Molecular Cloud Cores with High Deuterium Fractions: Nobeyama Mapping Survey

Because the number of maps (44) is large, most maps are presented in the online Figure Set 19, whereas seven representative examples are shown here as Figures 1–7. Table 3 indicates the relation between the map field and figure number. These figures show that for most of the SCUBA-2 cores, the N₂H⁺ emission distribution is similar to the 850 μm dust continuum distribution. The former is slightly larger than the latter in distribution extent. Difference in the beam sizes for the respective observations may explain part of this difference, but probably not all. The N₂H⁺ emission intensity becomes saturated due to high optical depths for very high densities of ≳2 × 10⁶ cm⁻³, for which the dust continuum will still be sensitive. As a result, the dust continuum traces high-density core centers better, resulting in smaller overall sizes. The HC₃N emission shows a distribution similar to the 850 μm dust continuum distribution in most of the cores (∼2/3), again with a slightly larger extent, whereas in the remaining cores (∼1/3), the emission is not detected or surrounds the central region of the 850 μm dust continuum emission.

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N₂H⁺ can be destroyed by CO evaporated from the dust in warm environments (T_dust ≳ 25 K) (Jørgensen et al. 2004; Lee et al. 2004; Tatematsu et al. 2014). CCS is basically an early-type molecule, but may have a second abundance enhancement due to the CO depletion before protostar formation (Li et al. 2002; Lee et al. 2003). Occasionally, the CCS distribution surrounds the YSO, which reflects different stages of the chemical evolution, or has an intensity peak toward the YSO position due to locally high excitation. These variations limit the effectiveness of the N₂H⁺/CCS as a chemical evolution tracer in general.

In general, the agreement between the SCUBA-2 cores and N₂H⁺ distribution is good. In some cases, the peak positions of the N₂H⁺ emission and the 850 μm continuum do not coincide with each other. The star-forming core G208.68−19.20North1 (Figure 4; N(DNC)/N(HN¹³C) = 2.6 ± 1.8, T_bol = 38 ± 13 K, T_kin = 19.7 K) shows such a case. It seems that N₂H⁺ here has been destroyed due to CO evaporated by local heating due to the YSO. This variation limits the effectiveness of N₂H⁺ as a late-type gas tracer in general. Typically, the spatial variation of the N₂H⁺ abundance including chemical evolution will result in a different N₂H⁺ distribution from that of the dust continuum. For example, the southern SCUBA-2 core G211.16–19.33South was detected in the N₂H⁺ emission, but it does not have a prominent peak there. Instead, a prominent N₂H⁺ emission feature is located 1' east of the SCUBA-2 position. This isolated N₂H⁺ feature is an exceptional example in all the fields in this study, however. It is likely that this isolated feature represents a starless core with lower concentration. G211.16–19.33North1, North2 (T_bol = 70 ± 20 K), North4, and North5 (T_bol = 112 ± 16 K), which were detected in both the continuum and N₂H⁺, are star-forming cores. Note that the starless core G211.16–19.33North3 detected in the continuum and N₂H⁺ shows infall motions in ALMA ACA observations (Tatematsu et al. 2020).

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The CCS emission shows a clumpy distribution, which is frequently very different from the 850 μm dust continuum distribution, or is simply not detected in most of the cores. The spatial distribution of the line emission is variable from core to core. For the star-forming core G204.4−11.3A2East (Figure 1; N(N₂D⁺)/N(N₂H⁺) = 0.27 ± 0.07), the N₂H⁺ and HC₃N lines show a distribution similar to the 850 μm distribution, whereas the CCS-H and -L lines show clumpy distributions, which are very different from the 850 μm distribution. Furthermore, the CCS-L emission appears to surround the dust continuum core, which can be explained in terms of the chemical evolution; the gas in the vicinity of the YSO is more evolved. All four lines are detected in the star-forming core G206.93−16.61West3 (Figure 3) and show distributions similar to the 850 μm distribution. It is possible that local warmer temperatures around the YSO provide high excitation for both the CCS-H and -L emission lines to be detected. The upper energy levels of the CCS-H and CCS-L are 19.9 K and 15.3 K, respectively. Toward the starless cores G206.93−16.61West4 and West5 (Figure 3), we did not detect CCS emission, but only N₂H⁺ emission. Their CEF2.0 values are −27 ± 14 and −34 ± 3, respectively, and they are thought to be evolved starless cores. Furthermore, it is possible that CCS depletion occurs in cold starless cores. The star-forming core G212.10−19.15South (Figure 7, N(N₂D⁺)/N(N₂H⁺) = 0.39 ± 0.06) with a YSO with a low bolometric temperature (T_bol = 43 ± 12 K) does not show any CCS emission. Another YSO with a low bolometric temperature (T_bol = 49 ± 21 K) associated with G211.47−19.27South (Figure 6) does show CCS-H emission, whereas CCS-L emission surrounds it as if it were avoiding the YSO. The YSO associated with G211.16–19.27North1 (Figure 5) accompanies the CCS-L emission, but does not show intense CCS-H emission. We detected both CCS-H and -L emission toward the YSO in G206.93−16.61West3 (Figure 3, N(N₂D⁺)/N(N₂H⁺) = 0.04 ± 0.02, N(DNC)/N(HN¹³C) = 1.7 ± 1.2). The star-forming core G212.10−19.15North2 (Figure 7) accompanying a YSO having T_bol =114 ± 10 K is associated with CCS-L emission, and also with very weak CCS-H emission. The CCL-H emission has a higher upper energy level (Table 2), but we do not see a very clear tendency that it is more concentrated on the YSO position than the CCS-L emission. 12% of the Orion starless cores show local CCS peak emission toward YSOs in either CCS-H or -L emission.

