THE CARBON INVENTORY IN A QUIESCENT, FILAMENTARY MOLECULAR CLOUD IN G328

Giant molecular clouds (GMCs) play a fundamental role in the evolution of a spiral galaxy. They represent the end result of the continual collection of diffuse gas into molecular form in the interstellar medium (ISM), some of it having been recycled from past generations of stars. GMCs are also the sites where the bulk of ongoing star formation in a galaxy then occurs. They can form from the atomic substrate, as evident in global views of other galaxies (e.g., M33; Engargiola et al. 2003), or perhaps from the assembly of smaller molecular clouds. How this occurs within our own Galaxy remains unclear as the process has not yet been seen. Models range from quasi-static self-gravitational collapse, for instance along magnetic field lines (e.g., Ostriker & Kim 2004), to transient phenomena such as the coalescence of clouds in converging flows in a turbulent medium (e.g., Hennebelle & Pérault 2000; Hartmann et al. 2012). Since stars appear to form almost as soon as molecular gas is present, then the rate of formation of GMCs is also instrumental in determining the star formation rate.

Furthermore, despite being molecular, forming clouds will not necessarily be evident through CO line emission, normally the tracer used to delineate their locations. This is because, in the low molecular column densities of clouds forming from the diffuse atomic medium, far-UV radiation will dissociate the CO, whereas self-shielding can allow H₂ to exist; i.e., a pure H₂ molecular cloud (sometimes also known as "dark" H₂ due to the absence of an emitting molecular species; Wolfire et al. 2010). The carbon in such clouds cannot be hidden, however, and will exist primarily in neutral form where it can emit through the [C i] lines at 492 and 809 GHz (610 and 371 μm, respectively), or in singly ionized form, emitting as [C ii] 1.90 THz (158 μm), or in both. In either case, its detection is difficult, for observations at these frequencies require exceedingly dry atmospheric conditions or airborne/space platforms. Facilities able to map these species at good spectral and spatial resolution, and over the large areas of sky that may encompass the environs of forming GMCs, have not previously been available.

We present the first data from a new facility at the summit of the Antarctic plateau, Ridge A (Saunders et al. 2009). The 62 cm aperture High Elevation Antarctic Terahertz (HEAT) telescope (C. Kulesa et al. 2014, in preparation) currently provides spectroscopic imaging in the 810 GHz lines of CO J = 7–6 and [C i] J = 2–1, with upcoming capabilities at 1.46 THz [N ii] and 1.90 THz [C ii]. It can already map [C i] emission over significant regions of the Galactic plane, and so be able to search for forming molecular clouds and "dark" H₂. The exceedingly low and stable columns of precipitable water vapor at Ridge A (falling below 100 μm for more than 25% of winter; Saunders et al. 2009; Yang et al. 2010) make this possible. We have identified a filament in [C i] in the G328 region that is also evident in molecular (CO) and atomic (H i) survey data taken with similar resolution. The results of our mapping of this filament are the subject of this paper. [C ii] emission has also been identified along a sightline near to this filament by the GOT C+ program using the Herschel telescope (Langer et al. 2014).

The observations are summarized in Section 2 and the results presented in Section 3. They are then discussed in Section 4 with reference to the physical characteristics of the G328 filament, a photodissociation region (PDR) model for its line emission, and the carbon abundance within it.

The data presented here comes from three separate spectral line surveys of submillimeter [C i], mm CO and cm H i emission in the southern Galactic plane. HEAT is imaging the [C i] 809.3 GHz line ($\rm ^3{{P}}_2 - ^3{P}_1$) from Ridge A, Antarctica, yielding data cubes with 2' and 0.7 km  s⁻¹ resolution. ¹²CO, ¹³CO and C¹⁸O J = 1–0 emission lines (115.3, 110.2 and 109.8 GHz, respectively) were imaged as part of the 22 m Mopra Southern Galactic Plane CO Survey (Burton et al. 2013), with 06 and 0.1 km  s⁻¹ resolution. The 1.420 GHz H i line comes from archival data in the Parkes–ATCA Southern Galactic Plane Survey (McClure-Griffiths et al. 2005) and provides 2' and 3 km  s⁻¹ resolution. The contiguous data set for these species covers l = 3280–3285, b = −04 to +04, although the CO and H i images presented here in fact cover a larger region, of l = 328°–329°, b = −05 to +05. [C i] and CO emission extend over a velocity range from −100 to 0 km  s⁻¹ V_LSR in the data cube, the H i from −120 to +100 km  s⁻¹. Spatially, the emission from the three species across these velocity ranges covers the entire region mapped.

