six components are calculated to be less than 1 K. Increasing the spin temperature by hand does not significantly degrade the quality of the fit. Therefore, for these uncertain components, we set the spin temperature equal to the uncertainty in T_s derived from the iterations over CNM component orders along the line of sight and fraction of WNM absorbed. The error on this value is set to the median T_s error for components along all 26 lines of sight, or 6.75 K.

Figure 2 shows emission and absorption spectra for all sources except 4C+32.14, which has a saturated optical depth profile. Strong absorption lines were detected in the direction of all sources. In all cases, the strongest emission and absorption is found at ∼0 km s⁻¹, and is generally well confined within the range of −20 to 20 km s⁻¹ (see also Figure 6). However, in the case of four sources (4C+33.10, 4C+27.14, 3C133, and 3C131) there are strong emission and absorption features around −40 km s⁻¹. Visual inspection of velocity components close to Perseus using the GALFA-H i data cubes suggests that this secondary region is likely not associated with Perseus.

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We show results of our Gaussian component fitting for four example sources in Figures 3 and 4. In each panel of both figures, we plot the derived expected emission and optical depth profiles for an individual source. For the optical depth spectra, we overplot the individual CNM components (dotted lines), as well as the residuals for the fit (offset to the bottom of the panel) with the derived uncertainties for the spectrum for comparison. For the expected emission profiles, we overplot the sum of all WNM components (dot-dashed line), the total T_s-corrected contribution of the CNM (thick dashed line), and the fit residuals (shown below zero in the panel) with the uncertainties in the profile for comparison. The two sources in Figure 3, 3C131 and 4C+27.14, have broad H i profiles as likely include emission/absorption beyond Perseus, 3C092 in Figure 4 is located behind the main body of Perseus, and NVO0157+26 in the same figure is an example of a low optical depth profile.

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In Table 2, we list the Gaussian parameters associated with all CNM and WNM components for each source. In Column 1, we list the peak brightness temperature for each component. For the WNM components, this is equal to the unabsorbed Gaussian height and estimated error in the fit. For the CNM components, this is equal to the calculated spin temperature multiplied by (1 − e^−τ), as in Equation (3), and is quoted without uncertainty. In Columns 2 and 3, we list the centers and FWHM of CNM and WNM components with estimated fit uncertainties. In Column 4, we list the peak optical depth of each component. For the CNM components, this is equal to the height of each component (in τ), with associated uncertainty. For the WNM components, this is equal to the maximum contribution of each WNM component detected in emission to the absorption profile and is found by measuring the height of the absorption fit residuals at the central velocity of each WNM component. In Column 5, we list the spin temperatures, which for the CNM components is equal to the calculated values from the fit with fit uncertainties. For the WNM components, this is equal to a lower limit imposed by the upper limit on optical depth in Column 4, and these values are also quoted without error because the errors are extremely large due to the nature of the estimation process. In Column 6, we list the maximum kinetic temperature of each component based on the line widths. In Column 7, we list the H i column density of each individual component, and these values are quoted in units of 10²⁰ cm⁻². Finally, in Column 8 we list the fraction of each WNM component lying in front of all CNM components (F, either 0.0, 0.5, or 1.0; see Section 2.2) or the order of each CNM component along the line of sight (O, integer values).

4.1. Optical Depth

A summary of the fitting results is presented in Figures 5–8. As shown in Figure 5(a), the median peak optical depth τ_max for individual Gaussian components is 0.16 and only a handful of CNM components have τ_max > 1 (10/107). Perseus is an intermediate-mass GMC located about 20° below the Galactic plane and may not sample the densest molecular gas. In addition, a tighter grid of background sources may be able to sample better denser gas. Only two of our sources are located right behind the main body of Perseus. Their peak optical depth is 1.5.