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The line detection statistics, line profiles, and column density ratios toward the SCUBA-2 positions are fully presented in our single-pointing paper (Kim et al. 2020). We expect that the telescope error beam will not seriously affect the observed molecular distribution. Because the beam efficiency is high, the line emission distribution is very clumpy, with sizes of ∼1', and the apparent area filling factor of the emission is not very large.

We investigated two extreme cases in detail: case one, G212, in which all the four lines have the same peaks, and case two, G206.12, in which the distributions of the continuum, N₂H⁺, and HC₃N emission are different from that of the CCS emission.

First, we considered field G212 (Figure 7). We detect intense emission in CCS-H and -L toward the YSO associated with G212.10−19.15North3 (N(N₂D⁺)/N(N₂H⁺) = 0.06 ± 0.03 and N(DNC)/N(HN¹³C) = 2.8 ± 2.0). CCS is usually regarded as an early-type gas tracer, but the CCS emission peak coincides with the YSO in this core. In the SCUBA-2 peak G212.10−19.15North1 (N(N₂D⁺)/N(N₂H⁺) = 0.35 ± 0.07), the four molecular lines are all distributed similarly, but their peaks are displaced by ∼40'' or 0.08 pc from the SCUBA-2 peak. It is possible that the YSO is destroying the core. Another possibility is that the YSO has moved from its birth site due to proper motion (Tatematsu et al. 2014), although we do not know the accurate age of the YSO or the vector of its proper motion with respect to the sky plane.

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Next, we investigated the radial intensity distribution field G206.12 (Figure 2), which contains only one SCUBA-2 core G206.12−15.76 (N(DNC)/N(HN¹³C) < 4.8) but was detected with all four lines. This core contains a YSO (T_bol = 35 ± 9 K) near the SCUBA-2 position (29 SSW). We binned the continuum and integrated-intensity line maps to 20'' pixels, which is close to the NRO telescope beam size. Figure 8 compares the intensity normalized for the maximum pixel value in the SCUBA-2 850 μm continuum and the line against the offset from the map center. The values at the same offset from the map center (SCUBA-2 position) were averaged. For the 850 μm continuum, N₂H⁺ and HC₃N have their maxima at the core center, which is almost identical to the YSO position. The 850 μm continuum, however, decreases more sharply than those of N₂H⁺ and HC₃N. Differences in the telescope beam radius (7'' and 9''–10'' for the 850 μm continuum and the lines, respectively) may affect this difference, but also the molecular lines will be saturated for very high densities, as explained in Section 3. CCS-H and CCS-L seem to have a depression toward the core center. It is known that CCS also exists in evolved molecular gas as a secondary late-stage peak due to CO depletion. The observed emission could represent this gas. It seems that the gas near the core center is more chemically evolved so that the CCS abundance is reduced.

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We investigated the physical properties of the SCUBA-2 cores using the N₂H⁺ data toward the SCUBA-2 position (Kim et al. 2020). We adopted the hyperfine spectral fitting result for the N₂H⁺ spectrum. We neglected cores with two N₂H⁺ velocity components, as it was difficult to identify the component that corresponded to the SCUBA-2 emission. The nonthermal and total velocity dispersions, σ_nt and σ_tot, are defined as in Fuller & Myers (1992),

$$\begin{eqnarray}&&{\sigma }_{\mathrm{nt}}=\sqrt{\tfrac{{{\rm{\Delta }}{v}_{\mathrm{obs}}}^{2}}{8\,\mathrm{ln}\,2}-\tfrac{{k}_{{\rm{B}}}{T}_{\mathrm{kin}}}{{\mu }_{\mathrm{obs}}{m}_{{\rm{H}}}}}\end{eqnarray} \tag{ 1 }$$

