CATALOG OF DENSE CORES IN THE ORION A GIANT MOLECULAR CLOUD^*

2.1.1. Core Identification in the AzTEC 1.1 mm Dust Continuum Map

The overall distribution of the AzTEC 1.1 mm dust continuum emission was revealed by Shimajiri et al. (2011). Here, we identify cores using the two-dimensional Clumpfind method (Williams et al. 1994). This algorithm has been widely used for the identification of cores and clumps (e.g., Kirk et al. 2006; Rathborne et al. 2009; Ikeda & Kitamura 2011; Tanaka et al. 2013). The algorithm works well with reasonable parameters to identify cores or clumps, although several authors have pointed out some shortcomings of the Clumpfind algorithm (Pineda et al. 2009). Pineda et al. (2009) examined the behavior of the algorithm by changing the threshold level from 3–20σ, a wider range than Williams et al. (1994) did, and found that the power-law index of the core mass function (CMF) sensitively depends on the threshold for the higher threshold range >5σ. Ikeda & Kitamura (2009), however, demonstrated the weak dependence of core properties and CMF in Orion A on the threshold in a reasonable range from 2–5σ levels, which was also shown by Pineda et al. (2009). As described in Sections 2.1.2 and 2.2.2, the physical properties (radius, mass, velocity width, etc.) of the condensations identified by Clumpfind in this paper are similar to those of the star-forming dense cores traced by the H¹³CO⁺ line (Ikeda et al. 2007 and references therein; see also Appendix A of this paper). In this paper, we will therefore define cores identified by Clumpfind with a similar threshold value as they used.

The noise distribution of the AzTEC 1.1 mm continuum emission is not uniform over the image and is higher in the outer region. Before applying Clumpfind (Williams et al. 1994), we cut off the outer edge of the AzTEC image, where the coverage is less than 30% and the noise level is higher by a factor of 1.3 than that in the central part. This is because the observations were made by the raster scan that boresights in azimuth and elevation and because the AzTEC 1.1 mm dust continuum image was obtained by mosaicing observations of two fields. The noise level is ∼9 mJy beam⁻¹ in the central region and ∼12 mJy beam⁻¹ in the outer region of the trimmed image. We applied the Clumpfind method to the AzTEC 1.1 mm dust continuum image with the criteria that the threshold should be the 2σ level and the depth of the valley between adjacent peaks should be larger than the 2σ interval. We adopted 9 mJy beam⁻¹ which is the noise level (= 1σ) in the central region as the noise level in Clumpfind. Next, we removed cores whose FWHM sizes are less than the effective angular resolution (∼36''). Furthermore, we only took cores having peak intensities above the 4σ noise level. As described by Shimajiri et al. (2011), the emission around the central Orion-KL region could not be reconstructed as an accurate structure with the AzTEC data-reduction technique, because the continuum emission around Orion-KL is too bright. Thus, we removed cores in the central Orion-KL region. As a result, we identified 619 dust cores (see also Appendix B), as shown in Figure 1. Here, we note that the 257 cores are located in the C¹⁸O observed region, excluding the central part of the Orion-KL region (see Figure 2).

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To investigate the performance of the FRUIT data reduction, Shimajiri et al. (2011) performed a simulated source extraction in which Gaussian sources with various FWHM sizes and total flux densities were artificially embedded in the Orion data, and obtained the following result: the larger FWHM size of the model source, the lower the recovered fraction of the input total flux density of the source. In the case that the FWHM size of the input source is under 150'' (∼0.3 pc), the output total flux density is underestimated by less than 20%. The total flux density of the source with a peak flux density under 20 Jy is underestimated by less than 10%. Moreover, the restored image of the 1.1 mm dust continuum emission is consistent with that of the SCUBA 850 μm dust continuum emission. Consequently, the total flux densities of the sources in our map should be recovered by more than 80%, because the peak flux density FWHM size of the identified 1.1 mm dust cores are smaller than 20 Jy and 0.2 pc, respectively, as described in Section 2.1.2 (see also Appendix C).

2.1.2. Physical Properties of the 1.1 mm Dust Cores

The mass of the 1.1 mm dust core ($\equiv$ ${{M}_{{{{\rm H}}_{2}}}}$) was derived from the total flux density at 1.1 mm, ${{F}_{\nu }}$, on the assumption that all the 1.1 mm continuum emission arises from dust and that the emission is optically thin, using the formula,

$$\begin{eqnarray}&&{{M}_{{{{\rm H}}_{2}}}}=\frac{{{F}_{\nu }}{{D}^{2}}}{{{\kappa }_{\nu }}{{B}_{\nu }}({{T}_{{\rm d}}})}.\end{eqnarray} \tag{ 1 }$$

We adopted the dust mass opacity of ${{\kappa }_{\nu }}=0.1{{\left( \frac{\nu }{{{10}^{12}}{\rm Hz}} \right)}^{\beta }}$ cm² g⁻¹ with β = 2 (Hildebrand 1983; Chini et al. 1997) and D = 400 pc. For the dust temperature, we adopted ${{T}_{{\rm d}}}$ = 20 K (Cesaroni & Wilson 1994). We determined the apparent core–radius ${{R}_{{\rm obs}}}$ as

$$\begin{eqnarray}&&{{R}_{{\rm obs}}}={{\left( \frac{A}{\pi } \right)}^{\frac{1}{2}}},\end{eqnarray} \tag{ 2 }$$

assuming that the core is a sphere. Here, A is the projected area of the core, derived by Clumpfind. We further estimated the core–radius ${{R}_{{\rm core}}}$ corrected for the beam size on the assumption that the core has a Gaussian intensity profile as,

$$\begin{eqnarray}&&{{R}_{{\rm core}}}={{\left\{ R_{{\rm obs}}^{2}-{{\left[ \frac{{\Delta }\theta /2}{\sqrt{2{\rm ln} 2}}{{(2{\rm ln} \frac{{{T}_{{\rm peak}}}}{{\Delta }I})}^{1/2}} \right]}^{2}} \right\}}^{1/2}},\end{eqnarray} \tag{ 3 }$$

where ${\Delta }\theta$ (= 36'') is the effective beam size of the AzTEC 1.1 mm dust continuum map, ${{T}_{{\rm peak}}}$ is the peak intensity of the core, and ${\Delta }I$ is the threshold level in the core identification (see Williams et al. 1994). We note that the grid size of the map was set to the effective angular resolution in the Clumpfind analysis. The mean gas density ($\equiv$ n) of the core was derived as,

$$\begin{eqnarray}&&n=\frac{3{{M}_{{{{\rm H}}_{2}}}}}{4\pi \mu {{m}_{{\rm H}}}R_{{\rm core}}^{3}},\end{eqnarray} \tag{ 4 }$$

where μ is the mean molecular weight per free particle taken to be 2.33 and ${{m}_{{\rm H}}}$ is the mass of a hydrogen atom. The range of the radius ${{R}_{{\rm core}}}$, mass ${{M}_{{{{\rm H}}_{2}}}}$, and density n of the 1.1 mm dust cores are estimated to be 0.01–0.2 pc, 0.6–1.2 × 10² ${{M}_{\odot }}$, and 0.3 × 10⁴–9.2 × 10⁶ cm⁻³, respectively. Figure 3 shows histograms of the radius, mass, density of the 1.1 mm dust cores. In the distributions of ${{R}_{{\rm core}}}$, ${{M}_{{{{\rm H}}_{2}}}}$, and n of the 1.1 mm dust cores, peaks are seen at 0.09 pc, 1.3 ${{M}_{\odot }}$, and 1.0 ×10⁴ cm⁻³, respectively. The uncertainty of ${{R}_{{\rm core}}}$ is 0.07 pc, which is derived from the uncertainty in the estimation of the core projected area. As estimated in Section 2.1.1, the uncertainty of the total flux density of the identified 1.1mm core should be less than 20%, since the size of the core is less than 0.2 pc. Since the uncertainty of the total flux density of the identified 1.1mm core should be less than 20% (see Section 2.1.1), the uncertainty of ${{M}_{{{{\rm H}}_{2}}}}$ is 20%. We summarized the mean, minimum, and maximum values of each physical parameter in Table 1. Table 2 shows the physical properties of all the identified cores.

