A HUNT FOR MASSIVE STARLESS CORES

Figures 1 through 10 present summary maps of the 30 targets, with one column for each source. Note that, except in the cases of D2 and D5, the FOV is centered on the IRDC core/clump Σ peak from BT12. The D2 region includes both D2 and (part of) D4, whereas the D5 region includes both D5 and D7. In these cases, the FOV is centered in between the Σ peaks. In all panels, the colored background shows MIREX-estimated mass surface density, Σ, in ${\rm{g}}\ {\mathrm{cm}}^{-2}$, from BT12. All panels also show the primary beam diameter FOV, which delimits the region that is searched for ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cores. The locations ("+" signs) and names (XXA, XXB, XXC..., indicating the ordering of decreasing ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) line flux) of these cores are also shown. These cores are discussed below, in Section 4.2. The panels also indicate the locations ("×" signs) of ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) "clump-scale" structures with $\geqslant 4\sigma$ peaks in the 5 $\mathrm{km}\ {{\rm{s}}}^{-1}\,$velocity range 0th-moment map that are not found by our ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) core detection algorithm.

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In the top row, the contours show 1.3 mm continuum emission. All regions generally have very strong continuum detection (C3 only has a 3σ detection, while D2 has 4σ detection). There is often quite good correspondence between the 1.3 mm continuum structures and those seen in the BT12 MIREX maps. Note, however, that the mm continuum image is insensitive to the structures that are larger than the maximum recoverable scale of the observation (i.e., ≳20''), unlike the MIREX map. Still, there are many regions where a MIREX Σ peak is not an especially strong mm continuum source and vice versa. Such discrepancies may arise because of problems in the MIREX map (e.g., where MIR bright sources are present) and/or if the mm continuum emission is being enhanced by higher temperatures, e.g., from local protostellar heating. A lack of prominent mm continuum emission from high Σ MIREX peaks may indicate these regions are extremely cold.

In the second row, the contours show ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) integrated intensity (0th-moment map). Here, and for all 0th-moment maps, the integration spans a velocity range of 5 $\mathrm{km}\ {{\rm{s}}}^{-1}\,$centered on ${v}_{\mathrm{LSR}}$ of each IRDC⁹ (see Table 1). We find the strongest detections of ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) in the B1, C9, and H2 clumps, which all show extended structures that are also identified as some of the highest ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) line flux cores. In general, the strongest cores in a given region (e.g., A1A, A3A, etc) are easily visible in these 0th-moment maps, but many of the weaker cores do not stand out above the noise (lowest contour is 3σ ≃ 60 mJy bm⁻¹ $\mathrm{km}\ {{\rm{s}}}^{-1}$), which is higher than the noise resulting from the more localized velocity ranges used to detect the cores.

In addition, there remain some $\geqslant 4\sigma$ features visible in these region maps that have not been identified as cores (i.e., as connected structures in PPV space). Note, however, that our core search is confined to within the primary beam, so strong features beyond this scale would not have been identified. Because our focus is on the cores, we only note here the position of these "clump-scale" structures (on average, there are about two per region), and discuss below their likelihood of being real features or merely noise fluctuations, by comparison with other tracers.

The third to sixth rows show 0th-moments maps of DCO⁺(3-2), DCN(3-2), ${{\rm{C}}}^{18}{\rm{O}}$(2-1), and CH₃OH(v t = 0 5(1,4)-4(2,2)), respectively. These images contain a lot of ancillary information, which will not be discussed in detail in this paper. We note that all regions have strong ${{\rm{C}}}^{18}{\rm{O}}$(2-1) detection, which tends to trace spatially extended structures (again, subject to the constraints of spatial filtering of the largest scales). The other tracers tend to identify smaller scale structures.

One particular use of these images is to show the presence or absence of these species at the locations of identified ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cores and "clump-scale" structures. Cores will be discussed in more detail in Section 4.2. For the clump-scale structures, several are also seen in these ancillary tracers, e.g., in: DCO⁺(3-2), such as the source in A3; DCN(3-2), such as the MIR-bright source in B2; or 1.3 mm continuum, such as sources in C6 (north) and F3 (also seen in CH₃OH). When such coincident detections in independent tracers are seen, it increases our confidence in the reality of the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) detected structure. For the remainder, it is hard to be sure about their reality: more sensitive follow-up observations are needed. There may be several reasons these ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) structures are not identified as cores: they may not be well-connected in velocity space; they may not subtend a sufficient angular area compared to the beam; they may be too close to the boundary of the primary beam, where we truncate the core search algorithm; or they may already be attached to an identified core, but have their clump-scale 0th-moment peak slightly displaced from the core peak (e.g., near H2J and H3A).

Physically, some of the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) structures that are only seen in the broader, 5 $\mathrm{km}\ {{\rm{s}}}^{-1}\,$velocity range 0th-moment map may represent an early stage of ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) core formation, i.e., when the material is less concentrated in position–velocity space. Thus, the follow-up of such structures with higher sensitivity observations is warranted to investigate such a possibility.

In total, 141 ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cores are found in the 30 data cubes, based on the criteria stated in Section 3. They are labeled as + signs in the second row of Figures 1 through 10. The cores are named based on the ranking of their ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) flux within each surveyed region: e.g., A3A is the highest-flux core within the A3 region, followed by A3B, A3C, etc.

Most strong features in the 0th-moment maps are identified, along with many cores that do not show up in these maps. Note, these 0th-moment maps are integrated over a 5 $\mathrm{km}\ {{\rm{s}}}^{-1}\,$range. Meanwhile, many weak ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$ cores are typically found in a velocity range much less than 5 $\mathrm{km}\ {{\rm{s}}}^{-1}\,$(the narrowest velocity range is 0.30 $\mathrm{km}\ {{\rm{s}}}^{-1}\,$by definition, corresponding to two channels, see Section 3). As a result, many of the weak cores do not show up in the region figures, i.e., at the positions of these cores there is no corresponding ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$ contours seen.

We have ranked the cores based on their ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$ 0th-moment flux, and list the strongest 50 of these in Table 2, along with the six cores from T13. The table lists core positions (intensity-weighted center) in Galactic coordinates in columns 2 and 3. Columns 4 and 5 give the velocity range over which the core is detected. Note the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cube used for core finding has been smoothed to 0.15 $\mathrm{km}\ {{\rm{s}}}^{-1}$ velocity resolution. In general, cores with structures in more channels tend to be more significant. Column 6 shows the intensity-weighted ${v}_{\mathrm{LSR}}$. and Column 7 shows the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) total line flux, ${S}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$, for each core. Columns 8, 9, and 10 show fluxes at the core position in the continuum image, the ${\mathrm{DCO}}^{+}\,$(3-2) 0th-moment image, and the ${{\rm{C}}}^{18}{\rm{O}}\,$(2-1) 0th-moment image (note that the T13 spectral set-up did not have ${{\rm{C}}}^{18}{\rm{O}}\,$(2-1)). The 0th-moment images of ${\mathrm{DCO}}^{+}\,$and ${{\rm{C}}}^{18}{\rm{O}}\,$are integrated within the velocity ranges shown in columns 4 and 5. The relevant signal-to-noise ratio (S/N) is also listed in these columns. Note that sometimes these fluxes can be negative in the case of non-detections where noise or other fluctuations cause the signal to be negative.