and

$$\begin{eqnarray}&&{\sigma }_{\mathrm{tot}}=\sqrt{\tfrac{{{\rm{\Delta }}{v}_{\mathrm{obs}}}^{2}}{8\,\mathrm{ln}\,2}+\tfrac{{k}_{{\rm{B}}}{T}_{\mathrm{kin}}}{{m}_{{\rm{H}}}}\left(\tfrac{1}{\mu }-\tfrac{1}{{\mu }_{\mathrm{obs}}}\right)},\end{eqnarray} \tag{ 2 }$$

respectively, where Δv_obs is the FWHM line width, k_B is the Boltzmann constant, and T_kin is the kinetic temperature. We assume that the kinetic temperature is equal to the dust temperature. μ_obs is the molecular weight of the observed molecule in units of the hydrogen mass m_H. The mean molecular weight μ per particle in units of m_H is set to 2.33.

In this study, we adopted the HWHM radius R (dust) and mass M (dust) of the core from the SCUBA-2 results of Yi et al. (2018) to avoid uncertainties of the N₂H⁺ abundance. Yi et al. (2018) expressed the core size R in terms of the FWHM diameter, but we express R in terms of the HWHM radius here.

The virial mass M_vir of the uniform-density sphere is derived using the following formula (McKee & Zweibel 1992):

$$\begin{eqnarray}&&{M}_{\mathrm{vir}}=\displaystyle \frac{5R{\sigma }_{\mathrm{tot}}^{2}}{G},\end{eqnarray} \tag{ 3 }$$

where G is the gravitational constant. The virial parameter α_vir is estimated by dividing the virial mass by the SCUBA-2 core mass,

$$\begin{eqnarray}&&{\alpha }_{\mathrm{vir}}=\displaystyle \frac{{M}_{\mathrm{vir}}}{M(\mathrm{dust})}.\end{eqnarray} \tag{ 4 }$$

Table 4 lists the velocity dispersion, radius, mass, virial mass, and virial parameter for the SCUBA-2 cores. The virial parameter is as large as ∼5. Figure 9 plots the virial parameter as a function of SCUBA-2 core mass. We adopted the uncertainty in the core radius to be 8% from the uncertainty in the distance adopted by Yi et al. (2018), and derived the uncertainty in the virial parameter assuming the propagation of random errors. From this sample, we obtained the least-squares fit to be α_vir ∝ M (dust)^−0.7, which can be well described in terms of a pressure-confined core with a form α_vir ∝ M^−2/3 (Bertoldi & McKee 1992). For the core located near α_vir ∼unity, self-gravity is likely to be dominant if we assume that it is in hydrostatic equilibrium. The core with an α_vir value that is considerably higher than unity probably needs an appropriate external pressure to bind it if it is not a transient object. Similar results showing large virial parameters are obtained by Kirk et al. (2017) and Kerr et al. (2019) in Orion and in other Gould Belt clouds, respectively. Note that core G211.47−19.27South has a very small virial parameter, α_vir = 0.1, and was cataloged by Yi et al. (2018) with an exceptionally small size, which is one order of magnitude smaller than the other cores. Its deconvolved size is smaller than the telescope beam. We define a subcategory of M (dust) $\gt 2{{ \mathcal M }}_{\odot }^{N}$, which seems closer to virial equilibrium. We estimate α_vir to be 5.9 ± 4.6 and 2.5 ± 1.2 for all the cores and for the subcategory M (dust) $\gt 2{{ \mathcal M }}_{\odot }^{N}$, respectively. It should be noted that the virial parameter for the structure embedded in the larger structure can be affected by tidal forces (Mao et al. 2020).

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Table 4. Physical Properties of N₂H⁺ Core for SCUBA-2 Cores in the Orion Region