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Table 1.  Physical Properties of the 1.1 mm Dust Cores

Property	Meana	Minimum	Maximum
Peak flux density [Jy beam−1]	0.27 ± 0.45	0.05	5.95
Rcore [pc]	0.09 ± 0.03	0.01	0.20
${{M}_{{{{\rm H}}_{2}}}}$ [M⊙]	5.52 ± 9.55	0.60	116.95
Density [× 104 cm−3]	5.48 ± 38.94	0.31	915.01

^aErrors are the standard deviation.

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Table 2.  Identified AzTEC 1.1 mm Dust Cores

ID	R.A.	Decl.	Peak Flux Density	Aspect Ratio	Rcore	${{M}_{{{{\rm H}}_{2}}}}$	n	Category	Notea,b
AzTEC-Ori	(J2000)	(J2000)	[Jy beam−1]	Major/Minor	[pc]	[M⊙]	[× 104 cm−3]
1	5 31 28.6	−5 40 33.6	0.10	1.1	0.10	1.9	0.7	⋯
2	5 31 48.8	−5 23 4.2	0.11	1.2	0.08	1.5	1.2	⋯
3	5 32 11.2	−5 38 16.6	0.18	1.0	0.14	6.0	0.9	⋯
4	5 32 11.6	−5 36 46.6	0.09	2.1	0.08	1.3	1.1	⋯
5	5 32 14.8	−5 37 40.7	0.09	1.9	0.06	1.3	3.0	⋯
6	5 32 18.5	−5 37 46.7	0.10	1.0	0.10	1.9	0.8	⋯
7	5 32 19.3	−5 33 58.8	0.09	1.3	0.09	1.3	0.9	⋯
8	5 32 26.6	−5 26 34.9	0.06	1.1	0.08	1.1	0.8	⋯
9	5 32 28.5	−5 34 16.9	0.51	1.5	0.16	10.1	1.1	⋯
10	5 32 37.0	−5 35 53.1	0.25	1.4	0.14	7.6	1.3	⋯

^a[NW2007] #, [ISK2007] #, and [TKU2008] # are the SCUBA 850 μm dust core from Nutter & Ward-Thompson (2007), the H¹³CO⁺ (1–0) core from Ikeda et al. (2007), and the N₂H⁺ (1–0) core from Tatematsu et al. (2008), respectively. ^bThe Spitzer YSOs and disk sources, respectively, cataloged by Megeath et al. (2012).

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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2.2.1. Core Identification in the C¹⁸O Map

2.2.2. Physical Properties of the C¹⁸O Cores

We estimated the radius ${{R}_{{\rm core}}}$, velocity width in FWHM $d{{V}_{{\rm core}}}$, LTE mass ${{M}_{{\rm LTE}}}$, virial mass ${{M}_{{\rm VIR}}}$, and mean density n of the C¹⁸O cores. The definitions of these parameters are the same as those used by Ikeda et al. (2007) and Ikeda & Kitamura (2009). We estimated the core–radius ${{R}_{{\rm core}}}$ using Equation (3). To obtain the observed velocity width $d{{V}_{{\rm obs}}}$, we calculated a velocity dispersion within the C¹⁸O cores, and then we multiplied the factor $\sqrt{8{\rm ln} 2}$ to convert the core–velocity dispersion to the FWHM line width on the assumption of a Gaussian profile. Thus, the observed velocity width $d{{V}_{{\rm obs}}}$ is given by

$$\begin{eqnarray}&&d{{V}_{{\rm obs}}}=\sqrt{8{\rm ln} 2}{{\left[ \frac{{{{\Sigma }}_{i}}v_{i}^{2}{{I}_{i}}}{{{{\Sigma }}_{i}}{{I}_{i}}}-{{\left( \frac{{{{\Sigma }}_{i}}{{v}_{i}}{{I}_{i}}}{{{{\Sigma }}_{i}}{{I}_{i}}} \right)}^{2}} \right]}^{1/2}},\end{eqnarray} \tag{ 5 }$$

where v_i and I_i are the radial velocity and intensity of the ith pixel in each core, respectively. The velocity width $d{{V}_{{\rm core}}}$ should be corrected for the velocity resolution, $d{{V}_{{\rm spec}}}$ = 0.104 km s⁻¹ as

$$\begin{eqnarray}&&d{{V}_{{\rm core}}}=\sqrt{dV_{{\rm obs}}^{2}-dV_{{\rm spec}}^{2}}.\end{eqnarray} \tag{ 6 }$$

In the mass estimation, we adopted ${{T}_{{\rm ex}}}$ = 20 K (Cesaroni & Wilson 1994). For the fractional abundance of C¹⁸O relative to H₂, ${{X}_{{{{\rm C}}^{18}}{\rm O}}}$, we adopted 1.7 × 10⁻⁷ (Frerking et al. 1982). Assuming that the C¹⁸O(J = 1–0) emission is optically thin, we have

$$\begin{eqnarray}\begin{array}{rcl} {{M}_{{\rm LTE}}} & = & 3.47\times \;{{10}^{-2}}{{\left( \frac{{{X}_{{{{\rm C}}^{18}}{\rm O}}}}{1.7\times \;{{10}^{-7}}} \right)}^{-1}}{{T}_{{\rm ex}}}{{e}^{5.27/{{T}_{{\rm ex}}}}} \\ {} & {} & {{\left( \frac{D}{400\;{\rm pc}} \right)}^{2}}{{\left( \frac{{\Delta }\theta }{26^{\prime\prime} 4} \right)}^{2}}{{\left( \frac{{{\eta }_{{\rm MB}}}}{0.4} \right)}^{-1}}\left( \frac{{{{\Sigma }}_{i}}T_{{\rm A}}^{*}{\Delta }{{V}_{i}}}{{\rm K}\;{\rm km}\;{{{\rm s}}^{-1}}} \right){{M}_{\odot }}, \\ \end{array}\end{eqnarray} \tag{ 7 }$$

where Σ_i ${{T}_{{\rm A}}}$ $^{*}$ Δ V_i is the total integrated intensity of the core. We adopted a main beam efficiency ${{\eta }_{{\rm MB}}}$ of 38% for the 2010 season data and 36% for the 2013 season data (see Shimajiri et al. 2014). Note that we adopted the grid spacing of the data cube, ${\Delta }\theta$, set to the effective angular resolution of 264. The mean gas density of the core was derived by

$$\begin{eqnarray}&&n=\frac{3{{M}_{{\rm LTE}}}}{4\pi \mu {{m}_{{\rm H}}}R_{{\rm core}}^{3}}.\end{eqnarray} \tag{ 8 }$$

