IRAM 30 m LARGE SCALE SURVEY OF ¹²CO(2–1) AND ¹³CO(2–1) EMISSION IN THE ORION MOLECULAR CLOUD

The structure and dynamical properties of the interstellar medium in galaxies is deeply influenced by the feedback of massive stars. Their ionizing photons (extreme UV, E > 13.6 eV) generate H ii regions, which expand rapidly within their parental molecular cloud. This expansion compresses molecular clouds and can trigger their gravitational collapse toward the formation of a new generation of low-mass stars (Elmegreen 1998; Deharveng et al. 2010). The interaction of the H ii region with the surrounding cloud is also a source of hydrodynamical instabilities (Spitzer 1954; Frieman 1954; Berné et al. 2010), turbulence (Elmegreen & Scalo 2004), and chemical mixing (Roy & Kunth 1995; Berné & Matsumoto 2012) in the interstellar medium. In addition, outflows from young stellar objects can also inject kinetic energy into their parent molecular cloud (Bachiller 1996).

Given its proximity to us (414 pc; Menten et al. 2007), the Orion nebula is one of the most studied regions of massive star formation (see, e.g., Genzel & Stutzki 1989; Bally 2008; Muench et al. 2008 for reviews). Traditionally, the "Orion nebula" refers to the visible part of the region, the H ii region, powered by the ionizing radiation of the Trapezium OB association. It is part of a much larger complex, referred to as the Orion molecular cloud (OMC), itself lying at the border of the Eridanis super bubble. Numerous studies have focused on specific objects in the Orion nebula, such as the famous Proplyds, the Orion Kleinmann–Low (KL) nebula, or the Orion bar. Studies of the large-scale structure of the nebula are, however, sparse, because of the difficulty to obtain observations covering large areas of the sky with sufficient angular resolution, and because the interpretation of such data sets is challenging. Bally et al. (1987) reported a ¹³CO observation of the entire Orion molecular cloud, including the nebula, with a resolution of 1' (Figure 1). This study was the first to reveal the filamentary structure of the cloud. The Orion nebula was found to lie at the center of an "integral shaped filament" (ISF) of molecular gas, itself part of a larger filamentary structure extending from north to south over 4° (referred to as Orion A, see Bally et al. 1987 and Figure 1). Several studies have investigated the degree scale properties of the nebula in various molecular tracers. Using ¹²CO, ¹³CO, and C¹⁸O observations, Castets et al. (1990) provided a column density and an H₂ density map of the ISF with an angular resolution of the order of 100''. Using C¹⁸O observations, Dutrey et al. (1991) identified clumps inside filaments distributed periodically, suggestive of externally triggered cloud collapse and fragmentation. Recently, Buckle et al. (2012) obtained a new survey in CO(3–2) along the ISF with a 15'' resolution (see their field of view in Figure 1). Their study concluded that the cloud is magnetically supported and wrapped in a helical magnetic field. Shimajiri et al. (2011) recently reported a survey of the Orion molecular cloud in CO (1–0) with a spatial resolution of 20'' and a spectral resolution of 1 km s⁻¹. Using this data set, the authors suggest that the formation of some clumps or protostars might have been triggered by the pressure exerted by the H ii region (Shimajiri et al. 2011). The ISF was observed by Johnstone & Bally (1999) in the submillimeter continuum. These authors found a strong correlation between the CO and cold dust continuum emission. They also reported the presence of young stellar objects and prestellar clumps, mainly found in the northern part of the ISF. Spitzer observations have shown further evidence for this ongoing low-mass star formation (Megeath et al. 2012). The H ii region observed at large scales with VLA at 330 MHz by Subrahmanyan et al. (2001) shows a shell-like structure, suggesting high pressures exerted on the northern cloud, while the gas is escaping in the south toward the general interstellar medium though cavities in the molecular gas. A similar idea was pointed out by Güdel et al. (2008) who have discovered the presence of an X-ray-emitting plasma in thermodynamic equilibrium with the H ii gas. Finally, the veil of neutral gas situated in the foreground of the Orion nebula was recently mapped at high angular and spectral resolution by van der Werf et al. (2013), and seemingly confirms this idea that the H ii region is in the blister phase.