SCUBA-2 core	Δv(N2H+, SCUBA − 2)	σnt	σtot	R(dust)	M(dust)	Mvir	αvir	Tkin	Filament
	(km s−1)	(km s−1)	(km s−1)	(pc)	( ${{ \mathcal M }}_{\odot }^{N}$)	( ${{ \mathcal M }}_{\odot }^{N}$)		(K)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
G192.32−11.88North	0.66 ± 0.05	0.27 ± 0.02	0.37 ± 0.03	0.030	0.49 ± 0.05	4.7 ± 0.8	9.6 ± 1.7	17.3	N
G192.32−11.88South	0.54 ± 0.02	0.22 ± 0.01	0.33 ± 0.01	0.025	0.22 ± 0.02	3.2 ± 0.6	14.4 ± 2.1	17.3	N
G203.21−11.20East1	0.76 ± 0.04	0.32 ± 0.02	0.38 ± 0.02	0.060	2.50 ± 0.43	9.8 ± 1.7	3.9 ± 0.8	11.2	Y
G203.21−11.20East2	0.44 ± 0.03	0.18 ± 0.01	0.27 ± 0.02	0.060	2.65 ± 1.73	5.0 ± 0.9	1.9 ± 1.3	11.2	Y
G203.21−11.20West1	0.50 ± 0.01	0.20 ± 0.01	0.29 ± 0.01	0.060	2.81 ± 0.13	5.7 ± 1.0	2.0 ± 0.2	11.2	Y
G203.21−11.20West2	0.50 ± 0.01	0.20 ± 0.01	0.29 ± 0.01	0.050	2.51 ± 0.19	4.8 ± 0.8	1.9 ± 0.3	11.2	Y
G204.4−11.3A2East	0.47 ± 0.01	0.19 ± 0.01	0.28 ± 0.01	0.040	2.97 ± 0.23	3.5 ± 0.6	1.2 ± 0.2	11.1	N
G204.4−11.3A2West	0.83 ± 0.06	0.35 ± 0.03	0.40 ± 0.03	0.025	0.99 ± 0.24	4.7 ± 0.8	4.7 ± 1.3	11.1	N
G206.93−16.61West1	0.84 ± 0.03	0.35 ± 0.01	0.43 ± 0.02	0.040	1.55 ± 0.23	8.5 ± 1.5	5.5 ± 1.0	16.8	Y
G206.93−16.61West3	0.65 ± 0.04	0.27 ± 0.02	0.36 ± 0.02	0.030	3.38 ± 0.15	4.6 ± 0.8	1.4 ± 0.2	16.8	Y
G206.93−16.61West4	0.64 ± 0.04	0.26 ± 0.02	0.36 ± 0.02	0.040	1.25 ± 0.67	6.0 ± 1.0	4.8 ± 2.7	16.8	Y
G206.93−16.61West5	0.81 ± 0.07	0.34 ± 0.03	0.42 ± 0.04	0.055	7.10 ± 0.72	11.1 ± 1.9	1.6 ± 0.3	16.8	Y
G206.93−16.61West6	0.62 ± 0.07	0.25 ± 0.03	0.35 ± 0.04	0.040	1.15 ± 0.15	5.8 ± 1.0	5.0 ± 1.2	16.8	Y
G207.36−19.82North1	1.13 ± 0.04	0.48 ± 0.02	0.52 ± 0.02	0.030	1.13 ± 0.46	9.4 ± 1.6	8.3 ± 3.5	11.9	Y
G207.36−19.82North2	0.45 ± 0.02	0.18 ± 0.01	0.27 ± 0.01	0.020	0.44 ± 0.14	1.8 ± 0.3	4.0 ± 1.4	11.9	Y
G207.36−19.82North3	0.69 ± 0.04	0.29 ± 0.02	0.35 ± 0.02	0.020	0.47 ± 0.15	2.9 ± 0.5	6.2 ± 2.1	11.9	Y
G207.36−19.82North4	0.80 ± 0.06	0.33 ± 0.03	0.39 ± 0.03	0.015	0.15 ± 0.05	2.7 ± 0.5	18.0 ± 6.5	11.9	Y
G207.36−19.82South	0.38 ± 0.16	0.15 ± 0.06	0.26 ± 0.11	0.095	2.01 ± 0.91	7.2 ± 1.2	3.6 ± 2.7	11.9	N
G208.68−19.20North2	0.42 ± 0.01	0.16 ± 0.01	0.31 ± 0.01	0.025	2.22 ± 1.15	2.8 ± 0.5	1.3 ± 0.7	19.7	Y
G208.89−20.04East	0.38 ± 0.01	0.14 ± 0.01	0.30 ± 0.01	0.065	3.86 ± 0.29	6.9 ± 1.2	1.8 ± 0.2	19.7	N
G209.05−19.73North	0.38 ± 0.02	0.15 ± 0.01	0.28 ± 0.01	0.115	2.83 ± 0.15	10.3 ± 1.8	3.6 ± 0.5	15.6	Y
G209.05−19.73South	0.43 ± 0.03	0.17 ± 0.01	0.29 ± 0.02	0.070	1.65 ± 0.29	6.9 ± 1.2	4.2 ± 0.9	15.6	Y