The virial mass assuming that the cores have spherical shapes and the virial ratio are estimated as

$$\begin{eqnarray}&&{{M}_{{\rm VIR}}}=209\left( \frac{{{R}_{{\rm core}}}}{{\rm pc}} \right){{\left( \frac{d{{V}_{{\rm core}}}}{{\rm km}\;{{{\rm s}}^{-1}}} \right)}^{2}}{{M}_{\odot }}\end{eqnarray} \tag{ 9 }$$

and

$$\begin{eqnarray}&&{{\mathcal{R}}_{{\rm vir}}}=\frac{{{M}_{{\rm VIR}}}}{{{M}_{{\rm LTE}}}},\end{eqnarray} \tag{ 10 }$$

respectively. The range of ${{R}_{{\rm core}}}$, $d{{V}_{{\rm core}}}$, ${{M}_{{\rm LTE}}}$, and n are 0.13–0.34 pc, 0.31–1.31 km s⁻¹, 1.0–61.8 ${{M}_{\odot }}$, and (0.8–17.5) × 10³ cm⁻³, respectively (see Table 3). Figure 3 shows histograms of ${{R}_{{\rm core}}}$, ${{M}_{{\rm LTE}}}$, and n of the C¹⁸O cores: peaks are seen at 0.22 pc, 15.1 ${{M}_{\odot }}$, and 2.9 ×10³ cm⁻³, respectively. The uncertainty of ${{R}_{{\rm core}}}$ is 0.05 pc derived from the uncertainty in the estimation of the core projected area. The uncertainty of $d{{V}_{{\rm core}}}$ is 0.104 km s⁻¹, corresponding to the velocity resolution. The uncertainty of ${{M}_{{\rm LTE}}}$ is a factor of 6, which is derived from the uncertainty in ${{X}_{{{{\rm C}}^{18}}{\rm O}}}$ (Shimajiri et al. 2014). The physical properties of the individual C¹⁸O cores are listed in Table 4.

Table 3.  Physical Properties of the C¹⁸O Cores

	Bound			Unbound			Total
Property	Meana	Minimum	Maximum	Meana	Minimum	Maximum	Meana	Minimum	Maximum
MLTE [M⊙]	15.3 ± 10.7	1.3	61.8	4.4 ± 2.5	1.0	13.4	12.4 ± 10.4	1.0	61.8
dVcore [km s−1]	0.59 ± 0.13	0.31	1.02	0.66 ± 0.18	0.40	1.31	0.61 ± 0.14	0.31	1.31
Rcore [pc]	0.23 ± 0.04	0.13	0.34	0.21 ± 0.04	0.13	0.32	0.23 ± 0.04	0.13	0.34
n [× 103 cm−3]	4.8 ± 2.8	1.1	17.5	2.0 ± 1.1	0.8	5.6	4.1 ± 2.8	0.8	17.5
$\mathcal{R}$ vir	1.5 ± 0.7	0.4	3.0	5.0 ± 2.8	3.1	20.1	2.4 ± 2.2	0.4	20.1
MJ [M⊙]	3.0 ± 2.7	0.2	20.2	5.6 ± 8.9	0.5	55.6	3.7 ± 5.2	0.2	55.6
Mϕ [M⊙]	0.4 ± 0.1	0.1	0.8	0.3 ± 0.1	0.1	0.7	0.4 ± 0.1	0.1	0.8
$\mathcal{R}$ c	5.5 ± 3.4	1.1	20.8	1.3 ± 0.7	0.1	2.6	4.4 ± 3.5	0.1	20.8

^aErrors are the standard deviation.

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Table 4.  Identified C¹⁸O Cores

ID	R.A.	Decl.	VLSR	Tpeak	Aspect	Rcore	dVcore	σ	MLTE	MVIR	${{\mathcal{R}}_{{\rm vir}}}$	${{M}_{{\rm J}}}$	${{M}_{{\Phi }}}$	${{\mathcal{R}}_{{\rm c}}}$	n	Area	Category	Note
C18O-Ori	(J2000)	(J2000)	[km s−1]	[K]		[pc]	[km s−1]	[km s−1]	[${{M}_{\odot }}$]	[${{M}_{\odot }}$]		[${{M}_{\odot }}$]	[${{M}_{\odot }}$]		[× 104 cm−3]
1	5 33 44.4	−5 28 19.0	8.0	1.7	1.2	0.20	0.63	0.27	8.8	16.7	1.9	3.0	0.3	2.7	0.5	Bending	C	⋯
2	5 33 50.4	−5 31 19.0	8.4	1.2	1.3	0.24	0.59	0.25	6.6	17.4	2.7	2.3	0.4	2.4	0.2	Bending	C	⋯
3	5 33 51.9	−5 35 26.5	8.0	1.9	1.7	0.25	0.55	0.23	8.7	15.8	1.8	1.7	0.4	4.0	0.2	Bending	A	AzTEC-Ori 69
4	5 33 53.4	−5 32 26.5	7.9	1.8	1.1	0.24	0.54	0.23	8.5	14.8	1.7	1.6	0.4	4.2	0.3	Bending	C	⋯
5	5 33 53.4	−5 22 41.5	8.1	3.2	1.3	0.24	0.50	0.21	15.0	12.1	0.8	1.1	0.4	9.8	0.5	Bending	A	AzTEC-Ori 72
6	5 33 56.4	−5 29 49.0	8.1	3.3	1.2	0.20	0.61	0.26	17.2	15.1	0.9	2.6	0.3	6.1	1.0	Bending	A	AzTEC-Ori 75
7	5 33 56.4	−5 27 11.5	7.8	0.9	1.1	0.23	0.44	0.19	2.6	9.3	3.6	0.7	0.4	2.4	0.1	Bending	A	AzTEC-Ori 71
8	5 33 57.9	−5 24 11.5	8.3	3.5	1.1	0.26	0.58	0.25	23.1	18.8	0.8	2.2	0.5	8.7	0.5	Bending	C	⋯
9	5 33 59.4	−5 28 41.5	8.0	3.7	1.2	0.22	0.51	0.22	13.9	12.2	0.9	1.3	0.3	8.4	0.5	Bending	A	AzTEC-Ori 79
10	5 34 0.9	−5 30 56.5	8.4	3.5	1.2	0.22	0.66	0.28	23.0	19.9	0.9	3.6	0.3	5.9	0.9	Bending	C	⋯

