GMF G214.5-1.8 as traced by CO: I – cloud-scale CO freeze-out as a result of a low cosmic-ray ionization rate

ABSTRACT

We present an analysis of the outer Galaxy giant molecular filament (GMF) G214.5-1.8 (G214.5) using IRAM 30m data of ¹²CO, ¹³CO, and C¹⁸O. We find that the ¹²CO (1-0) and (2-1) derived excitation temperatures are near identical and are very low, with a median of 8.2 K, showing that the gas is extremely cold across the whole cloud. Investigating the abundance of ¹³CO across G214.5, we find that there is a significantly lower abundance along the entire 13 pc spine of the filament, extending out to a radius of ∼0.8 pc, corresponding to A_v ≳ 2 mag and T_dust ≲ 13.5 K. Due to this, we attribute the decrease in abundance to CO freeze-out, making G214.5 the largest scale example of freeze-out yet. We construct an axisymmetric model of G214.5’s ¹³CO volume density considering freeze-out and find that to reproduce the observed profile significant depletion is required beginning at low volume densities, n ≳ 2000 cm⁻³. Freeze-out at this low number density is possible only if the cosmic-ray ionization rate is ∼1.9 × 10⁻¹⁸ s⁻¹, an order of magnitude below the typical value. Using time scale arguments, we posit that such a low ionization rate may lead to ambipolar diffusion being an important physical process along G214.5’s entire spine. We suggest that if low cosmic-ray ionization rates are more common in the outer Galaxy, and other quiescent regions, cloud-scale CO freeze-out occurring at low column and number densities may also be more prevalent, having consequences for CO observations and their interpretation.

1 INTRODUCTION

The interplay of gravity, turbulence and magnetic fields in the interstellar medium (ISM) leads to a complex hierarchy of structures of various morphologies across a range of spatial scales (see Pineda et al. 2023, for a recent review). One recent finding has been that the cold, dense molecular ISM is predominately arranged into filaments, and that these filaments are linked to the star formation process (André et al. 2014). This has lead to a surge of observational and theoretical works to better understand the role of these filamentary structures in the last decade (e.g. Arzoumanian et al. 2013; Smith, Glover & Klessen 2014; Clarke & Whitworth 2015; Könyves et al. 2015; Clarke, Whitworth & Hubber 2016; Cox et al. 2016; Marsh et al. 2016; Clarke et al. 2017, 2018; Williams et al. 2018; Howard et al. 2019; Suri et al. 2019; Clarke, Williams & Walch 2020; Bonne et al. 2020a,b; Abe et al. 2021; Li et al. 2022; Wang et al. 2022; Bonne et al. 2023).

Large-scale galactic surveys have been a highly important driver in our understanding of the complex web of structures in the ISM and provided a manner to investigate the nature of molecular clouds in a statistical sense (e.g. Heyer et al. 1998; Dame, Hartmann & Thaddeus 2001; Jackson et al. 2006; Schuller et al. 2009; Molinari et al. 2010; Burton et al. 2013; Dempsey, Thomas & Currie 2013; Beuther et al. 2016; Rigby et al. 2016; Schuller et al. 2017; Umemoto et al. 2017; Su et al. 2019). A common molecular line tracer used to study the kinematics of molecular clouds in these surveys is ¹²CO and its isotopologues ¹³CO and C¹⁸O. This is due to their relatively high abundance and brightness making them ideal when observing large areas. Numerous works have studied what gas is traced by CO, relating emission to physical quantities such as density and mass, as well as examining the chemical/radiative effects which impact the CO abundance and the ratio between isotopologues (e.g. van Dishoeck & Black 1988; Glover et al. 2010; Bolatto, Wolfire & Leroy 2013; Szűcs, Glover & Klessen 2014; Nishimura et al. 2015; Szűcs, Glover & Klessen 2016; Peñaloza et al. 2017, 2018; Areal et al. 2018, 2019; Clark et al. 2019; Rigby et al. 2019; Roueff et al. 2021; Borchert et al. 2022; Ebagezio et al. 2023).

One important discovery from Galactic surveys is the presence of giant molecular filaments (GMFs) which are typically defined as velocity coherent, large-scale (≳10 pc), high aspect ratio, massive clouds (Jackson et al. 2010; Goodman et al. 2014; Ragan et al. 2014; Wang et al. 2015, 2020; Abreu-Vicente et al. 2016; Zucker, Battersby & Goodman 2018; Zhang et al. 2019; Colombo et al. 2021; Ge et al. 2023). It is currently not known how GMFs form, or if there is a universal mechanism, but it is thought that the majority form from a combination of shear and the Galactic potential leading to the elongation of existing clouds (Dobbs & Bonnell 2006; Dobbs, Burkert & Pringle 2011; Duarte-Cabral & Dobbs 2016, 2017; Smith et al. 2020). As such, these large structures are potentially shaped by their Galactic environment whilst also being regions of extended star formation, making GMFs an excellent place to investigate how large-scale ISM processes affect the star formation process. One such GMF is the outer Galaxy cloud G214.5-1.8, which is the focus of this paper.

1.1 The giant molecular filament G214.5-1.8

G214.5-1.8 (hereafter G214.5) is a giant molecular filament associated with the larger Maddalena’s cloud and lies at a distance of 2301 ± 150 pc (Maddalena & Thaddeus 1985; Lee, Snell & Dickman 1991; Yan et al. 2019). It has recently been the focus of a Herschel study by Clarke et al. (2023). They find that G214.5 has a mass of ∼16, 000 M|$_{_{\odot }}$| and a length of approximately 35 pc from north to south, making it comparable to other GMFs studied (Zucker, Battersby & Goodman 2018; Zhang et al. 2019; Colombo et al. 2021). However, they also find that G214.5 is highly quiescent for its mass and size, hosting very few 70 µm sources. Due to this, as well as the paucity of dense gas, they posit that G214.5 is a young GMF that may not have began forming stars in earnest.

As can be seen in the column density map.¹ In Fig. 1, G214.5 has a unique morphology which consists of two distinct subregions, a north to south thin filament and an east to west flocculent structure; Clarke et al. (2023) name these the main filament and the head structure respectively. These two subregions are velocity coherent and a smooth velocity gradient exists across the cloud from ∼22–32 km s⁻¹ (Lee, Snell & Dickman 1991; Yan et al. 2019). While the average properties of the two subregions are similar, Clarke et al. (2023) find that the vast majority of the dense gas and protostellar clumps are located in the main filament and the head structure is more diffuse.

A possible explanation for the unusual morphology of G214.5 is that of an interaction with a neighbouring HI superbubble. This is suggested by Clarke et al. (2023) due to G214.5 lying on the edge of the superbubble GSH214.0+00.0 + 017.5, being coincident in both the plane of the sky and line-of-sight velocity. Further, Clarke et al. (2023) find evidence of an interaction in the strongly asymmetric radial profiles along the lower section of the main filament. These profiles are highly reminiscent of those found in filaments known to be impacted by external feedback (e.g. Peretto et al. 2012; Zavagno et al. 2020). Informed by the simulations of Goldsmith & Pittard (2020), Clarke et al. (2023) suggest that a mixture of compression and erosion by the superbubble front may lead to the formation of the narrow, dense main filament and the flocculent, extended head structure. Thus, G214.5 is an excellent candidate for studying the evolution of a young, quiescent GMF in the context of the bubble-dominated ISM (Inutsuka et al. 2015; Walch et al. 2015; Pineda et al. 2023).

The aim of this paper is to use IRAM 30m observations of the isotopologues ¹²CO, ¹³CO, and C¹⁸O to study the physical properties of G214.5 and better understand what CO observations may tell us of young GMFs in quiescent regions. The paper is structured as follows: in Section 2, we outline the details of the IRAM 30m, APEX, and SOFIA observations; in Section 3, we present moment maps and discuss general features seen in the observations; in Section 4, we detail the method used to calculate CO column densities, study the ¹²CO excitation temperatures, present ¹³CO and C¹⁸O abundances and determine the isotopologue ratio X_13/18 = N|$_{^{13}\textrm {CO}}$|/N|$_{\textrm {C}^{18}\textrm {O}}$|⁠; in Section 5, we summarize our results and explore their implications for CO observations in quiescent regions such as the outer Galaxy.