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In this paper, we present new observations of the ¹²CO and ¹³CO (2-1) rotational line at 1.3 mm observed with the IRAM 30 m telescope in Granada. This data set has an unprecedented spatial (∼11'') and spectral (∼0.4 km s⁻¹) resolution, together with a large field of view (1 × 08). This data are available at http://userpages.irap.omp.eu/~oberne/Olivier_Berne/Data.

The observations were conducted at the IRAM 30 m telescope in Granada, Spain, in 2008 March, April, and October. The data were obtained with the HERA receiver array, each polarization tuned to ¹²CO and ¹³CO lines (230.5 and 220.4 GHz respectively) with a spatial beamwidth of 11'', and main beam efficiencies of 0.524 and 0.545 for ¹²CO and ¹³CO, respectively. We used the versatile spectrometer VESPA as a backend providing 320 kHz of the spectral resolution, (0.4 km s⁻¹). We observed using the On-The-Fly (OTF) mapping mode, with 5'' of data sampling in right ascension, and with steps of 12'' in declination. Since the beam of the telescope is ∼11'', this implies that the resolution is equal to the telescope beam in right ascension, but is a factor of two larger in declination. Intensity calibration was performed every three to four minutes using two absorbers at different temperatures, resulting in system temperatures between 300 and 500 K. Atmospheric opacities were obtained from the measurement of the sky emissivity and the use of the ATM code (Cernicharo 1985; Pardo et al. 2001), and found to be between 0.1 and 0.2 corresponding to 1–3 mm of precipitable water vapor. Focus and pointing were checked every 3 hr and 1.5–2 hr respectively on intense nearby sources. The map is centered at the position of the infrared source IRc2 (α = 05^h35^m145, δ = −05^d22^m293 /α = 8381037, δ = −053748). The reference position, which is free of CO emission, was located at an offset (−3600'', −1800''). Data reduction was performed using the GILDAS software.⁵ Several corrections were applied to the data: one of the problems concerns the combination of submaps obtained over different observing sessions with different intensity calibration, weather conditions, and pointing errors. Position switching observations (PSW) were performed at the position of IRc2 before each OTF submap, and these were used afterwards to correct for such differences between submaps. Relative errors in pointing corrections were obtained comparing these PSW observations with the 4'' spacing ¹²CO map observed within the 2 × 2 line survey (see Esplugues et al. 2013 and Marcelino et al., in preparation). We have found pointing errors between submaps typically of 2–4'', with a few cases of large errors of 7–10'' in RA under poor weather conditions. Besides the pointing errors in the observations, we found that pixels in the array are not perfectly aligned. We obtained a measurement of pixel misalignment in both HERA1 and HERA2 arrays, using ¹²CO and ¹³CO maps of IRC+10216 (Cernicharo et al., in preparation). The errors found are between 0.1–2''. Further corrections on the intensity calibration are needed in order to account for the different response of each pixel within the HERA array. The different calibration between pixels is due to the fact that the image band rejection cannot be measured for each individual receiver in the array. Since this parameter will depend on the tuning, maps performed in different days will show different intensity calibrations. Therefore, the data were scaled using a factor that depends on the particular submap and pixel in the array. This factor was obtained comparing the emission in each pixel with respect to the central one in the array, which was found to be the most uniform over the whole map. After all of these corrections were applied, the final map was constructed using a pixel size of 55, i.e., half the beam size. The total number of positions in the map are 99415 after reduction, each with an on-source integration time of 10 s (∼1 s at the most external parts of the map) corresponding with an rms of ∼0.2 K (0.4–0.5 K at the map borders).

Figures 2 and 3 show the ¹²CO and ¹³CO J = 2–1 integrated emission maps between −5 to 25 km s⁻¹. While ¹²CO shows a widespread emission across the observed region, the less abundant and optically thin isotopomer ¹³CO, delineates the densest regions, showing a very clumpy and filamentary structure. The bulk of the gas is mainly distributed along the ISF (Bally et al. 1987), clearly delineated by the densest gas seen in ¹³CO emission (Figure 3). This filament contains the Orion molecular clouds 1–4 (see below). The gas distribution extends east and west of the main filament, but not equally. While emission spreads continuously to the east and southeast, showing numerous clumps and filaments, it is truncated sharply southwest to the filament, coincident with a region where X-ray emission is observed (Güdel et al. 2008). Further west of this empty region where no CO emission was found, a spherical clump and an elongated cloud (E-W) are observed. These features, are only seen at blue shifted velocities (see below), suggesting that they are being pushed toward the observer by a bubble of hot and ionized gas from massive stars. Indeed, the elongated cloud is composed of several clumps (or "ripples") whose geometry and velocity suggest they are the result of a Kelvin–Helmholtz instability produced by the expansion of the nebula (Berné et al. 2010).

