© ESO 2020

1 Introduction

The Aquila rift is part of a dark lane of cosmic dust flowing prominently through the central region of the galactic plane of the Milky Way, forming the Great Rift. The two known sites of star formation in the Aquila Rift cloud complex, namely the Serpens South (Bontemps et al. 2010) and the W 40 H II region (Smith et al. 1985), have become a hot spot for the study of star formation. Spitzer observations show that W 40 and the embedded cluster Serpens South are near to one another on the sky, such that the Serpens South is seemingly part of the more evolved W 40 region (Gutermuth et al. 2008). The distance to Serpens Main and W 40 was recently measured to be 436 pc, and the distance to Serpens South should be similar because the two sources are kinematically connected (Ortiz-León et al. 2017). Su et al. (2020) estimated a mass of ∽1.4 × 10⁵ M_⊙ for the W 40 giant molecular cloud, and determined a distance of ∽474 pc.

Recently, Könyves et al. (2015) presented the results of the Herschel Gould Belt survey (HGBS) observations in the Aquila molecular cloud AMC complex imaged with the SPIRE and PACS photometric cameras from 70 to 500 μm. These latter authors identified a complete sample of starless dense cores and embedded (Class 0–I) protostars in the AMC complex using the multi-scale, multi-wavelength source-extraction algorithm. In this study, we use the 70 and 250 μm data to describe the heating of the surrounding material and as an indicator of the evolutionary age of the core.

In this work, we encounter regions that are called photo-dissociation regions (PDRs) and regions where we suspect that selective dissociation also plays a role. We investigate the role of selective dissociation in the process of star formation by comparing the physical parameters of protostellar-prestellar cores and the distinct regions with the CO isotope distributions in PDRs. We seek to understand whether or not there is a close relationship between the evolutionary age of star formingregions and the effect of selective dissociation. A detailed description of how selective dissociation works is provided in Sect. 3.6. Breifly, as the star formation process progresses, far-ultraviolet photons start to regulate both the heating and the chemistry of the resulting PDR (Tielens & Hollenbach 1985). Selective dissociation of CO is an expected phenomenon in PDRs resulting from the UV radiation field (Glassgold et al. 1985; Yurimoto & Kuramoto 2004). In this process, UV radiation selectively dissociates less-abundant CO isotopologues more effectively than more-abundant ones owing to different levels of self-shielding (van Dishoeck & Black 1988; Liszt 2007; Shimajiri et al. 2014). As several regions have been identified as distinct star formation regions in the H₂ CO absorption map of the AMC (Komesh et al. 2019), here we compare the C¹⁸O distribution and the H₂CO absorption.

In the present paper, we show the results of the ¹²CO, ¹³CO, and C¹⁸O observations toward the W 40 and Serpens South regions of the Aquila Rift. In Sect. 2, we present the details of the observations. The results and discussions are described in Sect. 3. Finally, we present our conclusions in Sect. 4.

2 Archival data

The ¹²CO(1−0), ¹³CO (1−0), and C¹⁸O (1−0) data, simultaneously observed using the 13.7 m millimeter wave telescope of the Purple Mountain Observatory in Delingha, were taken from the Millimeter Wave Radio Astronomy Database¹. The central position of the on-the-fly (OTF) observing pattern is 18^h30^m03^s –2°02′40′′ (J2000). The half-power beam width (HPBW) of the observing system is ∽ 50′′, the velocity resolution is 0.17 km s⁻¹, and the system temperature ranged from 180 to 320 K. The ¹²CO(1−0), ¹³CO (1−0), and C ¹⁸O (1−0) data were smoothed to the same spatial resolution of 60′′ and the cell size is 30′′. The one-sigma noise levels of the ¹²CO, ¹³CO, and C¹⁸O data are 0.5, 0.35, and 0.35 K, respectively. Assuming a distance of 436 pc for the Aquila complex, the spatial scale of the maps is 0.124 pc arcmin⁻¹.

Infrared 70 and 250 μm images (André et al. 2010) were obtained from The Herschel Gould Belt Survey Archive².

3 Results and discussion

3.1 ¹²CO(1–0) emission line

The integrated intensity map of ¹²CO(1–0) over a velocity range 2 < V_LSR < 12 km s⁻¹ with signal-to-noise ratio (S/N) greater than three is presented in Fig. 1a. Enhanced core emission is present around W 40 on the north and west sides, which could result from heating by the H II region. There is weak emissions around Serpens South. The brightest position is at (RA,Dec) = (18^h31^m15^s, −2°08′ 13′′).