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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Figures 4(a) and (b) show virial ratio-LTE mass and virial ratio—density relations of the identified C¹⁸O cores, respectively. We consider that the cores with a ${{\mathcal{R}}_{{\rm vir}}}$ value less than three are under virial equilibrium according to Ikeda & Kitamura (2009) With the increasing LTE mass and density, the virial ratio decreases; a similar trend between the LTE mass and the virial ratio was also found by Dobashi et al. (1996), Yonekura et al. (1997), and Ikeda et al. (2007). Most of the bound C¹⁸O cores are distributed in the filamentary structure. On the other hand, most of the unbound C¹⁸O cores are distributed outside the filamentary structure (see Section 3.5). Figure 4(c) shows a LTE mass—${{R}_{{\rm core}}}$ relation of the C¹⁸O cores. The best-fit power-law functions for the unbound and bound cores are log₁₀(${{M}_{{\rm LTE}}}$/${{M}_{\odot }}$) = (3.8 ± 13.6)log₁₀(${{R}_{{\rm core}}}$/pc)+(3.2 ± 9.3) and log₁₀(${{M}_{{\rm LTE}}}$/${{M}_{\odot }}$) = (6.6 ± 16.5)log₁₀(${{R}_{{\rm core}}}$/pc)+(5.3 ± 10.5), respectively.⁹ No significant difference can be seen between the data distributions for the unbound and bound core due to the larger uncertainty in the estimation of the LTE mass, although the trend that the LTE mass of the bound core is larger than that of the unbound core can be recognized in Figure 4(c). Figure 4(d) shows a $d{{V}_{{\rm core}}}$–${{R}_{{\rm core}}}$ relation of the identified C¹⁸O cores. The best-fit power-law functions for the unbound and bound cores are log₁₀($d{{V}_{{\rm core}}}$/km s⁻¹) = (2.7 ± 14.6)log₁₀(${{R}_{{\rm core}}}$/pc)+(1.6 ± 10.0) and log₁₀($d{{V}_{{\rm core}}}$/km s⁻¹) = (2.4 ± 8.3)log₁₀(${{R}_{{\rm core}}}$/pc)+(1.3 ± 5.3), respectively. No significant difference can be seen between the data distributions for the unbound and bound cores.

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Figure 5 shows the change of the systemic velocity of the cores (i.e., the peak C¹⁸O velocity) along the decl., which is best fitted by the relation (${{V}_{{\rm sys}}}$/km s⁻¹)= (5.1 ± 0.3) (decl./deg)+(36.5 ± 1.8). This result suggests a presence of a large-scale velocity gradient along the south–north direction (∼0.7 km s⁻¹ pc⁻¹; cf., the velocity gradient along the integral-shaped filament is estimated to be 1.0 km s⁻¹ pc⁻¹ in the ¹²CO, ¹³CO, H¹³CO⁺, CS lines (Bally et al. 1987; Tatematsu et al. 1993; Ikeda et al. 2007; Shimajiri et al. 2011; Buckle et al. 2012; Shimajiri et al. 2014).

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Region-to-region variation of the dust core mass distribution can be recognized in Figure 1. The high-mass cores (${{M}_{{{{\rm H}}_{2}}}}$ $\geqslant$ 10.0 ${{M}_{\odot }}$) are mainly located in the integral-shaped filament. On the other hand, the intermediate-mass (1.0 ${{M}_{\odot }}$ $\leqslant$ ${{M}_{{{{\rm H}}_{2}}}}$ < 10.0 ${{M}_{\odot }}$) and low-mass (${{M}_{{{{\rm H}}_{2}}}}$ < 1.0 ${{M}_{\odot }}$) cores tend to appear on the outside of the integral-shaped filament. One of the reasons why the high-mass cores are concentrated in the integral-shaped filament is that the 1.1 mm dust cores in the integral-shaped filament could not be resolved in the AzTEC observations with an angular resolution of ∼36'' (corresponding to ∼0.07 pc at 400 pc). In fact, previous SCUBA 850 μm observations with an angular resolution of ∼14'' (Nutter & Ward-Thompson 2007) resolved each 13 1.1 mm dust core into two or three smaller cores (also see Table 2). Furthermore, interferometer observations with a high angular resolution of ∼1–3'' revealed that cores in OMC-2/FIR 4, OMC-2/FIR 6, and L1641 N consist of several smaller cores (Shimajiri et al. 2008, 2009; Stanke & Williams 2007). Observations with interferometers such as the Atacama Large Millimeter/Submilimeter Array are crucial to unveil the internal structures of the cores and confirm whether the trend of the region-to-region variation of the dust core mass distribution is significant.

Recently, Megeath et al. (2012) identified young stellar objects (YSOs) in the Orion A and B molecular clouds from the infrared array camera (IRAC)/Spitzer and multi-band imaging photometer for Spitzer (MIPS)/Spitzer data. They classified 2991 YSOs as pre-main sequence (PMS) stars with disks and 488 YSOs as protostars using the criterion that the spectral index α (=$\lambda {{F}_{\lambda }}$/$d\lambda$) $\geqslant$ −0.3 for protostars and α <−0.3 for PMS stars with disks. The active galactic nucleus, galaxies with polycyclic aromatic hydrocarbons (PAH) emission, outflow shock knots and stars contaminated by PAH emission are excluded from these YSO catalog (see Megeath et al. 2012). The AzTEC map includes 1801 of 2991 PMS stars with disks and 202 of 488 protostars. The central part of the Orion-KL region, which could not be well reconstructed by the AzTEC, includes 122 PMS stars with disks and 22 protostars. We removed these PMS stars with disks and protostars from the following comparison with our cores.

Figure 6 shows a histogram of the separations between the YSOs cataloged by Megeath et al. (2012) and the peak positions of the 1.1 mm dust cores nearest to them. In the figure, only the protostars and PMSs with separations less than 36'', which is the angular resolution of the AzTEC 1.1 mm dust continuum data, are counted. The distribution of the protostars has a peak at a separation of 7.5'' and decreases to 15''. Thus, we adopted the 15'' separation as a criterion to identify the YSOs associated with the 1.1 mm dust cores. As a result, 50/1679 (3.0%) of the PMS stars with disks are associated with the 1.1 mm dust cores and 49/180 (36.1%) of the protostars associated with the cores. Figures 7 show close-up images of the 1.1 mm dust cores associated with the YSOs. We note that the spatial resolution of the AzTEC 1.1 mm dust continuum map is ∼36'' (corresponding to ∼0.07 pc at 400 pc), which cannot resolve each dense core in a cluster-forming region where many dense cores are concentrated in small areas. This effect should lower the detection rate. For example, previous dust continuum observations in the 1.3 mm dust continuum emission with an angular resolution of 11'' found eleven dust cores in the OMC-2 region (Chini et al. 1997), but only three cores are identified in our AzTEC 1.1 mm dust continuum map. In addition, we cannot exclude the possibility that the dust cores and the YSOs overlap by chance on the same line of sight. However, this possibility is thought to be small, since the YSOs are likely to be in the Orion-A GMC.