Table 2.  ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) Cores

Core	l	b	${v}_{\min }$	${v}_{\max }$	$\bar{v}$	${S}_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$	${S}_{1.30\mathrm{mm}}$/S/N	${S}_{{\mathrm{DCO}}^{+}}$/S/N	${S}_{{{\rm{C}}}^{18}{\rm{O}}}$/S/N
	(deg)	(deg)	($\mathrm{km}\ {{\rm{s}}}^{-1}$)	($\mathrm{km}\ {{\rm{s}}}^{-1}$)	($\mathrm{km}\ {{\rm{s}}}^{-1}$)	(Jy $\mathrm{km}\ {{\rm{s}}}^{-1}$)	($\mathrm{Jy}\ {\mathrm{bm}}^{-1}\,$ $\mathrm{km}\ {{\rm{s}}}^{-1}$)	($\mathrm{Jy}\ {\mathrm{bm}}^{-1}\,$ $\mathrm{km}\ {{\rm{s}}}^{-1}$)	($\mathrm{Jy}\ {\mathrm{bm}}^{-1}\,$ $\mathrm{km}\ {{\rm{s}}}^{-1}$)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
1 C9A	28.39894	0.08112	77.05	80.35	78.44	1.4e+00	6.9e−03/30	−8.6e−03/−0.88	−2.3e−01/−21
C1S	28.32194	0.06737	76.90	81.90	79.40	6.3e−01	1.6e−02/59	6.7e−02/8.2	⋯/⋯
G2N	34.78101	−0.56816	38.95	43.95	41.45	6.1e−01	1.4e−03/8.3	1.5e−01/14	⋯/⋯
2 B1A	19.28744	0.08048	26.40	29.10	27.66	4.6e−01	3.4e−04/1.5	4.4e−02/5.0	2.6e−02/2.7
C1N	28.32508	0.06714	78.68	83.68	81.18	2.7e−01	1.9e−03/6.9	4.6e−02/5.6	⋯/⋯
3 H2A	35.48231	−0.28684	44.95	47.20	45.60	2.3e−01	5.4e−04/2.4	4.7e−02/4.7	2.7e−02/2.3
G2S	34.77842	−0.56838	39.30	44.30	41.80	2.2e−01	1.2e−03/6.7	1.1e−01/10	⋯/⋯
F1	34.41928	0.24588	53.62	58.62	56.12	1.6e−01	2.9e−03/8.7	1.0e−01/12	⋯/⋯
F2	34.43525	0.24140	55.16	60.16	57.66	9.5e−02	3.5e−03/16	1.5e−01/16	⋯/⋯
4 B1B	19.28583	0.08304	26.40	27.15	26.76	6.5e−02	7.6e−03/23	3.3e−02/7.0	6.7e−03/1.3
5 C9B	28.39679	0.08314	76.45	77.95	77.30	6.5e−02	1.1e−04/0.32	−1.2e−02/−1.7	−5.4e−02/−7.5
6 H2B	35.48377	−0.28801	45.10	46.90	46.10	6.3e−02	2.6e−03/11	2.5e−02/2.7	4.1e−02/3.9
7 D6A	28.55294	−0.24057	85.50	86.85	86.39	6.0e−02	3.5e−04/0.93	−1.0e−02/−1.2	1.1e−02/1.2
8 D5A	28.56350	−0.23050	87.90	88.95	88.28	5.8e−02	4.3e−04/1.7	2.6e−03/0.33	−2.3e−02/−2.9
9 B2A	19.30983	0.06697	24.90	26.55	25.56	5.6e−02	2.8e−03/9.8	2.8e−02/4.2	5.5e−02/7.5
10 H5A	35.49591	−0.28680	45.10	46.30	45.34	5.2e−02	4.1e−04/1.7	3.3e−02/3.9	2.0e−02/2.2
11 H1A	35.47838	−0.30785	44.20	45.55	44.88	5.0e−02	−2.2e−04/−0.68	2.5e−02/3.0	2.3e−02/2.5
12 H2C	35.48314	−0.28847	44.95	46.45	45.69	4.9e−02	9.0e−04/3.6	2.1e−02/2.6	3.0e−02/3.1
13 F4A	34.45842	0.25645	56.95	58.15	57.40	4.9e−02	1.4e−03/6.4	4.7e−02/6.0	1.5e−02/1.7
14 C3A	28.34951	0.09583	77.35	79.00	78.29	4.9e−02	3.8e−04/1.1	6.7e−03/1.0	−1.7e−02/−2.4
15 C5A	28.35517	0.05754	76.45	77.65	76.80	4.8e−02	−7.0e−05/−0.29	4.0e−03/0.72	1.4e−03/0.22
16 D2A	28.53882	−0.27327	84.45	85.80	84.73	4.8e−02	1.2e−04/0.40	4.0e−04/0.048	−9.0e−03/−0.94
17 H2D	35.48285	−0.28575	44.35	47.20	45.68	4.6e−02	2.8e−04/1.2	2.7e−02/2.4	−5.6e−02/−4.3
18 H2E	35.48511	−0.28485	45.55	46.60	46.08	4.6e−02	1.9e−04/0.51	5.4e−02/7.5	3.5e−04/0.044
19 D2B	28.53645	−0.27670	85.50	86.55	86.11	4.6e−02	1.3e−05/0.047	−1.0e−02/−1.3	−2.5e−03/−0.31
20 C4A	28.35450	0.07184	79.15	80.65	79.87	4.4e−02	5.0e−04/2.2	8.5e−03/1.4	2.3e−02/3.3
21 C2A	28.34592	0.05881	77.35	79.75	78.36	4.3e−02	5.9e−04/1.9	8.1e−03/0.94	−1.6e−02/−1.7
22 C2B	28.34677	0.05918	79.45	79.60	79.50	4.1e−02	2.4e−03/6.5	−3.1e−03/−0.92	−4.9e−03/−1.8
23 A3A	18.80730	−0.30530	64.10	66.05	65.16	3.9e−02	1.8e−03/8.2	2.4e−02/3.3	1.8e−02/2.4
24 D1A	28.52688	−0.25208	87.30	87.90	87.46	3.8e−02	1.3e−04/0.50	1.1e−02/1.8	3.0e−02/4.5
25 A3B	18.80692	−0.30445	63.95	65.90	65.15	3.7e−02	4.3e−05/0.18	1.5e−02/2.1	2.3e−02/3.1
26 H1B	35.47858	−0.31096	43.90	45.40	44.49	3.6e−02	5.5e−04/2.4	9.3e−03/1.1	−8.1e−03/−0.84
27 D2C	28.53883	−0.27762	88.65	88.80	88.75	3.5e−02	1.9e−04/0.57	−3.3e−03/−0.79	4.3e−03/1.0
28 D1B	28.52548	−0.25163	86.40	86.70	86.58	3.5e−02	6.6e−04/2.4	3.3e−03/0.74	1.1e−05/2.1e−3
29 C7A	28.36254	0.12185	79.45	80.50	80.20	3.4e−02	2.8e−04/0.76	−2.5e−03/−0.42	−2.7e−02/−4.6
30 D7A	28.56324	−0.23270	84.45	84.90	84.65	3.3e−02	1.2e−04/0.40	−2.4e−03/−0.46	−1.1e−02/−1.8
31 D2D	28.54054	−0.27463	88.80	89.25	89.09	3.3e−02	−1.0e−04/−0.29	6.1e−04/0.12	−2.6e−03/−0.48
32 D8A	28.57531	−0.23401	84.45	85.50	84.65	3.3e−02	−2.5e−04/−0.78	1.3e−02/1.8	−2.7e−03/−0.32
33 D3A	28.54180	−0.23689	85.80	86.85	86.66	3.3e−02	2.8e−04/1.1	−3.3e−02/−4.5	1.6e−02/2.0
34 C4B	28.35479	0.07069	80.05	80.20	80.14	3.2e−02	9.8e−04/4.4	2.7e−02/8.6	8.2e−03/3.3
35 D9A	28.58601	−0.22902	85.95	87.45	86.63	3.2e−02	−8.4e−05/−0.34	2.1e−03/0.25	−4.8e−04/−0.049
36 D2E	28.53890	−0.27550	87.15	88.65	88.01	3.0e−02	−1.7e−04/−0.71	−5.9e−03/−0.71	−3.1e−02/−3.1
37 B2B	19.30633	0.06616	25.95	27.45	26.74	2.9e−02	1.2e−03/5.2	3.0e−02/4.4	3.1e−02/4.4
38 C9C	28.40155	0.07969	78.70	79.30	78.97	2.8e−02	−8.8e−04/−2.2	4.2e−03/0.92	−5.2e−03/−1.1
39 C4C	28.35621	0.07074	79.15	80.95	79.95	2.8e−02	−2.0e−05/−0.074	5.1e−03/0.72	1.2e−02/1.6
40 H6A	35.52262	−0.27226	44.95	46.15	45.49	2.7e−02	4.8e−03/22	5.0e−02/6.1	1.6e−01/18
41 D1C	28.52562	−0.25044	86.55	86.70	86.64	2.6e−02	3.0e−05/0.12	1.1e−03/0.36	−5.4e−03/−1.2
42 C2C	28.34311	0.06017	78.40	80.20	79.14	2.6e−02	8.8e−03/39	2.9e−02/3.8	1.3e−01/15
43 H2F	35.48063	−0.28927	45.10	46.60	46.02	2.5e−02	5.2e−04/1.4	−5.6e−04/−0.068	−2.4e−02/−2.5
44 H3A	35.48931	−0.29409	42.40	44.65	43.33	2.5e−02	2.9e−04/1.1	4.0e−02/3.9	−3.4e−03/−0.28
45 D7B	28.56577	−0.23133	89.10	89.25	89.24	2.5e−02	−1.4e−04/−0.62	2.7e−03/0.65	−7.8e−03/−2.3
46 C6A	28.36492	0.05084	80.20	81.25	80.63	2.4e−02	−3.2e−04/−1.1	1.2e−02/2.3	8.0e−03/1.4
47 H2G	35.48368	−0.28475	45.10	45.25	45.25	2.4e−02	3.2e−05/0.11	1.7e−02/5.9	6.4e−03/1.5
48 D3B	28.54043	−0.23394	87.60	88.65	87.83	2.4e−02	4.6e−04/1.9	1.5e−02/2.0	3.8e−02/4.7
49 D8B	28.57318	−0.23559	88.50	89.25	88.72	2.3e−02	1.2e−04/0.35	−2.4e−03/−0.36	−8.2e−03/−1.2
50 D2F	28.53729	−0.27641	87.30	87.45	87.40	2.3e−02	7.2e−04/3.0	−2.8e−03/−0.67	−4.0e−03/−1.2

