Gas Kinematics and Excitation in G035.39-00.33

# Gas Kinematics and Excitation in the Filamentary IRDC G035.39-00.33

## Abstract

Some theories of dense molecular cloud formation involve dynamical environments driven by converging atomic flows or collisions between preexisting molecular clouds. The determination of the dynamics and physical conditions of the gas in clouds at the early stages of their evolution is essential to establish the dynamical imprints of such collisions, and to infer the processes involved in their formation. We present multi-transition CO and CO maps toward the IRDC G035.39-00.33, believed to be at the earliest stages of evolution. The CO and CO gas is distributed in three filaments (Filaments 1, 2 and 3), where the most massive cores are preferentially found at the intersecting regions between them. The filaments have a similar kinematic structure with smooth velocity gradients of 0.4-0.8kmspc. Several scenarios are proposed to explain these gradients, including cloud rotation, gas accretion along the filaments, global gravitational collapse, and unresolved sub-filament structures. These results are complemented by HCO, HNC, HCO and HNC single-pointing data to search for gas infall signatures. The CO and CO gas motions are supersonic across G035.39-00.33, with the emission showing broader linewidths toward the edges of the IRDC. This could be due to energy dissipation at the densest regions in the cloud. The average H densities are 5000-7000cm, with Filaments 2 and 3 being denser and more massive than Filament 1. The CO data unveils three regions with high CO depletion factors (5-12), similar to those found in massive starless cores.

###### keywords:
stars: formation — ISM: individual (G035.39-00.33) — ISM: molecules
12

## 1 Introduction

In order to explain the global properties and evolution of Giant Molecular Clouds (GMCs) and the star formation processes within these clouds, several scenarios of molecular cloud formation have been proposed. In models of flow-driven (e.g. Hennebelle & Pérault, 1999; Ballesteros-Paredes et al., 1999; Heitsch et al., 2009) and shock-induced GMC formation (Koyama & Inutsuka, 2000, 2002; van Loo et al., 2007), molecular clouds are born in a highly dynamical environment characterized by the collision of large-scale, warm atomic flows that give rise to thermal and dynamical instabilities yielding filamentary molecular structures. Alternatively, Tan (2000) and Tasker & Tan (2009) have proposed that dense molecular clumps and filaments are expected to be formed during GMC-GMC collisions, i.e. of already mostly molecular gas, induced by shear in galactic disks.

Observationally, the Herschel Space Telescope has recently revealed that the dusty interstellar medium (ISM) across the Galaxy is highly structured and organized in filaments (Molinari et al., 2010). Among these structures, Infrared Dark Clouds (IRDCs), first detected in extinction by the Infrared Space Observatory (ISO) and by the Midcourse Space Experiment (MSX) (Pérault et al., 1996; Egan et al., 1998), are believed to represent the initial conditions of massive star and star cluster formation. Indeed, IRDCs are cold (T25K; Pillai et al., 2007) and massive (masses from some 100M to 10M, depending on the scale of the region considered; Rathborne et al., 2006; Kainulainen & Tan, 2013), and their clumps and cores show a range of densities (from 10cm to even up to 10cm; see e.g. Peretto & Fuller, 2010; Rathborne et al., 2010; Butler & Tan, 2012) similar to regions known to be forming massive stars and star clusters.

Although the general properties of IRDCs (and of their cores and clumps) have been characterized thanks to the analysis of dust extinction in the mid-IR and of dust emission at millimeter wavelengths (see e.g. Rathborne et al., 2006; Butler & Tan, 2012; Peretto & Fuller, 2010), few studies have been devoted to analyze the dynamical properties of the molecular gas associated with IRDCs (Hernandez & Tan 2011; Hernandez et al. 2012; Kainulainen & Tan, 2013; Peretto et al., 2013). In this context, we have recently carried out a comprehensive study of the molecular line emission and chemical composition of the gas toward the very filamentary IRDC G035.39-00.33 (distance of 2.9kpc; Rathborne et al., 2006), in order to obtain a global understanding of the dynamics, history, and physical properties of the molecular gas at the initial conditions of molecular cloud formation.

The first results obtained from this study were presented by Jiménez-Serra et al. (2010, Paper I), who reported the detection of faint and widespread SiO emission over parsec-scales across this IRDC. In Paper I, widespread SiO in G035.39-00.33 was interpreted as a fossil record of the large-scale shock interaction induced by a flow-flow collision that may have been involved in the formation of the IRDC3. An alternative scenario considers a widespread and deeply-embedded population of low-mass stars driving molecular outflows in G035.39-00.33. This scenario cannot be ruled out at present due to the limited angular resolution of the SiO single-dish observations (Paper I).