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To investigate the region-to-region variation of the environments and evolutionary phases of star formation, we compared the number density of the 1.1 mm dust cores, protostars, and PMS stars in OMC-1, OMC-2/3, OMC-4, DLSF, the bending structure, and the southern part in the 1.1 mm dust continuum map. The OMC-1 region is known to be a high-mass star-forming region (Furuya & Shinnaga 2009; Bally et al. 2011; Lee et al. 2013). The OMC-2/3 region is known to be an intermediate-mass star-forming region (Takahashi et al. 2006, 2008, 2009, 2013; Shimajiri et al. 2008, 2009; Takahashi & Ho 2012). The DLSF is influenced by the far-ultraviolet (FUV) radiation from the trapezium cluster (Rodríguez-Franco et al. 2001; Shimajiri et al. 2011, 2013, 2014). In the southern area of the 1.1 mm dust continuum map, cloud–cloud collision is suggested to be occurring by Nakamura et al. (2012). We summarize numbers and number densities of the 1.1 mm dust cores, protostars, and PMS stars in each region in Table 5. Although the six areas/regions are not uniquely and rigorously defined and this is likely to introduce some uncertainties in statistical analyzes and discussions, the number density of the 1.1 mm dust cores in the southern part of the 1.1 mm dust continuum map (4.2 cores pc⁻²) is found to be the lowest. In the integral-shaped filament, the number densities of the protostars in OMC-1, OMC-2/3, and OMC-4 (6.3–8.0 protostars pc⁻²) are similar. On the other hand, the number densities of protostars in the other regions of DLSF, the bending structure, and the southern part are 3–27 times lower than those in the integral-shaped filament. This is consistent with the fact that the OMC-1, OMC-2/3, and OMC-4 regions are more active star-forming regions than the DLSF, bending structure, and southern regions. The number density ratios of the 1.1 mm dust cores without YSOs to YSOs including protostars and PMS stars with disk in OMC-2/3 (6.8 cores pc⁻²/41.8 YSOs pc⁻² = 0.16) and OMC-4 (7.4 cores pc⁻²/81.3 YSOs pc⁻² = 0.09) are 2.6–6.0 times lower than those in the other regions of DLSF (11.1 cores pc⁻²/20.3 YSOs pc⁻²= 0.54), the bending structure (8.4 cores pc⁻²/18.1YSOs pc⁻²= 0.46), and the southern part (4.2 cores pc⁻²/8.6 YSOs pc⁻² = 0.49). Thus, we speculate that the DLSF, bending structure, and southern regions are in younger evolutionary stages than that of the integral-shaped filament.

Table 5.  Numbers and Number Densities of the 1.1 mm Dust Cores, Protostars, and Pre-main Sequence Stars in the Six Distinct Regions

	Area Definition			Number			Number Density
Region	BLC	TRC	Area	1.1 mma	Protostar	PMS Star	1.1 mma	Protostar	PMS Star
	R.A.$_{{\rm J}2000}$, Decl.$_{{\rm J}2000}$	R.A.$_{{\rm J}2000}$, Decl.$_{{\rm J}2000}$	[pc2]				[pc−2]	[pc−2]	[pc−2]
OMC1	5 36 00, −5 32 35	5 34 35, −5 13 35	5.6	⋯	45	621	⋯	8.0	110.2
OMC2/3	5 36 05, −5 14 40	5 34 40, −4 46 40	8.1	55	51	286	6.8	6.3	35.5
OMC4	5 35 22, −5 47 42	5 34 42, −5 28 42	2.6	19	19	190	7.4	7.4	73.9
DLSF	5 36 15, −5 48 35	5 35 35, −5 24 35	3.2	36	1	65	11.1	0.3	20.0
Bending	5 34 45, −5 43 30	5 33 30, −5 21 30	5.6	47	11	90	8.4	2.0	16.1
South	5 38 00, −6 55 30	5 34 30, −5 45 30	49.8	209	61	366	4.2	1.2	7.4

^aNumbers of 1.1 mm dust cores without YSOs.

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This interpretation is supported by the spatial variation of the mean density of the 1.1mm dust core. The mean densities of the 1.1mm dust cores in OMC-2/3 and OMC-4 are 6.2 × 10⁴ and 18.9 × 10⁴ cm⁻³, respectively, while those in the bending, DLSF, and south regions are 1.7 × 10⁴, 2.1 × 10⁴, and 3.0 × 10⁴ cm⁻³, respectively. Consequently, the mean densities of the 1.1 mm dust cores in the integral-shaped filament is 2.1–11.1 times higher than those in the DLSF, bending structure, and southern regions. Since the gas density is generally thought to increase as star formation progresses, the difference in mean density suggests that the integral-shaped filament is most evolved. We must consider another possibility that the OMC-2/3 and OMC-4 regions are forming higher mass stars. In fact, the OMC-2/3 region is known as an intermediate star-forming region (Takahashi et al. 2006). However, as shown in Figure 8(c), the difference in the ${{M}_{{\rm LTE}}}$ distribution between OMC-2/3 and Bending as well as between DLSF and OMC-4 is not significant, suggesting that the stars with similar masses will form on the assumption of the same star formation rate among the regions.

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In the Orion-A GMC, the environments and evolutional phases of star formation have considerable region-to-region variations as discussed in Section 3.2. To investigate the influence of the different environment and evolutional phase on physical properties of the dense cores, we compare the physical properties of the C¹⁸O cores in the OMC-1, OMC-2/3, OMC-4, DLSF, and bending structure regions. Figure 8 shows histograms of the radius, velocity width, LTE mass, and virial ratio of the C¹⁸O cores, respectively, in the five regions. To quantitatively examine the similarities of the physical properties among the five regions, we applied the Kolmogorov–Smirnov (KS) test, which considers the maximum deviation between the distributions of two samples (e.g., Wall & Jenkins 2012), to the five histograms in each panel (see Tables 6 and 7). The results of the KS test show that there is no significant difference among the five regions for most of the physical properties. Although the ${{R}_{{\rm core}}}$ values in DLSF are relatively small as shown in Figure 8(a), the KS test shows no significant difference for the ${{R}_{{\rm core}}}$ values due to the small sample for DLSF. The $d{{V}_{{\rm core}}}$ distribution in DLSF is significantly different from that in the OMC-2/3 region with a significant level of 5% (p-value = 3.1%). The $d{{V}_{{\rm core}}}$ value in DLSF is relatively small as shown in Figure 8(b). The LTE-mass distribution in DLSF is significantly different from those in OMC-1 and OMC-2/3 with a significant level of 5% (p-value = 0.7%). As described in the above, the LTE-mass distributions in DLSF and OMC-4 have two distinct peaks at ${{M}_{{\rm LTE}}}$ = 2.9 ${{M}_{\odot }}$ and 24.2 ${{M}_{\odot }}$.

Table 7.  Kolmogorov–Smirnov Test for R_vir and M_LTE ^a,b

$\mathcal{R}$ vir \MLTE	OMC1	OMC23	OMC4	DLSF	Bending
OMC1	⋯	97.5%	11.1%	0.7%	67.5%
OMC23	97.5%	⋯	11.1%	0.7%	67.5%
OMC4	67.5%	31.3%	⋯	67.5%	67.5%
DLSF	31.3%	11.1%	31.3%	⋯	11.1%
Bending	97.5%	67.5%	97.5%	67.5%	⋯

^aValues in the upper triangular portion are the probabilities of the KS test for M_LTE. ^bValues in the lower triangular portion are the probabilities of the KS test for R_vir.

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The external pressure and internal magnetic (B) field in the cores are important factors to determine their dynamical states. Recently, Li et al. (2013) performed high angular (5'') resolution observations with a velocity resolution of 0.6 km s⁻¹ in NH₃ using the Very Large Array and Green Bank Telescope toward the OMC-2/3 region (c.f., the mean velocity width of the C¹⁸O cores is 0.61 km s⁻¹). They found that most of the massive cores are supercritical from the comparison between mass and critical mass, suggesting that cores will collapse or fragment. The critical mass ${{M}_{{\rm critical}}}$ is defined as ${{M}_{{\rm critical}}}$ = ${{M}_{{\rm J}}}$ + ${{M}_{{\Phi }}}$, where ${{M}_{{\rm J}}}$ and ${{M}_{{\Phi }}}$ are the Jeans mass and the maximum mass that can be supported by a steady B field (e.g., McKee & Zweibel 1992). Here, we investigate the dynamical states of the C¹⁸O cores with the external pressure and the internal magnetic field according to Li et al. (2013).