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Figures 11–13 show the top 15 newly detected ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cores, ordered by ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) line flux. Each figure row shows a 10'' by 10'' zoom-in view of the core, centering at the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) intensity weighted center. The first panel in each row shows the 1.3 mm continuum contours, overlaid on the MIREX map (BT12). For all figures, we use the same color scale for the MIREX image.

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The second panel shows the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$(3-2) integrated intensity (black solid contours) on top of the 1.3 mm continuum emission (same color scale for all sources). The integration for these ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$(3-2) 0th-moment maps is only over velocity channels in which the core is defined and only including voxels flagged to be in the core. We also show a full 0th-moment integration map as gray dotted contours, which includes all voxels within the velocity ranges. Both types of contour maps start at 2σ and increase with a step of 1σ, with σ being the noise of the full integration map. The gray dotted contours always extend over a wider area than the black ones because the full integration picks up more flux at the core boundary, which is also why the black solid contours are sometimes separated. At the top of the panel, several properties of the core: ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) flux, ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) 0th-moment map rms, and ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) intensity weighted core velocity (sub- and super-scripts are velocity boundaries over which core is detected).

The third, fourth and fifth panels show DCO⁺(3-2), ${{\rm{C}}}^{18}{\rm{O}}\,$(2-1) and SiO(5-4) 0th-moment maps on top of the dust continuum. For DCO⁺(3-2) and ${{\rm{C}}}^{18}{\rm{O}}\,$(2-1), the integrations are over the same velocity ranges as the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) 0th-moment map. For SiO(5-4) the velocity range is the 5 $\mathrm{km}\ {{\rm{s}}}^{-1}\,$range used in the region maps (note a full analysis of the SiO(5-4) data from the region maps will be presented in a companion paper by M. Liu et al. 2016, in preparation).

Comparing some of the top ranked cores, including those of T13 (see Table 2), C9A has more than twice the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) flux of C1-S. B1A ranks above C1-N, and H2A ranks above F1. Note that the integration for C9A, B1B, H2A only includes voxels in the connected components (the defined cores), so their fluxes are higher in a full integration (i.e., gray dotted contours in these core figures). However, we also note that the sensitivity in this data set is about 3 times worse than T13, so the uncertainty in core fluxes is also higher.