3.2 ¹³CO(1–0) emission line

The integrated intensity map of ¹³CO(1−0) over a velocity range 2 < V_LSR < 12 km s⁻¹ and a S/N greater than three is presented in Fig. 1b. Here, enhanced emission is also seen to the north and west of W 40. There are several elongated structures at Serpens South.

3.3 C¹⁸O(1–0) emission line

The integrated intensity map of C¹⁸O(1−0) over a velocity range 2 < V_LSR < 12 km s⁻¹ is presented in Fig. 1c with its S/N greater than three. Several integrated intensity concentrations are present in this map including both the W 40 H II region and Serpens South. The distribution of the C ¹⁸O (1−0) emission shows some similarity to the Herschel 250 μm large-scale (∽0.124 pc) image presented in Fig. 1d. Both the C¹⁸O and the Herschel data trace the same regions, which suggests that the C¹⁸O and the Herschel 250 μm emission arise from similar regions.

3.4 Column densities and abundance ratios

The excitation temperature, T_ex, was estimated from the peak brightness temperature of ¹²CO(1−0), by the following equation with the assumption that the ¹²CO(1−0) line is optically thick and taking into account a beam-filling factor of one (e.g. Pineda et al. 2010; Kong et al. 2015; Lin et al. 2016): $$T_{\text{ex}}=\text{frac{}hv\text{\_{^}12\text{CO}}}k\text{[}\ln \text{(}1+\text{frac{}hv\text{\_{^}12\text{CO}}/k\text{}}{T}_{\text{mb}{,}^{12}\text{CO}}+J_v(T_{\text{bg}})\text{)}\text{]}-1\text{Knn}=5.53{\left[\ln \left(1+\frac{5.53}{T_{\text{mb}{,}^{12}\text{CO}}+0.818}\right)\right]}^{-1}\text{K},$$(1)

where $T_{\text{mb}{,}^{12}\text{CO}}$ is the peak intensity of ¹²CO(1−0) in units of K, $J_v(T)=\frac{hv/k}{\exp (hv/(kT))-1}$ is the effective radiation temperature (Ulich & Haas 1976), and T_bg = 2.7 K is the temperature of cosmic microwave background radiation. The estimated excitation temperatures in the whole observed region range from 3.6 to 23.6 K, but these values are underestimates in locations where the ¹²CO emission is affected by self-absorption. We assume that the excitation temperatures (T_ex) of ¹³CO and C¹⁸O lines have the same value as that of the optically thick ¹²CO line. The optical depth and the column densities of ¹³CO(1−0) and C¹⁸O(1−0) were estimated using the following equations on the assumption that the cloud is in local thermodynamic equilibrium (LTE; e.g. Lada et al. 1994; Kawamura et al. 1998; Lin et al. 2016): $$\tau ({\text{C}}^{\text{18}}\text{O})=-\ln \left[1-\frac{T_{\text{mb},{\text{C}}^{18}\text{O}}}{5.27[J_1(T_{\text{ex}})-0.166]}\right],$$(2) $$\tau (\text{textrm{^}13CO\text{}})=-\ln \left[1-\frac{T_{\text{mb}{,}^{13}\text{CO}}}{5.29[J_2(T_{\text{ex}})-0.164]}\right],$$(3)

and $$N({\text{C}}^{18}\text{O})=2.42\times {10}^{14}\frac{\tau ({\text{C}}^{18}\text{O})\Delta V({\text{C}}^{18}\text{O})T_{\text{ex}}}{1-\exp (-5.27/T_{\text{ex}})},$$(4) $$N(\text{{^}13\text{CO}})=2.42\times {10}^{14}\text{frac{}\tau (\text{{^}13\text{CO}})\Delta V(\text{{^}13\text{CO}})T_{\text{ex}}\text{}}1-\exp (-5.29/T_{\text{ex}}),$$(5)

where J₁(T_ex) = 1∕[exp(5.27∕T_ex) − 1], J₂ (T_ex) = 1∕ [exp (5.29∕T_ex) − 1], and ΔV is the FWHM in km s⁻¹. The abundance ratio, $X{(}^{13}\text{CO})/X({\text{C}}^{18}\text{O})$, is equivalent to the $N{(}^{13}\text{CO})/N({\text{C}}^{18}\text{O})$ column density ratio.