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The same figure shows τ_max for the components from HT03, dotted lines show median rms noise in optical depth for two studies. The two studies agree very well and have relatively similar (median) sensitivity, but we are missing the low τ_max portion of the distribution. This could be partially due to our small survey area relative to HT03 who had more sources at high Galactic latitudes. We note that HT03's sensitivity varies across sources as their survey was searching for strong sources suitable for Zeeman measurements.

Very recently, Fukui et al. (2014b) suggested a new approach to estimate properties (optical depth and spin temperature) of cold H i by utilizing dust emission. They noticed that the Planck dust optical depth τ₃₅₃ at 353 μm correlates with N(H i), but the scatter in this relation is much smaller when different dust temperature regimes are considered separately. By assuming that the highest dust temperature sub-sample is associated with the optically thin H i, the saturation seen in the τ₃₅₃–N(H i) relation was attributed to the existence of the high optical depth H i solely. By inverting the relation, they estimated a single value of T_s and τ_H i per pixel from their all-sky τ₃₅₃ images (after masking low-latitude regions with |b| < 15° and regions with internal dust heating as traced by the Hα emission). They found that 85% of data points have τ_H i > 0.5 and T_s < 40 K. Similar results were obtained for the high latitude clouds MBM 53-55 (Fukui et al. 2014a), increasing the H i mass of MBM 53-55 clouds by a factor of two. Fukui et al. (2014b) suggested that the local interstellar medium (ISM) may be dominated by the high optical depth H i, and that this component may explain all of the CO-dark gas in the Milky Way.

Around Perseus we find τ_max > 0.5 only for 21 out of 107 (20%) individual (Gaussian) components. This is clearly in stark contrast with Fukui et al. (2014b), who claimed that 85% of lines of sight at essentially |b| > 15° have τ > 0.5 based on their comparison of τ₃₅₃ and N(H i).

4.2. Spin Temperature

4.3. H i Column Density and the CNM Fraction

4.4. What Determines the CNM Fraction?

While the Perseus region has on average a higher CNM fraction relative to an average ISM field, as shown in Figure 7, interestingly almost all directions (25 of 26) in our study have the CNM fraction smaller than 50%. We emphasize that this result is not an artifact of our applied T_s < 200 K cutoff. If we do not apply any temperature cutoff, the median CNM fraction is 35%, and 23 of 26 directions have a CNM fraction <50%.

In Figure 8, we show the CNM fraction as a function of the total H i column density for our sources as well as HT03 data. It is obvious that the CNM fraction never gets higher than ∼80% (for both studies). This shows that there are no lines of sight without the WNM, even in the directions where the CNM hugely dominates the WNM fraction is at least ∼20%. Although the scatter in this figure is large, the CNM fraction appears to increase from 0% to ∼40% at N(H i) ∼ 10²¹ cm⁻², and then levels off (purple points show median values for Perseus observations). As pointed out by Heiles & Troland (2003b), this transition occurs right around the column density required for shielding H₂, suggesting that the CNM transitions into H₂ as soon as the adequate shielding is achieved. This column density also agrees with Lee et al. (2012) who showed that the H i-to-H₂ transition (defined as having a H₂ fraction of 0.25) occurs in Perseus at N(H i) = (6–12) × 10²⁰ cm⁻².

In Figure 9 (top), crosses show the CNM fraction as a function of the column density weighted average spin temperature along the line of sight. A recent study by Kim et al. (2014), which produced synthetic H i spectra based on their three-dimensional hydrodynamic simulations of a Milky Way-like disk, suggested that for the observed T_s < 400 K, the CNM fraction is proportional to the inverse of T_s. While their synthetic spectra represent random directions, most of the simulated data are located between 50K/T_s and 100K/T_s lines. Furthermore, for the observed T_s < 200 K the simulated CNM fraction ranges between 40% and 70%, with a median value being 52% (97% of simulated data points have a CNM fraction <70%; C.-G. Kim et al. 2014 private communication). We overplot the 1/T_s relation in the figure for three representative temperature values of 20, 50, and 100 K (the simulation applied a CNM temperature cutoff of T_k < 184 K, where T_k is the true kinetic temperature). To bracket most of our data points, we need to expand the T_s range to lower temperatures of ≲ 20 K. With our observed CNM fraction being largely in the range of 10%–50%, we overlap with the 40%–70% range expected by the simulation, although the simulated fraction is generally slightly higher than what we observe. Square symbols in this plot show the difference introduced in the CNM fraction when a 350 K threshold is applied (instead of 200 K) to select the CNM. The difference is very small, only three data points are noticeably affected.

