A cold and diffuse giant molecular filament in the region of l = 41°, b = −1°

The average spectra of ¹²CO/¹³CO/C¹⁸O emission in the analysed region are shown in Figure 1. The GMF exhibits velocities in the range marked as the near portion of the Sagittarius arm.

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The integrated intensity map of the ¹²CO/¹³CO/C¹⁸O lines in the velocity range between 25 km s⁻¹ and 40 km s⁻¹ is shown in Figure 2. The GMF can be clearly distinguished from the surrounding clouds. It was about 5° in length and about 0.6° in width, and has an angle about 30° with respect to the b = 0° plane. In our assumed distance of 1.7 kpc, the length is about 160 pc, and the largest separation from the Galactic plane is about 80 pc. Both the large length and the relatively high latitude are unusual compared to other GMFs listed in Zucker et al. (2018). As the C¹⁸O flux is barely detected, future discussion is limited to the ¹²CO and ¹³CO data.

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The channel maps, i.e. the integrated intensity map in 1 km s⁻¹ bins, of ¹²CO and ¹³CO lines are shown in Figures 3 and 4, respectively. The GMF lies from northeast to southwest in this region. Clouds to the east of the GMF, around (43.5°, – 0.5°), have much higher LSR velocity and are farther than the GMF. Clouds to the northwest, around (39°, +1°), are the southern part of a much larger cloud that has a trigonometric distance about 1.9 kpc (Reid et al. 2014). Cloud at around (40°, 0°) is GMF 41 in Zucker et al. (2018). They placed it at 2.5 kpc. However, the dust absorption data from Green et al. (2018) have provide a similar distance for GMF 41 as the GMF in this work.

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The moment-1 map, i.e. the flux-weighted mean velocity map, of the ¹³CO line emission for the analysed region is shown in Figure 5. The northeast part of the GMF has three velocity components, with velocities of 29 km s⁻¹, 34 km s⁻¹ and 38 km s⁻¹. There is a significant velocity gradient in the south-west part (SWP) of the GMF along its main axis.

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To show the velocity structures of the GMF more clearly, a velocity-position map of ¹³CO line emission along the GMF is shown as Figure 6. The position is from (l,b) = (42.9°, – 0.2°) to (38.5°, – 2.7°) and the integral width is 1 degree (about 30 pc). Two main velocity components at 29 km s⁻¹ and 34 km s⁻¹ can be seen at the position offset around 1.5°. The velocity gradient of the SWP is clearly shown in Figure 6 and has a value of about 4 km s⁻¹ deg⁻¹, or 0.14 km s⁻¹ pc⁻¹.

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Since these components are distinguishable both in space and velocity, we divide the GMF into three filamentary parts (F1 to F3) and one cloudy part (the SWP), and show their boundaries in Figure 6.

As F3 is relatively weak in ¹³CO emission, its ¹²CO integral intensity is shown in Figure 7. In this map, F3 shows a "∼" shape and is fragmented into several clumps, with more clumps being located at its two ends.

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The molecular hydrogen gas column density N_H2 can be derived by the X-factor method as

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}_{2}}({X}_{{\rm{CO}}})={X}_{{}^{12}{\rm{CO}}}\displaystyle \int {T}_{{\rm{MB}}}{(}^{12}{\rm{CO}})dv\end{eqnarray} \tag{ 1 }$$

where X_¹²CO is the ¹²CO-to-H₂ conversion factor and we adopt the value of 2 × 10²⁰ molecules cm⁻² (K km s⁻¹)⁻¹ from Bolatto et al. (2013). T_MB(¹²CO) is the main beam brightness temperature of ¹²CO emission.

Another way to estimate N_H2 is the standard local thermodynamic equilibrium (LTE) radiation transfer method. The ¹²CO line is assumed to be optically thick and the excitation temperature T_ex is derived from the peak intensity of ¹²CO line T_{¹²CO peak} as

$$\begin{eqnarray}&&{J}_{{\nu }_{12}}({T}_{{\rm{ex}}})={k}_{B}{T}_{{}^{12}{\rm{COpeak}}}/h{\nu }_{12}+{J}_{{\nu }_{12}}({T}_{{\rm{bg}}})\end{eqnarray} \tag{ 2 }$$