In the regions where the ¹²CO emission is affected by self-absorption, the column densities of ¹³CO and C¹⁸O are effected by underestimates of T_ex from the ¹²CO data. This leads to underestimation of the column densities of ¹³CO and C¹⁸O in those areas. The resulting ranges of $N(\text{{^}13\text{CO}})$ and N(C¹⁸O) are 3.8 × 10¹⁴–5.5 × 10¹⁶ cm⁻² and 2 × 10¹⁴–3.4 × 10¹⁵, respectively, and the resulting range of the abundance ratio of R_13∕18 is 1.02–41.9. A map of the column density of C¹⁸O(1−0) is represented in Fig. 2.

The column density of C¹⁸O(1−0) versus the number of pixels with C¹⁸O(1−0) is displayed in the diagrams of Fig. 3 together with the observed column densities at the location of the prestellar and protostellar cores. The cores sample locations with increasing C¹⁸O column density confirming that star formation first happens in regions with the highest column densities. Most of the C ¹⁸O(1−0) detection points correspond to the column densities in the range 0.5 × 10¹⁵–1.6 × 10¹⁵ cm⁻² (see panel a). The prestellar and protostellar cores correlate well with the C¹⁸O column density. The majority of the prestellar cores column densities in the range of 0.5 × 10¹⁵–2 × 10¹⁵ cm⁻² while the locations of the protostellar cores coincide with the column densities in the range of 0.5 × 10¹⁵–2.8 × 10¹⁵ cm⁻².

Fig. 1 Aquila maps of the intensities of (a) 12CO (1−0), (b) 13CO (1−0), and (c) C 18O (1−0) integrated from 2 to 12 km s−1. White filled circles in the bottom-right corner of each panel illustrate the beam size of 60′′. (d) The Herschel 250 μm image (the beam size is 18.2′′) taken from André et al. (2010). The circle and star mark the locations of the W 40 H II region (radius ∽ 3′) and the Serpens South, respectively.

3.5 Far-infrared distribution

The peak flux density at the prestellar and protostellar cores at 70 and 250 μm is presented versus the column density of C¹⁸O(1−0) diagrams in Fig. 4. The 70 μm diagram (panel a) shows a clear separation indicated with a dotted line between the prestellar and protostellar core distributions; most of prestellar cores have a lower flux density while most of the protostellar cores have a higher flux that may increase slightly at higher column densities. However, excluding the uncertainty on the N(C¹⁸O) emission, the 250 μm distribution in panel b shows an increasing trend with column density suggesting that star formation is more advanced athigher column densities and that an increasing volume is affected by the ongoing star formation. Star formation processes are slower in regions of lower column density and more time is required to heat the surrounding environment. In addition, the number of protostellar (or prestellar) cores may be larger because of fragmentation which will accelerate the heating process. The number of cores with very high column density is much smaller than for low-column-density cores, which agrees with the histogram of the stellar core number versus the C¹⁸O column density in Fig. 3.

3.6 Selective photodissociation

A map of the abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ is presentedin Fig. 5. The contours show the value of $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ = 4. We selected nine unique regions (A–I) in the map where the abundance ratio has a lower value (A, B, C, E, F, and G), one region with a much higher value (region D), and two regions on the outskirts with medium values (H and I). The abundance ratio located in region D next to the W 40 H II region is as high as 42, which is significantly higher than the value of 5.5 seen in the Solar System (Anders & Grevesse 1989). Region D is located next to the W 40 (northwest side), region B is Serpens South, and region G was identified as a distinct star formation region by Komesh et al. (2019). The far-ultraviolet (FUV) emission with sufficient energy to photo-dissociate ¹²CO promptly becomes optically thick as it penetrates molecular clouds. On the contrary, C¹⁸O self-shielding is relatively less significant because of its low abundance and the shift of its absorption lines. Hence, this infers that the FUV emission with higher energy than the C¹⁸O dissociation level will penetrate deeper into a molecular cloud and will also increase the abundance ratio of ¹³CO and C¹⁸O, $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$, at the instance when C¹⁸O self-shielding is not yet dominant. When both self-shielding effects of ¹³CO and C¹⁸O become significant, the abundance ratio will decrease towards its intrinsic value, which is derived from ¹²C,¹³C, ¹⁶O, and ¹⁸C abundances (van Dishoeck & Black 1988; Liszt 2007; Shimajiri et al. 2014). We can therefore confirm that selective FUV photodissociation of C 18 O indeed occurs.

Figure 6 presents the averaged spectra of ¹²CO(1−0), ¹³CO(1−0), and C ¹⁸O(1−0) emission in the nine selected regions. The central component of the broader ¹²CO can clearly be seen to be depleted by self-absorption. However, the spectrum shapes of ¹³CO and C¹⁸O appear different from that of ¹²CO.