2 OBSERVATIONS

The IRAM 30m telescope was used in the on-the-fly (OTF) mapping mode between 2019 September 4 and 10 under project 009–19 (PI: S. Clarke). The mapped region is approximately 8 × 19 arcmin and is shown as the magenta, dashed rectangle in the left-hand panel of Fig. 1. To ensure reasonable observing times per OTF map, the region was divided into 80 × 80 arcsec squares with a total of 73 square maps observed. Each square was observed twice, once using right ascension aligned scans and once using declination aligned scans, to minimize mapping artefacts. Position-switching was employed using the OFF position at (RA,DEC) = (06:48:37.7,-02:08:48.7). The accuracy of the pointing was checked every 1–2 h.

Observations were performed using the EMIR heterodyne receiver tuned to observe the E090 band at 107.4–115.4 GHz and the E230 band at 228.0–236.0 GHz simultaneously. This allowed coverage of the ¹²CO, ¹³CO, and C¹⁸O (1-0) lines at 115.27, 110.20, and 109.78 GHz, respectively, and the ¹²CO (2-1) line at 230.54 GHz. This results in spatial resolutions of ∼22 and ∼11 arcsec for the two bands, respectively. The FTS200 spectrometer was set as the backend leading to a spectral resolution of 195 kHz, corresponding to ∼0.6 km s⁻¹ velocity resolution for the E090 band and ∼0.3 km s⁻¹ for the E230 band. The VESPA backend was also used to cover the ¹³CO and C¹⁸O (1-0) lines to provide 0.2 km s⁻¹ resolution data; these data are not considered here but will be used in a companion work focusing on the kinematics of G214.5 (Clarke et al. in prep.).

The data were reduced using the class and greg programs from the gildas software package². To convert from antenna temperature (T|$_a^{*}$|⁠) to main beam temperature (T_mb), we used the equation T_mb = (F_eff/B_eff)T|$_a^{*}$|⁠, where F_eff is the forward efficiency and B_eff is the main beam efficiency; for the E090 band, we used B_eff = 0.78 and F_eff = 0.94, and for the E230 band, we used B_eff = 0.59 and F_eff = 0.92.³ All data were binned to a common 0.6 km s⁻¹ velocity resolution and mapped to 4 arcsec pixel size. Due to the varying spatial resolutions across the lines, we smoothed all data to a common 23.5 arcsec resolution. The resulting noise maps can be seen in Fig. B1 in Appendix  B; the mean noise levels are 206, 96, and 96 mK for the ¹²CO, ¹³CO, and C¹⁸O (1-0) lines, respectively, and 217 mK for the ¹²CO (2-1) line.

Additional observations were taken with the APEX telescope using the LASMA instrument between 2019 October 11 and 18 under project O-0103.F-9318A-2019 (PI: S. Clarke); only the single central pixel of the LASMA instrument was used. A region of approximately 250 arcsec by 60 arcsec was mapped, which lies across the spine of G214.5 away from the clumps, see the cyan, dashed rectangle in the middle panel of Fig. 1, using the OTF mode. The same OFF position as that used for the IRAM 30m observations was used. These observations allowed the simultaneous observations of the ¹²CO and ¹³CO (3-2) lines at 345.80 and 330.59 GHz, respectively. The beam size at these frequencies is ∼19 arcsec. The data were binned onto a 9.5 arcsec pixel size map with a velocity resolution of 0.25 km s⁻¹, and a main beam efficiency of 0.74 was used to convert from antenna temperature to main beam temperature. The mean noise levels are 34 and 41 mK for the ¹²CO and ¹³CO lines, respectively.

Observations were also taken using the upGREAT instrument (Risacher et al. 2018) on the Stratospheric Observatory for Far-Infrared Astronomy (SOFIA) on 2020 March 11 under project 83_0723 (PI: S. Clarke). These observations consisted of three pointings towards the clumps C11, C14, and C15 in G214.5 with positions (RA,DEC) = (06:47:50.2,-02:12:53), (06:47:55,-02:08:38) and (06:47:51,-02:05:01), respectively. Each pointing contains 7 pixels; their locations are shown in Fig. A1 in Appendix  A. The OFF position was the same as that used for the IRAM 30m and APEX observations. Main beam efficiencies for each pixel were determined through observations of Mars, resulting in efficiencies between 0.63 and 0.69. The low-frequency and high-frequency arrays, upGREAT/LFA and upGREAT/HFA, were used to simultaneously observe the 157.7 µm [CII] and 63.2 µm [OI] fine structure lines, respectively; however, in this work, we consider only the [CII] data. The beam size at 157.7 µm is 14.1 arcsec, and the data were smoothed to a velocity resolution of 0.38 km s⁻¹. The achieved noise level for the [CII] spectra are between 0.2 and 0.5 K depending on the pixel and the pointing, with a mean of 0.32 K.

3 RESULTS

We use a moment masking technique to create moment zero, one and two maps from the ¹²CO (1-0), ¹²CO (2-1), ¹³CO (1-0), and C¹⁸O (1-0) lines. We use the moment masking technique presented by Dame (2011) as it is shown to produce ‘cleaner’ and more accurate moment maps compared to the typical clipping technique. We modify the technique slightly to aid in detecting weaker emission. Dame (2011) unmask voxels which are within the smoothing kernel of voxels which themselves are unmasked by some threshold, T_C (step vii in their section 3). Here we use an iterative method that unmasks voxels that neighbour previously unmasked voxels as long as they have a value above some threshold, T_L where T_L < T_C. We use the |$\small {MAKE\_MOMENTS}$| function in the latest version of |$\small {BTS}$| for this purpose (Clarke et al. 2018), and full details of the moment masking method can be found in its documentation.⁴ After testing various values of T_C and T_L, we find that 8σ and 3σ, respectively, produce moment maps that are least affected by noise while capturing weaker emission. The resulting moment zero, one and two maps are shown in Fig. 2. The uncertainty on the moment zero values can be found in the online supplementary materials.

One can see from the moment zeros maps that ¹²CO and ¹³CO are detected across the entire mapped region, while C¹⁸O is only detected in the dense filament, i.e. approximately A_v > 2 mag. Further, while the spatial distribution of ¹³CO and C¹⁸O are similar to the column density derived from dust emission, the ¹²CO lines show a flatter spatial distribution with a large bright bar protruding from the southern massive clump, C11, and a less prominent x-shaped feature towards a the northern clump, C15. These are the result of large-scale outflows from these clumps, as evidenced by the associated large red-blue velocities in the moment one map and the localized, elevated dispersion in the moment two maps (outflows are identified as black, dashed lines in the ¹²CO (1-0) moment 2 panel of Fig. 2). A bipolar outflow from clump C11 has been previously reported in CS (Larionov et al. 1999), but examination of the moment one and moment two maps suggests two potential outflows with position angles of 45.6° and 109.5° with respect to north. These outflow lobes have approximate lengths of 96 and 54 arcsec, respectively, which, at a distance of 2.3 kpc, results in sizes of 1.07 and 0.60 pc. The two outflows do not intersect at the centre of clump C11; however, higher-resolution observations are needed to determine if this is accurate or a result of low spatial resolution. The x-shaped feature from the northern clump C15 has a clear red-blue gradient, indicative of an outflow, along only one of its ‘strokes’. This outflow has not previously been reported and has a position angle of 71.8°, making it approximately perpendicular to the filament spine, and a length of 78 arcsec or 0.87 pc. Clarke et al. (2023) note that C15 contains two 70 μm sources, S8 and S9; on close inspection, it appears that the outflow from this clump originates from the dimmer S8 source. Investigating the moment 1 velocity from the ¹²CO (1-0) map along these outflow axes, we find the difference between the most blueshifted and most redshifted velocities, ΔV. We may define a dynamical time of these outflows as 2L/ΔV, resulting in values of 0.58 and 0.31 Myr for the two outflows from C11 and 0.60 Myr for the outflow from C15. These dynamical time scales are only approximate as the large beam size does not allow one to resolve the internal structures of the outflows, but their low values do support the youth of G214.5 proposed by Clarke et al. (2023).

