Nobeyama 45 m mapping observations toward Orion A. II. Classification of cloud structures and variation of the ¹³CO/C¹⁸O abundance ratio due to far-UV radiation

Abstract

1 Introduction

The process of star formation is deeply connected with the structures of giant molecular clouds (GMCs). GMCs are composed of hierarchical structures: small-scale dense cores are contained inside filaments that are enveloped in lower density gas (Rosolowsky et al. 2008). Over the wide scale of these structures, self-gravity plays an important role in leading star formation (Goodman et al. 2009). However, its role in individual star-forming regions remains to be elucidated partly because of a lack of sufficient observational data and the difficulty in the unbiased identification of cloud structures. In addition to self-gravity, stellar feedback such as protostellar H ii regions, outflows, and stellar radiation also significantly influence cloud structure and star formation therein.

The far-ultraviolet (FUV: 6 eV < hν < 13.6 eV) radiation from massive stars affects the thermal balance, structure, chemistry, and evolution of neutral interstellar medium (Hollenbach & Tielens 1999). Furthermore, the cloud surfaces tend to be photodissociated in the presence of FUV. In such photon-dominated regions (PDRs), rarer isotopologues of CO can be dissociated deeper inside the clouds due to the difference in self-shielding effects by up to 1–2 orders of magnitude in the photodissociation rate (van Dishoeck & Black 1988; Visser et al. 2009). Since the self-shielding is more effective for abundant species, C¹⁸O is dissociated more than ¹³CO and the abundance ratio of ¹³CO and C¹⁸O is likely to become larger under the influence of FUV radiation. This isotope-selective effect is called selective photodissociation. Thus, the spatial variation of the ¹³CO|$/$|C¹⁸O abundance ratio, |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$|⁠, is expected to reveal the area where the FUV radiation affects the cloud structure and properties. The effect of selective photodissociation is observed in several star-forming regions (Bally & Langer 1982; Lada et al. 1994; Kong et al. 2015; Lin et al. 2016; Paron et al. 2018). Shimajiri et al. (2014) revealed the distribution of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| toward the northern part of the Orion A GMC. They found that |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| values are higher than the solar system value throughout the region. In particular, the abundance ratio in the nearly edge-on PDRs are ∼3 times as large. The difference of the ratio is most likely due to the selective FUV photodissociation of C¹⁸O. Enhancement of the abundance of ¹³CO due to the chemical fractionation, ¹³C⁺ + ¹²CO → ¹³CO + ¹²C⁺ + 35K

(Langer et al. 1980), was also discussed by Shimajiri et al. (2014). However, in the Orion-A GMC, the temperature is high (T_ex = 28.4 ± 9.7 K) in regions with low column density and thus this isotopic exchange reaction would not be dominant.

The structures within Orion A have been recognized along with the progress of millimeter, submillimeter, and infrared observations. Orion molecular cloud 1 (OMC-1) was identified as a dense gas directly associated with Orion KL (Wilson et al. 1970; Zuckerman 1973; Liszt et al. 1974), then OMC-2 (Gatley et al. 1974) and OMC-3 (Kutner et al. 1976) were detected as subsequent condensations in CO emission located about |${15^{\prime}}$| and |${25^{\prime }}$| to the north of OMC-1. The ¹³CO (J = 1–0) observations by Bally et al. (1987) revealed that these clouds consist of the integral-shaped filament. After that, the SCUBA maps at 450 and 850 μm presented concentrations of submillimeter continuum emission in the southern part of the integral-shaped filament, which are now referred to as OMC-4 (Johnstone & Bally 1999) and OMC-5 (Johnstone & Bally 2006). In parallel with these observations, the distribution of molecular gas in Orion A GMC has been quite extensively studied in multiple rotational transition lines of CO and its isotopologues: ¹²CO (J = 1–0) (Maddalena et al. 1986; Wilson et al. 2005; Shimajiri et al. 2011; Nakamura et al. 2012), ¹²CO (J = 1–0) and ¹³CO (J = 1–0) (Ripple et al. 2013), ¹²CO (J = 2–1) and ¹³CO (J = 2–1) (Berné et al. 2014), ¹²CO (J = 2–1), ¹³CO (J = 2–1) and C¹⁸O(J = 2–1) (Nishimura et al. 2015), ¹²CO (J = 2–1) (Sakamoto et al. 1994), ¹²CO (J = 3–2) (Takahashi et al. 2008), ¹²CO (J = 4–3) (Ishii et al. 2016), ¹³CO (J = 1–0) (Nagahama et al. 1998), ¹³CO (J = 1–0) and C¹⁸O (J = 1–0) (Shimajiri et al. 2014), and ¹³CO (J = 3–2) and C¹⁸O (J = 3–2) (Buckle et al. 2012).

This paper investigates how the FUV radiation affects individual clouds in a GMC by combining the results of the identification of cloud structure and estimation of the abundances of CO isotopologues ¹³CO and C¹⁸O in three-dimensional space. The target is the nearest high-mass star-forming giant molecular cloud, Orion A (d = 414 ± 7 pc by Menten et al. 2007), which are newly observed over a 7 pc × 15 pc region. This wide-field observation allows us to examine the relation between cloud properties and the FUV radiation in an extensive range of field strength, i.e., from a strong FUV (G₀ ∼ 10⁴⁻⁵ in units of the local interstellar radiation field by Habing 1968) environment in the northern part to a weaker (G₀ ∼ 10¹) environment in the southern part of the GMC. Following a description of the observations and data sets analyzed here in section 2, we derive distributions of excitation temperature, optical depth, and column density and provide an overview of structures within Orion A in section 3. The three-dimensional distribution of the abundance ratio of ¹³CO and C¹⁸O is also estimated. In section 4, the details of the identification of molecular clouds and clustering analysis by SCIMES and the results are reported. In section 5, we discuss the interpretation of the results of the clustering analysis and scaling relations between physical properties such as size, line width, mass, and virial parameter. Finally, we examine the effect of the selective photodissociation of C¹⁸O for defined clouds.