Fig. 2 Map of the column density of C18O(1− 0). The black stars and triangles present the locations of protostellar and prestellar cores, respectively. The coordinates of the protostellar and prestellar cores were taken from Könyves et al. (2015). The black circle marks the location of the W 40 H II region (radius ∽ 3′) and the black filled circle in the bottom-right corner illustrates the beam size of 60′′. The clippinglevel for the 13CO and C18O data corresponds to a signal-to-noise ratio greater than five. Gaussian fitting to each pixel was done.

Fig. 3 Histograms of the distributions of (a) the number of pixels with certain column density of C18O(1−0), (b) the number of prestellar cores with this density, and (c) the protostellar cores with this column density. The prestellar and protostellar sources clearly sample the larger C18O column densities.

3.7 Integrated properties of the distinct regions

The molecular hydrogen gas masses ($M_{{\text{H}}_2}$) of the selected regions A to I were derived using equations from Tan et al. (2013). In order to estimate the original mass of the selected regions, we fitted the profile of the ¹²CO emission line with a Gaussian using the line wings of the self-absorbed ¹²CO lines (see Fig. 7).

We compute the ¹²CO luminosity as follows: $$L_{\text{CO}}=I_{\text{avg}}\times N_{\text{pix}}\times 23.5\times {(D\times {\Delta }_{\text{pix}})}^2,$$(6)

where L_CO is the ¹²CO luminosity in K km s⁻¹ pc², I_avg is the average ¹²CO intensity (K km s⁻¹) obtained from the integrated intensity map on a main-beam temperature scale, N_pix is the number of pixels included, D is the distance to the sources in megaparsec, and Δ_pix is the pixel size in arcseconds. The mass of the molecular gas is computed using: $$M_{{\text{H}}_2}=1.6\times {10}^{-20}\times L_{\text{CO}}\times X_{\text{CO}}(M_{\odot }),$$(7)

where ${\text{X}}_{\text{CO}}=2\times {10}^{20}{(\text{K}\text{km}{\text{s}}^{-1})}^{-1}$ (Strong et al. 1988).

The average fluxes of the infrared 70 and 250 μm images of the selected regions (see Table 1) were obtained from the Herschel Gould Belt Survey Archive. The average 70 μm flux is higher in regions A, B, C, D, E, F, and G, with the highest flux being ∽ 2172 MJy sr⁻¹ in region D next to the W 40 HII region. However, the average 70 μm flux is significantly lower in regions H and I. This means that regions A, B, C, D, E, F, and G are enhanced, and that the star-forming processes therein are more active than those in regions H and I. The integrated properties of the distinct regions are summarised in Table 1. The columns have the following meaning: Col. 1: the distinct region, Cols. 2 and 3: the right ascension and declination (J2000) of the centre position, Col. 4: the radius of the region, Col. 5: the average flux of Herschel 70 μm image, Col. 6: the average flux of Herschel 250 μm image, Col. 7: the original mass based on the best Gaussian fitting, and Col. 8: the original luminosity of the ¹²CO based on the best Gaussian fitting.

Fig. 4 Column density of C18O vs. the peak flux densities of protostellar (red triangles) and prestellar (black triangles) cores at (a) 70 μm and (b) 250 μm selected from Könyves et al. (2015). The number of prestellar cores in panel a is less than the total number because some have no 70 μm flux. A clear separation is found between prestellar and protostellar cores in panel a (shown with a dotted line). Panel b: increasing trend of the 250 μm flux density with the C18O column density suggesting that star formation is more advanced at higher column densities and that an increasing volume is affected by the ongoing star formation.

Fig. 5 Map of the abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$. The contours show the value of $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ = 4. The letters A to I present the selected regions where the abundance ratio is lower (A, B, C, E, F, and G) and much higher (region D), and the outskirts (H and I). The black circle presents the location of the W 40 H II region (radius ∽ 3′) and the black filled circle in the bottom-right illustrates the beam size of 60′′. The clippinglevel for the 13CO and C18O data is the S/N greater than five. High abundance-ratio values are distributed only in region D and reach up to 42.

Fig. 6 Averaged spectra of 12CO(1−0) (red), 13CO(1−0) (green), and C18O(1−0) (blue) emission at the selected regions from Fig. 5. The name of the selected region is presented in the top-left corner of each panel.

Fig. 7 Examples of the 12CO self-absorption correction. The blue dashed line presents the best single Gaussian fitting for the original 12CO profile using the remaining wings of the emission line. The name of the selected region is presented in the top-left corner of each panel.