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The Orion molecular cloud 1 (OMC-1), located behind the Orion nebula, is the brightest region seen at the center of the filament and contains well-known features such as the BN/KL infrared nebula, the Orion–south region (Ori-S), and the Bar, whose positions are indicated in Figure 2.

In contrast to the bright emission of the Bar, the KL nebula, and Ori-S, there is a small region of weak emission that corresponds to the position of the Trapezium stars. This region is limited by the M42 H ii region ionization fronts (the Northern Ionization Front and the Bar to the south), and by the molecular ridge to the west. It is easy to see, in the ¹²CO maps, the close relation of these bright features with the cone-like ionized structure of M42 observed in the radio-continuum emission (Yusef-Zadeh 1990). The north ionization front (NIF) is formed by several filaments running sorthwest–southeast (see ¹³CO emission in Figure 3). The NIF is the counterpart of the obscured filament seen in the optical images of the Orion nebula and known as the "Dark Lane." Further east, other clumps appear that follow the same direction as the NIF, indicating that they might be related. In ¹²CO (Figure 2), low density gas east to the NIF is observed. This emission ends abruptly in a wall-like structure from which few thin filaments or streamers spread toward the east, like tunnels blowing the molecular gas to the clumps seen at the easternmost part of the map. South of the NIF, a filamentary structure going nearly north–south is seen (Figure 3), which should also be related to the expansion of the H ii region (see Rodriguez-Franco et al. 1998). Cometary shaped pillars are very visible in this region (Figure 3). The fact that these are pointing toward the Trapezium stars strongly suggests that these structures are the result of the selective photo-erosion of the nebula, following the model proposed by Reipurth (1983). This is illustrated in more detail in Figure 4, where we overlay the ¹³CO emission and the Spitzer-IRAC 3.6 μm image in this particular region. While ¹³CO traces the inner molecular cloud, the IRAC image is thought to trace the emission from UV heated polycyclic aromatic hydrocarbons (PAHs), present in the mostly atomic gas at the surface of the molecular cloud. It is clear from Figure 4 that the PAH emission enshrouds the molecular pillars and peaks systematically closer to the Trapezium stars as compared to CO. This stratification is classical in photon-dominated regions (PDRs, see for instance Tielens et al. 1993 for a classical example in the Orion Bar), and hence also favors the idea that selective photo-erosion is at the origin of these Pillars. Immediately to the west of Orion-KL, elongated structures or Fingers (Rodriguez-Franco et al. 1992) are detected. These structures are believed to be the result of the interaction of the molecular cloud with the extreme environment (especially the flow of ionized gas, see discussion in Rodriguez-Franco et al. 1992).

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The northern part of the ISF shows strong ¹²CO emission (Figure 2), which is separated in several clumps in the ¹³CO map (see Figure 3). This region corresponds to the molecular clouds OMC-2 and OMC-3. Both regions are known to be very active in star formation since many young protostars and premain sequence stars have been detected in the infrared and submillimeter wavelengths, together with molecular outflows and jets (see Peterson & Megeath 2008, for a review). Indeed, the turbulent ¹²CO emission in OMC-2/3 indicates the presence of such outflows (see Section 4.3). The ¹³CO emission on the other hand, is very clumpy (Figure 3), showing the densest cores where star formation is taking place. To the southeast of OMC-2, there is a cavity empty of molecular emission, clearly seen in the ¹³CO map (Figure 3), which corresponds to the H ii region M43. This cavity, which in the optical is nearly spherical, is a small H ii region illuminated by the B0.5 star ν Ori (Thum et al. 1978). M43 is limited in molecular emission by the ISF to the west, and a thin filament to the east that connects OMC-2 to the NIF. To the south, the ISF seems less clumpy and active in star formation than the northern filament (e.g., no outflow signatures observed). There is a local maximum located about 700'' south of Orion-KL, corresponding to the OMC-4 molecular cloud. This molecular core was identified in the CO maps of Loren (1979) and in the SCUBA 450 and 850 μm emission observed by Johnstone & Bally (1999). In their submillimeter maps, this cloud is seen as a bright concentration of knots in a V-shaped structure.