One of the features of the 6 ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cores found by T13 was their extended DCO⁺(3-2) envelopes. This is still true for most of the new cores presented here, however, now we also see some cores, like C9A, C9B, D5A, C3A and C5A, which have relatively weak DCO⁺(3-2) emission. This chemical diversity may reflect different environmental conditions among the core sample.

We note that there is often a dearth of ${{\rm{C}}}^{18}{\rm{O}}$(2-1) emission associated with the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cores, which likely indicates that there is a high degree of gas phase depletion of CO, i.e., due to freeze out onto dust grain ice mantles. Such CO depletion is thought to boost the deuteration of ${{\rm{N}}}_{2}{{\rm{H}}}^{+}\,$(e.g., K15), and so this anti-correlation of CO emission with ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$ emission is expected theoretically.

SiO(5-4) emission is a known tracer of protostellar outflows and so can help us assess such activity within the cores. C9A and C9B show extended SiO emission in their vicinity, which is however thought to mostly arise from a separate massive protostellar source (e.g., that is seen as a strong DCN(3-2) source in the lower right of the region Figure 5) (M. Liu et al. 2016, in preparation). However, there is some localized, potentially elongated SiO emission that is spatially coincident with C9A, which likely indicates that this core is already forming a protostar (similar to that present in C1-S Feng et al. 2016; Tan et al. 2016). Most other cores do not show strong SiO(5-4) emission. We discuss more details about the six strongest ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cores below.

In order to study basic core properties and, for the best cases of C9A, B1A, H2A, B1B, B2A and F4A, compare to simple dynamical models, we fit 2D elliptical Gaussians to the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) integrated intensity maps. We define an ellipse at the $3\sigma$ value of the 2D Gaussian (Case 1), which is shown as the white, solid ellipses in the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) columns of Figures 11 to 13. These fitting results are listed in Table 3 for the best six cores. Note that the 2D Gaussian center is sometimes slightly different from the intensity weighted core center defined earlier (Table 2). Note also that the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) 0th-moment image, e.g., for C9A, has an rms of 13 mJy per 15 × 10 beam $\mathrm{km}\ {{\rm{s}}}^{-1}$, roughly corresponding to 23 mJy per 23 × 20 $\mathrm{km}\ {{\rm{s}}}^{-1}$, which is about twice the rms of C1 region rms reported by T13. Thus the core sizes reported here are likely to be systematically somewhat smaller than if they had been measured with the same sensitivity used by T13. Still, we will use these ellipses for our following study of core dynamics. For C9A, B1A, H2A, B1B, B2A and F4A we also consider their properties on the scale of larger ellipses (Case 2), shown by the dashed ellipses in Figures 11–13). These geometries are based on total ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) intensities: they cover most of the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$ flux within the 2σ contours from the full integration images. These ellipses also cover most of the 1.3 mm continuum flux that is seen to be associated with these cores. These core properties are shown inside square brackets in Table 3. We note that given these uncertainties in defining core sizes, we have not attempted to derive deconvolved sizes. As discussed above, our Case 1 radii are probably lower limits, and deconvolution would have only a very minor effect on the derived Case 2 radii.

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Table 3.  Physical Properties of the Six "Best" ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$ Cores