3.8 Correlating the infrared and photo-dissociation data

The heating of the interstellar dust by the star formation processes first results in 250 μm infrared emission and at a later stage produces 70 μm emission (e.g. Bendo et al. 2015). Therefore, the 70/250 μm ratio could be an indicator of the evolutionary age of the star formation process and the state of the interstellar dust. On the other hand, photo-dissociation is clearly a time-dependent effect resulting from the UV exposure of the molecular gas and the photo-dissociation rate also reflects the evolutionary age of the selected distinct regions.

The peak flux density at the prestellar and protostellar cores at a wavelength of 70 μm versus the column density of C¹⁸O(1−0) reveals a separationbetween the prestellar and protostellar core distributions (Fig. 4a). The variation of the 250 μm emission data suggests a flux density increase at higher C¹⁸O column densities, such that the more intense star formation is able to heat a larger volume of the surrounding dust, which is also time dependent (Fig. 4b). Figure 8 displays the column density of C¹⁸O versus the peak flux density ratio F_70μm∕F_250μm of protostellar and prestellar cores. Excluding some improperly distributed stellar cores, most evolved protostellar cores are in the upper part, and the youthfulprestellar cores are in the lower part in the diagram. However, the dividing line between the flux ratio decreases with an increasing C¹⁸O column density because at higher C¹⁸O columns the star formation has time and energy to heat larger volumes of dust. The flux ratio F_70μm∕F_250μm diagram confirms that the C¹⁸O column density is related to the evolutionary age of the cores.

The abundance ratio of $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ for the prestellar and protostellar locations plotted against the C¹⁸O column density shows a similar distribution for prestellar and protostellar cores, which indicates that the effects of photodissociation only depend on the presence of star formation at this C¹⁸O column density (Fig. 9). The $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ abundance ratio decreases with increasing C¹⁸O column density indicating an enhancement of C¹⁸O in the interstellar medium. The strong variation of the abundance ratio with the C¹⁸O column density shows that the more massive and fragmented star formation has a strong effect on the surrounding area.

The actual mass of the star formation region containing young stellar objects plays a critical role in distinguishing between evolutionary paths and their timescales. In order to depict the evolutionary path of star formation regions in the AMC, the original mass estimated from the reconstructed ¹²CO emission line in the nine selected regions is plotted against the 70 μm flux density in Fig. 10a. This diagram shows that the regions lie along a string of points indicating five stages of evolution. Region D, next to the W 40 HII, belongs to the oldest evolutionary stage with the highest amount of photo-dissociated mass (∽ 74 M_⊙), and with the highest 70 μm flux density. The regions B and E form the next oldest stage of evolution, where region B is the Serpens South region and region E is a filament located southeast of the W 40 HII. Region E has lost more mass to photo-dissociation than region B. Regions G, F, A, and C resemble regions of an earlier stage of evolution, where region C has lost a little more mass than the others because it is larger. The youngest star formation region H is just starting to show up in 70 μm images. Region I is the youngest region located on the outskirts of the cloud; it does not yet show any 70 μm flux and has the least estimated mass of all the selected regions.

As UV radiation selectively dissociates less-abundant CO isotopologues more effectively than more-abundant ones (van Dishoeck & Black 1988; Liszt 2007; Shimajiri et al. 2014) the ratio $X\text{\_{^}13\text{CO}}/X_{{\text{C}}^{18}\text{O}}$ is equivalent to the dissociation rate of the C 18O. A similar evolutionary sequence is found when plotting the ratio $X\text{\_{^}13\text{CO}}/X_{{\text{C}}^{18}\text{O}}$ against the flux ratio F_70μm∕F_250μm of the selected regions in Fig. 10b. However, the mid-range evolutionary regions cluster together in this case, possibly because of inaccuracies in estimating the abundance ratio. The two diagrams of Fig. 10 present the original mass, and the rate of photodissociation combined with the infrared properties are useful to determine the evolutionary age of the star-forming regions.

Fig. 8 Column density of C18O vs. the peak fluxdensity ratio of the bandwidth of 70 and 250 μm of the protostellar (red triangles) and prestellar (black triangles) cores selected from Könyves et al. (2015). The dotted line indicates the dividing line between prestellar and protostellar cores and shows the gradual change of the ratio.

Fig. 9 Column density of C18O vs. the abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ in the protostellar (red triangles) and prestellar (black triangles) cores.