It is likely, however, that G035.39-00.33 is at an early stage of evolution and that its current star formation rate is relatively low. This is supported by the detection of widespread CO depletion (by up to a factor of 5) across the cloud (see Hernandez et al. 2011; Paper II, ), suggesting that the molecular gas in G035.39-00.33 has been affected very little by stellar feedback. The Herschel satellite has recently mapped this IRDC at 70, 160, 250, 350 and 500m, revealing 13 massive dense cores (masses 20M and H densities 210cm) inside the cloud (Nguyen Luong et al., 2011). Some of these cores are indeed quiescent (i.e. they contain no 24m sources or H shock-excited emission; Chambers et al., 2009), and therefore are at pre-stellar/pre-cluster phase (Rathborne et al., 2006; Butler & Tan, 2012).

By using combined near-IR and mid-IR extinction maps, Kainulainen & Tan (2013) have recently obtained more accurate measurements of the total mass of G035.39-00.33. These maps have shown that the central parsec-wide region of the IRDC is close to virial equilibrium (Hernandez et al. 2012; Paper III, ). The global kinematics of the molecular gas associated with this cloud are, however, rather complex, and reveals the presence of several secondary molecular filaments that could be interacting (Henshaw et al. 2013a, Paper IV). This interaction may have started 1Myr ago (Paper IV, ), implying that the gas in the IRDC would have had enough time to reach virial equilibrium with the surrounding environment (Paper III, ).

In Paper IV (), we concentrated on the large-scale dynamics and physical properties of the dense gas in the IRDC G035.39-00.33. In this paper (Paper V of this series), we present a multi-transition analysis of the low-density gas associated with this cloud and traced by CO and CO. These data are complemented by single-pointing spectra of typical gas infall tracers such as HCO and HNC, and of their C isotopologues (HCO and HNC) toward one of the most massive cores in the region (Core H6), to try to find evidence of gas infall toward this core. The observations of the CO and CO =10, =21, and =32 lines toward G035.39-0.33 are described in Section2. In Section3, we present the detailed analysis of the large-scale kinematics of the CO and CO emission toward the three filaments detected in the cloud (Filaments 1, 2 and 3). In section3.5, we report the spectra of HCO, HNC, HCO and HNC measured toward core H6 to find evidence of molecular gas infall in the core. The physical conditions of the CO and CO gas (e.g. H number density, CO/CO column density, excitation temperature and optical depth) are presented in Section4. The results are discussed in Section5, and in Section6 we summarize our conclusions.

## 2 Observations

### 2.1 13CO and C18O line observations.

The =10 and =21 rotational transitions of CO and CO were mapped toward the IRDC G035.39-00.33 in August and December 2008 over an area of 24 (1.7pc3.4pc at a distance of 2.9kpc), with the Instituto de Radioastronomía Milimétrica (IRAM) 30m telescope at Pico Veleta (Spain). We imaged this emission using the On-The-Fly (OTF) mode. The central coordinates of the map were (J2000)=185708, (J2000)=021030 (l=35.517, b=-0.274), and the off-position was set at offset (1830, 658) with respect to the map central coordinates. While the =10 lines of CO and CO were observed with the old SIS ABCD receivers, the =21 line emission was imaged with the HERA multi-beam receiver. The receivers were tuned to single sideband (SSB) with rejections 10dB. The beam sizes were 22 for the =10 lines at 110GHz, and 11 for the =21 transitions at 220GHz. The VESPA spectrometer provided spectral resolutions of 20 and 80kHz, which correspond to velocity resolutions of 0.05 and 0.1kms at 110 and 220GHz, respectively. All maps were smoothed in velocity to channel widths of 0.1kms. Typical system temperatures were 150-220K. Intensities were calibrated in units of antenna temperature, T, and converted into units of main beam temperature, T, by using beam efficiencies of 0.64 for the CO and CO =10 data, and of 0.52 for the =21 lines.

The =32 rotational lines of CO and CO were simultaneously observed in August 2008 at the James Clerk Maxwell Telescope (JCMT) with the 16-pixel array receiver HARP-B toward the same 24 area as that mapped by the IRAM 30m telescope. We imaged this emission by using the jiggle-map observing mode. Since this mode only covers a field area of 22, we placed two adjacent fields centered at (J2000)=185708, (J2000)=021130 and (J2000)=185708, (J2000)=020930. The selected off-position was (J2000)=190241.5 and (J2000)=025738.1 (i.e. l=36.85 and b=-1.15 in Galactic coordinates). The beam size of the JCMT telescope was 14 at 330GHz. The spectral resolution provided by the ACSIS spectrometer was 60kHz, which corresponds to a velocity resolution of 0.05kms. In order to compare these data with the CO and CO =10 and =21 maps, we smoothed the =32 line spectra to a velocity resolution of 0.1kms. The system temperatures ranged from 340 to 410K. Intensities were calibrated in units of T, and converted into T by using a beam efficiency of 0.63. A summary of the observed line frequencies, telescopes, receivers, beam sizes and beam efficiencies of the CO and CO observations, is shown in TableLABEL:tab1.