G209.29−19.65South1	1.42 ± 0.04	0.60 ± 0.02	0.65 ± 0.02	0.035	1.49 ± 0.26	17.1 ± 3.0	11.5 ± 2.4	17.3	Y
G209.29−19.65South3	0.66 ± 0.03	0.27 ± 0.01	0.37 ± 0.02	0.030	0.50 ± 0.05	4.7 ± 0.8	9.4 ± 1.5	17.3	Y
G209.77−19.40East1	0.35 ± 0.01	0.13 ± 0.01	0.26 ± 0.01	0.025	0.35 ± 0.09	2.0 ± 0.3	5.6 ± 1.6	13.9	Y
G209.77−19.40East2	0.47 ± 0.01	0.19 ± 0.01	0.29 ± 0.01	0.035	1.20 ± 0.56	3.5 ± 0.6	2.9 ± 1.4	13.9	Y
G209.94−19.52North	0.60 ± 0.01	0.25 ± 0.01	0.34 ± 0.01	0.065	2.81 ± 0.28	8.9 ± 1.5	3.2 ± 0.5	16.3	N
G210.82−19.47North1	0.44 ± 0.01	0.17 ± 0.01	0.30 ± 0.01	0.070	0.72 ± 0.08	7.2 ± 1.2	10.0 ± 1.5	16.2	Y
G210.82−19.47North2	0.35 ± 0.01	0.13 ± 0.01	0.27 ± 0.01	0.030	0.15 ± 0.05	2.6 ± 0.5	17.5 ± 6.1	16.2	Y
G211.16–19.33North1	0.44 ± 0.02	0.18 ± 0.01	0.28 ± 0.01	0.055	0.79 ± 0.05	4.9 ± 0.8	6.1 ± 0.8	12.5	Y
G211.16–19.33North2	0.46 ± 0.01	0.19 ± 0.01	0.28 ± 0.01	0.050	0.50 ± 0.20	4.6 ± 0.8	9.2 ± 3.8	12.5	Y
G211.16–19.33North3	0.35 ± 0.01	0.14 ± 0.01	0.25 ± 0.01	0.050	0.41 ± 0.12	3.7 ± 0.6	8.9 ± 2.8	12.5	Y
G211.16–19.33North5	0.48 ± 0.01	0.19 ± 0.01	0.29 ± 0.01	0.060	0.64 ± 0.18	5.8 ± 1.0	9.0 ± 2.7	12.5	Y
G211.47−19.27North	0.52 ± 0.01	0.21 ± 0.01	0.30 ± 0.01	0.035	1.66 ± 0.43	3.6 ± 0.6	2.2 ± 0.6	12.4	N
G211.47−19.27South	1.03 ± 0.03	0.43 ± 0.01	0.48 ± 0.01	0.005	12.25 ± 3.18	1.3 ± 0.2	0.1 ± 0.03	12.4	N
G211.72−19.25North	0.38 ± 0.02	0.15 ± 0.01	0.26 ± 0.01	0.015	0.07 ± 0.06	1.2 ± 0.2	16.8 ± 14.5	12.6	Y
G211.72−19.25South1	0.40 ± 0.05	0.16 ± 0.02	0.26 ± 0.03	0.060	1.15 ± 0.82	4.9 ± 0.8	4.3 ± 3.2	12.6	Y
G212.10−19.15North1	0.84 ± 0.04	0.35 ± 0.02	0.40 ± 0.02	0.090	3.52 ± 1.68	17.0 ± 2.9	4.8 ± 2.4	10.8	Y
G212.10−19.15North2	0.69 ± 0.02	0.29 ± 0.01	0.35 ± 0.01	0.060	1.65 ± 0.72	8.5 ± 1.5	5.1 ± 2.3	10.8	Y
G212.10−19.15North3	0.55 ± 0.05	0.23 ± 0.02	0.30 ± 0.03	0.055	1.36 ± 0.78	5.8 ± 1.0	4.2 ± 2.5	10.8	Y
G212.10−19.15South	0.38 ± 0.01	0.15 ± 0.01	0.25 ± 0.01	0.075	2.41 ± 1.00	5.4 ± 0.9	2.2 ± 1.0	10.8	Y
Mean (All)	0.59 ± 0.23	0.24 ± 0.10	0.33 ± 0.08	0.047 ± 0.023	1.90 ± 2.14	5.9 ± 3.6	5.9 ± 4.6	13.9 ± 2.7
Median (All)	0.50	0.20	0.30	0.040	1.36	4.9	4.7	12.5
Mean (Starless)	0.64 ± 0.11	0.26 ± 0.11	0.35 ± 0.09	0.048 ± 0.025	1.81 ± 1.53	6.8 ± 4.1	5.8 ± 4.5
Median (Starless)	0.63	0.26	0.35	0.040	1.37	5.4	4.5
Mean (Star-forming)	0.51 ± 0.16	0.21 ± 0.07	0.31 ± 0.05	0.045 ± 0.021	2.03 ± 2.84	4.6 ± 2.0	6.0 ± 4.8
Median (Star-forming)	0.48	0.19	0.30	0.050	1.36	4.8	5.1