The present observations of Orion A were made as a part of the Nobeyama Star Formation Legacy Project at the Nobeyama Radio Observatory (NRO) to observe nearby star-forming regions, Orion A, Aquila Rift, and M 17. The overview of the project will be presented in a separate paper (Nakamura et al. 2019a) and the detailed observational results for the individual regions are given in other articles (Orion A: Tanabe et al. 2018, Nakamura et al. 2019b; Aquila Rift: Shimoikura et al. 2019b, Kusune et al. 2019; M 17: Shimoikura et al. 2019a; other regions: Dobashi et al. 2019a, 2019b).

2 Observations and data

2.1 Observations with the Nobeyama 45 m radio telescope

We carried out observations in the emission lines of ¹²CO (J = 1–0), ¹³ CO (J = 1–0), and C¹⁸O (J = 1–0) toward the Orion A GMC using the 45 m radio telescope of the NRO. The |${2{^{\circ}_{.}}0} \times {1{^{\circ}_{.}}5}$| region in Orion A was simultaneously mapped in ¹²CO (J = 1–0) and ¹³ CO (J = 1–0) in 2015 May and the period from 2015 December to 2016 May. The observations in C¹⁸O (J = 1–0) were done with the same observing method in the period from 2016 December to 2017 March. The telescope has a beam size of |${14{^{\prime\prime}_{.}}1}$| (half-power beamwidth) at 115 GHz. We used a new four-beam receiver, FOREST, which is a dual-polarization sideband-separating SIS receiver (Minamidani et al. 2016). FOREST has 16 intermediate frequency (IF) outputs in total; eight IFs in the upper-sideband and the other eight IFs in the lower-sideband were used. The beam separation of FOREST is |${51{^{\prime\prime}_{.}}7}$| on the sky. As the receiver backend, we used a digital spectrometer based on an FX-type correlator, SAM45, that has 16 sets of 4096-channel arrays. In these observations, the total bandwidth and frequency resolution of all spectrometer arrays were set to 62.5 MHz and 15.26 kHz, respectively, which correspond to 163 km s⁻¹ and 0.04 km s⁻¹ at 115 GHz. The observed region was covered by a combination of small observation boxes with a size of |${10^{\prime }} \times {10^{\prime }}$|⁠. The on-the-fly (OTF) technique (Sawada et al. 2008) was adopted to map each observation box. Scans of the OTF observations are separated by |${5{^{\prime\prime}_{.}}17}$|⁠, so that individual scans by the four beams of FOREST are overlapped.

As an “off” position, we used an emission-free area at (⁠|$\alpha _{\mathrm{J2000.0}}, \delta _{\mathrm{J2000.0}}) = ({5^{\rm h}29^{\rm m}00{^{\rm s}_{.}}0}, {-5^{\circ}25^{\prime }30{^{\prime\prime}_{.}}0}$|⁠) that is |${\sim } {2^{\circ}}$| away from the mapping area. The typical system noise temperature was in the range from 350 K to 400 K for ¹²CO (J = 1–0) and from 150 K to 200 K for ¹³CO (J = 1–0) and C¹⁸O (J = 1–0) in the single sideband mode at the observed elevation |$\mbox{El}={30^{\circ}}\!-\!{50^{\circ}}$|⁠. The temperature scale was determined by the chopper-wheel method. The telescope pointing was checked every 1 hour by observing the SiO maser line from Orion KL (⁠|$\alpha _{\mathrm{J2000.0}}, \delta _{\mathrm{J2000.0}} = {5^{\rm h}35^{\rm m}14{^{\rm s}_{.}}5}, {-5^{\circ}22^{\prime }30{^{\prime\prime}_{.}}4}$|⁠). The pointing accuracy was better than ∼5″ throughout the observations. The parameters of observations are summarized in table 1. In order to minimize the scanning effects, the data with orthogonal scanning directions along the right ascension and declination axes were combined into a single map. We adopted a spheroidal function as a gridding convolution function to calculate the intensity at each grid point of the final cube data with a spatial grid size of |${7{^{\prime\prime}_{.}}5}$|⁠. The final effective angular resolutions are |${21{^{\prime\prime}_{.}}6}$| for ¹²CO (J = 1–0) and |${22{^{\prime\prime}_{.}}0}$| for ¹³CO (J = 1–0) and C¹⁸O (J = 1–0), respectively. The spheroidal function used in the NRO reduction software is explained by Sawada et al. (2008) and the function itself is described by Schwab (1984) in detail. We applied the parameters m = 6 and α = 1, which define the shape of the function. The intensity scale of the data was calibrated by comparing with the previous survey data taken by the BEARS receiver (Shimajiri et al. 2011, 2014; Nakamura et al. 2012), which was already converted to T_mb, the brightness temperature scale corrected for the main beam efficiency. We determine a scale factor for the data of each observation box and spectrometer array. We produced the integrated intensity maps of the FOREST and BEARS data after matching the grid of the FOREST data to that of the BEARS data. We then defined the scale factor as the ratio of the mean integrated intensities of the FOREST and BEARS maps. The scale factors of the arrays range between 2.0–2.6 for ¹²CO (J = 1–0) and between 2.7–3.2 for both ¹³CO (J = 1–0) and C¹⁸O (J = 1–0) . The velocity resolutions of the final datasets after merging the FOREST and BEARS data are 0.198 km s⁻¹ for the ¹²CO (J = 1–0) data, and 0.220 km s⁻¹ for the ¹³CO (J = 1–0) and C¹⁸O (J = 1–0) data. The noise levels were ΔT_mb = 0.48 ± 0.08 K for ¹²CO data, ΔT_mb = 0.18 ± 0.04 K for ¹³CO data, and ΔT_mb = 0.24 ± 0.03 K for C¹⁸O data. See Nakamura et al. (2019) for more details.