where ${J}_{\nu }(T)=\displaystyle \frac{1}{{e}^{h\nu /{k}_{B}T}-1}$, ν₁₂ = 115271202 kHz is the frequency of ¹²CO J = 1 → 0 line, k_B is the Boltzmann constant, T_{¹² CO peak} is the peak intensity of the pixel and T_bg = 2.726 K is the temperature of the cosmic microwave background. Here we assumed the beam filling factor is 1 as the ¹²CO emission is relatively extended. This results in a derived excitation temperature of

$$\begin{eqnarray}&&{T}_{{\rm{ex}}}=\displaystyle \frac{5.532\,{\rm{K}}}{\mathrm{ln}(\displaystyle \frac{5.532}{{T}_{12{\rm{COpeak}}}/{\rm{K}}+0.837+1})}.\end{eqnarray} \tag{ 3 }$$

Under the assumption of LTE, excitation temperatures for ¹²CO and ¹³CO are the same. Then the optical depth of ¹³CO is

$$\begin{eqnarray}&&{\tau }_{{}^{13}{\rm{CO}}}=-\mathrm{ln}\left(1-\displaystyle \frac{{k}_{B}\,{T}_{{\rm{MB}}}\left(^{13}{\rm{CO}}\right)}{h{\nu }_{13}}\displaystyle \frac{1}{{J}_{{\nu }_{13}}\left({T}_{{\rm{ex}}}\right)-{J}_{{\nu }_{13}}({T}_{{\rm{bg}}})}\right)\end{eqnarray} \tag{ 4 }$$

or equivalently

$$\begin{eqnarray}&&{\tau }_{{}^{13}{\rm{CO}}}=-\mathrm{ln}\left(1-\displaystyle \frac{{T}_{{\rm{MB}}}{(}^{13}{\rm{CO}})/5.289\,{\rm{K}}}{{{\rm{J}}}_{{\nu }_{13}}({{\rm{T}}}_{{\rm{ex}}})-0.168)}\right)\end{eqnarray} \tag{ 5 }$$

Following Pineda et al. (2010), the column density of ¹³CO is

$$\begin{eqnarray}\begin{array}{ll}{N}_{{}^{13}{\rm{CO}}}= & \displaystyle \frac{2.42\times {10}^{14}\,{{\rm{cm}}}^{-2}\,{{\rm{K}}}^{-1}\,{{\rm{km}}}^{-1}\,{\rm{s}}}{1-{e}^{-5.289{\rm{K}}/{T}_{{\rm{ex}}}}}\displaystyle \frac{{\tau }_{{}^{13}{\rm{CO}}}}{1-{e}^{-{\tau }_{{}^{13}{\rm{CO}}}}}\\ & \displaystyle \int {T}_{{\rm{MB}}}{(}^{13}{\rm{CO}})dv\end{array}\end{eqnarray} \tag{ 6 }$$

where T_MB(¹³CO) is the main beam brightness temperature of ¹³CO emission. The number ratio for conversion used in this paper is f(H₂/¹²CO) = 1.1 × 10⁴ (Frerking et al. 1982) and f(¹²C / ¹³C) = 77 (Wilson & Rood 1994). The H₂ column density is thus

$$\begin{eqnarray}\begin{array}{ll}{N}_{{{\rm{H}}}_{2}}({\rm{LTE}})= & f({{\rm{H}}}_{2}{/}^{12}{\rm{CO}})\times f{(}^{12}C{/}^{13}C)\times {N}_{{}^{13}{\rm{CO}}}\\ & \simeq 8.5\times {10}^{5}\times {N}_{{}^{13}{\rm{CO}}}.\end{array}\end{eqnarray} \tag{ 7 }$$

The distributions of the excitation temperature T_ex, ¹³CO optical depth τ_{¹³ CO}, and H₂ column density N_H2 for the whole GMF are shown in Figure 8(a), 8(b) and 8(c), respectively. The median excitation temperature is about 7.5 K. The ¹³CO optical depth has a median value of 0.26. The column density of this GMF is at the order of 10²¹ cm⁻², and the distribution does not follow a power-law relation at the high-density end. Compared with the GMFs analysed by Zucker et al. (2018), this GMF is much colder (7.5 K compared to 20.8 K) and about 5 times lower in column density. The peak T_ex of our GMF is smaller than 13 K, close to the lowest value of other GMFs. We note that, both the excitation temperature and column density of our GMF are derived from CO spectroscopic data while these parameters for the known low-latitude GMFs are usually derived from SED fitting of dust continuum or ammonia spectra. Due to the effect of the beam filling fact, our results for the excitation temperature of our GMF are underestimated while the column densities are overestimated because we use a lower excitation temperature. However, Gong et al. (2019) have pointed out that the kinematic temperature derived from RADEX non-LTE analysis for the L1188 filament (distance about 0.8 kpc) is about 13–23 K, not much higher than the excitation temperature (about 10–20 K) derived from the optical thick ¹²CO J = 1 → 0 line in their previous work (Gong et al. 2017). Keeping those caveats in mind, it is still reasonable to believe that this GMF is very cold and very diffuse compared to other GMFs in the literature.