4.1. Column Density Map

4.1.1. Method

Assuming local thermodynamic equilibrium and optically thin emission (which is mostly the case for ¹³CO), the ¹³CO column density can be obtained using an excitation temperature derived from the peak temperature of the ¹²CO line (see, e.g., Goldsmith & Langer 1999). The ¹³CO column density can be converted into a column density N(H₂) using the abundance ratio [H₂]/[¹³CO] = 7 × 10⁵. Of course, the derivation of column density in this manner is limited by the assumptions made, in particular, that ¹³CO may become moderately optically thick in some regions of the nebula with high column densities (see, e.g., Castets et al. 1990). In dense and cold regions, CO is also expected to be depleted on grains and the [H₂]/[¹³CO] ratio may become larger than the one used. Both of these effects will imply an underestimation of the total column density of the order of a few for dense regions. In the rest of the nebula, we expect our estimation to be relatively robust. We have computed N_H on each pixel of the map (Figure 5). Column densities derived in this way range between a few times 10¹⁸ and a few times 10²³ cm⁻². We have mapped the points that correspond to column densities below 3 × 10²¹ cm⁻², corresponding to the typical visual extinction at which CO can survive (e.g., Draine 2011). We found that these points correspond to noisy ¹³CO spectra, i.e., with a peak brightness below 0.6 K, i.e., three times the typical sensitivity of ∼0.2 K per channel, where the column density cannot be evaluated with confidence. Therefore, we have thresholded our map at 3 × 10²¹ cm⁻² (Figure 5). We also arbitrarly define three subregions in the map presented in Figure 5: the north region, which contains OMC-2/3 and corresponds to the regions where many low-mass stars are present, the south region, which contains OMC4, the ripples, and the cometary shaped pillars, and corresponds to the parts of the cloud that enshroud the M42 H ii region, and, finally, the central region, corresponding to the most active and complex parts of the nebula, in which Orion-KL, the Bar, the molecular Fingers and the NIF are found.

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4.1.2. General Properties

The map of column density derived from the ¹³CO data is shown in Figure 5. Moderate column densities of a few times 10²¹–10²² cm⁻² are found along the ISF. The column density for the Orion-KL is of the order of 5 × 10²³ cm⁻² (Figure 5) close to the values reported recently by Plume et al. (2012). Figure 6 presents a close-up view of the column density map in the Orion Bar region. The Bar has a typical maximum column density of 10²³ cm⁻². This map suggests the presence of clumpy structures, and we have identified four specific clumps. They correspond well in position (Table 1) and shape to the clumps seen in the ¹³CO (3–2) and C¹⁸O (3–2) maps of Buckle et al. (2012) (see their Figure 7). The good match between the positions of these clumps in ¹³CO (2–1), ¹³CO (3–2), and C¹⁸O (3–2) indicates that the emission in these transitions is only moderately affected by optical depth effects in the Bar. We note that these clumps appear relatively large (diameter > 14'', see Table 1) and, therefore, differ from the arcsecond scale clumps proposed to exist by van der Werf et al. (1996) and Goicoechea et al. (2011). For the case in which these mini-clumps also exist in the Bar, this would suggest that clumpy structures with different spatial scales coexist. The maximum column densities for these clumps are 9, 10, 11, and 13 × 10²² cm⁻² for clumps number 4, 3, 2, and 1 respectively. These values are comparable with the column densities derived for the Orion bar based on far infrared dust emission by Arab et al. (2012). Apart from the ISF and classical structures described above, other notable structures are found with significant column densities: the ripples (a few times 10²¹ cm⁻²), the clump just north of the ripples (a few times 10²² cm⁻²) as well as the wall of pillars at the edge the Veil in the southeast. The molecular fingers also appear with high column densities (10²²–10²³ cm⁻²).⁶

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Table 1. Properties of the Clumps in the Orion Bar