2.2 Dust continuum data

In order to examine relations among cloud properties and to probe into the environmental effects in Orion A, we compare the dataset of CO lines with the dust continuum observations from the Herschel Gould Belt Survey (André et al. 2010) and the Planck satellite (Planck Collaboration et al. 2011). Based on the map of the optical depth at |$850\, \mu$|m and the dust temperature derived by fitting the spectral energy distribution (Lombardi et al. 2014), we converted τ_850μm to visual extinction (A_V) using A_V = A_K/0.112 (Rieke & Lebofsky 1985) and A_K = γ_Orion Aτ_850μm + δ_Orion A, where γ_Orion A and δ_Orion A are estimated to be 2640 mag and 0.012 mag, respectively. The photometric data at |$70\, \mu$|m taken by PACS on Herschel is also taken from the science archive (obsid: 1342218967). The pixel scale of the original data is |${3{^{\prime\prime}_{.}}2}$|⁠. The bandwidth of the 70 μm band is |$\Delta \lambda = 10.6\, \mu$|m. The map of the FUV radiation field G₀ can be estimated by following equations (9) and (10) in Shimajiri et al. (2017). Note that we use only the 70 μm map to estimate G₀ because the 100 μm map is currently not available.

3 Results

3.1 Excitation temperature, optical depth, and column density

Fig. 1.

Maps of (a) the excitation temperature derived from the peak intensity of ¹²CO (J = 1–0), (b) the optical depth and (c) the column density of ¹³CO (J = 1–0), (d) the optical depth and (e) the column density of C¹⁸O(J = 1–0), and (f) the ratio of the fractional abundances of ¹³CO and C¹⁸O, |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$|⁠. (Color online)

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Figures 1b–1e show spatial distributions of |$\tau _{^{13}\mathrm{CO}}(\alpha , \delta )$|⁠, |$N_{^{13}\mathrm{CO}}(\alpha , \delta )$|⁠, |$\tau _{\mathrm{C^{18}O}}(\alpha , \delta )$|⁠, and |$N_{\mathrm{C^{18}O}}(\alpha , \delta )$|⁠. The mean and maximum values of optical depths and the column densities are summarized in table 2. The distributions of the optical depth and column density of ¹³CO and C¹⁸O are similar to each other. The values of the optical depths are high in the northern edge of OMC-3, OMC-4/5, and L1641-N regions in both emission lines. The optical depth of ¹³CO integrated along the velocity axis exceeds 1.0 in these regions, however the mean value of the optical depth per velocity channel is 0.21 ± 0.18, which means that emission of ¹³CO (J = 1–0) can be assumed to be optically thin in the position–position–velocity space. The distributions of the column density show that ¹³CO and C¹⁸O are highly concentrated in the integral-shaped filament and L1641-N, with |$N_{^{13}\mathrm{CO}}(\alpha , \delta ) \gtrsim 5 \times 10^{16}\:$|cm⁻² and |$N_{\mathrm{C}^{18}\mathrm{O}}(\alpha , \delta ) \gtrsim 3 \times 10^{15}\:$|cm⁻². These distributions also clearly exhibit that the dense components can be identified as sub-filamentary structures in the integral-shaped filament. As revealed by previous ¹³CO maps over Orion A (e.g., Bally et al. 1987; Castets et al. 1990; Nagahama et al. 1998; Berné et al. 2014), a number of clumpy and filamentary structures are seen in the distribution of |$N_{^{13}\mathrm{CO}}(\alpha , \delta )$|⁠. In the northern part of Orion A, these condensations would be separated into structures associated with the integral-shaped filament and others that are located in the eastern or western sides of the filament such as the DLSF and the bending structure (Shimajiri et al. 2011). In contrast, the structures of condensation in the southern part of the map are not elongated compared with filamentary structures in the northern part of Orion A. The integral-shaped filament extending from OMC-4/5 is connected to a cloud structure at |$\delta _\mathrm{J2000.0} = {-6^{\circ}12^{\prime }}$|⁠. The L1641-N cluster is located at the position of (α_J2000.0, δ_J2000.0) = (⁠|${5^{\rm h}36^{\rm m}18{^{\rm s}}}$|⁠, |${-6^{\circ}21^{\prime }48^{\prime \prime }}$|⁠) (Nakamura et al. 2012) and is contained in an extended cloud between |$\delta _\mathrm{J2000.0}= {-6^{\circ}20^{\prime }}$| and |${-6^{\circ}30^{\prime }}$|⁠. Further south, there is a cloud associated with V380 Ori at (α_J2000.0, δ_J2000.0) = (⁠|${5^{\rm h}36^{\rm m}25{^{\rm s}_{.}}43}$|⁠, |${-6^{\circ}42^{\prime }57{^{\prime\prime}_{.}}7}$|⁠). This cloud has almost uniform values of |$N_{^{13}\mathrm{CO}}(\alpha , \delta ) \lesssim 2 \times 10^{16}\:$|cm⁻².