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In the same figure (bottom panel), instead of using our calculated T_s, we follow exactly Kim et al. (2014) and calculate the observed temperature as the optical depth weighted average spin temperature along the line of sight (Equation (15) from Kim et al.). Most of our data points follow the 50/T_s line, which agrees well with our median T_s estimate and is in excellent agreement with the Kim et al (2014) prediction. Considering that in the simulation the CNM fraction is known, while the observed CNM fraction is based on the Gaussian decomposition T_s derivation method, this excellent agreement is an indirect evidence that the observational method provides consistent and reliable CNM fractions.

While the optical depth weighted average spin temperature (shown in the bottom panel) is on average higher than our column density weighted spin temperature (top panel), at the lowest temperatures the observed CNM fraction is in the 10%–50% range, while the simulation suggests a CNM fraction of 40%–70%. The simulated fraction is slightly higher that what is observed; however, it is very encouraging to see that the simulated CNM fractions are so close to observations and that the observed CNM fraction follow the 50/T_s prediction so closely. Considering that Kim et al. (2014) do not include interstellar chemistry, they likely slightly overestimate the amount of cold H i as the conversion from atomic to molecular phase is not taking place in the simulation.

In summary, the CNM fraction in and close to Perseus is surprisingly low, being largely below 50% (median value of 30%), even at the lowest observed temperature where H i absorption should be tracing only the CNM with essentially no confusion by the thermally unstable WNM. This is a somewhat surprising result as suggests that even close to the dense molecular clouds the CNM fraction (CNM/CNM+WNM column density) is never very high. As a consequence, this suggests that even lines of sight that probe deep inside the GMCs have of the order of 50% contribution from the WNM (thermally unstable and/or stable). The geometry and the level of mixing of the CNM and WNM are still not understood. For example, it is not clear if the WNM is located primarily in outer regions of the H i envelope or if it is being brought closer to the inner regions via turbulence. From the observational point of view, the H i absorption may not be tracing the densest H i regions as optical depth profiles may become saturated, like in the case of 4C+32.14, which is the source we had to exclude from analysis due to its highly saturated H i absorption profile (this source is located behind the main body of Perseus). It will be important to investigate the CNM fraction using alternative tracers in the future, such as C ii and C i (e.g., Pineda et al. 2013).

As the mixture of CNM and WNM phases exists in the diffuse ISM, Hennebelle & Inutsuka (2006) asked the question of whether the WNM can persist deep inside molecular clouds. Considering that H i halos surround molecular clouds, interstellar turbulence will naturally mix in some H i with molecular gas. However, in about one cooling time, it is expected that any WNM mixed with molecular gas will cool down if the internal pressure is about 10 times higher than the typical ISM pressure. Hennebelle & Inutsuka (2006) showed that the dissipation of magnetic waves can provide substantial heating and therefore serve as an additional source of energy that can maintain the WNM inside even high-pressure molecular clouds.

To compare H i absorption with CO, we use data from two surveys: the CO (1–0) emission data from the CfA survey at 84 resolution (Dame et al. 2001), and the integrated CO intensity (W_CO) from Planck (Planck Collaboration et al. 2013) smoothed and regridded to match the CfA's angular resolution and pixel size. We extract CO spectra from Dame et al. and show W_CO in Figure 10 (left) as black data points. The Dame et al. observed area covers 14 out of 26 sources. The dashed black line in this figure shows the median 1σ uncertainty on W_CO calculated from the line-free channels. The results from Planck are shown in Figure 10 (left and right) in blue, as well as their median 1σ uncertainty. We noticed that Dame et al.'s integrated intensity is systematically higher relative to the Planck data. A median scaling of 1.37 was applied on the Planck data to roughly match Dame et al. observations.