Name	Position	Radius	Mass	Velocity Dispersion	Virial Paramater
	(R.A., decl.) (deg.)	Rclump (")	Mclump (M☉)	δV (km s−1)	α
Clump 1	(83.8075, −5.44827)	46.3	52.1	3.03	18.9
Clump 2	(83.8192, −5.43942)	23.4	13.6	2.08	17.3
Clump 3	(83.8431, −5.42102)	23.8	11.3	2.11	21.8
Clump 4	(83.8559, −5.41123)	14.7	4.30	2.12	35.6

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4.2. Mass

We can derive the total mass of the cloud using:

$$\begin{equation} M = \mu m_H \int _S{N({\rm H_2}) dS} \protect, \protect \end{equation} \tag{ 1 }$$

where μ = 2.8 is the mean molecular weight and m_H is the atomic hydrogen mass. This integral is calculated on each pixel of the column density map, using the map pixel size (5'' × 5'' at 414 pc) as the unit of surface. The total mass is then derived by summing all the integrals. Using this approach, we find a total mass of ∼7700 M_☉, close to the value derived by Castets et al. (1990) using ¹³CO (1–0) for a similar field of view. We computed the mass of the integral-shaped filament, using Equation (1), but considering the field of view of Buckle et al. (2012) (see Figure 1). This field is centered on Orion KL and follows the brightest emission of the ISF. With this field of view, we find a mass of 4300 M_☉, in excellent agreement with the mass of 4290 M_☉ derived by Buckle et al. (2012) using ¹³CO (3–2), but smaller than the value reported by Bally et al. (1987) of 5000 M_☉. Considering that these latter authors used a distance of 500 pc (instead of 414 pc here) and a mean molecular weight of 2.6 (while we use a value of 2.8) to estimate the mass of the ISF, their value could be overestimated by a factor of (2.6 × 500²)/(2.8 × 414²) = 1.35 as compared to ours. On the other hand, in their computation, Bally et al. (1987) consider a north-to-south extent of about 15 for the ISF, compared to 085 in our case. Overall, we conclude that the mass we derive for the ISF is in very good agreement with the value of Buckle et al. (2012), where a direct comparison is possible. As compared the value of Bally et al. (1987), the agreement is reasonable considering the uncertainty in the area used to derive the mass. Since the total mass we derive for the cloud is about 7700 M_☉, dense molecular gas present in the ISF actually represents only about half of the cloud mass. Hence, a large fraction of the cloud mass resides in more diffuse extended filamentary structures. Using the column density map, we have estimated that most of this mass in the diffuse molecular gas lies in regions of column densities lower than 3 × 10²² cm⁻², or at a visual extinction A_V below 10. The diffuse and filamentary molecular gas in these regions can be observed thanks to the high sensitivity obtained with the 30 m telescope. These results stress the importance of sensitive surveys in order to calculate accurate masses of molecular gas in nearby and extragalactic environments. Using the same method as above, we derive the masses of the clumps identified in the Orion Bar (see Figure 6). We have assumed a circular geometry with radii given in Table 1. The masses are found to range between 4.3 and 52 solar masses (Table 1). Condensations with similar masses are often observed around H ii regions (see, e.g., Deharveng et al. 2009), and it is believed that they result from the compression of the molecular cloud due to the expansion of the ionized bubble.

4.3. Kinematics

4.3.1. Subtraction of the North–South Velocity Gradient

As mentioned in Bally et al. (1987, see their Figure 5), the Orion A cloud is subject to a velocity gradient over a scale of about 25 pc from north to south. This is also visible at the small scale which we study here, and was reported as well in Buckle et al. (2012) (see their Figure 3 for a position–velocity diagram illustrating this effect). When trying to study the small scale fluctuations of the velocity field, it is, therefore, useful to subtract this velocity gradient. Hence, both our ¹²CO and ¹³CO spectral cubes are corrected from a 0.7 km s⁻¹ pc⁻¹ velocity gradient. This gives spectral cubes that are in the rest frame of the ISF, and can be used to spatially study the fluctuations of the velocity field without contamination from the large-scale falling backwards effect. For these two cubes, we redefine v = 0 at the peak of the line obtained by averaging the cube over the spatial dimensions.