Examination of the moment one maps show that the filament is velocity coherent across its length and has a velocity gradient from north to south, seen in all three isotopologues. The line-of-sight velocity varies from ∼27 km s⁻¹ in the south to ∼30 km s⁻¹ in the north. The velocity dispersion, σ_v, of the ¹³CO and C¹⁸O lines is low within the filament having values of 0.5–2 km s⁻¹, with higher values located in the south around the C11 clump, potentially connected to the outflows. Further analysis of the kinematics of G214.5 is left to a companion paper (Clarke et al. in prep.).

Clarke et al. (2023) note that their estimate of the mass of the entire G214.5 GMF using Herschel data is approximately half that of the estimate from Yan et al. (2019), who use the canonical CO-to-H₂ conversion factor, X_CO = 2 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹ (Bolatto, Wolfire & Leroy 2013). For our mapped region we calculate the average X_CO factor, defined as |$\sum N_{\rm H_2}/\sum I_{\rm CO}$|⁠, where I_CO is the moment zero of ¹²CO, to be 1.12 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹. If this value held across the whole cloud, then it would bring the Herschel derived mass estimate of G214.5 into much closer agreement with the CO derived mass estimate by Yan et al. (2019). Further, low X_CO values (∼1 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹) are expected in young molecular clouds in which widespread star formation are yet to occur, due to the time delay between H₂ and CO formation (Borchert et al. 2022). Thus, the low average X_CO factor calculated here is in agreement with the potential youth of G214.5 proposed by Clarke et al. (2023).

3.1 SOFIA [CII] spectra

It has previously been shown that [CII] may be used as a tracer of the FUV field due to it being produced by the ionization of neutral carbon by UV photons above an energy of 11.2 eV (e.g. Tielens & Hollenbach 1985). Out of the 21 individual SOFIA spectra, 20 spectra show no detections. As such, we follow the method of Bonne et al. (2020a) and use the non-detection of [CII] to place upper limits on G214.5’s external FUV-field; details may be found in Appendix  A. Using this method, we find that the ambient FUV-field has a strength less than ∼1.1–2.5 G₀. Such a weak external radiation field is consistent with the low dust temperatures and the quiescent environment found by Clarke et al. (2023).

As mentioned above, 1 pixel shows significant detection of [CII], with a peak intensity of ∼1.1 K ≈5σ (see Fig. A3). This is the central pixel towards clump C11, i.e. the most massive clump in G214.5, ∼230 M|$_{_{\odot }}$|⁠. With the lack of detections at all other positions, it is likely that the [CII] emission at this location is not from external radiation but is internal to the clump. This may be the first evidence that clump C11 may harbour an intermediate/high-mass protostar, as previous searches using H₂O and class II methanol masers have found no such sign (Slysh et al. 1999; Furuya et al. 2003; Sunada et al. 2007), as well as the clump being found to be radio-quiet at 5 GHz with the VLA (Urquhart et al. 2009). A more detailed analysis of the [CII] detection will be presented in a future work focusing on clump C11.

4 CO COLUMN DENSITY AND ABUNDANCES

In this section, we use the assumption of local thermodynamic equilibrium (LTE) and a beam-filling factor of 1 to determine the column density of ¹³CO and C¹⁸O without the assumption of canonical isotopologue ratios relative to ¹²CO (see e.g. Mangum & Shirley 2015). Using this method, one determines the ¹²CO excitation temperature and, assuming it is equal to that of ¹³CO and C¹⁸O, one may use it to calculate column densities of the two species. Note that this method does not allow an estimate of the ¹²CO column density, but it does allow one to determine the isotopologue abundance ratio ¹³CO over C¹⁸O, X_13/18, which has been shown to vary across clouds (e.g. Areal et al. 2018, 2019; Lin et al. 2021; Roueff et al. 2021).

To calculate uncertainties on the quantities of interest in this section, we use a Monte Carlo method that takes the noise of each individual spectrum and propagates it forward. This is fully discussed in Appendix  B, and maps of the uncertainty in quantities are shown in the online supplementary material. This method results in 10 000 instances of each quantity calculated. When reporting the quantity of interest (e.g. ¹³CO column density), we report the mean of this distribution, and the uncertainty is taken as the distribution’s standard deviation unless otherwise stated. Note that throughout this paper, the notation |$A^{+b}_{-c}$| is used to denote the median (A) and interquartile range (-c, + b) of a quantity, where the range is over all the pixels; therefore, it is not a measure of uncertainty but of variation. Uncertainties will be stated as such or use the ± notation.

4.1 ¹²CO excitation temperature

The excitation temperature of ¹²CO may be estimated under the assumption that emission is optically thick using the equation:

where T_ul is the energy gap of the transition in Kelvin, T_bg is the background temperature taken to be the CMB temperature of 2.7 K, and T_R is the radiation temperature taken as the peak temperature of each spectrum. We may use equation (1) for both the (1-0) and (2-1) transitions of ¹²CO due to the high-optical depth of both lines; for the (1-0) transition, T_ul is set to 5.53 K and for the (2-1) transition T_ul is set to 11.07 K. Note that if the ¹²CO emission suffers from strong self-absorption features, this method produces reduced estimates of the excitation temperature; however, inspection of even the brightest spectra show no such absorption features so we believe this effect has minimal impact on the excitation temperature estimates.

Fig. 3 shows the excitation temperature maps for both transitions of ¹²CO. One sees that the (1-0) and (2-1) transitions produce near identical maps of the excitation temperature, and that the measured excitation temperatures are low. The fact that the two transitions produce such similar excitation temperatures (the median of the ratio T_{ex, (2-1)}/T_{ex, (1-0)} = 1.07|$^{+0.04}_{-0.04}$|⁠) shows that the assumption that the gas is thermalized is valid and that the population levels may be well described by a single temperature. The low-excitation temperature (median values over the whole map of 8.2|$^{+0.7}_{-0.6}$| and 8.7|$^{+0.9}_{-0.6}$| K from the (1-0) and (2-1) lines, respectively) is in agreement with that first reported for G214.5 by Lee, Snell & Dickman (1994) which found excitation temperatures below 7.3 K to be common across G214.5 and the neighbouring Maddalena’s cloud. The median error on the (1-0) line derived excitation temperature is 0.21 K, and as a percentage of the excitation temperature, the median error is 2.6 per cent, i.e. the excitation temperature is well constrained. Such low-excitation temperatures are atypical and other molecular clouds (e.g. Serpens North, Ophiuchus and Orion B) show ¹²CO excitation temperatures lying in the range of 10–50 K (Graves et al. 2010; White et al. 2015; Roueff et al. 2021). There is some variation in the excitation temperature across the map in Fig. 3, with a slight gradient of ∼0.5 K/10²¹ cm⁻²; however, the results presented in the following sections are not affected by this variation as calculations using a fixed excitation temperature of 8.2 K (the median ¹²CO (1-0) derived temperature) across the map yield the same results, as shown in the online supplementary material.

Low-excitation temperatures may result from sub-thermal excitation (see Goldsmith et al. 2008; Peñaloza et al. 2017) rather than low kinetic temperatures. However, as mentioned above, the near identical excitation temperatures derived from the (1-0) and (2-1) transitions show that the gas is thermalized and as such the excitation temperature is close to the gas kinetic temperature. This would mean that the CO bright gas in G214.5 is unusually cold. Clarke et al. (2023) show that the dust temperatures are also low, with values of around 12.5 K in the spine and 13.5–14.0 K at larger radii (see Fig. 1), making it colder than any previously studied inner Galaxy GMF. As there are few internal heating sources, all of which are localized to their immediate surroundings, i.e. the protostellar clumps C11, C14, and C15, no nearby OB stars/clusters (Lee, Snell & Dickman 1994; Wright et al. 2023) and the [CII] non-detections constrain the ambient UV field to values below ∼1.1G₀, it is likely that the dominant heating mechanism is that due to cosmic rays. Thus, the low gas and dust temperatures indicate a decrease in the cosmic ray flux in G214.5’s vicinity, in agreement with gamma-ray studies showing such a decrease with galactocentric radius (e.g. Yang, Aharonian & Evoli 2016).