3.2 Abundance ratio of ¹³CO and C¹⁸O

Fig. 2.

(a) Correlation between |$N_{^{13}\mathrm{CO}}$| and |$N_{\mathrm{C^{18}O}}$| over the mapped area, and (b) relation between |$N_{\mathrm{C}^{18}\mathrm{O}}$| and |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| over the mapped area. The solid and dashed lines indicate |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}} = 5.5$| and 9.31.

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4 Identification of molecular clouds

4.1 Clustering analysis by SCIMES

We identify internal cloud structures that compose Orion A. Colombo et al. (2015) designed SCIMES (Spectral Clustering for Interstellar Molecular Emission Segmentation) for the analysis of cloud structures based on graph theory and cluster analysis. SCIMES offers a novel and robust approach to finding discrete regions with similar emission properties using the hierarchical structure of molecular gas extracted by dendrogram (Rosolowsky et al. 2008). ¹³CO is an appropriate tracer to analyze internal structures through entire molecular clouds. ¹²CO is optically thick and is a good probe to estimate the kinematic temperature near the surface of the cloud. As we derived in section 3, the isotopolog ¹³CO is optically thin in most directions and its emission is a probe of the column density. It is demonstrated that the integrated intensity of the ¹³CO emission shows a good correlation with A_V (Nakamura et al. 2017). The emission of C¹⁸O is also optically thin and therefore traces the internal structure of the molecular cloud. However, it is difficult to identify extended emission associated molecular clouds due to weak emission as C¹⁸O is less abundant compared with ¹³CO.

Here we apply SCIMES to the three-dimensional data cube of the column density of ¹³CO (J = 1–0) that would trace physical structures of the Orion A GMC in position–position–velocity space. In order to reduce computational complexity, the data is binned by 3 pixels in spatial directions before the analysis, and thus the size of a pixel is equivalent to |${22{^{\prime\prime}_{.}}5}$|⁠. However, this is still comparable with the effective angular resolution of the original dataset and the information of spatial structures should not be lost. We did not apply binning to the velocity direction to detect cloud structures that have velocity dispersions similar to the velocity resolution of 0.22 km s⁻¹. There are three parameters to input to SCIMES: min_value, min_delta, and min_npix. min_value is the threshold of the intensity that the dendrogram uses for analyzing. A single local maximum that exceeds min_value is labeled as a leaf. min_delta represents the minimum height of a local maximum measured from a nearby local minimum. Only local maximums higher than min_delta are determined as independent leaves and these form branches with their neighbors. If the height of a local maximum is less than min_delta, it just becomes a part of another leaf. This parameter prevents identifying a local peak produced by the noise. Both min_value and min_delta are usually given in units of σ_rms, which corresponds to the noise level of the dataset. min_npix is the minimum volume for a leaf in the position–position–velocity space that is specified by the number of pixels. Using the result of identification of the hierarchical structure by the dendrogram, SCIMES applies a clustering analysis to find discrete regions with similar emission properties based on graph theory. In this paper, we refer to the identified structure of the column density of ¹³CO by SCIMES as a “cloud”.

We adopt min_value = 3σ_rms, min_delta = 3σ_rms, and min_npix = 8 pixel with σ_rms = 5.61 × 10¹³ cm⁻². The value of σ_rms corresponds to the rms noise of 0.18 K in T_mb when we adopt the average excitation temperature of T_ex = 23.7 K and the dataset achieves this noise level for most of inner parts of the mapped area (Nakamura et al. 2019a). The distribution of the rms noise is non-uniform over the observed area. The value of σ_rms was chosen to be suitable for detecting faint structures in the region that has relatively low rms noise, but the dendrogram can wrongly identify structures in the region that has higher rms noise. We evaluated the local maximum of each structure with the local rms after the identification by SCIMES and filtered it out from the catalog of clouds if the signal-to-noise ratio was less than 3. The structures that have a peak on the map edge were also removed from the catalog as they would be artificial. We choose min_npix so that identified structures contain more than 2 pixels in average along each axis, which are equivalent to |${45{^{\prime\prime}_{.}}0}$| in spatial scale and 0.44 km s⁻¹ in velocity. The “volume” option is selected for the analysis.

4.2 Cloud identification

Figure 3 shows the spatial distribution of the final result of the identification of clouds by SCIMES with filtering. SCIMES has identified 78 clouds including well-known structures such as OMC-1 (cloud #5 in figure 3), OMC-2/3 (#4), OMC-4 (#10), OMC-5 (#14), NGC 1977 (#6), L1641-N (#16), and the DLSF (#63) as summarized in table 3. These famous clouds are naturally identified in our analysis without any fine tuning of the input parameters. All clouds contain at least 2 pixels along individual axes of the data cube. The radius of each cloud is calculated by |$R = 1.91 \sqrt{R_{\mathrm{max}} R_{\mathrm{min}}}$| as defined by Rosolowsky et al. (2008). It is expected that a typical concentration of emission from the cloud is included within an equivalent spherical cloud that has a radius of R. The rms sizes of the region, R_max and R_min, are estimated from the intensity-weighted second moments along the two spatial dimensions using all pixels within the isosurface of the identified cloud. Most of the spatially larger clouds are located in the integral-shaped filament or the L1641-N region. These clouds in the integral-shaped filament are elongated along the north–south direction. In contrast, clouds in the L1641-N region tend to show elongated shapes in the east–west direction and to overlap each other.