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¹³CO cores in each component are searched using Python package astroDendro (Rosolowsky et al. 2008) and we use the minimum structures as the cores. The settings are min_npix = 30, min_value = min_delta = 0.6 K. This means that the cores we find will include 30 voxels at least, the intensity of each voxel should be greater than 0.6 K (two times of noise), and two contiguous voxels with intensity difference below 0.6 K will not be considered as belonging to different structures. These values are selected to let the resultant cores be real and robust against noise. The 1σ radius R and velocity dispersion σ_v, ¹³ CO are calculated automatically from the moment method and without deconvolution by the beam size. Excitation temperature for each core is derived using the peak ¹²CO intensity within the corresponding voxels with Equation (3). The peak optical depth of ¹³CO is derived using peak ¹³CO intensity within the corresponding voxels of each core with Equation (5). We derived the mass of each core using the LTE method with Equation (7) and the mean molecular weight per H₂ molecule is μ_H2 = 2.8 (Kauffmann et al. 2008). The total flux is calculated from the voxels that define in the cores, without any extrapolation. The distributions for these physical parameters of the cores are shown in Figure 9. This shows that those cores have masses of 10 ∼ 100 M_⊙, sizes of ∼0.3 pc and excitation temperatures of about 9 K.

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Table 1. Cloud Mass and Total Core Mass of each Component

Part	M(XCO)	M(LTE)	M(cores)	N(cores)	$\displaystyle \frac{M({\rm{LTE}})}{M({X}_{{\rm{CO}}})}$	$\displaystyle \frac{M({\rm{cores}})}{M({X}_{{\rm{CO}}})}$	$\displaystyle \frac{M({\rm{cores}})}{M({\rm{LTE}})}$
	(103M⊙)	(103M⊙)	(103M⊙)
F1	53	22	4.6	116	0.41	0.086	0.21
F2	67	22	4.9	138	0.33	0.072	0.22
F3	10	2.5	0.8	27	0.24	0.082	0.34
SWP	66	23	4.2	137	0.35	0.063	0.18
Entire	202	72	13.8	385	0.36	0.068	0.19

The derived masses for cloud and the sum for cores in each component are shown in Table 1. F3 has a relative low $\displaystyle \frac{M({\rm{LTE}})}{M({X}_{{\rm{CO}}})}$ ratio and a high $\displaystyle \frac{M({\rm{cores}})}{M({\rm{LTE}})}$ ratio, but its $\displaystyle \frac{M({\rm{cores}})}{M({X}_{{\rm{CO}}})}$ ratio is comparable to others. This means that F3 is faint in ¹³CO line emission and therefore has a relative lower LTE mass, but it has nearly the same mass fraction (about 7%) of dense cores as traced by ¹³CO to the diffuse molecular cloud as traced by ¹²CO emission. Taken together with the morphology, it is possible that F3 is not physically associated with other components of the GMF.

The one-dimensional velocity dispersion for free particles is related to that of ¹³CO through the following equation,

$$\begin{eqnarray}&&{\sigma }_{v}=\sqrt{{\sigma }_{v{,}^{13}{\rm{CO}}}^{2}+{k}_{B}{T}_{{\rm{ex}}}(\displaystyle \frac{1}{{\mu }_{p}{m}_{{\rm{H}}}}-\displaystyle \frac{1}{{m}_{{}^{13}{\rm{CO}}}})}\end{eqnarray} \tag{ 8 }$$

where μ_p = 2.37 is the mean molecular weight per free particle (Kauffmann et al. 2008), m_H is the mass of H atom and m¹³CO = 29 m_H is the mass of ¹³CO molecule. The virial mass is derived as ${M}_{{\rm{vir}}}=5{\sigma }_{v}^{2}{R}_{{\rm{eff}}}/G$ where G is the gravitational constant and R_eff is the core radius derived from the moment method and deconvolved by the beam size of the telescope. The virial parameter is α ≡ M_vir / M(LTE) (Kauffmann et al. 2013). If the virial parameter of a structure is significantly larger than 2, then it will expand and dissolve in the future, or need external pressure to be stable. Alternatively, if the virial parameter is much lower than 2, then the structure will collapse due to gravity (Kauffmann et al. 2008). As shown in Figure 9(f), the median value of virial parameter is about 2.5, showing that the majority of the cores are nearly gravitationally stable.