4.3.2. Kinematics from ¹²CO

¹²CO has the advantage of being bright, but, on the other hand, this line quickly becomes optically thick. Hence, it is useful to study detailed spatial structures corresponding to emission in the optically thin high velocity wings of this line. This is particularly suited for the study of outflows and jets emanating from protostars. Using the velocity gradient subtracted cube of ¹²CO, we compute two maps corresponding to the emission in the high velocity wings of this line. The "blue" map (corresponding to blue shifted velocities in the frame of the ISF) is obtained by integrating the cube in velocity between [ − ∞, −4.8] km s⁻¹. The "red" map instead is obtained by integrating over the [ + 3.2, ∞] km s⁻¹ range. In Figure 7, we present an overlay of the "blue" and "red" maps. In the south region, OMC-4 appears blue-shifted, most likely because it sits in front of the H ii region, and is pushed toward the observer. To the east of OMC-4, an arc-shaped structure is clearly visible. This structure was identified by Loren (1979) and most likely represents the back of the cloud situated behind the H ii region. The difference between the mean velocity of the blue- and red-shifted parts of the cloud in the south region is of the order of Δv ∼ 10 km s⁻¹. With a radius of 1.8 pc for the H ii region, this implies a—short—dynamical age of about t_dyn ∼ 0.2 Myr for the expansion of the nebula due to the growth of the H ii region. The ripples also appear in blue, and hence seem to be part of a foreground cloud as was already proposed by Berné et al. (2010). In the north region, ¹²CO looks more mixed/turbulent due to red and blue emission most likely arising due to the intense star formation and hence outflow activity in this region (e.g., Chini et al. 1997; Aso et al. 2000; Williams et al. 2003). In Figure 8, we overlay the red and blue maps of ¹²CO to the MIPS 24 μm image obtained by Spitzer, focusing on the northern region of the nebula only. In addition, we indicate the positions of the far infrared clumpy structures that can be identified (by eye) in the SCUBA 850 μm map obtained by Johnstone & Bally (1999). It clearly appears that numerous elongated blue/redshifted structures find their origin at positions of 24 μm sources and/or FIR clumps, which are both indicators of the positions of young stellar objects. We do not study these structures individually since this has been done in great detail by Aso et al. (2000) and Williams et al. (2003). Nevertheless, Figure 8 suggests that most of the red and blueshifted structures seen in Figure 8 correspond to protostellar outflows, and that the dynamical properties of the nebula in this region are likely to be affected, or perhaps dominated (Williams et al. 2003), by this activity.

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4.3.3. Kinematics from ¹³CO

As opposed to ¹²CO, ¹³CO has the advantage of being more optically thin, but less bright. Hence, it is a useful tracer to study the inner structure of the molecular gas. Using the velocity gradient subtracted cube of ¹³CO, we compute two maps corresponding to the emission in the blue and redshifted sides of the line, i.e., the "blue" map is obtained by integrating the cube in velocity between [ − ∞, 0] km s⁻¹ and the "red" map instead is obtained by integrating over the [0, ∞] km s⁻¹ range. In Figure 9, we present an overlay of the corresponding "blue" and "red" maps. Following the ISF from Orion KL, toward the north or the south, the filament successively appears in red and then blue, with a periodicity of the order of about 20'. This pattern is compatible with a rotating helical filament, which could be due to the structure of the large-scale magnetic field, which has been suggested to be helical (see Uchida et al. 1991; Matthews et al. 2001; Poidevin et al. 2011; Buckle et al. 2012). Whether this structure is at the origin of the formation of Orion KL (e.g., by the Parker instability as suggested by Shibata & Matsumoto 1991) or resulting from the formation of Orion KL (e.g., acting as a drain of angular momentum as suggested by Uchida et al. 1991) is unclear and should be investigated in more detail. In any case, this suggests that the magnetic field plays a dominant role in the evolution of the cloud. The comparative study between the kinematics of the cloud and the magnetic field combining the present CO data with the large-scale polarization data from the Planck satellite will be particularly useful to investigate this subject.

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4.4. Energy Balance

4.5. Probability Density Functions

We derive the probability density functions (PDF) of the column density N_H, turbulent velocity dispersion δv, and kinetic energy E_k. In addition, we derive the PDF of the turbulent Mach number $\mathcal {M}$, given by the ratio δv/c_s, where c_s is the sound speed. c_s is derived assuming that the gas temperature is equal to the excitation temperature derived from the ¹²CO line. For each one of these parameters, we compute the PDF for the whole region, but also for the three sub-regions identified in Figure 5. The resulting PDFs are presented in Figure 10.