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Figure 10 shows that 8 out of 26 sources have a clearly detected CO emission that is above 1σ uncertainty in both Dame et al. (2001) and Planck data. Almost all detections have the total H i column density >10²¹ cm⁻². Their CNM fraction ranges from 20% to 55%. While H i absorption is detected in the case of all sources, 18 sources were not detected in CO. Most non-detections pile up at N(H i) < 10²¹ cm⁻² and likely probe diffuse H i regions. As shown in Figure 10 (right), where we use the Planck data for E(B − V) × 3.19 as a measure of A_V (R_V = 3.19 was measured for Perseus star BD+31°643 by (Snow et al. 1994)), most non-detections have A_V < 1. Lee et al. (2014) showed that in Perseus A_V ∼1 mag is a necessary condition for the existence (shielding against photodissociation) of CO. Considering all this, most CO non-detections probe diffuse (A_V < 1 mag) regions without necessary shielding for CO formation.

However, there are three CO non-detections with N(H i) = 10–35 × 10²⁰ cm⁻², which probe regions with A_V ∼ 1 mag and therefore likely contain H₂, while CO could be just forming and still be underabundant. Considering that we detect H i absorption with large column density but no CO emission, these three positions are excellent candidates for probing the CO-dark gas, which contains H₂ but not CO. Interestingly, CO is detected both at lower and higher total H i column density relative to these non-detection, at ≲ 10²¹ and >3 × 10²¹ cm⁻². The three sources are 3C132, 3C093.1, and B20411+34. As shown in Figure 2, their H i absorption spectra have only components around 0 km s⁻¹, suggesting that a contamination from non-Perseus H i clouds can not be the reason for H i absorption detections without CO emission.

We now compare closely the kinematics of CO (from Dame et al. 2001) and H i absorption of eight sources with detected CO, which have A_V ≳ 1 mag (Figure 11). One of the eight sources, 3C092, is particularly interesting as it is located right behind the main body of Perseus, this source has the highest integrated CO intensity (>30 K km s⁻¹) and the CNM fraction of ∼0.4. As shown in the figure, in most cases CO and H i absorption agree well in terms of velocity range and profile shapes, although there is a large diversity among sources. This suggests that H i in absorption appears to trace not just cloud envelopes but also central regions. In three cases (3C092, 3C108, and 4C+25.14) CO emission and H i absorption cover the same velocity range. In the case of 3C131, 3C133, and 4C+27.14, while the strongest H i absorption agrees well with the CO emission peak, a weaker secondary component is seen at a velocity of 0 km s⁻¹, which is not detected in CO, possibly due to low sensitivity. Only for two sources, 4C+30.04 and 4C+33.10, there is significant difference in that the H i absorption profile is broader than CO emission and a CO peak is found in the middle of the H i absorption profile.

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We show in Figure 11, the corresponding spin temperature and the CNM column density of the H i component that is the closest in velocity to the CO peak. The spin temperature ranges from 30 to 80 K and the CNM column density of the component closest to CO ranges from 0.8 to 8 × 10²⁰ cm⁻², which corresponds to the higher portion of the CNM column density measured for the whole population of CNM components in this study. On the other hand, the remaining CNM column density along these lines of sight ranges from ∼3 × 10²⁰ to 13 × 10²⁰ cm⁻². All sources except 4C+25+14 have the total H i column density >10²¹ cm⁻² (A_V ≳ 1 mag), suggesting conditions suitable for formation of CO (and H₂).