A sinuous emission feature was identified in the CO data cubes, extending ∼08 × 005 in angular size and centered at −78 km  s⁻¹, with a narrow spectral range of just 4 km  s⁻¹. This filament is analyzed in this paper, with an analysis across the full spectral emission range of the cubes presented in C. Kulesa et al. 2014 (in preparation).

Figure 1 presents integrated flux images of the [C i], ¹²CO and H i for the G328 filament, together with a 250 μm continuum image of the dust emission from the Herschel HiGal program (Molinari et al. 2010). The ¹³CO image (not shown) looks essentially the same as ¹²CO (albeit at ∼30% the flux), and is used to determine the CO optical depth. C¹⁸O is also detected at the brightest portions of the filament at the 3σ level, indicative of high optical depths. It is also notable that the H i is evident as a depression in the level of the extended atomic emission found across the entire G328 region (i.e., H i self-absorption or HISA⁷), whereas the CO and [C i] emission are primarily confined to just the filament itself in this velocity range. Also notable is that the filament is not apparent in the dust emission map.⁸ There also do not appear to be any IR sources that are clearly associated with the filament, as might be expected if star formation were active in it.

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Figure 2 shows the H i image overlaid with contours of the CO and [C i]. It is clear that these features are closely related. The HEAT [C i] data set so far spans only the NW portion of the filament (the "Head"). However, given the similarity of the CO and [C i] here, both spectrally and in morphology, it seems likely that the [C i] emission will be co-extensive with the CO along the rest of the filament.

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Figure 3 presents profiles for the lines averaged over the Head of the filament. We show both the entire spectrum along the sight line as well as zoomed into the velocity range for the G328 filament, for clarity. The CO and [C i] are clearly similar for the filament (i.e., same line center and narrow FWHM), but for H i this is evident as a dip in the profile, which extends considerably beyond the spectral limits shown. Figure 4 shows a spatial cut perpendicular to the filament in the integrated flux images. The filament is narrow and shows similar structure in CO and [C i].⁹ As for the velocity profiles, there is a dip in the H i flux across the filament. The reduction amounts to approx 40% of the flux level found either side of the filament.

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Line parameters are then calculated for three different apertures associated with the filament. The first is for the integrated flux for its Head, and the other two are for the peak pixels seen in the [C i] image. These apertures are defined in Table 1 and their line fluxes are listed in Table 2. ¹²CO optical depths are also calculated from the ¹²CO/¹³CO flux ratio, R (i.e., τ ∼ X/R with $X = [\rm ^{12}C/^{13}C] \sim 50$ appropriate to a Galactocentric radius of ∼5 kpc; the derived values are only mildly sensitive to its likely variation—see Burton et al. 2013). The CO optical depths are significant(>10) and greatest at the brightest pixels.

Table 1. Apertures

Aperture		l	b	Δl	Δb	V1	V2
Number	Name	($\deg$)	($\deg$)	(')	(')	(km s−1)	(km s−1)
1	Filament Head	328.375	−0.085	15	10	−80	−76
2	Peak 1	328.420	−0.120	2	2	−80	−76
3	Peak 2	328.345	−0.025	2	2	−80	−76

Notes. Apertures used for this analysis. l and b are the centers for each aperture in Galactic coordinates, Δl and Δb their widths, and V₁ and V₂ the velocity limits.