Fig. 3.

Result of the identification of clouds in Orion A by SCIMES. The map of the column density of ¹³CO is shown in grayscale. The numbers on the clouds show the identification number of the individual clouds in this analysis. (Color online)

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The other clouds are seen as emission extending to the east from Orion KL (⁠|$\alpha _{\mathrm{J2000.0}}, \delta _{\mathrm{J2000.0}} = {5^{\rm h}35^{\rm m}14{^{\rm s}_{.}}5},\ {-5^{\circ}22^{\prime }30{^{\prime\prime}_{.}}4}$|⁠), diffuse emission at the west of the integral-shaped filament, and small structures near the edge of the map. The clouds in diffuse emission at the west of the integral-shaped filament form a filamentary structure that connects with the northern end of the integral-shaped filament and the bending structure in the west of OMC-4. Figure 4a shows the distribution of clouds in the position–velocity diagram along the direction of right ascension with the column density map of ¹³CO. A number of clouds are overlapping each other in the diagram. This indicates that clouds in the same declination have similar systemic velocity regardless of its position in right ascension. The global velocity gradient of the emission in the integral-shaped filament (Bally et al. 1987) is clearly traced by clouds from the north (V_LSR ∼ 14 km s⁻¹) to the south (∼8 km s⁻¹) of the filament. The clouds in the filamentary structure in the west of the integral-shaped filament also show a gradient in velocity. The largest velocity dispersion of a cloud is at OMC-1 that ranges from 4.2 to 11.0 km s⁻¹. The most blueshifted velocity is seen at |$\delta _{\mathrm{J2000.0}} = {-5^{\circ}24^{\prime }14{^{\prime\prime}_{.}}3}$| in figure 4a. This blueshifted component of cloud #5 traces a V-shaped profile in the position–velocity diagram that may correspond to the accelerated inflow of materials towards the Orion Nebula Cluster (ONC) from N₂H⁺(1–0) observations (Hacar et al. 2017). The clouds extending to the east from Orion KL shows the velocity between 9 and 10 km s⁻¹, which is almost same with the systemic velocity of the cloud in OMC-1. Clouds in OMC-5 and L1641-N regions have a unity velocity of ∼8 km s⁻¹ with the dispersion of ∼2.5 km s⁻¹. We note that the velocities of diffuse clouds near the edge of the map are blueshifted from the main structure of Orion A. These clouds are distributed from |$\delta _{\mathrm{J2000.0}} ={-5^{\circ}20^{\prime }}$| to |${-6^{\circ}50^{\prime }}$| with a system velocity of 7 km s⁻¹ (Sakamoto et al. 1997).

Fig. 4.

Distribution of the identified clouds in the position–velocity diagram along the direction of right ascension. The clouds are overlaid with maps of (a) the column density of ¹³CO and (b) the abundance ratio of ¹³CO and C¹⁸O. The clouds are outlined with a color that shows the velocity of the center of the cloud in V_LSR. (Color online)

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4.3 Classification of cloud structures in Orion A

The dendrogram of the analysis by SCIMES is shown in figure 5. The color of each region in the dendrogram corresponds to the velocity of the cloud. The leaves with S/N < 3 are shown in black and not regarded as clouds in this paper. The dendrogram represents the hierarchical structures in the identified clouds in Orion A and the identified clouds can be categorized into three groups based on segregation in the dendrogram. The first group contains in clouds that are known as OMC-1–5 and NGC 1977 in the integral-shaped filament (e.g., O’Dell et al. 2008). These clouds dominate the column density of ¹³CO in Orion A as we see in figure 1c. The group contains several small clouds in the outer part (e.g., clouds #8 and #12) and the northern end (e.g., clouds #6, #9, and #13) of integrated shaped filament. A small cloud, cloud #11, is located between OMC-4 and OMC-5 and also belongs to this group. Thus the integral-shaped filament and clouds in the filament are naturally separated from other parts of Orion A by SCIMES, although OMC-2 and OMC-3 are identified as a single cloud in this analysis. The length of a leaf indicates the range of the column density within a cloud. OMC-1, OMC-2/3, and OMC-4 consist of relatively long leaves compared with other clouds in this group. This demonstrates that these clouds have a high contrast in column density within the clouds.

Fig. 5.

Dendrogram of the identified clouds in Orion A. Each region outlines structures belonging to an identified cloud with a color corresponding to the velocity of a cloud. The identification numbers of structures in SCIMES are used for unnamed clouds. (Color online)

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The second group includes the majority of clouds in the remaining part of Orion A, such as the southern regions of Orion A, the extended structure to the east of Ori-KL, and the filamentary structure in the west of the integral-shaped filament. Clouds #16 and #17 appear on the right-hand side of this group in the dendrogram. In figure 3, cloud #16 is the molecular cloud associated with the L1641-N cluster. Cloud #17 is located at the southern end of the integral-shaped filament between OMC-5 and L1641-N. Interestingly, the M 43 shell shows up as an independent leaf in this group. Several sub-groups can be seen in the dendrogram of the second group. The clouds in the filamentary structure in the west of the integral-shaped filament (e.g., clouds #20, #24, #32, #48, #49, and #53) tend to be located in the middle of the group in figure 5. Cloud #32 is known as the “bending structure” (Shimajiri et al. 2011). In contrast, the leaves of clouds extending to the east of Ori-KL are distributed over the group. However, some clouds in this region make a cluster on the left-hand side of the dendrogram of this group.