Core property (% error)	C9A	B1A	H2A	B1B	B2A	F4A	Average
l (°)	28.39896	19.28747	35.48231	19.28584	19.30986	34.45843	...
	[28.39896]	[19.28747]	[35.48231]	[19.28567]	[19.30983]	[34.45846]	...
b (°)	0.08113	0.08050	−0.28681	0.08305	0.06689	0.25643	...
	[0.08113]	[0.08050]	[−0.28681]	[0.08308]	[0.06699]	[0.25651]	...
${\theta }_{c}$ ('')	1.94	1.65	1.42	0.707	0.745	0.606	...
	[3.30]	[3.05]	[2.28]	[1.44]	[1.80]	[1.53]	...
e	0.747	0.877	0.852	0.881	0.672	0.955	...
	[0.904]	[0.866]	[0.781]	[0.00]	[0.00]	[0.866]	...
P.A. (°)	16	42	45	58	83	85	...
	[16]	[20]	[45]	[0]	[0]	[70]	...
d (kpc) (20%)	5.0	2.4	2.9	2.4	2.4	3.7	...
${R}_{{\rm{c}}}$ (0.01 pc) (20%)	4.71	1.92	2.00	0.822	0.867	1.09	...
	[7.99]	[3.55]	[3.20]	[1.67]	[2.09]	[2.74]	...
${V}_{\mathrm{LSR},{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ $(\mathrm{km}\ {{\rm{s}}}^{-1})$	78.40 ± 0.02	27.60 ± 0.02	45.50 ± 0.02	26.60 ± 0.04	25.50 ± 0.03	57.10 ± 0.05	...
	[78.40 ± 0.03]	[27.50 ± 0.02]	[45.50 ± 0.03]	[26.70 ± 0.04]	[25.50 ± 0.04]	[57.10 ± 0.11]	...
${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+},\mathrm{obs}}$ $(\mathrm{km}\ {{\rm{s}}}^{-1})$	0.579 ± 0.028	0.351 ± 0.025	0.245 ± 0.029	0.296 ± 0.068	0.180 ± 0.029	0.329 ± 0.053	...
	[0.579 ± 0.028]	[0.351 ± 0.025]	[0.245 ± 0.029]	[0.296 ± 0.068]	[0.180 ± 0.029]	[0.329 ± 0.053]	...
${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+},\mathrm{nt}}$ $(\mathrm{km}\ {{\rm{s}}}^{-1})$	0.576 ± 0.028	0.347 ± 0.025	0.239 ± 0.030	0.291 ± 0.069	0.172 ± 0.030	0.325 ± 0.053	...
	[0.576 ± 0.028]	[0.347 ± 0.025]	[0.239 ± 0.030]	[0.291 ± 0.069]	[0.172 ± 0.030]	[0.325 ± 0.053]	...
${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ $(\mathrm{km}\ {{\rm{s}}}^{-1})$	0.606 ± 0.028	0.395 ± 0.026	0.304 ± 0.029	0.347 ± 0.062	0.255 ± 0.029	0.375 ± 0.049	...
	[0.606 ± 0.028]	[0.395 ± 0.026]	[0.304 ± 0.029]	[0.347 ± 0.062]	[0.255 ± 0.029]	[0.375 ± 0.049]	...
${{\rm{\Sigma }}}_{\mathrm{cl}}$ $({\rm{g}}\ {\mathrm{cm}}^{-2})$ (30%)	0.317	0.394	0.321	0.361	0.293	0.313	...
	[0.312]	[0.321]	[0.292]	[0.362]	[0.273]	[0.288]	...
${{\rm{\Sigma }}}_{{\rm{c}},\max }$ $({\rm{g}}\ {\mathrm{cm}}^{-2})$ (30%)	0.282	0.492	0.327	0.391	0.302	0.349	...
	[0.308]	[0.438]	[0.326]	[0.437]	[0.297]	[0.334]	...
${M}_{{\rm{c}},\max }$ $({M}_{\odot })$ (50%)	9.34	2.70	1.95	0.394	0.338	0.616	...
	[29.3]	[8.24]	[4.99]	[1.83]	[1.94]	[3.74]	...
${n}_{{\rm{H}},{\rm{c}},\max }({10}^{5}\,{\mathrm{cm}}^{-3})$ (36%)	6.17	26.5	16.9	49.1	35.9	33.1	...
	[3.97]	[12.7]	[10.5]	[26.9]	[14.6]	[12.6]	...
${\sigma }_{{\rm{c}},\mathrm{vir},\max }$ $(\mathrm{km}\ {{\rm{s}}}^{-1})$	0.514 ± 0.064	0.398 ± 0.050	0.348 ± 0.044	0.241 ± 0.030	0.220 ± 0.027	0.259 ± 0.032	...
	[0.681 ± 0.086]	[0.500 ± 0.063]	[0.430 ± 0.054]	[0.353 ± 0.044]	[0.334 ± 0.042]	[0.399 ± 0.050]	...
${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}/{\sigma }_{{\rm{c}},\mathrm{vir},\max }$	1.18 ± 0.14	0.992 ± 0.129	0.873 ± 0.130	1.44 ± 0.30	1.16 ± 0.18	1.45 ± 0.25	1.18 ± 0.08
	[0.890 ± 0.108]	[0.790 ± 0.103]	[0.707 ± 0.105]	[0.982 ± 0.208]	[0.763 ± 0.123]	[0.941 ± 0.163]	[0.845 ± 0.057]
${R}_{{\rm{c}},\mathrm{vir},\max }$ (0.01 pc)	4.02 ± 1.03	1.94 ± 0.49	1.83 ± 0.46	0.774 ± 0.198	0.796 ± 0.204	1.04 ± 0.26	...
	[7.18 ± 1.84]	[3.75 ± 0.96]	[3.06 ± 0.78]	[1.66 ± 0.42]	[1.98 ± 0.50]	[2.67 ± 0.68]	...
${R}_{c}/{R}_{{\rm{c}},\mathrm{vir},\max }$	1.17 ± 0.33	0.989 ± 0.282	1.09 ± 0.31	1.06 ± 0.30	1.09 ± 0.31	1.05 ± 0.29	1.07 ± 0.12
	[1.11 ± 0.31]	[0.946 ± 0.270]	[1.05 ± 0.29]	[1.01 ± 0.28]	[1.06 ± 0.30]	[1.03 ± 0.29]	[1.03 ± 0.12]
${{\rm{\Sigma }}}_{{\rm{c}},\min }$ $({\rm{g}}\ {\mathrm{cm}}^{-2})$ (30%)	-	0.0979	6.37e−3	0.0303	8.68e−3	0.0368	...
	-	[0.117]	[0.0342]	[0.0743]	[0.0243]	[0.0457]	...
${M}_{{\rm{c}},\min }$ $({M}_{\odot })$ (50%)	-	0.537	0.0380	0.0305	9.72e−3	0.0650	...
	-	[2.20]	[0.522]	[0.311]	[0.159]	[0.511]	...
${n}_{{\rm{H}},{\rm{c}},\min }({10}^{5}\,{\mathrm{cm}}^{-3})$ (36%)	-	5.26	0.329	3.80	1.03	3.49	...
	-	[3.39]	[1.10]	[4.58]	[1.20]	[1.72]	...
${\sigma }_{{\rm{c}},\mathrm{vir},\min }$ $(\mathrm{km}\ {{\rm{s}}}^{-1})$	-	0.266 ± 0.033	0.130 ± 0.016	0.127 ± 0.016	0.0905 ± 0.0114	0.148 ± 0.018	...
	-	[0.359 ± 0.045]	[0.245 ± 0.030]	[0.227 ± 0.028]	[0.179 ± 0.022]	[0.243 ± 0.030]	...
${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}/{\sigma }_{{\rm{c}},\mathrm{vir},\min }$	-	1.49 ± 0.19	2.34 ± 0.34	2.74 ± 0.57	2.82 ± 0.45	2.54 ± 0.43	2.38 ± 0.18
	-	[1.10 ± 0.14]	[1.24 ± 0.18]	[1.53 ± 0.32]	[1.43 ± 0.23]	[1.55 ± 0.26]	[1.37 ± 0.10]
${R}_{{\rm{c}},\mathrm{vir},\min }$ (0.01 pc)	-	0.865 ± 0.222	0.255 ± 0.065	0.215 ± 0.055	0.135 ± 0.034	0.338 ± 0.086	...
	-	[1.94 ± 0.49]	[0.991 ± 0.254]	[0.687 ± 0.176]	[0.565 ± 0.145]	[0.987 ± 0.253]	...
${R}_{c}/{R}_{{\rm{c}},\mathrm{vir},\min }$	-	2.22 ± 0.63	7.84 ± 2.24	3.82 ± 1.09	6.42 ± 1.83	3.22 ± 0.92	4.70 ± 0.65
	-	[1.83 ± 0.52]	[3.23 ± 0.92]	[2.44 ± 0.69]	[3.71 ± 1.06]	[2.78 ± 0.79]	[2.80 ± 0.36]
${S}_{1.30\mathrm{mm}}$ (mJy)	31.3 ± 0.8	9.63 ± 0.69	5.52 ± 0.61	10.3 ± 0.3	4.36 ± 0.31	1.96 ± 0.26	...
	[76.4 ± 1.3]	[20.1 ± 1.2]	[10.7 ± 0.9]	[27.6 ± 0.6]	[14.2 ± 0.7]	[7.24 ± 0.66]	...
${S}_{1.30\mathrm{mm}}/{\rm{\Omega }}$ (MJy/sr)	112 ± 2	47.6 ± 3.4	37.1 ± 4.1	274 ± 7	107 ± 7	71.9 ± 9.6	...
	[95.0 ± 1.7]	[29.1 ± 1.8]	[28.2 ± 2.5]	[183 ± 3]	[59.3 ± 3.1]	[41.5 ± 3.8]	...
${{\rm{\Sigma }}}_{{\rm{c}},\mathrm{mm}}$ $({\rm{g}}\ {\mathrm{cm}}^{-2})$	${2.10}_{1.24}^{4.21}$	${0.895}_{0.530}^{1.79}$	${0.698}_{0.413}^{1.40}$	${5.15}_{3.05}^{10.3}$	${2.01}_{1.19}^{4.03}$	${1.35}_{0.800}^{2.71}$	...
	[1.79${}_{1.06}^{3.58}]$	[0.547${}_{0.324}^{1.10}]$	[0.531${}_{0.314}^{1.06}]$	[3.44${}_{2.03}^{6.89}]$	[1.12${}_{0.660}^{2.23}]$	[0.781${}_{0.462}^{1.56}]$	...
${M}_{{\rm{c}},\mathrm{mm}}$ $({M}_{\odot })$	${69.7}_{31.7}^{146}$	${4.91}_{2.24}^{10.3}$	${4.16}_{1.90}^{8.71}$	${5.19}_{2.36}^{10.9}$	${2.26}_{1.03}^{4.73}$	${2.39}_{1.09}^{5.00}$	...
	[170${}_{77.6}^{357}]$	[10.3${}_{4.69}^{21.6}]$	[8.11${}_{3.70}^{17.0}]$	[14.4${}_{6.55}^{30.1}]$	[7.29${}_{3.32}^{15.3}]$	[8.73${}_{3.98}^{18.3}]$	...
${n}_{{\rm{H}},{\rm{c}},\mathrm{mm}}$ $({10}^{5}\,{\mathrm{cm}}^{-3})$	${45.9}_{25.5}^{93.8}$	${48.0}_{26.6}^{98.1}$	${35.9}_{19.9}^{73.4}$	${644}_{357}^{1320}$	${239}_{133}^{489}$	${128}_{71.0}^{261}$	...
	[23.0${}_{12.8}^{47.0}]$	[15.8${}_{8.79}^{32.4}]$	[17.1${}_{9.47}^{34.9}]$	[211${}_{117}^{432}]$	[54.8${}_{30.4}^{112}]$	[29.3${}_{16.3}^{59.9}]$	...
${\sigma }_{{\rm{c}},\mathrm{vir},\mathrm{mm}}$ $(\mathrm{km}\ {{\rm{s}}}^{-1})$	${0.849}_{0.681}^{1.03}$	${0.462}_{0.371}^{0.561}$	${0.421}_{0.338}^{0.511}$	${0.458}_{0.368}^{0.556}$	${0.353}_{0.283}^{0.429}$	${0.364}_{0.292}^{0.442}$	...
	[1.06${}_{0.849}^{1.28}]$	[0.528${}_{0.424}^{0.641}]$	[0.486${}_{0.390}^{0.590}]$	[0.592${}_{0.475}^{0.718}]$	[0.465${}_{0.373}^{0.565}]$	[0.493${}_{0.396}^{0.599}]$	...
${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}/{\sigma }_{{\rm{c}},\mathrm{vir},\mathrm{mm}}$	${0.714}_{0.588}^{0.890}$	${0.854}_{0.703}^{1.06}$	${0.723}_{0.595}^{0.901}$	${0.758}_{0.624}^{0.944}$	${0.722}_{0.594}^{0.900}$	${1.03}_{0.850}^{1.29}$	${0.800}_{0.742}^{0.882}$
	[0.573${}_{0.472}^{0.715}]$	[0.747${}_{0.615}^{0.931}]$	[0.626${}_{0.516}^{0.781}]$	[0.586${}_{0.483}^{0.731}]$	[0.548${}_{0.451}^{0.683}]$	[0.761${}_{0.627}^{0.948}]$	[0.640${}_{0.594}^{0.705}]$
${R}_{{\rm{c}},\mathrm{vir},\mathrm{mm}}$ (0.01 pc)	${11.0}_{6.82}^{16.1}$	${2.62}_{1.62}^{3.83}$	${2.67}_{1.66}^{3.91}$	${2.81}_{1.74}^{4.11}$	${2.06}_{1.28}^{3.01}$	${2.05}_{1.27}^{3.00}$	...
	[17.3${}_{10.7}^{25.3}]$	[4.20${}_{2.61}^{6.14}]$	[3.90${}_{2.42}^{5.72}]$	[4.67${}_{2.90}^{6.83}]$	[3.83${}_{2.38}^{5.61}]$	[4.08${}_{2.53}^{5.97}]$	...
${R}_{c}/{R}_{{\rm{c}},\mathrm{vir},\mathrm{mm}}$	${0.429}_{0.288}^{0.657}$	${0.733}_{0.493}^{1.12}$	${0.749}_{0.504}^{1.15}$	${0.293}_{0.197}^{0.448}$	${0.421}_{0.283}^{0.646}$	${0.531}_{0.357}^{0.814}$	${0.526}_{0.452}^{0.646}$
	[0.462${}_{0.310}^{0.708}]$	[0.846${}_{0.569}^{1.30}]$	[0.820${}_{0.551}^{1.26}]$	[0.359${}_{0.241}^{0.550}]$	[0.547${}_{0.367}^{0.838}]$	[0.672${}_{0.451}^{1.03}]$	[0.617${}_{0.531}^{0.757}]$