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Table 2. Line Fluxes

Aperture	12CO	13CO	C18O	[C i]	H i	τCO	$\rm H\,{\scriptsize{I}}_{{\rm min}}$	$\rm H\,{\scriptsize{I}}_{{\rm interp}}$	τHISA
Number	(K km s−1)	(K km s−1)	(K km s−1)	(K km s−1)	(K km s−1)		(K)	(K)
1	12 ± 1	3.0 ± 0.4	<0.4	1.7 ± 0.2	380 ± 10	13	58	105	1.0
2	26 ± 1	9.2 ± 0.5	1.6 ± 0.5	4.1 ± 0.3	360 ± 10	18	67	118	0.9
3	21 ± 1	6.1 ± 0.4	0.7 ± 0.4	3.0 ± 0.3	340 ± 10	15	63	115	1.0

Notes. Average fluxes calculated over each aperture, ∫T_MBdV, for the five lines listed. The error includes an estimate for the uncertainty of the continuum level as well as the statistical noise in the data. The ¹²CO optical depth is calculated from the ¹²CO/¹³CO line ratio, assuming an intrinsic [¹²C/¹³C] ratio of 50. $\rm H\,{\scriptsize{I}}_{{\rm min}}$ and $\rm H\,{\scriptsize{I}}_{{\rm interp}}$ are the brightness temperatures in the H i cube at the bottom of the self-absorption profile, and when interpolated across the profile, respectively. τ_HISA is the derived optical depth due to this self-absorption, assuming T_S = 30 K and p = 1 (see Section 3).

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Column densities for CO, C and H are then given in Table 3. These are calculated using a standard excitation analysis from the upper level column density given by radiative transfer (e.g., Goldsmith & Langer 1999; Burton et al. 2013), with standard notation:

$$\begin{equation} N_J = T_{{\rm MB}} \delta V \frac{8 \pi k \nu _{JJ^{\prime }}^2}{A_{JJ^{\prime } hc^{3}}}\frac{\tau }{1 - e^{-\tau }}. \end{equation} \tag{ 1 }$$

The column density for the species is then determined from

$$\begin{equation} N = \frac{N_J}{g_J} \, Q(T_{{\rm ex}}) \, e^{T_J/T_{{\rm ex}}}. \end{equation} \tag{ 2 }$$

Here Q(T) is the partition function, taken to be 2T_ex/T₁ (T₁ = 5.5 K) for CO, 4 for H i, and from fitting to the tabulated values in the Cologne Database for Molecular Spectroscopy for [C i] (Müller et al. 2001, 2005). The principal assumptions made in these calculations are of a beam filling factor of unity and in the value of the excitation temperature, here taken to be T_ex = 20 K. τ is determined for CO as described above and the optically thin limit is assumed for C.¹⁰ Motivating the temperature assumption, in the PDR model we discuss in Section 4.2 the [C i] and CO lines arise in regions of similar temperature of ∼20 K. Also, combining the [C i] 809 GHz flux with a low signal-to-noise ratio spectrum for the 492 GHz ³P₁ − ³P₀ [C i] line obtained with the Nanten2 telescope at the filament's peak (C. Glück et al. 2014, in preparation) yields a similar value. Changing T_ex by ±10 K likewise changes N(CO) by about one-third. The Boltzmann factor applied to the 60 K energy level of the 809 GHz [C i] line makes N(C) particularly sensitive to lower values of T_ex. For 10 K, it would increase by an order of magnitude; however, for 30 K N(C) falls by only a half. On the other hand, if T_ex were significantly less than 20 K then the Nanten2 492 GHz flux would have been much higher, given the measured value for the 809 GHz line. The range in the derived columns for N(CO) and N(C), considering all such likely variations in these parameters, does not alter the essential results that are given below.