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The column density PDF is found to be non-Gaussian and relatively flat. Column density histograms in star-forming regions are known to exhibit power-law tails (see for instance recent examples in Kainulainen et al. 2011). In our case, the combination of a Gaussian and a power law gives poor fits to the observed histogram. A collection of power laws can give a reasonably good fit, but this is at the expense of many arbitrary choices such as the number of power laws used. It is interesting to note that similarly flat column density PDFs have been produced by MHD simulations of the turbulent saturation of the Kelvin–Helmholtz instability (Hendrix & Keppens 2014), which has been proposed as a source of small-scale turbulence in the Orion molecular cloud by Berné & Matsumoto (2012). When comparing the PDFs of the three subregions, it clearly appears that the central regions host the largest column densities, present in the Orion Bar and Orion-KL. The north region also appears to have higher column densities than the more diffuse south region. The north region shows a sharp decrease at a column density of N_H ∼ 4 × 10²² cm⁻², perhaps corresponding to the limit of gravitational stability. Both the higher column density and presence of this sharp edge are consistent with the fact that the north region is much more active in terms of star formation than the south region.

The PDFs of the velocity dispersion show a peak between 1 and 2 km s⁻¹, typical for molecular clouds and a log linear tail toward larger velocities. The north and south regions show very similar δv PDFs, while the PDF of the central region is shifted toward larger velocities due to the intense kinetic activity of Orion-KL. The PDFs of the Mach number peak around two to three, indicating that turbulence is highly supersonic in Orion. The PDF of the north region appears sharper than in the central and south regions, and peaks at a lower Mach number. This is likely the result of the low-mass star-formation activity, i.e., linked to the fact that turbulence in this region is dominated by the outflow activity.

Finally, the last panel of Figure 10 shows the distribution of the kinetic energy. Logically, the central region contains the pixels with the highest kinetic energies, due to the presence of Orion KL. The north region also displays higher kinetic energies than the south region. This is most likely because of the intense outflow activity in the north region, which can inject kinetic energy efficiently in the molecular cloud.

4.6. Distribution of the Feedback Processes

4.7. Fraction of Radiated Energy Converted into Kinetic Energy

4.8. On Triggered Star Formation in Orion

We presented new large-scale maps of the Orion molecular cloud in the ¹²CO and ¹³CO (2–1) lines. The nebula appears filamentary and turbulent. Using this data set we derive the following parameters: a dynamical age for the nebula t_dyn ∼ 0.2 Myr and a total mass of the nebula M = 7700 M_☉. About half of this mass resides in the dense integral-shaped filament at the center of the nebula, while the other half resides in more diffuse and filamentary structures distributed around the filament. We find a total kinetic energy E_k = 3.6 × 10⁴⁰ J for the cloud, about 40% of which emanates from the outflows and the rest from feedback of the H ii region. However, the relative importance of the feedback processes depends on the considered subregions within the cloud. The north region of the cloud, (OMC-2/3) seems to be dominated by feedback from outflows. In the central region (OMC-1), the feedback is shared between the protostellar outflows and feedback from the H ii region. The south region, instead, seems dominated by the feedback due to the expansion of the H ii region. Overall, it seems that the feedback from the H ii region, which is often invoked as a major trigger of star formation, is not significantly larger than the feedback from outflows, and, therefore, both mechanisms may be important. In addition, we find that the triggering of star formation by the expansion of the H ii region seems inefficient in Orion. We find that only about ∼0.01% of the energy radiated by θ¹C has been converted into kinetic energy in the molecular cloud. Over the lifetime of this star, a few 10⁴¹ J may be injected in the ISM. This is much smaller than what can be injected by a supernova but can still have a significant influence on the shaping of the ISM and the regulation of star formation, since this occurs on larger timescales. Finally, we suggest that magnetic fields probably play an important role in the energy balance at both small and large scales. We propose that the integral shaped filament has a helical shape, perhaps following the magnetic field lines and is rotating about its main axis.

We acknowledge the two referees of this paper who helped improve the manuscript. We thank Paul Goldsmith for his comments. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.