The Jeans mass is estimated as

$$\begin{eqnarray}&&{{M}_{{\rm J}}}=1.182\frac{{{\sigma }^{4}}}{{{G}^{3/2}}P_{{\rm ic}}^{1/2}},\end{eqnarray} \tag{ 11 }$$

where G is the gravitational constant, σ is the one-dimensional velocity dispersion within the core, and ${{P}_{{\rm ic}}}$ is the external pressure. The pressure ${{P}_{{\rm ic}}}$ can be expressed as ${{P}_{{\rm ic}}}={{n}_{{\rm ic}}}\mu {{m}_{{\rm H}}}\sigma _{{\rm ic}}^{2}$. We considered the tenuous gas traced by the ¹³CO (1–0) emission line as the external gas of the C¹⁸O cores. Thus, we adopted the density ${{n}_{{\rm ic}}}$ of 2.0 × 10³ cm⁻³ (Nagahama et al. 1998) and the velocity dispersion ${{\sigma }_{{\rm ic}}}$ of 0.67 km s⁻¹ (Shimajiri et al. 2014). The velocity dispersion in the core, σ, can be estimated from the core–velocity width $d{{V}_{{\rm core}}}$ as σ = $d{{V}_{{\rm core}}}$ / $\sqrt{8{\rm ln} 2}$, assuming a Gaussian velocity profile. As a result, the Jeans mass ${{M}_{{\rm J}}}$ of the C¹⁸O cores is estimated to be 0.2–55.6 ${{M}_{\odot }}$ (see Table 3). On the other hand, the maximum mass can be estimated using the formula,

$$\begin{eqnarray}&&{{M}_{{\Phi }}}={{c}_{{\Phi }}}\frac{\pi BR_{{\rm core}}^{2}}{{{G}^{1/2}}},\end{eqnarray} \tag{ 12 }$$

where ${{c}_{{\Phi }}}$ is a non-dimensional scaling factor and is 0.12 for an axisymmetric isothermal cloud (Tomisaka et al. 1988) and B is the magnetic field strength. Crutcher et al. (1999) derived the field strength from the observations of the Zeeman effect in CN toward OMC-1 and found B ∼0.19–0.36 mG. Here, we adopted 0.1 mG as the field strength according to Li et al. (2013). Thus, the estimated maximum mass could be the lower limit. As a result, the maximum mass ${{M}_{{\Phi }}}$ of the C¹⁸O cores is estimated to be 0.1–0.8 ${{M}_{\odot }}$ (see Table 3). Here we define the critical mass ratio ${{\mathcal{R}}_{{\rm c}}}$ as,

$$\begin{eqnarray}&&{{\mathcal{R}}_{{\rm c}}}=\frac{{{M}_{{\rm LTE}}}}{{{M}_{{\rm J}}}+{{M}_{{\Phi }}}}.\end{eqnarray} \tag{ 13 }$$

We list ${{M}_{{\rm J}}}$, ${{M}_{{\Phi }}}$, and ${{\mathcal{R}}_{{\rm c}}}$ of each C¹⁸O core in Table 4. Figure 9 shows a relation between the virial and critical mass ratios of the C¹⁸O cores. The ${{\mathcal{R}}_{{\rm c}}}$ value decreases with the increasing the ${{\mathcal{R}}_{{\rm vir}}}$ value. The difference between ${{\mathcal{R}}_{{\rm vir}}}$–${{\mathcal{R}}_{{\rm c}}}$ relations for the bound and unbound C¹⁸O cores are recognized in Figure 9. The slopes for the bound C¹⁸O cores are larger than those for the unbound C¹⁸O cores. The best-fit power-law functions are ${{\mathcal{R}}_{{\rm c}}}$ = 6.6 ± 0.12 ${{\mathcal{R}}_{{\rm vir}}}$ $^{-1.16\pm 0.04}$ for the unbound C¹⁸O cores and ${{\mathcal{R}}_{{\rm c}}}$ = 12.3 ± 2.9 ${{\mathcal{R}}_{{\rm vir}}}$ $^{-1.56\pm 0.18}$ for the bound C¹⁸O cores. We found that all the bound C¹⁸O cores are supercritical (${{\mathcal{R}}_{{\rm c}}}$ $\geqslant$ 1) and 25 of the 61 unbound C¹⁸O cores are subcritical (${{\mathcal{R}}_{{\rm c}}}$ < 1) as seen in Figure 9. Here, we note that there are large uncertainties in the estimates of the Jeans mass owing to the relation of ${{M}_{{\rm J}}}$ $\propto$ ${{\sigma }^{4}}$ and in the estimation of the maximum mass owing to the large uncertainty in B. For further investigation of the dynamical states of the dense cores, observations with higher spectral resolution and measurements of the magnetic field strength would be crucial.

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In Sections 2.1 and 2.2, we have identified the 257 dust and 213 C¹⁸O cores using the Clumpfind method and estimated their physical properties in the C¹⁸O observing area. The mean ${{R}_{{\rm core}}}$ value of the C¹⁸O cores (0.22 ± 0.04 pc) is 2.4 times larger than that of the 1.1 mm dust cores (0.09 ± 0.03 pc). The 1.1 mm dust continuum emission probably traces the inner part of the dense cores, while the C¹⁸O emission line probably traces the outer part of the dense cores. The n value range of the 1.1 mm dust cores ((0.3–915.0) × 10⁴ cm⁻³) is 13 times larger than that of the C¹⁸O cores ((0.8–17.5) × 10³ cm⁻³).

We compared the spatial distribution of the 1.1 mm dust cores with that of the C¹⁸O cores. Figures 10 –13 show the positions of the 213 C¹⁸O cores on the AzTEC 1.1 mm dust continuum map in the OMC-2/3, OMC-4, DLSF, and bending structure regions. Figure 14 shows the positions of the C¹⁸O cores in the OMC-1 region where the 1.1 mm image could not be well reconstructed there. Figure 15 shows the positions of the 1.1 mm dust cores in the southern part of the 1.1 mm dust continuum map where there is no C¹⁸O data. We found that the spatial relation between the 1.1 mm dust and C¹⁸O cores can be categorized into the following four types as shown in Figure 16.

• [Category A] The peak positions of the 1.1 mm dust and C¹⁸O cores agree with each other within the 1.1 mm map resolution of 36''.
• [Category B] Several C¹⁸O cores are distributed around the peak positions of the 1.1 mm dust cores within the 1.1 mm map resolution of 36''.
• [Category C] The C¹⁸O cores not associated with any 1.1 mm dust cores.
• [Category D] The 1.1 mm dust cores not associated with any C¹⁸O cores.