The reduction of the CO and CO =10 and =21 IRAM 30m data was carried out with the package reduction software GILDAS4. The final molecular line data cubes were also generated with this software. The map size, pixel size, angular resolution, spectral resolution and RMS noise level (per channel and pixel) of these images are shown in TableLABEL:tab2. For the CO and CO =32 emission lines, the observed JCMT data cubes were merged and converted into fits format within the Starlink package software. These data were then reduced and used to generate the final CO and CO =32 images within GILDAS. Their data cube parameters are also reported in TableLABEL:tab2.

### 2.2 Observations of gas infall tracers.

The molecular species HCO and HNC are known to be good probes of infalling gas in molecular cloud cores (Myers, 1996; Kirk et al., 2013). The infall signatures are characterized by blue-shifted asymmetries in the molecular line profiles caused by the large optical depths of the HCO and HNC emission (see e.g. Myers, 1996). In order to determine the presence of infall signatures, comparison with optically thin tracers such as HCO and HNC, are needed.

The =10 line emission of HCO, HCO and HNC, and the =32 line transition of HCO, were OTF mapped with the IRAM 30m telescope toward the IRDC G035.39-00.33 in August 2008 and February 2009. The HNC =10 line emission was observed toward this cloud with the IRAM 30m in September 2013. For the HCO, HCO and HNC line observations, we used the old SIS ABCD receivers (SSB rejections 10dB) while the HNC =10 transition was observed with the new EMIR receivers. The VESPA spectrometer provided spectral resolutions of 40kHz for the =10 lines of HCO, HNC, HCO and HNC (velocity resolution of 0.12-0.14kms), and of 80kHz for the HCO =32 line (i.e. 0.09kms). Typical system temperatures ranged from 100-140K at 90GHz, and 340-480K at 270GHz. The beam efficiencies used to convert the intensities from units of T into T are shown in TableLABEL:tab1.

In this paper, we report only the single-pointing spectra measured toward the most massive core in the mapped region, core H6 (Butler & Tan, 2012, and below), in an attempt to detect gas infall signatures in the line emission of HCO and HNC toward this core.

## 3 Results

In Figure1, we present the integrated intensity map of the CO =21 line emission from =40 to 50kms (white contours) observed with the IRAM 30m telescope toward the IRDC G035.39-00.33. This image has been superimposed on the mass surface density map of the cloud (in colour scale) derived by Kainulainen & Tan (2013) by combining a NIR extinction map with the MIR map of Butler & Tan (2012). In Figure1, we also show the locations of the massive cores reported by Butler & Tan (2012) toward this cloud. The low-mass and the IR-quiet massive cores found by Nguyen Luong et al. (2011, see yellow and light-blue filled diamonds, respectively) from Herschel PACS and Spire data, are also shown. All these cores show emission at 70m in the Herschel data. We note that the massive dense cores (filled light-blue diamonds) tend to cluster around the northern core H6 and the southern cores H2 and H3.

From Figure1, we find that the observed CO =21 emission toward G035.39-00.33 mainly follows the filamentary structure of the IRDC seen in extinction. However, besides the main filament, two other molecular structures are detected toward the north-east and north-west of the cloud with faint counterparts seen in the mass surface density map.

The CO =21 main emission peaks are associated with the regions with highest extinction (i.e. densest) in the cloud at offsets (-4,10) and (10,-130). These are the regions where most of the IR-quiet massive cores are found (black crosses and light-blue diamonds; Rathborne et al., 2006; Butler & Tan, 2012; Nguyen Luong et al., 2011). While the CO =21 emission toward cores H3, H2 and H4 in the south of G035.39-00.33 traces the peaks of the mass surface density map, this emission is offset with respect to the densest peak in core H6. This is consistent with the significant CO depletion measured toward this core (depletion factor 5 (Paper II, ; Paper III, ).

In Figure2, we compare the morphology of the CO =21 emission with that from the CO =10 and =32 transitions, and from the CO =10, =21 and =32 lines. The integrated intensity emission from 40 to 50kms for all these lines is shown superimposed on the mass surface density map of Kainulainen & Tan (2013). Like for CO =21, the other CO and CO transitions follow the filamentary structure seen in extinction. The CO =10 and =21 lines and the CO =10 transition show the molecular extensions toward the north-east and north-west of G035.39-00.33. However, the higher-J CO =32 and CO =21 and =32 lines probe denser (and therefore deeper) regions into the cloud as expected from their higher critical densities (310cm, i.e. a factor of 10 higher than those of the low-J lines, 210cm). The high-J transitions of CO and CO, therefore, suffer less from contamination from the diffuse molecular envelope of the IRDC.

### 3.1 Single-beam 13CO and C18O line spectra

In Figure3, we show a sample of the CO and CO spectra observed at different positions across the IRDC. The spectra have been smoothed to the largest beam in the dataset (of 22), corresponding to the =10 transition data. The positions are selected across the IRDC and are representative of cores H3 and H6 [offsets (10,-125) and (0,20)], of a position at half-distance between cores H2 and H4 [offset (-25,-115)], and of the more quiescent regions in the cloud [offsets (0,-50) and (-30,120)]. We have also selected a position off the main filament toward the northwest of the cloud [see offset (-60,110)].