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In the following sections, we study the core dynamics, following the methods of T13. We focus on 6 cores C9A, B1A, H2A, B1B, B2A, and F4A. The first four of these are the top four in terms of ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) flux of the new cores presented in this paper (see Table 2). They all have clear associations with 1.3 mm continuum structures, which will be the preferred method of estimated masses. B2A and F4A have relatively weak ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) fluxes, but also show quite good correspondence with continuum sources.

Only the top four ranked ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cores are significantly larger than the beam. For these, Figure 14 shows the first-moment maps of this species, along with DCO⁺(3-2) and ${{\rm{C}}}^{18}{\rm{O}}$(3-2). Only voxels with $\geqslant 3\sigma$ detection are considered. C9A shows a strong velocity gradient in ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2): in the upper left part of the image, the mean velocities are $\simeq -1.5\mathrm{km}\ {{\rm{s}}}^{-1}$, whereas they are $\simeq +0.5\ \mathrm{km}\ {{\rm{s}}}^{-1}$ on the lower right. The core diameter is about 0.1 pc, so the velocity gradient is ∼20 $\mathrm{km}\ {{\rm{s}}}^{-1}\,$ pc⁻¹. Given the bimodal morphology of the 0th-moment map, it is possible that we are seeing two ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) cores in the process of merging. The other cores, B1A and H2A, do not show such large velocity gradients.

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Figure 15 shows the second-moment (velocity dispersion) maps of C9A, B1A and H2A in ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2), DCO⁺(3-2) and ${{\rm{C}}}^{18}{\rm{O}}$(3-2). Again, only voxels with $\geqslant 3\sigma$ detection are considered. A 0.242 $\mathrm{km}\ {{\rm{s}}}^{-1}\,$effective dispersion from the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) main hyperfine group is subtracted in quadrature from its maps. Regions that then have a negative result are shown as blank; here, the sensitivity is probably too low to obtain a good measure of the velocity dispersion. Note also this effect leads to the appearance of artificially low dispersion halos around the main features. The C9A ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) second-moment map shows a higher velocity dispersion on its left-hand side than its right. Again, this may be evidence in favor of the two merging cores scenario.