It is known that there may exist differences in the excitation temperatures of the different CO isotopologues due to opacity and/or kinetic temperature gradients along the line of sight (e.g. see Roueff et al. 2021, who find ¹²CO excitation temperatures in general 70 per cent greater than that for ¹³CO in Orion B). However, an assumption we make in the following section when calculating the column densities of ¹³CO and C¹⁸O is that their excitation temperatures are equal to that of ¹²CO. We find that this assumption is valid, within uncertainties, in the region in which the ¹³CO (3-2) line was observed with APEX. This is done by using non-LTE RADEX calculations to model the brightness and ratio of the ¹³CO (3-2) and (1-0) transitions; full details can be found in Appendix  C. As the region mapped by APEX is a typical off-clump area across the spine, we believe that our finding that the ¹²CO and ¹³CO excitation temperatures are approximately equal is likely to hold across the rest of the map; however, this may not be valid in the outflow effected regions close to clumps C11 and C15, where elevated ¹²CO excitation temperatures are found.

4.2 ¹³CO and C¹⁸O column densities and abundances

We use the general formulation to estimate the column density from Mangum & Shirley (2015; their equation 84) that includes the effects of opacity:

where h is Planck’s constant, S is the line strength of the observed transition, µ is the dipole moment of the molecule, Q is the partition function, g_u is the upper level degeneracy, and J is the function defined as |$J(T) \equiv T_{ul}/(e^{T_{ul}/T}-1)$|⁠. As we consider the (1-0) rotational transition, the level degeneracy is given as g_u = 2J_u + 1 and the line strength as S = J_u/(2J_u + 1) where J_u = 1. Further, as ¹³CO and C¹⁸O are diatomic linear molecules the rotational partition function may be approximated as

where B₀ is the rigid rotor rotation constant of the molecule and k_b is Boltzmann’s constant. The values we use for B₀ are 55101.01 and 54891.42 MHz for ¹³CO and C¹⁸O, respectively (Cazzoli, Puzzarini & Lapinov 2003, 2004). For the dipole moment, we use 0.11046 Debye and 0.11049 Debye for ¹³CO and C¹⁸O, respectively (Goorvitch 1994).

We evaluate equation (2) using the same mask as that used to generate the moment maps to ensure that velocity channels containing only noise do not influence the calculation. The resulting column density maps for ¹³CO and C¹⁸O are shown in Fig. 4. One sees that the ¹³CO and C¹⁸O column densities roughly follow the contours of the dust derived H₂ column densities, though there are some clear differences in the high column density clumps. The interquartile range of the error on the column density of ¹³CO is 3.9–8.4 per cent, while for C¹⁸O it is 14.7–29.3 per cent due to the much weaker emission. The opacities of these lines are also calculated; the median opacities of ¹³CO and C¹⁸O are 0.34|$^{+0.15}_{-0.10}$| and 0.07|$^{+0.02}_{-0.02}$| respectively, showing that neither are highly optically thick. Maps of the ¹³CO and C¹⁸O opacities, and their errors, are shown in the supplementary materials. One can see that even in the filament spine, the ¹³CO opacity only reaches values of ∼0.7. Assuming typical relative abundances between ¹²CO and ¹³CO leads to high ¹²CO opacities, >12.5 across 95 per cent of the observed map and with a minimum value of ∼5.2, justifying the use of equation (1) to calculate the excitation temperature even in the least dense regions.

To investigate further we show the ¹³CO and C¹⁸O column density plotted against H₂ column density in Fig. 5. Note that here only pixels in which the CO column density has an error of less than 30 per cent are shown. One sees a large increase in ¹³CO column density around N|$_{\rm H_2} \sim 10^{21}$| cm⁻² (A_v ∼ 1 mag), which may be attributed to the regime in which CO formation may efficiently proceed due to self-shielding (Röllig et al. 2007; Bisbas, Schruba & van Dishoeck 2019). At higher column densities, the relationship is roughly linear indicating a constant abundance, though at even higher column densities (>3 × 10²¹ cm⁻²), two branches appear. For C¹⁸O, the relationship between C¹⁸O column density and H₂ column density is simpler and appears to be roughly linear with scatter.

One may consider the abundance of ¹³CO and C¹⁸O with respect to H₂ from these data. We use the isotopic gradient equations from Wilson & Rood (1994) to determine the expected abundance of ¹³CO and C¹⁸O. These are:

and

where R_GC is the galactocentric distance in kiloparsec. At G214.5’s galactocentric distance of 10.1 kpc this results in |$^{12}\rm {C}/^{13}\rm {C} = 83.4 \pm 23.1$| and |$^{16}\rm {O}/^{18}\rm {O} = 631.0 \pm 145.1$|⁠.⁵ Assuming that the abundance of carbon relative to hydrogen is 1.4 × 10⁻⁴ (Gerin et al. 2015), this leads to expected abundances of ¹³CO and C¹⁸O with respect to H₂ of X|$_{^{13}\textrm {CO}} = 3.4^{+1.2}_{-0.7} \times 10^{-6}$| and X|$_{\textrm {C}^{18}\textrm {O}} = 4.4^{+1.4}_{-0.8} \times 10^{-7}$|⁠.⁶ It is important to note that these expected abundances assumes no isotopic fractionation, all carbon is found in CO and that there is no depletion from the gas phase. Using these abundances, the expected relationship between the column density of ¹³CO and C¹⁸O, and H₂ is shown in Fig. 5. One sees that clearly, even considering the uncertainties, that the observed abundances of both isotopologues are mostly below the expected one.

The abundance of ¹³CO in G214.5 is |$1.9^{+0.4}_{-0.4} \times 10^{-6}$|⁠, which is approximately half what is expected. For C¹⁸O the abundance is |$1.7^{+0.5}_{-0.3} \times 10^{-7}$|⁠, nearly a third of what is expected. However, as seen in Fig. 5, the abundance is not independent of H₂ column density. As such we show X|$_{^{13}\textrm {CO}}$| and X|$_{\textrm {C}^{18}\textrm {O}}$| against H₂ column density in Fig. 6. For X|$_{^{13}\textrm {CO}}$|⁠, one sees the abundance increases until around A_v ∼2 mag, at which point it decreases with increasing H₂ column density until it is below ∼1 × 10⁻⁶. For X|$_{\textrm {C}^{18}\textrm {O}}$|⁠, the abundance is roughly constant but there exists a slight decrease with increasing H₂ column density. This is confirmed by the use of Kendall’s τ correlation test which reports τ = −0.12 and p ≪ 10⁻¹⁰. As mentioned above, the increasing abundance of ¹³CO between an A_v of 1 and 2 magnitudes indicates that this is the regime in which CO formation may efficiently proceed due to self-shielding. The decrease in abundance with increasing column density is most readily explained by CO depletion (or CO freeze-out), which is when gaseous CO molecules are locked onto the surfaces of dust grains in the form of ices (e.g. Caselli et al. 2002). This is supported by the fact that at a given column density, the abundances for both ¹³CO and C¹⁸O are lower with decreasing dust temperature.

To investigate the spatial distribution of X|$_{^{13}\textrm {CO}}$| and X|$_{\textrm {C}^{18}\textrm {O}}$|⁠, we show maps of these abundances in Fig. 7. A striking feature of the ¹³CO map is that the low abundances (∼1 × 10⁻⁶) associated with freeze-out are not confined to small, localized regions but are seen along the entire ∼13 pc long spine of G214.5. Typically such CO depletion is seen on the sub-parsec scale in cores and clumps (Kramer et al. 1999; Bergin et al. 2002; Caselli et al. 2002; Bacmann et al. 2003; Fontani et al. 2012; Sadavoy et al. 2015; Sabatini et al. 2022), though recent observations of infra-red dark clouds (IRDCs) have shown depletion on the parsec scale (Hernandez et al. 2011; Sabatini et al. 2019; Feng et al. 2020). Here, G214.5 shows CO depletion on the >10 pc scale across the whole cloud while not have column densities as high as typical IRDCs (Clarke et al. 2023). Thus such large-scale depletion may be apparent in non-IRDC clouds as long as it is accompanied by widespread low gas and dust temperatures. This may be common in the Outer Galaxy and so ought to be considered. The X|$_{\textrm {C}^{18}\textrm {O}}$| map shows the abundance is roughly uniform across the filament, with possibly lower abundances in the northern section with its lower dust temperatures; however, the C¹⁸O detection being limited to the spine of the filament makes it difficult to assess how depleted it is in the spine relative to material at larger radii.