From Figure3, we find that the CO and CO lines show complex molecular line profiles that change significantly across the IRDC. Consistent with the results from Paper IV (), three different velocity components are detected from the CO and CO emission. These velocity components are particularly clear toward (0,20), where the CO lines show three emission peaks. In TableLABEL:tab3, we report the central radial velocities (), linewidths (), and peak intensities (T) of every velocity component derived by fitting the lines with three-component Gaussian profiles. The errors in and are given by the uncertainties in the Gaussian fits, while the errors in T correspond to the measured 1 rms level in the spectra. For the non-detections, the upper limits correspond to the 3 level in the CO and CO spectra.

TableLABEL:tab3 shows that the observed velocity components are centered, approximately, at radial velocities 43, 45 and 46kms. However, a systematic trend is found for these velocities to become red-shifted (by 1.5kms) when one moves from the south to the north of G035.39-00.33 (note the systematic shift of the vertical dotted lines in Figure3 from left to right). For instance, for the 43kms-component, the radial central velocity of CO =10 shifts from 42.9kms toward (10,-125) in the south to 44.5kms toward (-60,110) in the north. The same applies to the other two velocity components. As shown in Section3.3, this velocity gradient in the CO isotopologue emission is confirmed by large-scale maps across G035.39-00.33 (velocity gradient of 0.4-0.8kmspc; see Section3.3).

The linewidths of the CO and CO lines typically range from 1 to 2kms (see Section3.4 for the distribution of the CO and CO linewidths), and the brightest CO and CO emission arises from the velocity component at 45kms. This component, which contains the bulk of the molecular gas, is associated with the filamentary IRDC seen in extinction (Section3.2). In the following, we describe in detail the morphology and kinematics of the different velocity components detected in CO and CO toward G035.39-00.33.

### 3.2 Channel maps of the 13CO and C18O emission

In Figures4 and 5, we show the channel maps of the CO and CO =21 line emission measured toward G035.39-00.33 between 41 and 49kms in velocity increments of 0.5kms. We use the CO and CO =21 line data cubes because they have the highest angular resolution available (beam of 11) within our CO isotopologue molecular line dataset.

As noted in Paper IV (), the general kinematics of the CO emission are characterized by the presence of several molecular filaments associated with the IRDC (Figure4). The CO gas concentrates along, at least, two clear elongated/filamentary structures extending over 300 (i.e. 4.4pc) along the north-south direction. The first filament is seen at the velocity component at =43kms (Filament 1). This filament runs from the north-east to the south-east, curving to the west towards the centre of the filament and showing a completely different morphology to that seen for the IRDC in extinction (the IRDC in extinction curves toward the east; see Figure1). At more red-shifted velocities (44.0-45.0kms), the CO molecular gas evolves from this filamentary morphology into a more complex structure. The dominant feature at these velocities has the same morphology as the IRDC seen in extinction and therefore it is associated with the densest part of the cloud (Filament 2; see Paper IV, ). Core H6 is approximately located at the intersecting region between Filaments 1 and 2 (Figure4). For velocities 46kms (Filament 3), the main filament develops two secondary extensions/arms toward the north-west and south-west of core H6. Although this new structure largely overlaps with Filament 2, it likely represents an additional feature different from Filaments 1 and 2 since it appears as an independent structure in velocity space with respect to the other two filaments (Paper IV, ). Figure6 shows the integrated intensity images of the three individual molecular filaments (Filaments 1, 2 and 3) identified in G035.39-00.33 from the CO =21 emission.

From Figures4 and 5, it is clear that the IR-quiet massive dense cores detected toward G035.39-00.33 tend to be found toward the regions where the filaments intersect, and where most of the molecular gas is concentrated. In particular, the chain of cores found toward the south follows the merged CO structure for Filaments 1 and 2 (see Figure4 for the velocity range 44.5-45.0kms), suggesting that these structures are physically connected and likely interacting. The detection of broader CO and CO line profiles toward these regions [offsets (10,-125) and (0,20) in Figure3], could be due to the merging of the filaments, although on-going star-formation could also be responsible for the broadening of the lines. As reported in Paper I (), broad SiO emission has been detected toward core H6 (SiO condensation named N) and toward core H4 (condensation S).

### 3.3 Distribution of vLSR across the CO filaments

By using the single-dish spectra of CO and CO measured across G035.39-00.33, we can derive the distribution of the central radial velocity, , and linewidth, , of the molecular gas for every position in this IRDC. We use the =21 and =32 transitions of CO and CO because they probe denser gas than the =10 lines, and their maps have a higher angular resolution (beam of 11-14; TableLABEL:tab1). In this Section, we will report the results from the maps, while the distribution of for the CO and CO lines will be presented in Section3.4.