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Within the defined Case 1 ellipses of C9A, B1A, H2A, B1B, B2A, and F4A, we extract total flux density from each channel (full velocity resolution of 0.04 $\mathrm{km}\ {{\rm{s}}}^{-1}$) and convert it to main beam temperature, ${T}_{\mathrm{mb}}$, to derive the total spectrum as a function of ${v}_{\mathrm{LSR}}$. These are shown in Figure 16. We then fit the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) line with full blended hyperfine components, utilizing the HFS method of the CLASS software package,¹⁰ assuming the line is optically thin (this was shown to be good approximation in the cores studied by T13). The resulting centroid velocity ${V}_{\mathrm{LSR},{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ and 1D velocity dispersion ${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+},\mathrm{obs}}$ are listed in Table 3. The velocity dispersions derived by this method range from about 0.2 to 0.6 $\mathrm{km}\ {{\rm{s}}}^{-1}$. However, to estimate the total velocity dispersion that is needed for the dynamical analysis, we subtract the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$ thermal component from its velocity dispersion in quadrature (assuming 10 K temperature), and add back the core sound speed in quadrature, assuming a mean particle mass $\mu =2.33{m}_{p}$ and gas temperature of 10 ± 3 K, following T13. These results, listed as ${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ in Table 3, are slightly larger, ranging from 0.26 to 0.61 $\mathrm{km}\ {{\rm{s}}}^{-1}$.

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Following the methods of T13, we measure core masses, M_c, within the Case 1 and Case 2 ellipses in two ways. First, we use the MIREX map of BT12. As a first MIREX-based estimate, we use the total mass surface density in the map integrated over the area of the core to yield a mass, ${M}_{c,\max }.$ As a second MIREX-based estimate, we account for the clump mass surface density, ${{\rm{\Sigma }}}_{\mathrm{cl}}$, in an elliptical annulus around the core (from R_c to 2R_c in the case of a circular core), and then subtract this contribution to Σ within the core ellipse, to then yield a mass, ${M}_{c,\min }.$

As discussed by T13, depending on the 3D structure of the core and clump, there can be large differences between ${M}_{c,\max }$ and ${M}_{c,\min }$. In some favorable situations where ${{\rm{\Sigma }}}_{\mathrm{cl}}$ is relatively small, both methods will yield similar mass estimates. However, there can be cases where the surrounding "clump" has a higher inferred mass surface density, and so ${M}_{c,\min }$ is formally negative; i.e., this mass estimate is not well-defined. In fact, this situation arises for C9A, because the ${{\rm{N}}}_{2}{{\rm{D}}}^{+}$(3-2) core is not co-located with a MIREX Σ peak. Another problem with the MIREX-based mass estimates is that the maps can suffer "saturation" in high Σ regions, i.e., where ${\rm{\Sigma }}\gtrsim 0.5\ {\rm{g}}\ {\mathrm{cm}}^{-2}$ (see BT12). This leads to the MIREX-based mass estimate being an underestimate of the true core mass.

As a second method, we calculate core masses from their 1.3 mm continuum emission, ${M}_{c,\mathrm{mm}}$. We use Equation (7) from T13. For consistency, we also assume a dust temperature of ${T}_{d}=10\pm 3$ K (such cold temperatures are expected for highly deuterated cores; see also discussion of T13) and adopt ${\kappa }_{\nu }=5.95\times {10}^{-3}\,{{\mathrm{cm}}^{2}{\rm{g}}}^{-1}$ (Ossenkopf & Henning 1994). We adopt a 30% uncertainty for ${\kappa }_{\nu }$. We do not attempt to carry out clump envelope subtraction with this method, because the ALMA observations tend to filter out the larger scale emission from the clump. Because the uncertainties in temperature cause quite asymmetric uncertainties in ${{\rm{\Sigma }}}_{c,\mathrm{mm}}$ and ${M}_{c,\mathrm{mm}}$, we calculate lower and upper boundaries and put them in sub- and super- scripts in Table 3. Overall, including temperature, opacity, and distance uncertainties, the total uncertainty is about a factor of two in the mass estimation (see detailed discussion in T13); however, because of the difficulties of clump envelope subtraction in the MIREX mass estimates, we prefer the mm continuum-based mass estimate as our fiducial method. We note that, for a "core" contained within the synthesized beam size, at a distance of 5 kpc and with a dust temperature of 10 K, the 1σ mass sensitivity is $0.51\ {M}_{\odot }$.

With these methods, we find that C9A is the most massive of the six cores suitable for dynamical analysis, with ${M}_{c,\mathrm{mm}}\simeq 70\ {M}_{\odot }$ in the Case 1 (i.e., inner) ellipse. The other cores are at least ten times smaller in mass. Considering the Case 2 (i.e., larger) ellipses, C9A rises in mass to ${M}_{c,\mathrm{mm}}\simeq 170\ {M}_{\odot }$. On these scales, the other cores have about $10\ {M}_{\odot }$.

Following T13 and MT03, we consider virialized singular polytropic quasi-spherical cores that have surfaces in approximate pressure equilibrium with their surrounding clump environments. Such cores have a radius ${R}_{{\rm{c}},\mathrm{vir}}$ and internal velocity dispersion ${\sigma }_{{\rm{c}},\mathrm{vir}}$ (assuming some contribution from large scale B-fields such that the Alfvén Mach number in the core is unity). The two quantities are calculated following T13 Equations (2) and (4), given core mass M_c and clump mass surface density ${{\rm{\Sigma }}}_{\mathrm{cl}}$. For each core, we calculate the properties in three cases: (1) using the core mass derived from the MIREX map without envelope subtraction; (2) using the core mass from the MIREX map with envelope subtraction; (3) using the core mass derived from the 1.3 mm continuum map. The clump mass surface density is estimated from the MIREX map in the region from R_c to 2R_c (in the case of a circular core). Table 3 lists the results for the six considered cores.

For our preferred mass estimates via 1.3 mm continuum emission, we find a mean ratio of the observed to predicted virial velocity dispersion for the six cores of $\langle {\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}/{\sigma }_{{\rm{c}},\mathrm{vir},\mathrm{mm}}\rangle =0.80$. This is very similar to the result found by T13 of a ratio of 0.83 for the six cores they analyzed. It suggests that this core population (of 12 cores) has properties that are consistent with the virial equilibrium assumption of the MT03 Turbulent Core model.