Note. Column 1: SCUBA-2 core name. Column 2: N₂H⁺ FWHM line width toward the SCUBA-2 position (Kim et al. 2020). Column 3: nonthermal velocity dispersion. Column 4: total velocity dispersion. Column 5: HWHM dust continuum radius (Yi et al. 2018). Column 6: mass from the dust continuum (Yi et al. 2018). Column 7: virial mass. Column 8: virial parameter. Column 9: kinetic temperature. Column 10: association with the filament.

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We statistically compared the emission distributions of the four lines on the basis of their integrated-intensity maps toward Orion cores. We selected the emission feature that was approximately coincident with the SCUBA-2 850 μm dust continuum emission through visual inspection and fitted a two-dimensional Gaussian to it. We identified the most prominent feature that was nearest to the SCUBA-2 position. Although this description may sound somewhat imprecise, the identification is practically straightforward.

The individual core data are listed in Tables A4 and A5 in the Appendix. Table 5 summarizes statistics for the offset θ_offset of the Gaussian-fit center from the SCUBA-2 position and the beam deconvolved radius R of the fit. Note that the offset of CCS-L is twice as large as the offsets of N₂H⁺ and CCS-H. Therefore, CCS-L emission is in general less correlated with the SCUBA-2 emission. We did not observe large differences in radius between the lines.

We also illustrate the offset and emission radius by a histogram. Figure 10 provides a comparison of the offset of the line emission fitted ellipse center from the SCUBA-2 position for the Orion cores. The offsets in N₂H⁺ and HC₃N are similarly distributed, having sharp peaks at θ_offset = 0–0.02 pc. These offsets are not significant, because 0.02 pc approximately corresponds to half the NRO beam size. The offsets in CCS-H and CCS-L appear to be less peaked. Figure 11 shows a comparison of the deconvolved radius values of the line emission feature for the Orion cores, in which no significant differences among the lines are observed.

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At the bottom of Table 4, we list parameter statistics for all the cores together and for starless and star-forming cores separately. The starless and star-forming cores have very similar radii, suggesting no evolutionary change in the core radius is detected at 0.027 pc linear resolution. Furthermore, their nonthermal velocity dispersions, masses, and virial masses are not appreciably different. Therefore no evidence for the dissipation of turbulence is identified at the employed spatial resolution, as already noted by Kim et al. (2020). The absence of differences in the velocity dispersion between the starless and star-forming cores contradicts the results of earlier studies (Beichman et al. 1986; Benson & Myers 1989; Zhou et al. 1989; Tatematsu et al. 1993). One possibility is that largely improved sensitivities allow the identification of low-luminosity YSOs that were previously undetectable. To test this possibility, we plotted the nonthermal velocity dispersion against the bolometric luminosity of the YSO taken from Dutta et al. (2020; Figure 12). Except for the core with the most luminous YSO (G211.47−19.27South, L = 180 ± 70 ${{ \mathcal L }}_{\odot }^{N}$), no clear positive correlation was observed. Our data were less affected by star formation activities because the tracer N₂H⁺ employed is insensitive to shocked gas (Turner & Thaddeus 1977; Womack et al. 1993; Bachiller 1996; Caselli et al. 2002), unlike CS and NH₃ employed in previous studies. Our samples contain warm T_bol YSOs, which are not too young to observe the impacts of YSO activities.

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We also compared the deconvolved radii (Yi et al. 2018) between the starless and star-forming cores. Figure 13 shows the histogram of the SCUBA-2 radius R (dust) of the two categories. The starless and star-forming cores have very similar radii. We corrected the semimajor axis a and semiminor axis b for the telescope beam in quadrature, and calculated the deconvolved radius R,

$$\begin{eqnarray}&&R={[{({a}^{2}-{(\mathrm{HPBW}/2)}^{2})({b}^{2}-(\mathrm{HPBW}/2)}^{2})]}^{1/4}.\end{eqnarray} \tag{ 5 }$$