As the CO depletion zone is confined to the entire spine of G214.5, we measure the radial extent of the freeze-out by using the spine identified by Clarke et al. (2023) and projecting the abundance map into the orthogonal radial-longitudinal distance space with the Python module FragMent (Clarke et al. 2019).⁷ From this, we construct the error-weighted mean abundance of ¹³CO as a function of radius, which is shown in Fig. 8, as well as the radial H₂ column density and dust temperature profiles. The weighting for the mean is taken as X|$_{^{13}\textrm {CO}}$|/ΔX|$_{^{13}\textrm {CO}}$|⁠, i.e. one over the uncertainty expressed as a fraction of the estimated abundance. Here, one sees that the abundance profile is approximately flat at large radii (>2 pc) before it begins to rise slightly, peaking at ∼0.8–1.0 pc. Within this radius, it monotonically decreases, just as total column density begins to the increase rapidly and the dust temperature decreases strongly. Thus, CO freeze-out seems to occur out to ∼0.8 pc in G214.5. We note that the beamsize of the CO observations is 23.5 arcsec, or ∼0.26 pc at a distance of 2300 pc, is much smaller than this observed radius at which the abundance decreases. As such, the abundance profile cannot be due to freeze-out in only the inner, unresolved region but must be radially extended.

4.3 Modelling cloud-scale freeze-out

To further investigate the extent of this widespread freeze-out, we construct an axisymmetric model of the H₂ and ¹³CO volume densities, which may be constrained by the radial profiles of the H₂ column density and X|$_{^{13}\textrm {CO}}$|⁠. This model is constructed in 2D using the unprojected radius, r, before being projected to produce a column density as a function of projected radius, R. This allows the conversion between volume and column densities, taking into account that the degree of freeze-out differs along the line-of-sight, and correcting for beam convolution.

The H₂ volume density takes the form of a Plummer-like distribution, commonly used in characterizing filaments (e.g. André et al. 2014),

where n_c is the central number density, r₀ is the inner, flattening radius, p is the profile’s exponent at large radii, and n_bg is the background density. We calculate the number density out to a radius of 5 pc; this has little effect on the estimates of the model parameters except n_bg which decreases as this outer radius increases.

The volume density of ¹³CO, which may be linked to the H₂ volume density by the equation

where X_bg is the abundance of ¹³CO with respect to H₂ unaffected by depletion, and f_gas is the fraction of ¹³CO which is located in the gas phase. To calculate f_gas, we use the freeze-out model from Glover & Clark (2016), which assumes an equilibrium between the rate at which CO accretes onto a dust grain, R_acc, the rate at which CO thermally evaporates from grains, R_therm, and the rate at which CO is desorbed due to cosmic rays, R_cr. This model produces the relation

These rates may be given as:

where T_g is the gas temperature, n_H is the number density of hydrogen nuclei (i.e. |$n_H = 2n_{H_2}$|⁠), and D is the gas-to-dust ratio which we set to 100 here;

where T_d is the dust temperature; and

where ζ_H is the cosmic ray ionization rate for atomic hydrogen. We assume that the rates of these reactions are identical for ¹²CO and ¹³CO.

Once the volume densities of H₂ and ¹³CO have been projected to column densities, |$N_{\rm H_2}$| and |$N_{^{13}\textrm {CO}}$|⁠, these are convolved with a beam of size 23.5 arcsec (i.e. the resolution of the observational data) assuming a distance of 2300 pc to G214.5. For the gas and dust temperatures we set T_g to 8 K and T_d to 13 K, informed by the gas temperatures found in Section 4.1 and the dust temperatures of Clarke et al. (2023). Our choices here have little effect on the final fitting; varying the dust temperatures in realistic ranges (10 K ≤T_d ≤ 15 K) changes the fitting parameters by only a few per cent, while changes to the gas temperature (5 K ≤T_g ≤ 10 K) result in |${\sim}10{{\ \rm per\ cent}}$| changes in only ζ_H. Further, uniform temperatures may not be realistic (as seen by the radial dust temperature gradient seen in Fig. 8); however, using radial temperature profiles of the form T(r) = T₀ + ΔT × r for both the gas and dust temperatures, also has minimal effect on the fitting parameters for a wide variety of gradients. This is because at these low dust temperatures, R_therm is negligible and variations of R_acc are dominated by changes in the number density, which covers orders of magnitudes, rather than the gas temperature which may vary by a factor of two at most. With the temperatures constrained, this model has six parameters which we aim to constrain: n_c, r₀, p, n_bg, X_bg, ζ_H.

As mentioned above, the data used to constrain the model are the radial profiles of H₂ column density and the abundance of ¹³CO, seen in Fig. 8. As the model is axisymmetric, we take the average of the left- and right-hand sides of the profiles to produce a single radial profile. We fit the column density profile out to a radius of 2 pc to ensure that the exponent p may be well-fitted and to avoid undue influence of further outside structures. The abundance profile is fitted out to a radius of 1 pc as it approximately peaks at this point; at larger radii, the abundance drops and this cannot be modelled using our freeze-out model as this drop is likely due to CO formation rather than depletion. The model is fitted using a least-squared method and may be done in two manners: a simultaneous fitting of the column density and abundance profiles and an independent fitting where the column density is fitted first before using the result to fit the abundance profile. We present the results of these fits in Fig. 9 as well as the best-fitting parameters in Table 1.

One sees from Fig. 9 that this simple axisymmetric freeze-out model well produces the observed column density and abundance profiles. Both methods of fitting produce relatively similar profiles and fitting parameters, with independent fitting leading to a slightly larger central volume density and smaller flattening radius. The independent fitting method leads to a moderately better fit to the column density profile, χ² = 25.0 compared to 42.7 for the simultaneous fitting method, while the fit to the abundance profile is moderately worse, χ² = 95.5 compared to 52.9.

An interesting result from the model is that due to the relatively low central densities determined, a low cosmic-ray ionization rate is needed to ensure the deep and wide depletion feature seen in the ¹³CO abundance profile, with best-fitting values of ∼1.9 × 10⁻¹⁸ s⁻¹. This is approximately an order of magnitude lower than the rate which is typically observed, a few times 10⁻¹⁷–10⁻¹⁶ s⁻¹ (de Boisanger, Helmich & van Dishoeck 1996; Caselli et al. 1998; van der Tak & van Dishoeck 2000; Indriolo & McCall 2012; Indriolo et al. 2015), although there have been some measurements of the order of a few times 10⁻¹⁸ s⁻¹ in a selection of dense cores (e.g. Caselli et al. 1998). Further, this low cosmic-ray ionization rate is consistent with the low gas temperatures we find in Section 4.1.

Cosmic-ray ionization rates of the order of 2–5 × 10⁻¹⁸ s⁻¹ have also been estimated in the IRDC G28.37 + 00.07 by Entekhabi et al. (2022) using a gas-grain astrochemical model towards 10 lines of sight constrained by numerous molecular line observations. This is a highly different environment to G214.5 as the IRDC is much denser (n > 5–10 × 10⁴ cm⁻³) and at higher column densities (N > 10²³ cm⁻²). It is possible that the low cosmic ray ionization rate observed by Entekhabi et al. (2022) may be the result of the attenuation of the lower energy cosmic-rays (i.e. those important for ionization and chemistry) due to the high column densities in G28.37 + 00.07. Such attenuation of these lower energy cosmic rays is predicted by cosmic-ray transport models (e.g. Padovani, Galli & Glassgold 2009; Schlickeiser, Caglar & Lazarian 2016; Ivlev et al. 2018; Padovani et al. 2018; Gaches, Bisbas & Bialy 2022). However, attenuation is unlikely the reason for the measured low cosmic-ray ionization rate in G214.5 as the column densities at which freeze-out occurs is nearly two orders of magnitude lower (N ∼ 2–3 × 10²¹ cm⁻²). Thus, the measured cosmic-ray ionization rate in G214.5 is likely close to the value in G214.5’s diffuse environment.