The most massive core, C9A, has a ratio of 0.71, which is modestly subvirial. As discussed by T13, apparently subvirial cores may indicate that stronger large scale magnetic fields are present: the fiducial MT03 model assumes that large-scale B-fields are present, which would produce an Alfvén Mach number of unity for turbulence in the core. T13 argued that stronger B-fields, ∼1 mG, were needed in the massive cores of their sample, especially C1-S, if the cores were to be in virial equilibrium. We carry out a similar analysis here, to work out what B-field strengths are needed for virial equilibrium, summarizing the results in Table 4. The magnetic field strengths that are implied by the fiducial MT03 model are again ∼1 mG. They need to be raised modestly to achieve precise virial equilibrium. Also listed is the B-field strength, ${B}_{{\rm{c}},\mathrm{crit}}$, needed to make the core mass equal to the magnetic critical mass (Bertoldi & McKee 1992): these also tend to be slightly higher.

Table 4.  Dynamical Properties of the Six "Best" ${{\rm{N}}}_{2}{{\rm{D}}}^{+}\,$ Cores

Core property (% error)	C9A	B1A	H2A	B1B	B2A	F4A
${R}_{{\rm{c}}}$ (0.01 pc) (20%)	4.71	1.92	2.00	0.822	0.867	1.09
${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}$ $(\mathrm{km}\ {{\rm{s}}}^{-1})$	0.606 ± 0.028	0.395 ± 0.026	0.304 ± 0.029	0.347 ± 0.062	0.255 ± 0.029	0.375 ± 0.049
${{\rm{\Sigma }}}_{\mathrm{cl}}$ $({\rm{g}}\ {\mathrm{cm}}^{-2})$ (30%)	0.317	0.394	0.321	0.361	0.293	0.313
${M}_{{\rm{c}},\mathrm{mm}}$ $({M}_{\odot })$	${69.7}_{31.7}^{146}$	${4.91}_{2.24}^{10.3}$	${4.16}_{1.90}^{8.71}$	${5.19}_{2.36}^{10.9}$	${2.26}_{1.03}^{4.73}$	${2.39}_{1.09}^{5.00}$
${\alpha }_{{\rm{c}}}\equiv 5{\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}^{2}{R}_{{\rm{c}}}/({{GM}}_{{\rm{c}},\mathrm{mm}})$ a	${0.287}_{0.124}^{0.636}$	${0.702}_{0.299}^{1.56}$	${0.514}_{0.211}^{1.14}$	${0.220}_{0.0775}^{0.501}$	${0.288}_{0.115}^{0.644}$	${0.742}_{0.288}^{1.66}$
${n}_{{\rm{H}},{\rm{c}},\mathrm{mm}}$ $({10}^{5}\,{\mathrm{cm}}^{-3})$	${45.9}_{25.5}^{93.8}$	${48.0}_{26.6}^{98.1}$	${35.9}_{19.9}^{73.4}$	${644}_{357}^{1320}$	${239}_{133}^{489}$	${128}_{71.0}^{261}$
${t}_{{\rm{c}},\mathrm{ff}}$ $({10}^{5}\,\mathrm{yr})$ b	${0.204}_{0.142}^{0.273}$	${0.199}_{0.139}^{0.267}$	${0.230}_{0.161}^{0.309}$	${0.0544}_{0.0380}^{0.0730}$	${0.0892}_{0.0624}^{0.120}$	${0.122}_{0.0853}^{0.164}$
Bc (μG) (mA = 1)	${1220}_{903}^{1750}$	${812}_{598}^{1160}$	${541}_{393}^{780}$	${2620}_{1800}^{3830}$	${1170}_{842}^{1690}$	${1260}_{899}^{1830}$
${R}_{{\rm{c}},\mathrm{vir},\mathrm{mm}}$ (0.01 pc)	${11.0}_{16.3}^{7.17}$	${2.62}_{3.89}^{1.71}$	${2.67}_{3.97}^{1.74}$	${2.81}_{4.18}^{1.83}$	${2.06}_{3.06}^{1.34}$	${2.05}_{3.05}^{1.34}$
${R}_{c}/{R}_{{\rm{c}},\mathrm{vir},\mathrm{mm}}$	${0.429}_{0.288}^{0.657}$	${0.733}_{0.493}^{1.12}$	${0.749}_{0.504}^{1.15}$	${0.293}_{0.197}^{0.448}$	${0.421}_{0.283}^{0.646}$	${0.531}_{0.357}^{0.814}$
${\sigma }_{{\rm{c}},\mathrm{vir},\mathrm{mm}}$ $(\mathrm{km}\ {{\rm{s}}}^{-1})$	${0.849}_{0.681}^{1.03}$	${0.462}_{0.371}^{0.561}$	${0.421}_{0.338}^{0.511}$	${0.458}_{0.368}^{0.556}$	${0.353}_{0.283}^{0.429}$	${0.364}_{0.292}^{0.442}$
${\sigma }_{{{\rm{N}}}_{2}{{\rm{D}}}^{+}}/{\sigma }_{{\rm{c}},\mathrm{vir},\mathrm{mm}}$	${0.714}_{0.588}^{0.890}$	${0.854}_{0.703}^{1.06}$	${0.723}_{0.595}^{0.901}$	${0.758}_{0.624}^{0.944}$	${0.722}_{0.594}^{0.900}$	${1.03}_{0.850}^{1.29}$
${\phi }_{{\rm{B}},\mathrm{vir}}$	${6.87}_{3.82}^{11.5}$	${4.27}_{2.37}^{7.16}$	${6.65}_{3.70}^{11.2}$	${5.87}_{3.26}^{9.85}$	${6.68}_{3.71}^{11.2}$	${2.58}_{1.43}^{4.32}$
${m}_{{\rm{A}},\mathrm{vir}}$	${0.519}_{0.383}^{0.772}$	${0.711}_{0.506}^{1.18}$	${0.529}_{0.390}^{0.791}$	${0.573}_{0.419}^{0.874}$	${0.528}_{0.389}^{0.788}$	${1.08}_{0.704}^{3.36}$
${B}_{{\rm{c}},\mathrm{vir}}$ (μG)	${2350}_{1360}^{3670}$	${1140}_{582}^{1830}$	${1020}_{564}^{1620}$	${4570}_{2500}^{7230}$	${2220}_{1200}^{3530}$	${1160}_{307}^{1980}$
${B}_{{\rm{c}},\mathrm{crit}}$ (μG)	${2830}_{1700}^{4730}$	${1200}_{725}^{2010}$	${939}_{565}^{1570}$	${6930}_{4170}^{11600}$	${2710}_{1630}^{4530}$	${1820}_{1090}^{3040}$

Notes.

^aVirial parameter (Bertoldi & McKee 1992). ^bCore free-fall time, ${t}_{{\rm{c}},\mathrm{ff}}={[3\pi /{(32G{\rho }_{c})]}^{1/2}={1.38}^{5}({n}_{{\rm{H}},{\rm{c}},\mathrm{mm}}/{10}^{5}{\mathrm{cm}}^{-3})}^{-1/2}\,\mathrm{yr}$.

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4.6.1. C9A

4.6.2. B1A

4.6.3. H2A

4.6.4. B1B

4.6.5. B2A

4.6.6. F4A