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Table 8 summarizes the numbers of the 1.1 mm dust and C¹⁸O cores in each category. We found 69 pairs of the dust and C¹⁸O cores in Category A. In this category, one C¹⁸O core seems to be associated with one 1.1 mm dust core. In Category B, there are 23 C¹⁸O cores (10.8%) and 10 dust cores (3.9%). There are three possible explanations for the B type cores. One is the several cores are overlapped in the same line of sight. The ${{V}_{{\rm LSR}}}$ is different among the C¹⁸O cores which are associated with the same 1.1 mm dust core (see Tables 2 and 4). Furthermore, the peak positions of 6/10 dust cores (AzTEC-Ori 110, 232, 234, 242, 272, and 482) coincide with those on the C¹⁸O integrated intensity map which includes all velocity components as well as the dust continuum map. These results suggest that several cores are distributed on the same line of sight. Second is due to the poor angular resolution of the AzTEC data. The resolution of the AzTEC data (=36'') is larger than in the C¹⁸O data (=26''). To confirm this possibility, we identified the C¹⁸O cores using the C¹⁸O data smoothed to the same angular resolution as the AzTEC 1.1 mm map (=36''). As a result, 5 of 10 dust cores (AzTEC-Ori 162, 232, 242, 273, and 482) are associated with one C¹⁸O core identified on the 36'' map, although these dust cores are associated with two C¹⁸O cores identified on the 264 map. This result suggests that these 1.1 mm dust cores are not resolved due to the poor angular resolution. Hence, distinct condensations resolved by the C¹⁸O observations may remain unresolved by the AzTEC observations. The other is the depletion of the C¹⁸O molecules in the central parts of dust cores. Such depletion in the central part of the dust condensation has been reported in the B 68 and L 1498 regions (Bergin et al. 2002; Tafalla et al. 2002). Although the inter-core diffuse gas in the Orion-A GMC is warmer than those in low-mass star-forming regions, the dense cores are well-shielded from nearby radiation and become cool enough for CO molecules to freeze onto dust grains. In fact, the CO depletion in the dense cores in the Orion-A GMC has been reported by several authors (Ripple et al. 2013; Ren et al. 2014; Tatematsu et al. 2014).

In Category C, we identified 121 C¹⁸O isolated cores. There are two possible origins of these cores. First is due to the poor angular resolution of the AzTEC data. Some 1.1 mm dust cores are associated with two cores in the 850 μm data with an angular resolution of 14'', suggesting that the 850 μm data with the higher angular resolution resolved the 1.1 mm dust cores. Some 850 μm cores associated with the C¹⁸O cores are not associated with any 1.1 mm dust cores. These cores are located between two 1.1 mm dust cores or on elongated structures in the 1.1 mm dust map as shown in Figures 19 and 20. The reason why the 1.1 mm dust cores are not associated with any 850 μm cores is probably that the 850 μm counterparts in the 1.1 mm map are not identified due to the poor angular resolution. We note that the smoothed 850 μm map with the same angular resolution as in the 1.1 mm map is quite consistent with the 1.1 mm map (see Figure 18 in Shimajiri et al. 2011). Second is that these C¹⁸O cores do not have high enough column density to be detected in the dust continuum. Figure 17 shows the histogram of each column densities of the 1.1 mm dust, all C¹⁸O cores, and C¹⁸O cores in Category C. The column densities of each cores is estimated from the equation, ${{N}_{{{{\rm H}}_{2}}}}$ = n × 2 ${{R}_{{\rm core}}}$. The minimum column density of the 1.1 mm cores (2.4 × 10²¹ cm⁻²) is twice larger than that of the C¹⁸O cores (1.0 × 10²¹ cm⁻²). The column density sensitivity of the C¹⁸O data is higher than that of the 1.1 mm data. On the contrary, the mass sensitivity of the C¹⁸O data is worse than that of the 1.1 mm data as shown in Figure 3(b), since the mean radius ${{R}_{{\rm core}}}$ of the C¹⁸O cores is twice larger than that of the 1.1 mm dust cores. Although the column density estimation has uncertainties, there is a possibility that the C¹⁸O cores lacking 1.1 mm cores are due to the lack of the sensitivity of the column density of the 1.1 mm data. For the 81 bound C¹⁸O cores (51.9%), we speculate that the central part of the cores have not yet evolved to reach the density > ∼10⁴ cm⁻³ and are not detected in the dust continuum, as described in the beginning of this section. For the 40 unbound C¹⁸O cores, we speculate that the unbound C¹⁸O cores are transient structures created by turbulent compression and do not have high enough column density. Most of the unbound C¹⁸O cores (∼70.2%) are in Category C and are not located on the integral-shaped filament. Here, we define the integral-shaped filament as the area having signal-to-noise ratios above 15 for the 1.1 mm flux density in the OMC 2, 3, and 4 regions for this study. Recent three-dimensional MHD simulations have suggested that the turbulent compression creates a local dense part that is gravitationally unbound and cannot produce stars (Nakamura & Li 2011).

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In Category D, there are 178 dust cores that are not associated with any C¹⁸O cores out of the 257 dust cores that were in the C¹⁸O-observed region (excluding Orion-KL). We discuss three possible origins of these cores as follows.

The first possible origin is that the C¹⁸O molecule is selectively dissociated by the FUV radiation from the massive stars in the trapezium cluster and NU Ori. The FUV intensity at the wavelengths of the dissociation lines for abundant CO decays rapidly on the surface of molecular clouds owing to very large optical depths of the FUV emission at these wavelengths (Glassgold et al. 1985; Yurimoto & Kuramoto 2004; Liszt 2007; Röllig & Ossenkopf 2013). Bethell et al. (2007) suggested that the photoionization may play a significant role at ${{A}_{{\rm v}}}\sim 10$ in the case that the cores are sufficiently clumpy using a reverse Monte Carlo radiative transfer code and spectral modeling. They also mentioned that the cosmic-ray ionization is dominant in such high ${{A}_{{\rm v}}}$ regions. For less abundant C¹⁸O, which has shifted absorption lines owing to the difference in the vibrational–rotational energy levels, the decay of FUV is much lower. The FUV radiation can penetrate the dense region owing to the clumpiness of the cloud. Shimajiri et al. (2013) have found that the distributions of the [CI] emission coincide with those of the ¹²CO emission in the PDRs of Orion bar, M43, and DLSF as well as the entire of the cloud, suggesting that these PDRs and the entire of the Orion A cloud have the clumpy structures (Spaans 1996; Kramer et al. 2008). For the three PDRs, the ionizing sources are the neighboring OB stars, because the 8 μm (PAH), 1.1 mm, and ¹²CO emission are located sequentially as a function of the distance from the OB stars, i.e., the edge-on view for the OB star/PDR system (Shimajiri et al. 2011). This result suggests that these PDRs are located on the plane of the sky against OB stars. As a result, C¹⁸O molecules are expected to be selectively dissociated by FUV photons even in the inner part of the cloud. It is possible that the structure of the cloud is clumpy and full of holes such that the mean extinction through the cloud from the perspective of the exciting stars is generally ${{A}_{{\rm V}}}$ $\lt \lt$ 5, even though the apparent extinction (based on the observed dust emission) is much greater. Figure 18 shows the correlation between the 1.1 mm dust and C¹⁸O intensities at the position of the 1.1 mm dust cores. The 1.1 mm dust cores associated with the C¹⁸O cores, which are categorized into A or B, have stronger C¹⁸O intensity. The number of the 1.1 mm dust cores not associated with any C¹⁸O cores (Category D) increases with decreasing C¹⁸O peak intensity. Most of the 1.1 mm dust cores (56/70 cores) in the PDRs are not associated with any C¹⁸O cores. Here, we defined the area of PDRs, DLSF, M43, and Regions A–D, as listed in Table 9 (also see regions A–D shown by Shimajiri et al. 2011). The C¹⁸O intensity at the position of the 1.1 mm dust cores in the PDRs is lower than the intensity expected from the best-fit line for the 1.1 mm dust cores associated with the C¹⁸O cores as shown in Figure 18. The C¹⁸O intensity at the position of several 1.1 mm dust cores not in PDRs is below the 3σ level. These dust cores are located around NGC1977 and DLSF. Thus, these cores seem to be also influenced by the FUV radiation. These facts suggest that the C¹⁸O molecule is selectively dissociated by the FUV radiation in the low 1.1 mm flux density range. Shimajiri et al. (2014) found that the abundance ratio of ¹³CO to C¹⁸O, ${{X}_{^{13}{\rm CO}}}$/${{X}_{{{{\rm C}}^{18}}{\rm O}}}$, in the Orion A GMC decreases with the increasing C¹⁸O column density, implying that the effect of the selective FUV dissociation of C¹⁸O becomes smaller in the higher 1.1 mm flux density range where it becomes hard for the FUV radiation to penetrate owing to the dust shielding. Note that several 1.1 mm dust cores in the large 1.1 mm flux density range are categorized into D. This might be because the FUV radiation can penetrate the large 1.1 mm flux density regions owing to the clumpiness of the cloud. In fact, the ${{X}_{^{13}{\rm CO}}}$/${{X}_{{{{\rm C}}^{18}}{\rm O}}}$ value is larger than the solar system value of 5.5 even in the inner part of the cloud (Shimajiri et al. 2014). Meanwhile, Shimajiri et al. (2011) found that the ¹²CO peak intensity range in the DLSF region is ∼20–50 K. Especially, at the outer layers of the cloud surface in DLSF, it increases up to 50 K. On the assumption that the ¹²CO (J = 1–0) line is optically thick, the result shows that the the temperature is 20–50 K in DLSF, suggesting that the regions with bright dust but faint C¹⁸O emission have dust temperatures higher than the assumed 20 K. Thus, there is a possibility that the outer layers of the cloud surface is significantly heated, driving up dust emission and (self-shielded)¹²CO emission, but the FUV radiation could still penetrate far enough into the unshielded C¹⁸O layer to photodissociate the C¹⁸O molecule without heating it.