The column density of cold atomic gas is estimated from the HISA profiles following the method of Sato & Fukui (1978) and Gibson et al. (2000) to determine the absorption optical depth. We use the difference in fluxes between the bottom of the absorption profile (T_min) and its value if no absorption had occurred (T_interp, obtained by interpolating across the line profile from the values either side) to determine τ_HISA = ln [(pT_interp − T_S)/(T_min + (p − 1)T_interp − T_S)] (see Table 2), where T_S is the spin temperature and p is the fraction of the H i emission assumed to originate from behind the filament (we have also implicitly assumed that the background continuum brightness temperature is very much less than the line brightness temperature in deriving this formula). We take T_S = 30 K, intermediate between the value in the cold molecular gas (∼20 K) and an upper limit equal to the lowest value found in the H i data cube over the entire filament (∼50 K). Following the discussion in Gibson et al. (2000), p is likely to be close to 1 for HISA to be prominent (but note also that it has minimum value given by p_low = 1 + (T_S − T_min)/T_interp in the limit that τ → ∞; for the values used here this is ∼0.6). The column of cold atomic gas in the filament is then given by $N{\rm (H_{{\rm HISA}})} = 1.8 \times 10^{18} \, T_S \, \tau \, \Delta V\,{\rm cm^{-2}}$ and is listed in Table 3. For T_S = (20 K, 50 K) these columns should be multiplied by ∼(0.5, 3) times, respectively. If only two-thirds of the H i emission was from behind the filament (i.e., p = 2/3) then the H i columns should be multiplied by a further factor of ∼3.

For C and CO the derived columns are of order a few × 10¹⁷ cm⁻². It is clear that the average C and CO abundances are comparable. Their ratio is a few times higher than that found in the dense PDR of Carina, where Nanten2 measurements found [C/CO] ∼ 0.2 (Kramer et al. 2008).

For H, the total column in emission is found to be ∼10²¹ cm⁻² in the velocity range of the filament (and so assumed to be at its distance). However, this gas is extended over the whole field seen in Figure 1 and so this column cannot be directly associated with atomic gas around the filament, although its projected distance is only 10–20 pc away. The cold atomic gas is evident as the HISA and has a column estimated to be ∼2 × 10²⁰ cm⁻², though this figure could readily be increased by ∼3 times, dependent upon the assumed value for T_S, the background continuum and particularly the foreground H i contribution, as discussed above.

Along a sightline at (l, b) = (328.085, 0.0) the GOT C+ program with Herschel has detected [C ii] emission in the same narrow velocity range as the CO, [C i] and H i discussed above (Langer et al. 2010, 2014). This sightline does not intersect the G328 filament, and lies ∼03 (∼ 25 pc) away from its Head, in a region where [C i] emission is absent and the CO emission diffuse and weak (see Figure 1). The H i here, however, is seen in emission rather than absorption. Thus, while this [C ii] emission cannot be used to determine the C⁺ column density associated with the filament, it does suggest that C⁺ emission is widespread and extends beyond the molecular cloud. The C⁺ column density at this position is estimated by Langer et al. to be several times 10¹⁷ cm⁻², so comparable in magnitude to that of the CO and C we have derived for the Head.

4.1. Physical Parameters for the G328 Filament

4.2. PDR Models

We have examined a range of cloud properties using a modified form of the Wolfire et al. (2010) PDR code to calculate column densities and line emission to compare with the data. The model consists of a slab of gas illuminated by the interstellar radiation field on two sides. The gas temperature and the abundances of atomic/molecular species are calculated as a function of optical depth, A_V, under the assumptions of thermal balance, chemical equilibrium and constant thermal pressure. We have made a simple approximation to include ¹³CO line transfer by assuming a constant ¹²CO/¹³CO abundance ratio of 50. For details on the chemistry and thermal processes we refer to Tielens & Hollenbach (1985), Kaufman et al. (2006), Wolfire et al. (2010), and Hollenbach et al. (2012). While not intended as a comprehensive attempt to fit the data, it has provided a representative model which approximates the observations for Aperture 2. The parameters and results are shown in Table 4.