The third group consists of the DLSF and clouds associated with diffuse emissions in the outer part of Orion A. The DLSF is the most prominent structure in this group and has the largest dynamic range of the column density among all the identified clouds in Orion A, which varies from |$\Delta N_{^{13}\mathrm{CO}} = 1.0 \times 10^{15}\:$|cm⁻² to 2.0 × 10¹⁶ cm⁻² with three peaks within the cloud. The second major cloud in this group, cloud #66, is located at the northeast of the DLSF. Most of the blueshifted clouds in figure 3b can be found in this group.

5 Discussion

5.1 Origins of clouds isolated in the dendrogram

The reason for the isolation of the DLSF from other clouds could be related to the origin of this structure. The DLSF is thought to be formed as the result of the interaction between the expansion of the H ii region in the ONC and the molecular cloud (Loren 1979; Sugitani et al. 1986; Berné et al. 2014). The interaction can cause separation in both spatial and velocity domains. This is consistent with the DLSF having a large velocity gradient from the north to south (Shimajiri et al. 2011; Kong et al. 2018). A similar situation can happen for the M 43 shell. This is also known as the northern ionization front (Berné et al. 2014) and could be the result of the H ii region in the ONC interacting with a foreground molecular cloud. In addition to DLSF and the M 43 shell, an expanding shell is recently identified in the northern edge of the DLSF using ¹³CO data (Shell 10 in Feddersen et al. 2018). It is clearly seen as an isolated cloud, cloud #30, with a C-shaped structure at 11.3 km s⁻¹. This distinct feature supports the shell having a different driving source, which is most likely to be stellar winds from T Ori as suggested by Feddersen et al. (2018). Thus, molecular clouds interacted with external motion would appear as isolated leaves of the dendrogram due to their prominent feature in the velocity space.

5.2 Relations between physical properties of the identified clouds

The relation between the line width and the radius of the cloud is widely investigated to analyze the internal motion of clouds dominated by turbulence. Figure 6a presents the FWHM linewidth–radius relation for the identified clouds. We fitted a power law to clouds in each group. For reference, we plot relations derived by Larson (1981) and Heyer and Brunt (2004) after modifications on the line width and the radius to make them consistent with the definition used here according to Maruta et al. (2010). The best-fitting lines for groups 1 and 2 are estimated to be ΔV = (2.31 ± 1.40)R^{0.70 ± 0.21} and (1.51 ± 1.21)R^{0.46 ± 0.12}, respectively. The line for group 1 has a similar power index derived by Heyer and Brunt (2004) but the coefficient is larger by a factor of 2. The clouds in group 2 follow Larson’s relation well. No significant correlation is found for the clouds in group 3. The almost independent relation for group 3 suggests that the internal motions of the clouds in this group are comparable to the inter-cloud motions as shown for ρ Oph cores (Maruta et al. 2010). All the molecular clouds discussed in the previous section (DLSF, M 43 shell, and cloud #30) have line widths larger than 1 km s⁻¹. The interaction with external motion would highly enhance turbulence in these clouds.

Fig. 6.

Physical properties of the identified clouds by groups. (a) FMHW linewidth–radius relation, (b) mass–radius relation, and (c) virial parameter–mass relation. In panels (a) and (b), red, green, and blue solid lines indicate fitting lines for clouds in groups 1, 2, and, 3 respectively. Dashed and dot–dashed lines in panel (a) represent relations derived by Larson (1981) and Heyer and Brunt (2004). Dashed and dot–dashed lines in panel (c) show α_vir = 2 and a fitted line decreasing with M^−2/3, respectively. (Color online)

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The mass–radius relation is plotted in figure 6b. For a certain radius, the mass of a cloud becomes less in the order of groups 1, 2, and 3. In other words, the density of the gas is highest for the clouds in the northern part, followed by those in the southern and outer parts of Orion A in this order. The differences by group clearly appear in the virial parameter–mass relation shown in figure 6c. For α_vir < 2, the cloud can be self-gravitating in the absence of other forces (Rosolowsky et al. 2008). All the clouds in group 1 show virial parameters of less than 2 and it is suggested that these clouds are self-gravitating. The virial parameters for group 3 tend to decrease with M^−2/3, which is pointed out by Bertoldi and McKee (1992) for pressure-confined clumps. For group 2, the clouds show features of both groups 1 and 3. 41 out of 47 clouds have α_vir < 2 and clouds tend to follow the virial parameter–mass relation with M^−2/3 as clouds in group 3.

5.3 Abundance ratio of ¹³CO to C¹⁸O and FUV radiation

The abundance ratio of ¹³CO and C¹⁸O, |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$|⁠, is one of the crucial parameters that characterizes molecular clouds and their environment. We overlaid the identified clouds on maps of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| in figure 7a. The clouds are outlined with a color that shows the median of the abundance ratio. Each median value of the cloud reported here is computed with pixels that have a signal-to-noise ratio larger than 5.0 within the identified cloud. As we see in subsection 3.2, the values of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| are significantly different by clouds. In clouds that correspond with OMC-1, OMC-2/3, OMC-4, OMC-5, and L1641-N, the median values of the |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| are 11.9 ± 2.1, 11.0 ± 2.8, 9.2 ± 2.3, 7.6 ± 1.6, and 7.7 ± 1.8, respectively. The DLSF shows a high abundance ratio of 13.2 ± 2.9, though the data do not fully cover the entire distribution of the cloud due to weak C¹⁸O(J = 1–0) emission. The median of the abundance ratio of each cloud ranges from 5.6 to 17.4. The highest ratio of 17.4 ± 1.9 is measured toward cloud #30, which is the expanding shell (Shell 10) in Feddersen et al. (2018). We produced the position–velocity diagram of the abundance ratio by integrating |$\Delta X_{^{13}\mathrm{CO}}(\alpha , \delta , V)/\Delta X_{\mathrm{C}^{18}\mathrm{O}} (\alpha , \delta , V)$| along right ascension (see figure 4b). In the southern part of Orion A (⁠|$\delta \lt {-5^{\circ}40^{\prime }}$|⁠), the velocity component between 8.0 and 10.0 km s⁻¹ shows high values of the ratio. In contrast, the ratio is ∼7 on average for the blueshifted component of the gas. However, it is still high compared to the typical value of 5.5 in the solar system (Wilson & Matteucci 1992).