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The SCUBA-2 beam radius is 7'' or 0.0135 pc; thus, the cores are well resolved. This similarity is not consistent with the result from H¹³CO⁺ observations toward Taurus by Mizuno et al. (1994), who concluded that starless cores are larger than star-forming cores, but it is consistent with that from N₂H⁺ observations by Tatematsu et al. (2004) for the same cores. A possible reason for this difference is the depletion of H¹³CO⁺ molecules in the starless cores, which could cause flat-topped radial intensity profiles toward cold starless cores, and correspondingly lead to larger radii (Tatematsu et al. 2004). It seems that when we use a molecular-line tracer affected by depletions we see a size difference between the starless and star-forming cores. In contrast, when we use the dust continuum or a tracer that is less affected by depletion, it seems difficult to observe differences in radii with HPBWs of 0.01−0.03 pc. When we adopt Welch's t-test for the null hypothesis that the starless and star-forming cores have equal radii, we obtain a p-value of 0.55, which is considerably higher than a standard threshold of 0.05 for statistical significance. Thus, we cannot statistically conclude that these two categories have different radii.

It is suggested that the sizes of identified cores are often very close to the telescope beam size, and this can be well explained if cores have power-law density profiles. Ladd et al. (1991) indicated that the observed emission size tends to be 10−80% larger than the original beam size if we assume the power-law radial intensity distribution. Young et al. (2003) showed an anticorrelation between the power-law index and the deconvolved emission size (see their Figure 27). Then, in these cases, the observed radius represents the radial density slope rather than the physical boundary. The mean HWHM radius (230 ± 114 or 0.045 ± 0.022 pc) and beam radius (7'' or 0.0135 pc) suggest a power-law index p of <1.4 for the radial density profile ρ (r) ∝ r^−p . Therefore the SCUBA-2 core in Orion studied by Yi et al. (2018) arguably has a shallow radial density profile.

We investigated how the physical parameters of the starless cores compare to evolutionary indications based on chemistry, as encoded by CEF2.0, which is the chemical evolution tracer based on the deuterium fraction. Table 6 lists the deuterium fraction and CEF2.0 for all cores observed. Note that CEF2.0 is defined only for the starless cores in Orion, but this table contains the starless and star-forming cores, and also the cores outside Orion. Kim et al. (2020) pointed out that the deuterium fraction will be seriously underestimated for distant (>1 kpc) cores due to beam dilution. The adopted distance is listed in Table A1. Table A2 in the appendix contains the YSO association information. The CEF2.0 values of the Orion starless cores were calculated from the column density ratios of N₂D⁺/N₂H⁺ and DNC/HN¹³C from our single-pointing observations (Kim et al. 2020). We question whether there is any evidence that stable cores change into unstable cores by changing physical properties such as turbulence.

Figure 14 shows the plot of the nonthermal velocity dispersion, radius, H₂ column density, mass, and virial parameter of the Orion starless cores against CEF2.0, in which no significant trend observed. Radius R and mass M increase with increasing CEF2.0 from CEF2.0 = −24 to −19, but this rise is probably not significant when we take the error in CEF2.0 into account. The virial parameter α_vir of the starless cores is as large as 1−20. If we allow 1σ uncertainty, four cores (44%) out of the nine starless cores in this figure may fit the range 0.5 < α_vir < 2. Large virial parameters for starless cores suggest that most of them are either pressure confined or transient. Chen et al. (2020) showed the evolution of unbound cores into bound cores in their simulation.

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Crapsi et al. (2005) noted that the chemical properties (including the deuterium fraction) and physical properties (density, line width, etc.) of starless cores as a whole can trace the evolutionary stage, although they did not find very tight dependences between these properties. Their samples included starless cores at younger stages such as B68, TMC-1, L492, L1498, and L1512 (Shirley et al. 2005; Hirota & Yamamoto 2006), which have values of −100 ≲ CEF2.0 ≲ −60 (Kim et al. 2020), implying lower deuterium fractions. They concluded that evolved starless cores with higher N(N₂D⁺)/N(N₂H⁺) tend to have higher central H₂ column densities and more compact density profiles. They employed multiple tracers including N₂H⁺, N₂D⁺, and the dust continuum emission, and the above physical parameters were derived at linear resolutions of 0.006−0.02 pc, 1.5−6 times better than our linear resolution (0.03−0.04 pc). The difference in the linear resolution and/or the CEF2.0 range may at least partially explain the difference in conclusion.

Marka et al. (2012) observed Bok globules in NH₃ and CCS to study their chemical evolution. They did not find any globules with extremely high CCS abundances and concluded that all of the observed Bok globules are in a relatively evolved chemical state. It is possible that the SCUBA-2 cores with high column densities selected in our study are similarly biased to evolved cores.