3.9 Uncertainties on the abundance ratio X_¹³CO/X_C¹⁸O introduced by the excitation temperature and the beam-filling factor

C¹⁸O and ¹³CO beam-filling factors were assumed to be unity when estimating their column densities and optical depths in Sect. 3.4. Also, the excitation temperatures (T_ex) for all three lines C¹⁸O, ¹³CO, and ¹²CO were presumed to have the same values, as derived from the optically thick line ¹²CO.

Calculation of the beam-filling factor is obtained through Eq. (8): $$f=\frac{{\theta }_{\text{s}}^2}{{\theta }_{\text{s}}^2+{\theta }_{\text{beam}}^2},$$(8)

where θ_beam is the beam size and θ_s is source diameter. The ¹³CO and C¹⁸O data have an effective beam size of 60′′ corresponding to 0.124 pc at the distance of the AMC. C¹⁸O emission is deemed as a tracer of dense cores, filaments, and clumps. In comparison, the ¹³CO emission will additionally trace extended components which could be seen via integrated intensity maps (Shimajiri et al. 2014). The nearest low-mass star forming region observations toward the Taurus cloud traced via C¹⁸O have dense cores of 0.1 pc in diameter (Onishi et al. 1996). Moreover, the constant encounter of parsec-scale filaments with narrow widths of typically 0.1 pc within molecular clouds were discovered through Herschel micrometre emission observations (Arzoumanian et al. 2011; Palmeirim et al. 2013). This infers that traced ¹³CO and C¹⁸O sources will have dimensions of over 0.1 pc. Assuming θ_source > 0.1 pc and θ_beam = 0.124 pc, we anticipate the beam to exceed 0.6. The affects of the beam filling factor on the abundance ratios and column densities are summarised in Table 2. The column density values for both C¹⁸O and ¹³CO are higher with the assumption of ϕ = 0.6 compared to those when ϕ = 1 is assumed. Nevertheless, the beam filling factor corrections play a insignificant role in estimating $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$.

As ¹²CO emission is affected by self-absorption, C¹⁸O and ¹³CO column densities are affected by underestimates of T_ex from the ¹²CO data. The influence of uncertainties related to the excitation temperature on the derived physical properties is investigated assuming T_ex (C¹⁸O) = 20 K and $T_{\text{ex}}{(}^{13}\text{CO})$ = 30 K. This is further illustrated in Table 2. The column density values for both ¹³CO and C¹⁸O with the assumption of T_ex(C¹⁸O) = 20 K and $T_{\text{ex}}{(}^{13}\text{CO})$ = 30 K increase compared with those where $T_{\text{ex}}{(}^{13}\text{CO})$ = T_ex(C¹⁸O) = $T_{\text{ex}}{(}^{12}\text{CO})$. However, the range of $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ with T_ex(C¹⁸O) = 20 K and $T_{\text{ex}}{(}^{13}\text{CO})$ = 30 K is slightly narrower compared with those of $T_{\text{ex}}{(}^{13}\text{CO})$ = T_ex(C¹⁸O) = $T_{\text{ex}}{(}^{12}\text{CO})$. The higher abundance ratios ($X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}>10$) in all assumptions correspond to region D next to the W 40 HII.

When including uncertainties on excitation temperatures and beam filling factors of ¹³CO and C¹⁸O, we are convinced that the abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ is lower towards more actively star-forming regions in the AMC, with the exception of one region showing a particularly high abundance ratio (next to the W 40 HII).

3.10 Comparison with H₂CO absorption

As regions B, D, and G have been identified as distinct star formation regions in the H₂ CO absorption map of the AMC, a comparison may be made between the C¹⁸O distribution and the H₂CO absorption (Komesh et al. 2019). Figure 11 shows a map of the C ¹⁸O(1−0) integrated intensity superposed on the integrated absorption contours of H₂ CO. The C¹⁸O(1−0) and H₂ CO data were smoothed to the same effective resolution and cell size of 10′ and 2.5′, respectively. The outer edges of the C¹⁸O emission (∽0.7 K km s⁻¹) follow the lower contours of H₂CO (∽0.4 K km s⁻¹) and the contours encompass all identified star formation regions in the C¹⁸O data. The stronger C¹⁸O emission surrounding W 40 does not correspond to the H₂CO absorption, because the H₂CO absorption is related to the radio continuum of the H II region while the enhanced C¹⁸O emission results from heating by the H II region. The C¹⁸O emission map at Serpens South shows several elongated structures that only partially follow the H₂ CO absorption structure. On a large scale the H₂CO absorption structure is similar to the C¹⁸O(1−0) distribution but does not identify all active star formation regions.