As the model constructs an underlying radial profile, unaffected by projection or beam convolution, we may investigate the radial profile of the depletion factor, f_D = 1/f_gas. This is shown in the lower panel of Fig. 9. Both fitting procedures lead to strongly centrally condensed depletion factor profiles, with peak values ∼5, i.e. only |${\sim}20{{\ \rm per\ cent}}$| of the ¹³CO is in the gas phase. The radius at which half of the ¹³CO is in the gas phase, f_D = 2, is ∼0.16 pc in both models, and the radius at which two thirds is in the gas phase, f_D = 1.5 is ∼0.30 pc. We may also determine the number density at these radii, ∼2200 and ∼720 cm⁻³, respectively. Thus, tracing even moderately dense gas using CO is affected by depletion. Using these volume densities, one may determine an estimate of the time scale over which this depletion occurs, |$\tau _{D} = 1/R_{acc} \sim 560 \,\,\rm {Myr}/n_{H_2}$|⁠. The central density of ∼8000 cm⁻³ yields a depletion time scale ∼0.07 Myr, and for the f_D = 2 density of ∼2200 cm⁻³, τ_D ∼ 0.25 Myr. These are much lower than the cloud free-fall time and cloud-crushing time scales calculated by Clarke et al. (2023) for G214.5, 13 and 2–3 Myr, respectively, showing that such depletion occurs sufficiently quickly for it to be feasible and consistent with the expected youth of G214.5.

Comparing to Hernandez et al. (2011) and Sabatini et al. (2019), which study the parsec-scale CO depletion in the filamentary IRDCs G035.39-00.33 and G351.77-00.51, respectively, we find similar peak depletion factors, f_D ∼ 5. Further, Sabatini et al. (2019) also model the radial extent of the CO depletion using multiple imposed abundance profiles and find a depletion radius in the range 0.02–0.15 pc, slightly smaller but comparable to the f_D = 2 radius we see in G214.5. Thus, the large-scale CO depletion along the spines of cold, giant filamentary clouds may be commonplace. However, here we find that depletion begins at volume densities an order of magnitude lower than Hernandez et al. (2011) and Sabatini et al. (2019), who find depletion to become important above |$n_{\rm H_2} \sim 2-50 \times 10^{4}$| cm⁻³. Further, freeze-out starts to appear in G214.5 at column densities of only ≥2 × 10²¹ cm⁻² compared to ≥1 × 10²² cm⁻² in the aforementioned IRDCs. This shift reflects the very low temperatures in G214.5, even off of the spine, related to its quiescent environment characterized by a low radiation field and cosmic ray ionization rate. This may suggest that in other quiescent environments (e.g. in the Outer Galaxy), one might expect to see widespread CO depletion at lower volume and column densities. A consequence of this is that estimates of masses and column densities made without considering cloud-scale CO freeze-out will be underestimates; for the case of G214.5, if one used the expected abundance of ¹³CO, X|$_{^{13}\textrm {CO}} = 3.4 \times 10^{-6}$|⁠, one would underestimate the total mass by roughly a factor of 2, and the mass at high column densities would be reduced by roughly a factor 3 due to decreasing X|$_{^{13}\textrm {CO}}$| with increasing column density (Fig. 6). Further, considering the kinematics of CO isotopologues, even moderately dense gas might not be probed as expected and measurements of velocity centroids/dispersion affected.

4.3.1 Ambipolar diffusion

As well as the low cosmic-ray ionization rate allowing widespread CO depletion to occur, it will have the consequence of lowering the ionization fraction of the gas as cosmic rays are the dominant ionization source in UV-shielded gas (Wolfire, Vallini & Chevance 2022). Low ionization fractions have the consequence of imperfect coupling between the gas and the magnetic field, meaning that non-ideal MHD effects like ambipolar diffusion become important (e.g. Ntormousi et al. 2016; Zhao et al. 2018; Wurster, Bate & Price 2019; Wurster & Lewis 2020; Wurster 2021; Zhao et al. 2021; Commerçon et al. 2022).

To consider if this may be relevant for G214.5, we use the Nicil code presented in Wurster (2016) to self-consistently determine the ionization fraction and ambipolar diffusivity, |$\eta _{\rm {\small AD}}$|⁠, at a given density, temperature, cosmic ray ionization rate, and magnetic field strength. For the density, we use the average density within the full-width half-maximum (FWHM) of the filament model profile described above, FWHM = 0.17–0.21 pc and 〈n〉 = 5500–6900 cm⁻³, where the variation comes from the two fitting methods. We use a range of gas temperatures of 5–10 K and a cosmic-ray ionization rate of 1.8–2.0 × 10⁻¹⁸ s⁻¹. Further, we use Nicil with a grain-size distribution proportional to a^−3.5 between a range of 0.03 µm–0.1 cm, discretized into 100 equal size bins. The B-field strength is unknown for G214.5 and not constrained; we thus use a range between 20–200 µG which are typical field strengths found across IRDCs (Hacar et al. 2023).⁸ One may construct an ambipolar time scale from these diffusivities which is related to the time scale over which magnetic flux is lost via ion-neutral drift,

where L is the length-scale considered (Pattle et al. 2023); here we use the FWHM of the filament model, 0.17–0.21 pc. The resulting ambipolar diffusivities and time scales are summarized in Table 2. One sees that the time scale ranges from ∼0.35 to 45 Myr, with shorter time scales corresponding to higher magnetic field strengths. Increasing the cosmic ray ionization rate by an order of magnitude (1.9 × 10⁻¹⁷ s⁻¹), i.e. within the typical range in other regions, the ambipolar time scale is increased by a factor of 4–5.

To compare to the ambipolar diffusion time scale, we may consider the cloud free-fall time and cloud crushing time calculated by Clarke et al. (2023), 13 and 2–3 Myr, respectively, for estimates of cloud-scale time scales. For smaller scales, we may consider the thermal and turbulent crossing time scales, L/c_s and L/σ_NT, where the sound speed c_s = 0.16 km s⁻¹ for a gas temperature of 8.2 K and σ_NT = 0.35 km s⁻¹ taken from typical line-widths of C¹⁸O along the filament spine using the 0.2 km s⁻¹ resolution VESPA data. This results in time scales of 1.1–1.3 and 0.5–0.6 Myr, respectively. Taken together, the ambipolar diffusion time scale is shorter than/comparable to cloud-scale time scales for magnetic field strengths above 50 µG and is shorter than/comparable to the crossing times when above 100 µG. Thus, even a low-to-moderate magnetic field strength results in ambipolar diffusion being an important process in the spine of G214.5 due to the low cosmic ray ionization rate.

4.4 The isotopologue ratio between ¹³CO and C¹⁸O

An advantage of the method used in Section 4.2 to determine the column densities of ¹³CO and C¹⁸O is that the two are independently calculated, allowing a study of the isotopologue ratio X_13/18 = N|$_{^{13}\textrm {CO}}$|/N|$_{\textrm {C}^{18}\textrm {O}}$|⁠. This isotopologue ratio is known to vary between clouds and within clouds for a number of reasons, such as local isotope enrichment, selective photodissociation and selective fractionation, and ranges from ∼4-50 (e.g. Areal et al. 2018, 2019; Lin et al. 2021; Roueff et al. 2021). One reason for the variation between clouds is the dependence of the ¹²C/¹³C and ¹⁶O/¹⁸O isotope ratios on Galactocentric radius mentioned above (equations (4) and (5)). Combining these two equations results in

which for G214.5’s Galactocentric radius of 10.1 kpc is equal to |$7.6^{+2.1}_{-1.6}$|⁠.⁹ Using the column densities of ¹³CO and C¹⁸O calculated above produce a map of the isotopologue ratio X_13/18 shown in the left-hand panel of Fig. 10. We find a median value of |$13.5^{+7.6}_{-3.9}$| and a median uncertainty of 25 per cent; these observed ratios are larger than the expected isotopologue ratio given G214.5’s Galactocentric radius. Further, as seen in Fig. 10 there are spatial variations of the ratio with higher values towards the edge of the filament spine, i.e. at lower column densities.