We did not observe intense CCS emission even at the starless core stage. Relatively late chemical evolution stages may be one reason, but we also suspect that serious depletion occurs in CCS at cold starless cores, which leads to the low values of the CCS column density. Some previous studies of core chemistry evolution used the abundance at the molecular line emission maximum (Ohashi et al. 2014; Tatematsu et al. 2014), which can be different from that at density peaks traced by the dust continuum emission. In these cases, the depletion of CCS can be alleviated. We used the SCUBA-2 position as the core centers where the CCS depletion could be severe.

We investigated the physical parameters of the star-forming cores against the bolometric temperature of associated YSOs (Dutta et al. 2020). The bolometric temperature is a reliable empirical tracer of star-forming core's evolution (Chen et al. 1995). The bolometric temperature T_bol can be obtained from the flux-weighted mean frequencies in the observed spectral energy distributions (SEDs; Myers & Ladd 1993). Dutta et al. (2020) used their ALMA 1.3 mm fluxes as well as fluxes at other wavelengths from Cutri et al. (2003), Lawrence et al. (2007), Wright et al. (2010), Megeath et al. (2012), Stutz et al. (2013), Tobin et al. (2015), Doi et al. (2015), and Yi et al. (2018). Figure 15 shows the nonthermal velocity dispersion, radius, H₂ column density, mass, and virial parameter versus T_bol for the star-forming cores (Dutta et al. 2020). We did not observe any significant trends in this figure. The virial parameter α_vir of the star-forming core ranged from 0.1 to 20. Six (55%) of the eleven star-forming cores in this figure may fit the range α_vir = 0.5–2 when we allow a 1σ uncertainty. The core that forms a protostar should be gravitationally bound or pressure confined at least when the protostar forms. Large virial parameters of the star-forming core suggest either a confining external pressure, a fast core dispersal after star formation, strong tidal forces from the ambient gas, or systematic bias in the estimation of the parameter. Furthermore, the associated outflow can stir up the core to some extent through magnetic fields, although N₂H⁺ is less affected by shocks.

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We also investigated the distribution of CCS (young-gas tracer) and N₂H⁺ (evolved-gas tracer) versus T_bol . Figure 16 shows the close-up maps of representative star-forming cores aligned in order of the bolometric temperature T_bol of the associated YSO as an evolutionary tracer for star-forming cores. Comparisons including HC₃N on the full-sized maps of the all star-forming Orion cores with T_bol can be seen with Table A2, Figures 1– 7, and Figure Set 19. Again, no clear trend is seen.

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Some of the observed cores are apparently located in filaments. Because filaments likely play an important role in inflow into cores, we investigate whether there are any differences between cores inside or outside filaments. The association with a filament was judged from the SCUBA-2 and N₂H⁺ distributions is shown in Table 4. Table 7 summarizes the statistics of the Orion core. Here, we do not distinguish the starless and star-forming cores. The nonthermal velocity dispersions and radii are similar between the two categories. The cores associated with filaments are slightly less massive and have smaller virial parameters, although the standard deviation is large and so the differences may not be significant.

Table 7. Core Properties with and without the Filaments

Filament	Calculation	σnt	R (dust)	M (dust)	αvir
		(km s−1)	(pc)	( ${{ \mathcal M }}_{\odot }^{N}$)
Y	mean	0.24 ± 0.11	0.05 ± 0.02	1.58 ± 1.41	6.29 ± 4.56
Y	median	0.20	0.05	1.23	4.93
N	mean	0.25 ± 0.09	0.04 ± 0.03	3.03 ± 3.66	4.54 ± 4.62
N	median	0.22	0.04	2.01	3.18

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Details of the kinematics of the cores discussed here are beyond the scope of this paper, but we consider here two example fields, each containing representative examples, G206.12 and G211.16. We selected them from Orion cores, as they have more accurate distances (Kounkel et al. 2017; Perryman et al. 1997), and they are less affected by beam dilution (Kim et al. 2020).

One field, G206.12, has only one SCUBA-2 core inside the mapped area (Figure 2), whereas the other field, G211.16, contains six SCUBA-2 cores (Figure 5). The N₂H⁺ emission was used for the analysis. We calculated the intensity-weighted radial velocity (moment 1) using the hyperfine group J = 1 → 0 F₁ = 2 → 1 containing the brightest hyperfine component to obtain better signal-to-noise ratios (S/Ns), and the velocity dispersion (moment 2) using the isolated hyperfine component J = 1 → 0, F₁, F = 0, 1 → 1, 2, which is optically thinner and less affected by the neighboring satellites.

Field G206.12 (Figure 17) does not exhibit any significant velocity gradients. The velocity dispersion seems to increase toward the core center harboring the YSO. This shift may represent the influence from the YSO. In field G211.16 (Figure 18), however, the velocity field shows distinct velocities for filaments.

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