This generally good spectral agreement we find between H i absorption and CO emission contrasts results from studies of the diffuse molecular gas (A_V < 1 mag), e.g., Liszt & Lucas (1996) and Liszt & Pety (2012), where commonly H i absorption is more extended in velocity relative to CO emission, and especially it was noticed that CO emission tends to avoid the deepest H i absorption (in other words, CO was associated only with weaker H i absorption features). This is usually explained as the deepest H i absorption arising mainly from the CO-free cloud envelopes, while CO tracing the central regions. The eight directions we investigate here all trace regions with A_V ≳ 1 and are therefore likely probing equilibrium chemistry relative to A_V < 1 likely largely non-equilibrium dominated regions.

It is generally expected that the CO-dark gas is found in uniform envelopes surrounding CO-bright molecular clouds (Wolfire et al. 2010). Numerical simulations by Smith et al. (2014) support this idea but show that CO-dark H₂ may be asymmetric and not necessarily trace the outlines of CO-bright clouds. Fukui et al. (2014a) proposed that the CO-dark gas could be dominated by the optically thick H i. In addition, considering that envelopes are likely to have small velocity offsets relative to the CO-bright cloud regions, we would expect to see kinematically more extended H i absorption profiles around CO peaks. However, in eight directions where we have both H i absorption and CO emission spectra, we generally find good agreement between the two. This suggests that in these directions H i absorption traces largely the central cloud regions where CO is bright, and to a smaller degree only the CO-dark cloud envelope. Of 26 directions, there are only 3 cases with strong H i absorption and the total N(H i)>10²¹ cm⁻², but without CO emission.

Another interesting result from our study is that cold H i with high H i column density is clearly present deep inside CO-bright GMCs, suggesting that its importance for GMC evolution, and star formation, may be more significant than previously thought. The origin of cold H i deep inside GMCs, and its morphology (e.g., filamentary flows versus clumps versus diffuse distribution throughout GMCs) are not well understood. The cold H i could be brought deep into the clouds via circulation of neutral gas from outer regions due to turbulence (Hennebelle & Inutsuka 2006) or could be a photodissociation product of H₂. Tighter grids of H i absorption sources across and around GMCs are greatly needed to map out the distribution of cold H i and distinguish between various formation mechanisms.

To investigate properties of cold H i in and around the Perseus molecular cloud, and especially to investigate the role of cold H i in the shielding of H₂ (Paper II), we have obtained and detected H i absorption in the direction of 26 background radio continuum sources. Using the corresponding H i emission spectra, and by employing a Gaussian decomposition of H i emission/absorption pairs, we have performed radiative transfer calculations to estimate T_s and τ(v) for 107 individual Gaussian components. This method represents the most direct way of measuring spin temperature and optical depth.

The peak optical depth of individual Gaussian components ranges from ∼0.01 to a few, with the median value of 0.16. The spin temperature ranges from 10 to 725 K and peaks at 50 K. The median values of the CNM and WNM column densities for individual components are 6 × 10¹⁹ cm⁻² and 1.5 × 10²⁰ cm⁻², respectively. All properties of individual components for Perseus are in excellent agreement with those of HT03, who observed 66 random lines of sight at |b| > 10°. This suggests that individual cold H i components have similar properties between a focused field around a GMC and an average ISM field.

However, when all CNM and WNM components are summed along each line of sight, we find a significant difference relative to an average ISM field. The Perseus region has a higher fraction of absorbing H i and a higher total H i column density relative to an average ISM field, suggesting environmental differences. This result is the first observational evidence that the CNM fraction in/around GMCs is likely higher than what is found in an average ISM field. Interestingly, the median CNM and WNM H i column density along the line of sight are roughly similar around Perseus, 4.6 × 10²⁰ cm⁻² versus 5.8 × 10²⁰ cm⁻², while in the case of HT03, the WNM column density was twice higher than the CNM column density.