Table 4. PDR Model

Input Parameters
Parameter	Value
AV	7.2 mag
Pth/k	2.0 × 104 K cm−3
G0	3 Habings
ΔV	2.4 km s−1
ζcrp	2.0 × 10−16 s−1
[C/H] abundance	1.6 × 10−4
Model Outputs
N(H i)	7.5 × 1020 cm−2
N(C+)	2.4 × 1017 cm−2
N(C)	4.7 × 1017 cm−2
N(CO)	1.4 × 1018 cm−2
I(12CO 1–0 115 GHz)	51 K km s−1
I(13CO 1–0 110 GHz)	15 K km s−1
I([C i] 492 GHz)	21 K km s−1
I([C i] 810 GHz)	9 K km s−1
I([C ii] 1.90 THz)	2.4 K km s−1
T(τCO = 1)	25 K
$n_{\rm H_2}(\tau _{\rm CO}=1)$	650 cm−3

Notes. Model parameters and predictions for a two-sided PDR (i.e., the model is one dimensional with radiation incident from both sides). $A_V=[N({\rm H\,{\scriptsize{I}}})+2N({\rm H_2})]/2.0\times 10^{21}$ cm⁻² is the optical depth through the cloud. P_th/k is the thermal pressure. G₀ is the radiation field strength in free space in units of the Habing field (1.6 × 10⁻³ erg s⁻¹ cm⁻²). ΔV is the Doppler line width in km s⁻¹. ζ_crp is the primary cosmic ray ionization rate per H nucleus. T(τ_CO = 1) is the gas temperature and $n_{\rm H_2}(\tau _{\rm CO}=1)$ the H₂ number density where CO 1–0 becomes optically thick.

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This model adopts an interstellar radiation field of G₀ = 3 (with G₀ = 1.5 incident on each side; G₀ is the interstellar field strength in units of Habing fields; Habing 1968). This field is roughly consistent with interstellar fields expected at a Galactocentric radius of 5 kpc (Wolfire et al. 2003). Somewhat surprisingly, the CO and [C i] flux results are not strongly dependent on G₀, as discussed in Wolfire et al. (1993), because stronger fields drive the C to CO transition deeper into the cloud, where the temperature is lower than at the surface. Higher fields will increase the C⁺ 1.9 THz flux, however. The model shown in Table 4 adopts a primary cosmic ray ionization rate of ζ_crp = 2 × 10⁻¹⁶ s⁻¹, consistent with rates for low column density diffuse clouds determined from observations of H$_3^+$ (Indriolo & McCall 2012), OH⁺, and H₃O⁺ (Hollenbach et al. 2012). There is some evidence that the ionization rate is depth dependent in clouds, varying from ∼2 × 10⁻¹⁶ s⁻¹ in low A_V clouds to values of ∼2 × 10⁻¹⁷ s⁻¹ in the centers of molecular clouds (e.g., Padovani et al. 2009; Hollenbach et al. 2012; Indriolo & McCall 2012; Rimmer et al. 2012). We present in Table 4 a model with the high cosmic ray rate, but an equally good fit to the data can be obtained with the low cosmic ray rate. We find that the low cosmic ray rate produces a higher fraction of the total CO cooling in the J = 1–0 line, because the CO gas is cooler.

The observed CO J = 1–0 luminosity of the whole filament is of order 0.1 L_☉. In the PDR models, this corresponds to a total CO luminosity of the cloud of 3–6 L_☉, depending on the cosmic ray rate. For the low cosmic ray rate, the total CO cooling is 3 L_☉ and most of the heating of the CO is provided by the FUV radiation at intermediate depths into the cloud. For the high cosmic ray rate the total CO cooling is 6 L_☉, of which about half the heating is provided by the FUV radiation at intermediate depths and half by cosmic rays distributed through the entire CO region.