Fig. 7.

Distribution of the identified clouds overlaid with maps of (a) |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$|⁠, (b) A_V, and (c) G₀. The clouds are outlined with a color that shows the velocity of the center of the cloud in panel (a) and |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| in panels (b) and (c). (Color online)

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We should note that the distribution of the ratio has a large deviation even within a cloud. Figure 8 represents the distribution of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| toward the identified clouds OMC-2/3, OMC-4, OMC-5, and L1641-N regions in the spatial maps and the position–velocity diagrams. In these regions, the ratio is high along the edge of the cloud clearly and it decreases in the inner parts of the clouds. This implies that the FUV field effects at least on a scale of individual cloud structures (∼ 0.3 pc) outlined with the column density of ¹³CO. The northern part of OMC-2/3 shows high values in both of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| and |$\Delta X_{^{13}\mathrm{CO}}/\Delta X_{\mathrm{C}^{18}\mathrm{O}}$| (see subsection 3.2). This area also presents a high CO (J = 4–3) to CO (J = 1–0) ratio that may be caused by interaction with OB stars or accumulation of diffuse CO components (Shimajiri et al. 2011; Ishii et al. 2016). The abundance ratio also tends to be high on the edge of clouds in the position–velocity diagrams, as shown in figure 8. For example, the ratio exceeds 15 on the northern edge of OMC-2/3 at |$(\delta _{\mathrm{J2000.0}}, V_{\mathrm{LSR}}) = ({-4^{\circ}54^{\prime }22^{\prime \prime }}$|⁠, 12.4 km s⁻¹), the northeastern edge of OMC-4 at |$({-5^{\circ}32^{\prime }}$|⁠, 5.2 km s⁻¹), and redshift (V_LSR = 8–10 km s⁻¹) components of OMC-5 and L1641-N.

Fig. 8.

Distribution of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| within the identified clouds toward (a) OMC-2/3, (b) OMC-4, (c) OMC-5, and (d) L1641-N. The spatial map and the position–velocity diagram are the same as shown in figure 1f and figure 4b, but are enlarged to the clouds that are outlined by blue lines. (Color online)

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These variations of the abundance ratio by clouds and within a cloud support the relation between the chemical difference and the PDR led by the selective photodissociation of C¹⁸O. Figures 7b and 7c show the clouds overlaid with the maps of A_V and the intensity of the FUV radiation field G₀ estimated from infrared continuum data as described in subsection 2.2. We derived properties of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$|⁠, A_V, and G₀ for the individual clouds. Figures 9a and 9b represent correlations of |$N_{\mathrm{C^{18}O}}$|– |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| and A_V–|$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$|⁠, respectively. The circles and error bars indicate the median and the standard deviation for the cloud with colors that correspond to the median intensity of the FUV radiation field. Clouds #71 and #78 were flagged in the plots because the estimated values of A_V and G₀ for these clouds have large uncertainty due to the effect of overlap with other large and dense clouds. In figure 9a, we overlaid the distribution of |$N_{\mathrm{C^{18}O}}$|–|$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| without averaging by clouds for reference. This is the same as the one shown in figure 2b, but the data is binned by 3 pixels in spatial directions for SCIMES analysis. The values of A_V and G₀ for clouds spatially overlapping each other are derived in the same way as the cloud mass using the weight calculated by equation (8). Maps of A_V and G₀ are calculated only in the pixels where |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| is measured.

Fig. 9.

Correlation plots of |$X_{\mathrm{C^{13}O}}/X_{\mathrm{^{18}CO}}$| with (a) the column density of C¹⁸O |$N_{\mathrm{C^{18}O}}$| and (b) the visual extinction A_V for the identified clouds. Each circle represents a cloud with a color that shows the intensity of the FUV radiation field and all parameters are median in the cloud. The error bars indicate the standard deviation of each parameter. Black dots in panel (a) represent pixel-by-pixel comparison without averaging by clouds as shown in figure 2b, but the data is binned by 3 pixels in spatial directions for SCIMES analysis. (Color online)