Our results for both the optical depth and spin temperature are in stark contrast to Fukui et al. (2014b), who used Planck data and assumed that all dust grains cooler than 22 K are mixed with the optically thick H i, suggesting that the amount of cold H i could be significant and even enough to explain all (or most) of the CO-dark gas. For 85% of their sky coverage, they estimated T_s = 20–40 K and τ_max > 0.5. Considering all our Gaussian components, we find such high τ_max only occasionally, with only 20% of components having τ_max > 0.5. Considering whole optical depth profiles, 54% of directions have τ_max > 0.5. Also, only ∼15% of lines of sight have a column density weighted average spin temperature lower than 40 K. We suspect that Fukui et al. results are caused by the inability to distinguish different gas components along the line of sight as well as by assigning all of the cooler dust to H i without allowing for contribution of the molecular gas (bright or dark).

The mean spin temperature appears uniform over the radius of 10–120 pc from the rough center of Perseus. Obtaining a tighter grid of H i absorption sources, and especially sampling better the inner 10 pc, in the future will be important to probe a potential radial increase in T_s away from the cloud center as suggested by Andersson et al. (1992).

While the CNM fraction is on average higher around Perseus relative to a random ISM field, surprisingly it rarely exceeds 50%. Even directions with the lowest T_s < 200 K clearly show the CNM fraction of <50%. It is highly encouraging to see that recent numerical simulations by Kim et al. (2014) produce the CNM fractions reasonably close to observations, 40%–70%, and also predict that the CNM fraction is inversely proportional to the optical depth weighted average T_s, which is in excellent agreement with observations. Further inclusion of interstellar chemistry and the H i-to-H₂ conversion will likely fine-tune the simulated fractions and bring them even closer to observations. Our results suggest that even directions that probe deep inside molecular clouds do not have high CNM fractions (e.g., >50%). This could result from extended WNM envelopes of GMCs and/or significant mixing of CNM and WNM throughout GMCs caused by interstellar turbulence or accretion flows. While the low CNM fraction in/around GMCs requires further theoretical work, at high column densities, the H i lines are likely to become saturated and therefore poorly trace the densest and coldest regions of GMCs. It is therefore also important to observationally test the usefulness of additional tracers of neutral gas inside GMCs, e.g., C i and C ii.

Finally, we have compared H i absorption with CO emission for our 26 directions and found that 8 of 26 have detected CO. Out of the remaining 18, 15 directions probe diffuse regions with A_V < 1 mag and likely do not have enough shielding for CO formation. Only 3 of 26 directions have N(H i)>10²¹ cm⁻² (A_V ≳ 1 mag) and therefore probe conditions suitable for CO formation, yet have no detected CO emission. These directions therefore likely contain molecular gas but not CO and are representative of so called CO-dark gas. Eight directions with detected CO have N(H i)>10²¹ cm⁻², A_V > 1 mag and good kinematic agreement between H i absorption and CO emission spectra. All of this suggests that these lines of sight probe largely central CO-bright regions, confirming the existence of cold H i deep inside GMCs. However, future observations of a tighter grid of background sources are necessary to map out the distribution of cold H i around GMCs and its origin.

We sincerely thank the telescope operators at the Arecibo Observatory for their help in conducting these observations. We are extremely grateful to Chang-Goo Kim and Eve Ostriker for extensive discussions and for providing detailed CNM fractions from Kim et al. (2014) for comparison with observations. We acknowledge stimulating discussions with Robert Lindner and Brian Babler, and thank Elijah Bernstein-Cooper for extracting Planck images around Perseus. We also thank an anonymous referee for emphasizing the importance of detailed chemistry in neutral gas estimates. We are grateful to John Dickey for stressing the importance of background diffuse emission in spin temperature calculations. S.S. thanks the Department of Astronomy at the Faculty of Mathematics, Belgrade University, for their kind hospitality during the final stage of manuscript preparation. This work was supported by the NSF Early Career Development (CAREER) Award AST-1056780. M.-Y. Lee acknowledges support from the DIM ACAV of the Region Ile de France. We also acknowledge the NSF REU grant AST-1004881, which funded summer research of Jesse Miller. The use of "Karma" visualization software (Gooch 1996) is gratefully acknowledged.