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The second possibility is the depletion of the C¹⁸O molecule in the central part of the dust cores. In this case, the C¹⁸O peak positions are distributed around the center positions of the dust cores. The peak positions of the C¹⁸O cores disagree with those of the 1.1 mm dust cores (Ripple et al. 2013; Ren et al. 2014; Tatematsu et al. 2014).

The third possibility is contaminations from the components by ambient gas and surrounding cores. As shown in Figure 18, many 1.1 mm dust cores are not associated with any C¹⁸O cores, in spite of the fact that these C¹⁸O intensities are more than 3σ and are not located in PDRs. In most cases, the C¹⁸O cores and/or extended emission are distributed around the 1.1 mm dust cores categorized into D (also see Figure 3(b) in Shimajiri et al. 2014). There is a possibility that the C¹⁸O cores associated with the 1.1 mm dust cores categorized into D are embedded in the components of other C¹⁸O cores and/or extended emission and and can not be extracted as cores.

We also compared the spatial distribution of the 1.1 mm dust cores with those of the SCUBA 850 μm dust (Nutter & Ward-Thompson 2007), H¹³CO⁺ (1–0)(Ikeda et al. 2007), and N₂H⁺ (1–0) cores (Tatematsu et al. 2008). The H¹³CO⁺ and N₂H⁺ emission are known as the dense gas tracers (e.g., Saito et al. 2001; Takakuwa et al. 2003; Friesen et al. 2010; Johnstone et al. 2010; Maruta et al. 2010; Tanaka et al. 2013). The angular resolution of the SCUBA 850 μm data is 14'' (0.03 pc) and Nutter & Ward-Thompson (2007) identified the condensations having a peak flux density more than 5σ relative to the local background as cores. The H¹³CO⁺ data has an angular resolution of 21'' (0.04 pc) and Ikeda et al. (2007) identified the H¹³CO⁺ dense cores by Clumpfind. The N₂H⁺ observations with a telescope beam size of 178 (0.03 pc) were performed with a grid spacing of 2055 (0.04 pc) and Tatematsu et al. (2008) identified the N₂H⁺ dense cores by eyes from the ${{F}_{1}},F$ = 0, 1–1, 2 component, which is an isolated component of the seven hyperfine components, and the most intense hyperfine component ${{F}_{1}},F$ = 2, 3–1, 2. In Table 2, we summarize the SCUBA 850 μm dust, H¹³CO⁺, and N₂H⁺ cores distributed around the peaks of the 1.1 mm cores within the spatial resolution of 36''. Figures 19–21 show the comparison of the spatial distribution among the 1.1 mm dust, C¹⁸O, 850 μm dust, H¹³CO⁺, and N₂H⁺ cores. Table 10summarizes the comparison.

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The AzTEC map excluding the Orion KL region contains 198 850 μm dust cores and 202 H¹³CO⁺ cores. The overall spatial distribution of the 1.1 mm dust cores has good agreement with that of the 850 μm dust cores. We found that 133 of the 215 850 μm dust cores (61.9%) are associated with the 1.1 mm dust cores. However, 82 850 μm dust cores (38.1%) are not detected in the 1.1 mm continuum emission, probably because of the insufficient sensitivity and beam dilution in the 1.1 mm map. The lowest mass of the dense cores detected in the SCUBA 850 μm observations is 0.13–0.15 ${{M}_{\odot }}$, which is four times smaller than those detected in the 1.1 mm dust continuum observations. In addition, the angular resolution of the SCUBA 850 μm observations is 2.6 times higher than that of the 1.1 mm dust continuum observations. These facts indicate that the sensitivity of the SCUBA data is 10 times higher than that of the AzTEC 1.1 mm dust continuum data. We found that 56.7% (119/210) of the H¹³CO⁺ cores are associated with the 1.1 mm dust cores. The fraction is 1.3 times higher than that for the C¹⁸O cores, in spite of the fact that the mass detection limit of the H¹³CO⁺ observations is twice higher than that of the C¹⁸O observations. Furthermore, the mean density of the 1.1mm dust cores (5.5 × 10⁴ cm⁻³) is closer to that of the H¹³CO⁺ cores (1.6 × 10⁴ cm⁻³) and smaller than that of the C¹⁸O cores (0.4 × 10⁴ cm⁻³). Thus, the 1.1 mm dust continuum and the H¹³CO⁺ emission line are thought to trace the similar density area. These facts suggest that the H¹³CO⁺ emission is a better tracer of the dense cores than the C¹⁸O emission.

In the comparison of the spatial distributions between the 1.1 mm dust and N₂H⁺ cores, the high fraction of 77.8% (21/27) of the N₂H⁺ cores are found to be associated with the 1.1 mm dust cores. Such a high fraction implies that both the N₂H⁺ and H¹³CO⁺ emission can trace well the dense cores compared to the C¹⁸O emission. The remaining six N₂H⁺ cores are not associated with any 1.1 mm dust cores probably owing to the insufficient spatial resolution of the 1.1 mm map. In fact, the six cores are located in the extended feature in the 1.1 mm map, and are associated with the SCUBA 850 μm dust cores. We note that the number of the N₂H⁺ cores is the smallest and the lowest mass of the detected N₂H⁺ cores is 7.3 ${{M}_{\odot }}$, which is much larger than those of the 1.1 mm, 850 μm, and H¹³CO⁺ cores.