4 Conclusion

Archival data of wide-field OTF observations of ¹²CO, ¹³CO, and C¹⁸O (J = 1–0) emission lines of the AMC were used to study star formation activity in the region and its influence on the surrounding areas. In the AMC, the distribution of protostellar and prestellar cores are a first indication of the locations of active star formation and their distribution is well correlated with the highest column densities within the structure of the extended C ¹⁸O(1−0) emission. This extended star formation structure is also found within the contours of the H₂ CO absorption against the continuum of the region.

The abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ in our observations confirms that selective FUV photodissociation of C¹⁸O indeed occurs. As photo-dissociation results from FUV exposure of the surrounding molecular gas, photo-dissociation is a time-dependent process that may serve as an indicator of the evolutionary age of star formation. This effect is confirmed by a strong reduction in the abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ with increasing C¹⁸O column density.

To evaluate how the beam filling factor affects the $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ abundance ratio, we consider the beam filling factor to exceed 0.6 for both C¹⁸O and ¹³CO gas. The abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ distribution in the AMC was found to be similar even after the consideration of uncertainties on the beam filling factor. The beam filling factor corrections play a insignificant role in estimating $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$.

As the ¹²CO emission is affected by self-absorption, C¹⁸O and ¹³CO column densities are effected by underestimates of T_ex (3.6–23.6 K)from the ¹²CO data. To study the affects of uncertainties related to excitation temperature measurements on derived physical properties,we used the assumption of T_ex(C¹⁸O) = 20 K and $T_{\text{ex}}{(}^{13}\text{CO})$ = 30 K. Even if we consider higher excitation temperatures for the ¹³CO and C¹⁸O lines, we come to the same conclusion, namely that with the exception of one region of high abundance ratio (next to the W 40 HII), the abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ is lower toward more actively star forming regions in the AMC.

The FUV radiation field originating at the location of massive and even fragmented star formation will also heat the surrounding molecular regions. This heating process will increasingly result in 250 μm FIR emission and also 70 μm emission after a certain evolutionary period. The 70/250 μm flux density ratio can therefore also serve as an evolutionary age indicator and this ratio is indeed found to vary with the C¹⁸O column density.

We tested these evolutionary indicators with a number of selected star-formation and non-star-formation regions for which we estimated the dissociation rate using the ratio $X\text{\_{^}13\text{CO}}/X_{{\text{C}}^{18}\text{O}}$. We find a clear sequence for these selected regions when correlating the 70 μm flux density with the estimated original mass of the regions. Similarly, we find a clear sequence when correlating the 70/250 μm flux density ratio with the estimated photo-dissociation rate. These observed parameters of the molecular medium surrounding the star formation provide a measure of the intensity of the star formation process as well as a measure of the evolutionary age of the region.

Fig. 10 (a) Mass-corrected self-absorption vs. 70 μm flux, and (b) the ratio $X\text{\_{^}13\text{CO}}/X_{{\text{C}}^{18}\text{O}}$, equivalent tothe dissociation rate of the C18O, vs. the flux ratio F70μm∕F250μm of the distinct regions. Selected regions are marked with the letters A to I. The average fluxes of the infrared 70 and 250 μm images of the distinct regions in both panels were obtained from the data of the Herschel Gould Belt Survey Archive.

Fig. 11 Map of the C18O(1−0) integrated intensity superposed on the contours of H2CO absorption toward the AMC. The C18O(1−0) and H2 CO data were smoothed to the same effective resolution and cell size of 10′ and 2.5′, respectively. Contour levels of the H2CO intensity map are −0.4 to − 1.8 in steps of −0.15 K km s−1. The white circle presents the location of the W 40 H II region (radius ∽3′) and the black circle in the bottom-right illustrates the resolution of 10′.

Acknowledgements

This work was sponsored by CAS-TWAS President’s Fellowship for International Doctoral Students, and The National Natural Science foundation of China under grants 11433008, 11973076, 11703074, 11703073 and 11603063. W.A.B. has been funded by Chinese Academy of Sciences President’s International Fellowship Initiative under grants 2021VMA0008 and 2019VMA0040. Collaboration between Z.R. and the main author was supported by the University of Malaya grant UMRG FG033-017AFR. This publication makes use of data products from the 13.7 m telescope of the Qinghai observation station of the Purple Mountain Observatory and the millimeter wave radio astronomy database, and the data from the Herschel Gould Belt survey (HGBS) project (http://gouldbelt-herschel.cea.fr). The HGBS is a Herschel Key Programme jointly carried out by SPIRE Specialist Astronomy Group 3 (SAG 3), scientists of several institutes in the PACS Consortium (CEA Saclay, INAF-IFSI Rome and INAF-Arcetri, KU Leuven, MPIA Heidelberg), and scientists of the Herschel Science Center (HSC).