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At low column densities (⁠|$N_{\mathrm{C^{18}O}} \lesssim 5 \times 10^{15}\:$|cm⁻²), the median values of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| for clouds show a large variation ranging from 5.6 to 17.4 as shown in figure 9a. In figure 9b, it seems that there are two trends of distribution. One is a set of clouds that has relatively low abundance ratios (⁠|$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}} \lesssim 10$|⁠) with low column densities (⁠|$N_{\mathrm{C^{18}O}} \lesssim 5 \times 10^{15}\:$|cm⁻²) and the other is a set of clouds that have abundance ratios higher than 10. The low-|$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| clouds range from 1 mag to 3 mag in A_V and there is no clear correlation between A_V and |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$|⁠. The intensity of FUV for these clouds is G₀ ≲ 10³. This means that the abundance ratios are almost independent of the visual extinction of the clouds under weak FUV environment. In contrast, the high-|$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| clouds are located in the upper edge of the distribution in the plot and the abundance ratios decrease with the column densities at |$N_{\mathrm{C^{18}O}} \gtrsim 1 \times 10^{15}\:$|cm⁻². Most of the high-|$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| clouds are located in the integral-shaped filament and are irradiated by strong FUV of G₀ ≳ 10³. In figure 10, we plot G₀ versus |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| for clouds with colors that correspond to the median values of A_V. This plot clearly shows that the abundance ratio increases with the intensity of the FUV radiation field and decreases with the visual extinction. These results are consistent with the abundance ratio being significantly affected by the selective photodissociation of C¹⁸O, which is dominant compared to the dissociation of ¹³CO under a strong FUV environment and is suppressed in the dense part of the clouds. The selective photodissociation of C¹⁸O also explains the high abundance ratio on the outer part of each cloud which is irradiated by the strong FUV and has a low column density.

Fig. 10.

Correlation plot of |$X_{\mathrm{C^{13}O}}/X_{\mathrm{^{18}CO}}$| with the intensity of the FUV radiation field G₀ for the identified clouds. Each circle represents a cloud with a color that shows the intensity of the FUV radiation field and all parameters are median in the cloud. The error bars indicate the standard deviation of each parameter. (Color online)

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5.4 Assumptions on derivations of the abundance ratio and the FUV radiation field

We examine the impact of assumptions used for deriving the abundance ratio and the FUV radiation field.

5.4.1 The assumptions of the excitation temperature and the beam filling factor

It has to be mentioned that optical depths and column densities of ¹³CO and C¹⁸O were derived based on several assumptions. T_ex is estimated by the peak temperature of ¹²CO. The excitation temperatures of ¹³CO (J = 1–0) and C¹⁸O (J = 1–0) are likely to be lower than that of ¹²CO (J = 1–0) since the result of these isotopologic lines trace inner parts of the cloud (Castets et al. 1990). As investigated by Shimajiri et al. (2014), this possibility of overestimation of T_ex has impacts for the absolute values of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$|⁠, but our discussion on the relative values of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| should be still reliable.

The beam filling factors are assumed to be 1.0 for the emission of ¹³CO (J = 1–0) and C¹⁸O (J = 1–0). The distribution of C¹⁸O (J = 1–0) is more concentrated on dense filaments and cores than that of ¹³CO (J = 1–0), as presented in figures 1c and 1e. This might lead to small beam filling factors of C¹⁸O (J = 1–0), |$\phi _{\mathrm{C^{18}O}}$|⁠, of less than 1.0. The beam size of the ¹³CO and C¹⁸O data is |${21{^{\prime\prime}_{.}}5}$|⁠, which corresponds to 0.04 pc at the distance of Orion A. Shimajiri et al. (2015) revealed that the mean size of dense cores traced by C¹⁸O (J = 1–0) in Orion A is 0.09 ± 0.03 pc and this gives |$\phi _{\mathrm{C^{18}O}} = 0.09^2/(0.09^2+0.04^2) = 0.84$|⁠. We investigate this effect on |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| using |$\phi _{\mathrm{^{13}CO}} = 1.0$| and |$\phi _{\mathrm{C^{18}O}} = 0.84$| as shown in figure 11a. |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| systematically decreases for the same |$N_{\mathrm{C}^{18}\mathrm{O}}$| compared with the result in figure 2b. The mean value of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| is evaluated to be 7.76 ± 2.21, which is 81% of the mean value when |$\phi _{\mathrm{C^{18}O}}=1.0$| is assumed. However, there is no change in the relative values of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| and the mean value is 1.4 times larger than the solar system value. We confirmed that the variation of the abundance ratio of |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$| is significant even after taking into account the possibility of the small beam filling factor.

Fig. 11.

(a) Effect by the small beam filling factor of the C¹⁸O (J = 1–0) line on the relation between |$N_{\mathrm{C}^{18}\mathrm{O}}$| and |$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$|⁠. The black and blue dots present values for |$\phi _{\mathrm{C^{18}O}} = 1.0$| and 0.84, respectively. The black and blue dashed lines indicate the mean values of 9.31 and 7.76 for |$\phi _{\mathrm{C^{18}O}} = 1.0$| and 0.84. (b) Map of the ratio of the radiation field estimated from the 60 μm and 100 μm maps by IRAS, G_{(60μm + 100μm)}/G_60μm. The identified clouds are presented using black lines. Note that the high ratio spots at δ = |${-6^{\circ}23^{\prime }}$| are due to an artificial pattern in the 100 μm map. (Color online)

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5.4.2 The omission of the 100 μm data from the estimation of the FUV radiation field

The lack of PACS dust continuum data at |$100\, \mu$|m might lead to an underestimation of the FUV radiation field. We estimate the effect of this omission using dust continuum maps at |$60\, \mu$|m and |$100\, \mu$|m taken by IRAS. Figure 11b represents the map of the ratio of the radiation field estimated by the 60 μm map and the |$60\, \mu \mbox{m} + 100\, \mu$|m maps, r = G_{(60μm + 100μm)}/G_60μm. The value of r ranges from 1.2 to 1.6 in regions with strong FUV field. In weak FUV regions such as the southern part of Orion A and OMC-2, r reaches 2.2. Since the mean values of G₀ for each cloud range over 3 orders of magnitude (see figure 10 and table 4), we conclude that the impact of the omission is small.