The relation between virial parameter and core mass is shown in Figure 10. It shows that virial parameters of the cores have a power-law relation against their masses with an index of –0.34. Such a power-law relation is widely observed, for example figure 1 of Kauffmann et al. (2013). The relation is a combination of the mass-size and linewidth-size relations. The slope is comparable to the theoretical value of –2/3 for pressure-confined fragments in Bertoldi & McKee (1992).

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The mean velocity of the GMF is at the center of the velocity range of Sagittarius – Carina arm in longitude-velocity space in the spiral arm model of Reid et al. (2019). The dust distance of the GMF from Green et al. (2018) is also within the range of Sagittarius – Carina arm in the model of Reid et al. (2019). Hence, we place the GMF at the Sagittarius – Carina arm. However, the GMF has a large angle with the Galactic plane, hence we can hardly to call it as the spine of the Milky Way (more like the rib). We note that, according to figure 5 of Reid et al. (2019), the Sagittarius – Carina arm is relatively thick and extended below the Galactic plane. The GMF is about 40 pc below the Galactic plane, which is compatible with their results.

We suggest a possible giant filament-filament collision scenario to explain the velocity features of F1 and F2. Three pieces of evidence are presented below for such a collision.

A position-velocity map with a narrow integral width of 40 pixels (1°/3) is shown as Figure 11. With a smaller integral range, the connection between F1 and F2 around position offsets 2.2° is more clearly shown than in Figure 6, as shown by the arrows. The bridge-like feature is widely used as evidence for collisions between molecular clouds. If they are overlapped, not physically interacting, then we would see just two main velocity components without the broad bridge feature between them. The simulations for collision of spherical clouds (Haworth et al. 2015) and for collision of filaments (Duarte-Cabral et al. 2011) both have verified that the broad bridge feature in the position-velocity diagram is a robust signature of collision.

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Bisbas et al. (2017) have made synthetic observations based on the simulation results of collision between two spherical clouds. Their results show that overlaps between integrated intensity maps of high-velocity gases (HVGs), i.e. gases with relative velocity higher than one-dimensional velocity dispersion (σ = 5 km s⁻¹ in their simulation), are a clear signature of collision of gas along the line of sight. We apply the results of this model to the collision between filaments,assuming that collision between different structures (filaments or clouds) will in general have similar physical parameters and results. The velocity dispersion in F1 and F2 are about 1 km s⁻¹, which are much smaller than the value of Bisbas et al. (2017). For our GMF, the velocity ranges for the HVGs are chosen to be between 1σ and 3σ from the mean velocity of each component. Map of ¹³CO HVGs in F1 and F2 is shown as Figure 12, with the integrated velocity range of 27∼29 and 35.5∼37.5 km s⁻¹ being shown in blue and red, respectively. The two HVG parts do overlap in the region around (41.5°, –0.8°) and (40.6°, –1.4°), a total projected length about 20 pc. The possible collision position is near the centre of both F1 and F2, which is expected as the gravity force in two parallel fluid bars is higher in their centres than the endpoints.

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A collision usually leads to higher excitation temperatures and column densities in the collision region. Maps of excitation temperature and column density for F1 and F2 are shown as Figures 13 and 14. It can be seen that the collision region roughly from (41.5° –0.8°) to (40.6°, –1.4°) is warmer and denser than the nearby non-collision region.

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To our knowledge, this is the first candidate for giant filament-filament collision in such a large scale (≥10 pc). However, Clarke et al. (2018) have found in their simulations that only about 50 percent of fibers identified in position-position-velocity space correspond to sub-filaments in position-position-position space, whereas the other 50 percent fibers are attributable either to the overlap of several physically separate sub-filaments or to the contamination from parcels of gas in the line-of-sight. Therefore, we note that the velocity bridge feature that we have identified in our position-velocity diagram of Figure 11 may be caused by projection effect of sub-filaments or gas parcels in the line-of-sight, rather than a collision of filament-filament.