To calculate the and maps across G035.39-00.33, we have smoothed the CO and CO single-dish =21 and =32 data to the same angular resolution of 14 (i.e. to the largest beam of the JCMT maps), so that the =21 and =32 spectra can be compared directly. The individual spectra are simultaneously fitted with three-component Gaussian line profiles as described in AppendixA. In our analysis of the CO lines, we have considered line spectra with peak intensities 9 only (with the rms in every spectrum). This criterion was first used in Paper IV () and takes into account that the typical detection threshold for Gaussian line profiles is 3 and that the CO emission toward G035.39-00.33 has three overlapping velocity components. For CO, the applied detection threshold is 5 since the CO lines are weaker (AppendixA). The derived values of and are then used to generate the and maps. This Gaussian decomposition allows to study not only the individual kinematic structure of every filament, but also the excitation conditions of the CO gas within them (see Section4).

In Figure7, we show the distribution of derived from the CO =21 data for Filaments 1, 2 and 3. The intensity-weighted average of for every filament is shown in the upper part of every panel, and is calculated as described in AppendixB. The intensity-weighted average of is 43.61kms for Filament 1, 45.16kms for Filament 2, and 46.47kms for Filament 3 (TableLABEL:tab4). In agreement with the results reported in Paper IV (), the filaments are separated in velocity space by 3kms. We note that these values change by 0.2% if data with peak intensities 5, instead of 9, are considered in our analysis.

For all three filaments, our data reveal a velocity gradient in the north-south direction with the red-shifted gas peaking toward the north-northwest of G035.39-00.33, and with the blue-shifted emission toward the south of this cloud. While the most red- and blue-shifted velocities are measured at distances further away from core H6, the CO gas motions in the vicinity of this core show radial velocities close to the average values (i.e. the gas radial velocities get more red- or blue-shifted with increasing distance to core H6; see Figure7). Although the velocity gradient is relatively smooth for Filament 2, we note that the kinematics of the CO gas in the vicinity of this core for Filaments 1 and 3 are more complex. This could be due either to feedback from local star formation (broad SiO emission is detected toward this position; see Paper I, ) or to smaller-scale structures unresolved in our single-dish observations (see Section5.4 and Henshaw et al. 2013b).

The derived values for the velocity gradient are 0.4-0.8kmspc from the northern part of G035.39-00.33 to core H6, and 0.6-0.8kmspc from the southern region to this core. This velocity gradient is consistent with that previously reported in Paper IV () (of 1kmspc) for Filament 2. Similar velocity gradients have also been reported toward the Orion molecular cloud (0.7kmspc; Bally et al., 1987), the DR21 filament (0.8-2.3kmspc; Schneider et al., 2010), or even toward the low-mass Serpens South cluster-forming region (1.4kmspc; Kirk et al., 2013). This smooth velocity gradient in G035.39-00.33 has become apparent thanks to the new CO and CO data, and contrasts with the sharp velocity transition found in Paper IV (). This is likely due to the lower-angular resolution of the NH and CO =10 data compared to our CO =21 line data (26 vs. 14, respectively). We also stress that the smooth velocity gradient reported for every filament cannot be attributed to an artifact of our three-component Gaussian fit method, since the close inspection of the single-pointing spectra (Section3.1) already revealed a systematic trend for the radial velocities of the filaments to shift from blue- to red-shifted velocities as one moves from the southern to the northern regions in the IRDC.

Besides CO =21, the analysis of the CO =32 and CO =21 data also reveals a similar behavior for the individual motions of the gas within every filament (see Figures13 and 14). This demonstrates that our analysis of the kinematics of the molecular gas toward G035.39-00.33 does not depend on the transition used, and provides robust results against the multi-Gaussian profile fitting method described in AppendixA. Indeed, the average derived for every filament is very similar in all transitions and CO isotopologues (see TableLABEL:tab4), except for Filament 2 where the CO =21 emission appears globally red-shifted (by 0.2kms) compared to the lower-density CO =21 line. This behavior is similar to that reported between CO =10 and NH =10, and has been interpreted as a signature of the ongoing interaction between Filaments 1 and 2 (Paper IV, ). This velocity shift cannot be attributed to large optical depth effects since CO and CO are moderately optically thick and optically thin, respectively (see Sections4.1 and 4.2).

The emission from the CO =32 is very faint throughout the map except for few positions (see Figure2). This has prevented us from generating the individual motions of the three filaments from this transition.

### 3.4 Distribution of Δv in the CO filaments

We have generated maps of the average linewidth of the CO and CO lines, , by using the linewidths measured for every velocity component (or filament) and position in the map (see AppendixB for the method to calculate this average). By doing this, we can infer the global level of turbulence across the cloud, and look for any systematic changes in the molecular linewidths between the densest regions in the IRDC and its lower-density envelope.