References

All Tables

All Figures

Fig. 1 Aquila maps of the intensities of (a) 12CO (1−0), (b) 13CO (1−0), and (c) C 18O (1−0) integrated from 2 to 12 km s−1. White filled circles in the bottom-right corner of each panel illustrate the beam size of 60′′. (d) The Herschel 250 μm image (the beam size is 18.2′′) taken from André et al. (2010). The circle and star mark the locations of the W 40 H II region (radius ∽ 3′) and the Serpens South, respectively.

In the text

Fig. 2 Map of the column density of C18O(1− 0). The black stars and triangles present the locations of protostellar and prestellar cores, respectively. The coordinates of the protostellar and prestellar cores were taken from Könyves et al. (2015). The black circle marks the location of the W 40 H II region (radius ∽ 3′) and the black filled circle in the bottom-right corner illustrates the beam size of 60′′. The clippinglevel for the 13CO and C18O data corresponds to a signal-to-noise ratio greater than five. Gaussian fitting to each pixel was done.

In the text

	Fig. 3 Histograms of the distributions of (a) the number of pixels with certain column density of C18O(1−0), (b) the number of prestellar cores with this density, and (c) the protostellar cores with this column density. The prestellar and protostellar sources clearly sample the larger C18O column densities.
In the text

Fig. 4 Column density of C18O vs. the peak flux densities of protostellar (red triangles) and prestellar (black triangles) cores at (a) 70 μm and (b) 250 μm selected from Könyves et al. (2015). The number of prestellar cores in panel a is less than the total number because some have no 70 μm flux. A clear separation is found between prestellar and protostellar cores in panel a (shown with a dotted line). Panel b: increasing trend of the 250 μm flux density with the C18O column density suggesting that star formation is more advanced at higher column densities and that an increasing volume is affected by the ongoing star formation.

In the text

Fig. 5 Map of the abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$. The contours show the value of $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ = 4. The letters A to I present the selected regions where the abundance ratio is lower (A, B, C, E, F, and G) and much higher (region D), and the outskirts (H and I). The black circle presents the location of the W 40 H II region (radius ∽ 3′) and the black filled circle in the bottom-right illustrates the beam size of 60′′. The clippinglevel for the 13CO and C18O data is the S/N greater than five. High abundance-ratio values are distributed only in region D and reach up to 42.

In the text

	Fig. 6 Averaged spectra of 12CO(1−0) (red), 13CO(1−0) (green), and C18O(1−0) (blue) emission at the selected regions from Fig. 5. The name of the selected region is presented in the top-left corner of each panel.
In the text

	Fig. 7 Examples of the 12CO self-absorption correction. The blue dashed line presents the best single Gaussian fitting for the original 12CO profile using the remaining wings of the emission line. The name of the selected region is presented in the top-left corner of each panel.
In the text

	Fig. 8 Column density of C18O vs. the peak fluxdensity ratio of the bandwidth of 70 and 250 μm of the protostellar (red triangles) and prestellar (black triangles) cores selected from Könyves et al. (2015). The dotted line indicates the dividing line between prestellar and protostellar cores and shows the gradual change of the ratio.
In the text

	Fig. 9 Column density of C18O vs. the abundance ratio $X\text{\_{^}13\text{CO}}$/$X_{{\text{C}}^{18}\text{O}}$ in the protostellar (red triangles) and prestellar (black triangles) cores.
In the text

Fig. 10 (a) Mass-corrected self-absorption vs. 70 μm flux, and (b) the ratio $X\text{\_{^}13\text{CO}}/X_{{\text{C}}^{18}\text{O}}$, equivalent tothe dissociation rate of the C18O, vs. the flux ratio F70μm∕F250μm of the distinct regions. Selected regions are marked with the letters A to I. The average fluxes of the infrared 70 and 250 μm images of the distinct regions in both panels were obtained from the data of the Herschel Gould Belt Survey Archive.

In the text

Fig. 11 Map of the C18O(1−0) integrated intensity superposed on the contours of H2CO absorption toward the AMC. The C18O(1−0) and H2 CO data were smoothed to the same effective resolution and cell size of 10′ and 2.5′, respectively. Contour levels of the H2CO intensity map are −0.4 to − 1.8 in steps of −0.15 K km s−1. The white circle presents the location of the W 40 H II region (radius ∽3′) and the black circle in the bottom-right illustrates the resolution of 10′.

In the text