When calculating the above isotopologue ratio the whole detected line-of-sight ¹³CO and C¹⁸O column densities are considered. However, due to the lower brightness of the C¹⁸O emission and the noise level of the observations, the detected C¹⁸O column density is likely tracing a less extended region of gas along the line of sight compared to the detected ¹³CO column density. Closer inspection of the spectra reveal that multiple velocity components are present in ¹³CO (pre-dominately in the south of the filament around the massive clump C11), which are not detected in the C¹⁸O spectra. Thus, using the total detected line of sight column densities to determine the isotopologue ratio will bias the result to larger values. To correct for this bias, we recalculate the ¹³CO column density using the mask derived from the C¹⁸O data cube, i.e. only using velocity channels in which C¹⁸O is detected. This attempts to ensure that the two column densities used to calculate the isotopologue ratio are tracing the same line-of-sight gas. The resulting ratio is shown in the right-hand panel of Fig. 10, and yields a median ratio of |$9.4^{+2.9}_{-2.1}$|⁠. This value is only slightly elevated compared to the expected ratio of |$7.6^{+2.1}_{-1.6}$| but consistent given the uncertainties. When considering only pixels which have uncertainties less than 30 per cent the median corrected ratio lowers further to |$8.2^{+1.8}_{-1.4}$|⁠. Moreover, as shown in Fig. 10, the spatial variation in the ratio is much reduced. This shows the importance of using the kinematic information to correct for this bias and ensure that the ¹³CO and C¹⁸O column densities used to calculate the isotopologue ratio are tracing the same gas.

To further investigate the variation across the cloud, we show the isotopologue ratio, both the total column density ratio and the corrected ratio, as a function of column density in Fig. 11. One sees a large spread in the ratio (mostly due to uncertainties in the ratio which are typically ∼1–2), especially in the total column density ratio, making a search for a correlation difficult. A better view is seen when using the error-weighted moving-mean (the solid lines) which reveals that the corrected ratio is lower on average (by ∼2–4) for all column densities and lies extremely close to the expected ratio independent of column density. Typically an anticorrelation is seen between the isotopologue ratio and column density due to the selective enhancement of ¹³CO due to fractionation and destruction of C¹⁸O via photodissociation at low column densities (e.g. Langer et al. 1980; Areal et al. 2019; Rodríguez-Baras et al. 2021; Roueff et al. 2021). However, the lack of such a correlation in G214.5 suggests that even the poorly shielded gas is relatively unaffected by the interstellar UV field, indicating that the background radiation field in G214.5’s vicinity is low. This is in agreement with the low upper limit placed on the ambient FUV-field by the non-detection of [CII] (Section 3.1), as well as the low dust/gas temperatures, the presence of ¹²CO and ¹³CO at low A_v, as well as the fact there are no nearby OB stars/cluster (Lee, Snell & Dickman 1994; Wright et al. 2023).

5 CONCLUSIONS

In this paper, we present CO observations taken from the IRAM 30m telescope of the northern region of the giant molecular filament G214.5-1.8. We use these data to study the CO excitation temperature, the abundances of ¹³CO and C¹⁸O, as well as isotopologue ratio X_13/18, revealing G214.5 to be a highly interesting object.

We use the ¹²CO (1-0) and (2-1) lines to estimate the excitation temperature and find a relatively uniform and low value across the entire mapped region, |$8.2^{+0.7}_{-0.6}$| K, with moderately elevated excitation temperatures close to the two observed outflows (Section 4.1). The excitation temperatures of these two lines are near identical, showing that the low excitation temperatures are not due to sub-thermal excitation but rather the gas is thermalized and as such the excitation temperatures are representative of low gas temperatures (∼7–9 K). This is in agreement with the low dust temperatures in G214.5 found by Clarke et al. (2023) who find the cloud to be the coldest GMF yet studied. Moreover, widespread low gas/dust temperatures at low column densities are in agreement with the upper limit placed on the ambient FUV-field by the non-detection of [CII], ≲ 1.1–2.5 G₀ (Section 3.1). It is potentially due to G214.5’s position in the Outer Galaxy that such temperatures and heating rates are found. As such, further studies of the thermal properties of GMFs in the Outer Galaxy and their comparison to those in the Inner Galaxy would be valuable.

Using the derived excitation temperatures, we calculate the column densities of ¹³CO and C¹⁸O independent of each other, i.e. no assumption is made about isotopologue ratios (Section 4.2). Further, we use the column density map produced from Herschel by Clarke et al. (2023) to calculate abundances for ¹³CO and C¹⁸O with respect to H₂, X|$_{^{13}\textrm {CO}}$| and X|$_{\textrm {C}^{18}\textrm {O}}$|⁠. We find abundances of X|$_{^{13}\textrm {CO}}$| = |$1.9^{+0.4}_{-0.4} \times 10^{-6}$| and X|$_{\textrm {C}^{18}\textrm {O}}$| = |$1.7^{+0.5}_{-0.3} \times 10^{-7}$|⁠; both are slightly lower than but similar to that found in nearby clouds (e.g. Pineda et al. 2010; Roueff et al. 2021). Investigating the ¹³CO abundance further, we find that it increases with column density below an A_v ∼ 2 mag, possibly indicating formation below this visual extinction.

We find that above an A_v ∼ 2 mag, the ¹³CO abundances drops with increasing column density, and this decrease coincides with a decreasing dust temperature. Due to this, we suggest that this is evidence of CO freeze-out in cold, dense gas. Investigating the spatial extent of this drop in the ¹³CO abundance, we see that it is found along the entire ∼13 pc filament spine and out to a radius of roughly 0.8 pc, making G214.5 a rare case of cloud-scale CO freeze-out.

To further investigate the widespread freeze-out, we construct a CO depletion model considering CO accretion, thermal desorption, and cosmic-ray-induced desorption. In concert with a model of the underlying volume density, we use this depletion model to fit the mean radial profiles of G214.5’s column density and ¹³CO abundance (Section 4.3). We find that to reproduce the large radial extent of the depletion, a very low cosmic-ray ionization rate is required, 1.8–2.0 × 10⁻¹⁸ s⁻¹. This is due to freeze-out occurring at low volume densities (f_gas = 0.5 at r∼0.2 pc, n∼2000 cm⁻³), which is unique to G214.5. An inferred cosmic-ray ionization rate of the order of 10⁻¹⁸ s⁻¹ is an order of magnitude lower than is typically measured but is consistent with the very low gas and dust temperatures seen in G214.5. It is possible that other clouds in the Outer Galaxy may experience such low cosmic-ray ionization rates due to their Galactocentric radii and quiescent environments (e.g. Yang, Aharonian & Evoli (2016) find a decrease in cosmic-ray flux with increasing galactocentric radius using gamma-ray observations), making cloud-scale CO freeze-out more common. Such cloud-scale CO freeze-out has consequences on mass and column density estimates, as well as the interpretation of kinematic signatures, and it is therefore imperative to better understand the prevalence of this phenomenon.

An additional consequence of the low cosmic-ray ionization rate found in G214.5 is that it leads to a low ionization fraction of the gas. This results in imperfect coupling between the predominately neutral gas and the magnetic field and the growing importance of non-ideal MHD terms. To study this, we use the Nicil code (Wurster 2016) to self-consistently determine the ambipolar diffusivity given the results of our depletion model (Section 4.3.1). From this, we estimate an ambipolar diffusion time scale for the filament spine and find that even a low-to-moderate magnetic field strength of above 50–100 µG is sufficient to result in an ambipolar diffusion time scale comparable to or smaller than other relevant time scales such as the cloud free-fall time, cloud crushing time as well as the sound and turbulent crossing time. Thus, it is possible that ambipolar diffusion is an important physical process on the relatively large-scale of G214.5’s 13 pc spine.

As the column densities of ¹³CO and C¹⁸O are calculated independently of each other, we determine the isotopologue ratio between them, X_13/18 (Section 4.4). We find a large spread in the measured ratio, X_13/18 = |$13.5^{+7.6}_{-3.9}$|⁠, and that it is elevated compared to the expected ratio considering G214.5’s Galactocentric radius, |$7.6^{+2.1}_{-1.6}$|⁠. However, due to the lower brightness of the C¹⁸O emission and presence of noise, the detected C¹⁸O column density is likely tracing a less extended region of gas along the line of sight compared to the detected ¹³CO column density, and thus introducing a bias elevating the observed abundance ratio. To address this bias, we calculate a corrected ratio that only considers velocity channels in which both are detected; this results in a lower ratio with considerably less spread which is consistent with the expected ratio, X_13/18 = |$9.4^{+2.9}_{-2.1}$|⁠. It is therefore important to use the kinematic information to ensure that the measured isotopologue ratio is not biased by the non-detection of C¹⁸O in some of the velocity channels in which ¹³CO is detected. Further, we show that X_13/18 is relatively independent of the column density, indicating that fractionation and selective photodissociation are only having minor effects on CO isotopologue abundances, suggesting a low interstellar radiation field in the vicinity of G214.5, consistent with the low upper limit placed using the non-detection of [CII].