The PDR models that fit the data have a total cloud optical depth of A_V ∼ 7 mag. and the interior gas temperature where CO 1–0 becomes optically thick is ∼25 K with an H₂ density of 650 cm⁻³. Note, however, that the model line fluxes are approximately twice that observed indicating that the beam filling factor is ∼0.5. For this beam filling factor, the estimated columns in Table 3 would be multiplied by a factor of ∼2. With this correction, the model column densities and line fluxes agree with observations to within a factor of two. We also provide estimates for the C 492 GHz and C⁺ 1.90 THz transitions. The models predict overlapping C⁺, C, and CO emission zones but their peaks are separated by ΔA_V ∼ 0.5 mag, equivalent to ∼0.5 pc, which is not resolvable at the resolution of the HEAT telescope at 809 GHz (Figure 4), but should begin to be discernible were it at the resolution of the Mopra data set.

We also note that the model incident field is G₀ = 1.5. This field produces dust temperatures at the surface of ∼17 K for silicates and ∼23 K for carbonaceous grains (Draine 2011). However, the bulk of radiation field is absorbed, and the dust emission is produced at greater depth, where the field strength is lower. At τ_UV = 1 the grain temperatures drop to 15 K and 20 K for silicates and carbonaceous grains respectively. The model dust temperatures are marginally within the limits set by the Herschel observations.

4.3. Carbon Abundance

We have found a quiescent, filamentary molecular cloud in the G328 region, situated about 5 kpc from the Sun and extending ∼75 × 5 pc, with a mass ∼4 × 10⁴ M_☉, comparable to that of a low mass GMC. The filament is evident in CO, [C i], and in HISA. The line width is small, ∼4 km s⁻¹ along its length, and no velocity gradient is discernible. Over the sightline through the cloud the average abundance of atomic carbon is similar to that of carbon in its molecular form (i.e., CO). The filament is not discernible in far-IR continuum images, and the flux limits imply that the dust must be cold, T_D < 20 K. The limits on its luminosity place it at the low end of the range in L/M previously found for IR-quiet GMCs. No clear evidence for star formation in the filament can be seen in the IR images, consistent with no significant internal heating. The molecular cloud is thus cold and has limited internal turbulence. We speculate that this filament represents a GMC that has recently formed, or indeed may still be in the process of forming. Star formation has not yet progressed far within it, and there are no, or limited, sources of turbulent energy injection into the gas.

This hypothesis can be tested through further wide-field THz spectral imaging, in both the [C ii] 158 μm (1.90 THz) line and the two [C i] lines. [C ii] would be expected to also show a similar structure to the CO and [C i]. As the gas transitions from atomic to molecular form a high ratio of C⁺ and C to CO is expected, for the external far-UV radiation field will limit the amount of gas that can exist as CO until sufficient column density has been built up to shield it from dissociating radiation. It would be of particular interest to determine whether the C and C⁺ associated with the filament has a more extended distribution than the CO as this scenario would suggest. It is first planned to upgrade HEAT to operate at 1.9 THz to measure the extended C⁺. Then a 5 m diameter THz telescope, such as the proposed DATE5 for Dome A in Antarctica, and the 0.8 m balloon-borne STO-2, to be launched from McMurdo Station in Antarctica, in late 2015, would provide similar resolution to the CO in the [C i] and [C ii] lines, accordingly, allowing one to examine this question further.

We thank the referee, Bill Langer, for his positive criticism of this paper. This has lead to a number of improvements in the text and the tightening of the arguments we have presented.

Funding for the HEAT telescope is provided by the National Science Foundation under grant number PLR-0944335. PLATO-R was funded by Astronomy Australia Limited, as well as the University of New South Wales, as an initiative of the Australian Government being conducted as part of the Super Science Initiative and financed from the Education Investment Fund. Logistical support for HEAT and PLATO-R is provided by the United States Antarctic Program.

The Mopra radio telescope is part of the Australia Telescope National Facility. Operations support was provided by the University of New South Wales and the University of Adelaide. The UNSW Digital Filter Bank (the MOPS) used for the observations with Mopra was provided with financial support from the Australian Research Council (ARC), UNSW, Sydney and Monash universities. We also acknowledge ARC support through Discovery Project DP120101585.

Facilities: Mopra - Mopra Radio Telescope, Parkes - Parkes Radio Telescope, ATCA - Australia Telescope Compact Array, Herschel - European Space Agency's Herschel space observatory