In Figure8, we report the maps of derived for CO =21, CO =32, and CO =21 toward G035.39-00.33. From Figure8, we find that the general distribution of for CO =21 is not uniform and shows broader line emission along the outer edges of the IRDC. This behaviour was already noted in Paper II, and resembles that reported by Pineda et al. (2010) toward the B5 low-mass star forming core. Since we only consider the positions in the CO =21 map with line detections 9, the line broadening toward the outer regions in G035.39-00.33 is not due to poorer quality of the Gaussian fits, but to a real increase in the velocity dispersion in the lower density gas. The spatial distribution of for CO =32 and CO =21 shows narrower linewidths toward the central regions of G035.39-00.33, supporting this idea. Indeed, the average linewidths of the individual filaments in G035.39-00.33 (see AppendixB and TableLABEL:tab4) are significantly narrower for CO =32 and CO =21 (i.e. 1.4-1.5 and 1.2-1.3kms, respectively) than for CO =21 (1.6-1.8kms), which could be related to energy dissipation. The derived values of are found to vary by 3% if data with peak intensities 5, instead of 9, are considered in our analysis.

The trend of increasing linewidth toward the low-density outer regions of the IRDC can also be seen from the distribution of the non-thermal (turbulent) velocity dispersion, , for the individual Filaments 1, 2 and 3. can be determined from the observed linewidth, , as follows (Myers, 1983):

 σNT=√Δv28ln2−kBTkinm, (1)

where is the Boltzmann’s constant, the kinetic temperature of the molecular gas, and the mass of the molecular species (either 29a.m.u. for CO or 30a.m.u. for CO). The thermal dispersion of the molecular gas, =, is 0.07kms assuming that the gas kinetic temperature is 15K (Pillai et al., 2006; Ragan et al., 2011; Fontani et al., 2012). TableLABEL:tab4 reports the values of derived for every filament.

In Figure9, we show the non-thermal velocity dispersion, , derived from the CO and CO data as a function of peak intensity, T, for every filament. To our knowledge, this is the first attempt made to measure the non-thermal velocity dispersion across different filaments within the same IRDC. The peak intensity, T, of these lines is used as a proxy of column density and, therefore, of the radial distance to the axis of the filaments. In order to better show the increasing trend of for decreasing T, we have carried out a power law fit to the data in the form = (see red lines in Figure9). For the fits, we have binned the data in temperature ranges of 0.25K. While the average parameter for CO =21 is 0.24, for CO =32 this parameter is 0.09, indicating a weaker dependency of with radial distance. As expected for a higher-density tracer, CO =21 shows almost a flat distribution with an average value 0.03.

From Figure9, we find that the gas in the individual molecular filaments of G035.39-00.33 is supersonic, with an average non-thermal velocity dispersion (see also TableLABEL:tab4) being factors 2-3 larger than the sound speed in the medium (i.e. sound Mach number 2-3 with the sound speed being =0.25kms)5. This is in agreement with the results by Vasyunina et al. (2011) and Ragan et al. (2012) toward two samples of IRDCs, and contrasts with the gas motions toward the molecular filaments in the L1517 and the L1495/B213 low-mass star forming regions, where these motions are, respectively, subsonic and mildly transonic toward both the high-density cores (seen in NH) and the lower-density envelope of the filaments probed by CO (see Hacar & Tafalla, 2011; Hacar et al., 2013).

### 3.5 Gas infall tracer lines toward core H6

In Section3.3, we have reported the detection of a relatively smooth velocity gradient of 0.4-0.8kmspc in the north-south direction, common to Filaments 1, 2 and 3. As discussed in Section5.2, one scenario that could explain this velocity gradient is gas accretion flows along Filaments 1, 2 and 3 onto the massive core H6. We investigate whether typical gas infall tracers such as HCO and HNC indeed show blue-shifted asymmetries in their self-absorbed molecular line profiles as a result of gas accretion onto this core.

In Figure10 we report the spectra of the =10 lines of HCO, HNC, HCO and HNC, and of the =32 transition of HCO, measured toward core H6, and smoothed to the same angular resolution of 29 (the largest beam of the IRAM 30m observations). All species show similar line profiles. In particular, the emission from optically thick tracers, HCO and HNC, peaks at the same (45.4kms, i.e. the derived for the dense CO =21 gas; see TableLABEL:tab4) as their optically thin C isotopologues, HCO and HNC. This clearly contrasts with the behaviour seen for self-absorbed spectra toward contracting cloud cores, for which the optically thin species show their emission peaks red-shifted compared to the optically thick lines (see Myers, 1995; Kirk et al., 2013; Peretto et al., 2013). The asymmetry in the line profiles of HCO and HNC found toward core H6 are probably not due to gas infalling onto this core (at least at angular scales of 29, or 0.4pc), but to the intrinsic kinematic structure of the IRDC (Section3.2). We note that infall motions are not likely to appear at the denser regions in this IRDC since the HCO =32 emission does not show any self-absorption toward core H6 either.