Taken together, our results show that G214.5 is a highly interesting object of study that may be used to understand the star formation process in a quiescent region. Low gas and dust temperatures as well as large-scale CO freeze-out may be common in such quiescent regions and should be considered, as well as their effects on CO observations. Further studies of G214.5 to investigate the physical and chemical consequences of its low cosmic-ray ionization rate and corresponding cloud-scale CO freeze-out will be the focus of future works.

ACKNOWLEDGEMENTS

The authors would like to thank the anonymous referee for their helpful and constructive comments. SDC would also like to thank James Wurster for kindly answering a number of questions about ambipolar diffusion and the Nicil code. SDC is supported by the Ministry of Science and Technology (MoST) in Taiwan through grant MoST 108-2112-M-001-004-MY2. A.S.M. acknowledges support from the RyC2021-032892-I grant funded by MCIN/AEI/10.13039/501100011033 and by the European Union ‘Next GenerationEU’/PRTR, as well as the program Unidad de Excelencia María de Maeztu CEX2020-001058-M and the grant PID2020-117710GBI00 (MCI-AEI-FEDER, UE). This work includes observations carried out under project number 009–19 with the IRAM 30m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). This publication includes data acquired with the Atacama Pathfinder Experiment (APEX) under programme ID O-0103.F-9318A-2019. APEX is a collaboration among the Max-Planck-Institut fur Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory. This work includes observations made with the NASA/DLR Stratospheric Observatory for Infrared Astronomy (SOFIA) under project ID 83_0723. SOFIA is jointly operated by the Universities Space Research Association, Inc. (USRA), under NASA contract NAS2-97001, and the Deutsches SOFIA Institut (DSI) under DLR contract 50 OK 0901 to the University of Stuttgart. SDC would also like to acknowledge the people developing and maintaining the open source packages which were used in this work: matplotlib (Hunter 2007), numpy (Harris et al. 2020), scipy (Virtanen et al. 2020), and astropy (Astropy Collaboration 2022).

6 DATA AVAILABILITY

The data underlying this article will be shared on reasonable request to the corresponding author. The analysis tools of this work, bts and FragMent, are made freely available at https://github.com/SeamusClarke/FragMent and https://github.com/SeamusClarke/BTS.

Footnotes

References

APPENDIX A: CONSTRAINING THE FUV FIELD USING SOFIA [CII] OBSERVATIONS

Fig. A1 shows the location of the 3 SOFIA [CII] pointings, 7 pixels per pointing, on top of the ¹²CO (1-0) moment zero for G214.5, as well as the individual spectra for the 7 pixels for the C14 pointing. We use the non-detection of [CII] in the pixels away from clump C11, to place an upper limit on the FUV in the vicinity of G214.5. For this purpose, we use the predicted ratio of [CII]/CO (J = 1-0) from the 2020 Wolfire/Kaufman PDR models included in PDR toolbox¹⁰ (Kaufman, Wolfire & Hollenbach 2006; Wolfire, Hollenbach & McKee 2010; Neufeld & Wolfire 2016).

The noise level from each spectrum ranges from ∼0.20 to 0.50 K depending on the pixel and the pointing. Assuming an FWHM of 1 km s⁻¹ for the [CII] line, using these noise levels results in 3σ upper limits of 4.49 × 10⁻⁶-1.10 × 10⁻⁵ erg/s/sr/cm⁻². Dividing these upper limits for the [CII] line by the observed ¹²CO moment zero at those positions results in ratios between 65.8 and 380.7, with a median value of 207.9. The minimum and median value of this ratio may be seen in Fig. A2 as the two contours. Using volume density information found when modelling the CO freeze-out in Section 4.3, we constrain the number density to below 10⁴ cm⁻³. With this constraint, it places upper limits for the FUV flux at ∼1.1 and ∼2.5 G₀.

The single detection of [CII] towards the centre of clump C11 can be seen in Fig. A3, with the ¹²CO, ¹³CO and C¹⁸O spectra at the same location. The detection is clear with a peak intensity of ∼1.1 K, and lies at the same velocity as the CO isotopologues.

APPENDIX B: MONTE CARLO ERROR PROPAGATION TO DETERMINE UNCERTAINTIES

To take into account the effects of noise in the observations on the calculated column densities and abundances we use a Monte Carlo error propagation method. This first requires knowledge of the pixel-by-pixel noise of the spectra; we determine this by calculating the standard deviation of the spectra intensity in velocity channels which are determined to be free of emission by the BTS moment-masking method described in Section 3. The resulting noise maps are shown in Fig. B1.

Using the pixel-by-pixel noise, we produce 10,000 realisations of the spectra per pixel where the random numbers are drawn from a normal distribution with a mean of the observed intensity in the velocity channel and the standard deviation is the pixel noise. Using these spectral realisations, we calculate the moment zero map, ¹²CO excitation temperatures, ¹³CO and C¹⁸O column densities and abundances, as well as the abundance ratio of ¹³CO over C¹⁸O in the same manner as that done in the main body of the text. The standard deviation of these 10,000 realisations may then be used as a measure of the error on the calculated quantity. The maps of these errors, both as an absolute value and as a fraction of the quantity, can be seen in the supplementary online material. It should be noted that the propagated error calculated in this way is solely due to the noise in the spectra and does not include the systematic errors/biases which may be introduced due to assumptions in the analysis.

APPENDIX C: Comparing the ¹²CO and ¹³CO excitation temperatures

To examine the assumption that the ¹²CO and ¹³CO excitation temperatures are comparable we determine the ¹³CO excitation temperature using non-LTE RADEX calculations constrained by the APEX ¹³CO (3-2) and IRAM 30m ¹³CO (1-0) lines. We run a set of 4096 RADEX models using the LVG approximation with temperatures ranging from 5–20 K in steps of 1 K, densities ranging from 10²-10⁵ cm⁻³ in steps of 0.2 dex, and column densities of ¹³CO ranging from 10¹⁴-10¹⁷ cm⁻² in steps of 0.2 dex. The linewidth is taken to be 1 km s⁻¹, comparable to the observed linewidths of ¹³CO.

We calculate the moment zero map for the APEX ¹³CO (3-2) using BTS as done for the (1-0) line, as well as the error on the moment zero. The APEX data is smoothed to the common |$23.5^{\prime\prime}$|resolution before the moment zero is calculated. The moment zero map can be seen in the top right panel of Fig. C1. To determine the excitation temperature we minimise the χ² as defined as:

where O_rat is the observed ratio of the (3-2) moment zero over the (1-0) moment one, M_rat is the predicted ratio from the RADEX model, and E_rat is the error on the observed ratio. The resulting excitation temperature map is shown in the lower right panel of Fig. C1. As in the main body of this work, we utilise a Monte Carlo method to propagate the errors from the moment maps to the estimate of the excitation temperature. To do this we calculate 10,000 realisations of the moment zero values for the (3-2) and (1-0) lines, and for each realisation we minimise the above χ² to determine 10,000 estimates of the ¹³CO excitation temperature, the standard deviation of which may be taken as the uncertainty in the excitation temperature.

In Fig. C2 we compare the excitation temperature calculated from ¹²CO and ¹³CO and find that within errors most are consistent with each other. There is a tendency for the ¹³CO excitation temperature to be slightly lower than the ¹²CO excitation temperature by around 0.5 K but this is minor compared to the 70 per cent difference seen in more active regions (e.g. Roueff et al. 2021). There is a group of pixels which lie around 2 K below the 1:1 line; however, these pixels also exhibit multiple velocity components in the ¹³CO (1-0) which are not seen in the (3-2) line (an example of a simple, single velocity component pixel and a multi-component pixel is shown in Fig. C3). For such pixels the moment zero ratio of (3-2) over (1-0) will be artificially lowered, thus resulting in a lower excitation temperature than is associated with the shared velocity component. As such we conclude that the ¹²CO derived and ¹³CO derived excitation temperatures are broadly consistent with each other and the ¹²CO excitation temperature may be used for ¹³CO and C¹⁸O column density estimates.