## 4 Excitation conditions of the CO gas in G035.39-00.33

We can now use the derived peak intensities and linewidths of the CO and CO =21 and =32 lines, to estimate the physical conditions of the gas such as H number density, n(H), CO/CO column density, N(CO) or N(CO), excitation temperature, T, and optical depth, , in the three molecular filaments detected toward G035.39-00.33 (Sections3.1 and 3.2). To do this, we have used the Large Velocity Gradient (LVG) approximation (Sobolev, 1947), for which we have considered the collisional coefficients of CO and CO with H calculated by Yang et al. (2010), and the first 18 rotational levels of these two molecules. We assume a kinetic temperature of the gas, T, of 15K, which is similar to those found in other IRDCs from NH observations (Pillai et al., 2006; Ragan et al., 2011; Fontani et al., 2012), and which is in close equilibrium with the temperature of the dust measured toward G035.39-00.33 (T16-17K; see Nguyen Luong et al., 2011). In Section4.3, we however evaluate the sensitivity of our LVG results to small changes in the kinetic temperature.

The average linewidth between the =21 and =32 lines of CO and CO was used as an input parameter in the LVG code. The =10 line emission from CO and CO was not employed in our calculations because 1) this transition probes lower-density gas in the IRDC (Paper II, ); and 2) all data would have to be smoothed to the poorer angular resolution of 22 of the =10 observations (TableLABEL:tab1). In Section4.4, we examine in what extent our LVG results are modified by the inclusion of the =10 data in the LVG analysis.

A grid of LVG models were run with H number densities ranging from 900cm to 10cm, and with CO and CO column densities ranging from 10cm to 10cm. For every grid position, the LVG code calculates the peak intensity of the rotational lines of a molecular species (i.e. CO or CO in our case) with quantum numbers from =1 to =18. The LVG solution is then obtained by means of a minimization technique by comparing the predicted intensities of the =21 line and the predicted line intensity ratio T(32)/T(21), with those observed toward every position in the map. For CO, only those positions across the IRDC where both transitions were detected above the 9 level, were considered in the calculations (i.e. we use the same dataset as that reported in Sections3.3 and 3.4). Note that this is important because it guarantees that the derived peak intensities and linewidths of the lines, key for the determination of the physical conditions of the gas, have been measured with good accuracy. The LVG results provide maps of n(H), N(CO), T and (see Section4.1). However, in the case of CO, the threshold of 5 for both transitions was exceeded only toward three positions across the IRDC (see Section4.2), including 1) core H6; 2) the CO emission peak toward the west of core H6; and 3) 10 north the position where narrow SiO emission lines have been detected (Paper I, ).

### 4.1 LVG results for 13Co

In Figure11, we present the H number density, n(H), CO column density, N(CO), and excitation temperature of the gas for the =21 transition, T(21), obtained for Filament 1 (upper panels), Filament 2 (middle panels), and Filament 3 (lower panels) by using the LVG approximation. TableLABEL:tab5 also reports the average values of these parameters measured for every filament. From Figure11, we find that the derived n(H) typically range between some 10cm to few 10cm, as expected for a low-density tracer such as CO, and in agreement with those H densities estimated toward low-mass molecular clouds such as Perseus (see e.g. Bensch, 2006; Pineda et al., 2008). The average H density for Filament 1 is somewhat smaller (5100cm) than those of Filaments 2 and 3 (7300-7500cm; see TableLABEL:tab5), indicating that the former filament is less dense than the latter ones. This was already noted in Paper IV () from the lack of NH =10 emission in Filament 1.

The derived CO column densities range from 2-310cm to 2-310cm in the three filaments. The average values of N(CO) are very similar in the three filaments and are 10cm (TableLABEL:tab5). Assuming an isotopic ratio C/C of 53 (Wilson & Rood, 1994), a CO abundance of (CO)210 (Lacy et al., 1994), and a mass per H nucleus of =2.3410g, we can derive the average mass surface density for every filament as:

 Σ13CO=1.24×10−2×[N(13CO)1016(cm−2)]gcm−2. (2)

The average values of N(CO) imply mass surface densities of 0.012gcm for Filaments 1 and 3, and of 0.02gcm for Filament 2 (TableLABEL:tab5). By adding up all these contributions, we obtain a total surface mass density 0.04gcm, which is consistent with the average value obtained in Paper II () from their CO data.

An estimate of the relative H gas masses between the filaments can be derived from the values of N(CO) shown in Figure11. As shown in TableLABEL:tab5, the derived H gas masses for Filaments 1, 2 and 3 are, respectively, 4300, 15000 and 10800M. This implies that Filament 1 is a factor of 2-3 less massive than Filaments 2 and 3, while the latter two filaments have very similar gas masses. One may think that the lower mass for Filament 1 could be a consequence of the smaller number of data points considered in the calculation. However, by using a similar area than that covered by Filaments 2 and 3, and by assuming an average column density6 of N(CO)=210cm, the estimated gas mass missing for Filament 1 is 300M (i.e. 7% its total gas mass). After including this gas mass correction, Filament 1 is still 2-3 times less massive than Filaments 2 and 3.

From Figure11, we also find that the excitation temperature for the =21 transition, T(21), ranges from 7K to 14K in the three filaments. The average values of T(21) are 10-11K (TableLABEL:tab5), showing that the CO gas is sub-thermally excited. These excitation temperatures are similar to those found toward low-mass dark clouds (Pineda et al., 2008). We note however that T(21) tends to increase to 13-14K toward the eastern edge of the IRDC for Filaments 2 and 3, as a consequence of the higher H densities found in these regions (Figure11). This behaviour is similar to that found in Paper IV () from NH data. The measured values of T(32) are typically 2K below those reported for T(21).

The average optical depth obtained from our LVG results for the CO =21 and =32 lines is, respectively, 2-3 and 1-2 (see TableLABEL:tab5). This indicates that the CO emission is moderately optically thick.

### 4.2 LVG results for C18O

The CO data toward G035.39-00.33 reveal only three positions in Filaments 2 and 3 where the =21 and =32 lines are both brighter than the 5 level in the CO spectra. These positions are: 1) core H6; 2) a CO emission peak toward the west of core H6 (the CO West Peak at offset (-9,24); Figure2); and 3) offset (-9,80) located 10 north the region where narrow SiO has been detected (the Narrow SiO Peak; see Paper I, ). In TableLABEL:tab6, we report the H density, CO column density, and excitation temperature and optical depth for the =21 and =32 transitions, obtained with the LVG approximation and by using the CO =21 and =32 spectra smoothed within a 14-beam toward each position. From this Table, we find that core H6 is the densest of the three regions with a H number density of 10cm. The H densities for the CO West peak and the Narrow SiO Peak are of 2-410cm. The CO column densities are however very similar toward the three positions, with values within a factor of 1.5. The derived excitation temperatures are similar to those measured for CO, and the optical depths are 1, indicating that the emission from the CO lines is optically thin. This is consistent with the results of Paper II ().

From CO =10 and =21 observations, in Paper II () we found that G035.39-00.33 shows widespread CO depletion with depletion factors, , as high as 5. Since the =32 line emission has a higher critical density (510cm) than the =10 and =21 lines (210cm and 810cm, respectively), our LVG results obtained using the CO =32 data have the potential to provide the depletion factor toward even denser regions with a higher degree of CO depletion. Following the notation used in Paper II (), we can calculate the depletion factor, , as:

 fD=ΣSMFΣC18O, (3)

where denotes the mass surface density derived from near- and mid-IR images (Kainulainen & Tan, 2013), and is the mass surface density obtained from the observed CO column density toward Filaments 2 and 3. To calculate , we have used Eq.5 from Paper II (), and assumed an O/O isotopic ratio of 327 (Wilson & Rood, 1994), and a CO fractional abundance of 210 (Lacy et al., 1994).

In TableLABEL:tab6, we report the , the and the CO depletion factor measured toward core H6, the CO West Peak, and the Narrow SiO Peak. The derived CO depletion factor is 5-12. In particular, toward core H6, this value is a factor of 2 higher than those reported in Paper II (). The CO depletion factors measured toward G035.39-00.33 are thus similar to those derived toward low-mass pre-stellar cores (e.g. Crapsi et al., 2005), and consistent with those recently estimated toward a sample of IRDCs (Fontani et al., 2012). This is expected to largely affect the deuterium chemistry, as found toward massive starless cores where the deuterium fractionation, D, is increased by a factor of 10 with respect to more evolved high-mass protostellar objects (see Fontani et al., 2011).

### 4.3 Sensitivity of the LVG results to Tkin

In Sections4.1 and 4.2, we have assumed that the kinetic temperature of the gas in G035.39-00.33 is T=15K. However, as measured from NH observations toward other IRDCs (see e.g. Pillai et al., 2006; Ragan et al., 2011), T could range from 11K to 18K. We evaluate the effects of T on our LVG study by considering a kinetic temperature of 2K with respect to T=15K. In TableLABEL:tab5, we compare the LVG results obtained for T=13K, 15K and 17K. The largest discrepancies between LVG runs are found for the H densities, which are higher by up to 50% for the case with T=13K and lower by up to 25% for T=17K. The derived CO column densities differ by 4-20%, while the excitation temperatures vary by less than 5%. The optical depths only show large discrepancies (by up to a factor of 1.8) for Filament 2 and T=13K due to the larger CO column density derived for this filament. In average, the gas mass of the filaments lie within 30% those calculated for T=15K, except for Filament 2 and T=13K for which the derived gas mass is a factor of 2 higher.

### 4.4 Effects of including the J=1→0 data in the LVG analysis

In this Section, we analyze in what extent our results from Section4.1 may change by considering the low-excitation =10 line data in the LVG analysis. As examples, we have used the CO line spectra shown in Figure3, which have been spatially smoothed to the angular resolution of 22