The ALMA Survey of 70 μm Dark High-mass Clumps in Early Stages (ASHES). IX. Physical Properties and Spatial Distribution of Cores in IRDCs

We selected massive prestellar clump candidates without bright infrared sources to reveal the very early phase of high-mass star formation from the first and fourth quadrants following Traficante et al. (2015) and the MALT90 survey (Foster et al. 2011, 2013; Jackson et al. 2013), respectively. In the MALT90 survey, Jackson et al. (2013) used the ATLASGAL 870 μm survey to select a sample of 3246 high-mass clumps, almost all in the fourth quadrant, that were observed in molecular lines. Combining Herschel and ATLASGAL dust continuum emission, Guzmán et al. (2015) derived column density and dust temperature maps for the whole sample. Whitaker et al. (2017) derived kinematic distances, and Contreras et al. (2017) calculated the mass, density, and luminosities of the clumps. Guzmán et al. (2015) classified clumps that lack from 3.6 to 70 μm (Spitzer/Herschel) compact emission as quiescent, which are the best prestellar clump candidates.

The mean temperature of these clumps is ∼15 K, with a range from 9 to 23 K, supporting the idea that these clumps host the early stages of star formation. We impose additional selection criteria for clump mass and density to ensure the selection of the best prestellar candidates with the potential to form high-mass stars. The clump mass, the mass surface density, and the volume density should be larger than 500 M_⊙, ∼0.1 g cm⁻², and 5 × 10³ cm⁻³, respectively. In addition, targets are limited to within a distance of 6 kpc to ensure good spatial resolutions. At this distance, the angular resolution is comparable to the size of low-mass cores (Kirk et al. 2006, e.g., ∼7000 au). For some clumps that are not included in the analysis of Contreras et al. (2017), ¹⁵ we estimate clump mass by using the column density and radius from Guzmán et al. (2015) and the distance from Whitaker et al. (2017). Finally, we selected 18 clumps only in the fourth quadrant satisfying the conditions above, from which 11 were presented in the pilot survey (Sanhueza et al. 2019).

We selected additional sources from the first quadrant, using the work by Traficante et al. (2015), who studied 3493 clumps using dust emission from Herschel and ¹³CO (J = 1 − 0) emission from the Galactic Ring Survey Jackson06, and identified 667 starless clump candidates with no counterpart(s) at 70 μm, without checking for Spitzer point sources. We used the physical properties in Traficante et al. (2015) for the sample selection. We followed the same procedure for clumps designated as starless, and selected 20 prestellar, high-mass clump candidates (one presented in the pilot survey) that we visually inspected to verify a lack of emission from compact Spitzer sources. We finally included one 70 μm dark prestellar clump candidate, G023.477+00.114, that has a potential to form high-mass stars satisfying all conditions above that had been previously studied by Beuther et al. (2013, 2015). A detailed study of this source was presented using ASHES data in Morii et al. (2021). In summary, the entire ASHES sample is composed of 39 IRDC clumps (see Table 1).

Table 1. Physical Properties of ASHES Clumps

Clump Name	R.A.	Decl.	σ	d	Tcl	Mref	Rcl	Mcl	Σcl	$n{({{\rm{H}}}_{2})}_{\mathrm{cl}}$
	(ICRS)	(ICRS)	(km s−1)	(kpc)	(K)	(M⊙)	(pc)	(M⊙)	(g cm−2)	(104 cm−3)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
G010.991–00.082	18:10:06.65	−19:27:50.7	1.1	3.7	12.0	2230	0.49	2300	0.64	6.74
G014.492–00.139	18:17:22.03	−16:25:01.9	1.8	3.9	13.0	5200	0.44	3200	1.11	13.30
G015.203–00.441	18:19:52.56	−15:56:00.2	1.0	2.4	20.1	930	0.27	400	0.33	7.14
G016.974–00.222	18:22:31.99	−14:16:02.3	1.2	3.6	12.8	1378	0.26	200	0.21	4.02
G018.801–00.297	18:26:19.27	−12:41:17.3	1.3	4.7	13.3	2809	0.72	4500	0.57	4.08
G018.931–00.029	18:25:35.70	−12:26:53.7	1.5	3.6	20.7	423	0.76	2500	0.30	2.00
G022.253+00.032	18:31:39.60	−09:28:39.5	1.0	5.2	13.8	3010	0.32	400	0.24	4.29
G022.692–00.452	18:34:13.78	−09:18:42.2	1.2	4.9	18.0	1426	0.39	300	0.13	1.70
G023.477+00.114	18:33:39.53	−08:21:09.6	1.3	5.3	13.9	1000	0.38	1300	0.61	8.48
G024.010+00.489	18:33:18.40	−07:42:28.1	1.0	5.7	12.7	3529	0.26	600	0.57	11.97
G024.524–00.139	18:36:30.82	−07:32:26.6	1.5	5.5	13.1	1555	0.76	3700	0.43	2.89
G025.163–00.304	18:38:17.20	−07:02:58.3	1.2	4.2	12.9	7245	0.46	1100	0.33	3.84
G028.273–00.167	18:43:31.32	−04:13:19.5	1.6	5.0	10.9	1722	0.47	1700	0.50	5.71
G028.541–00.237	18:44:15.80	−04:00:49.8	1.4	5.3	13.9	6028	0.63	2100	0.35	2.91
G028.564–00.236	18:44:18.09	−03:59:33.5	1.9	5.3	12.7	15276	0.59	4900	0.94	8.43
G028.927+00.394	18:42:43.18	−03:22:56.3	1.0	5.9	15.4	1616	0.46	700	0.22	2.45
G030.704+00.104	18:47:00.12	−01:56:03.9	1.5	5.9	15.0	1749	0.76	2200	0.25	1.76
G030.913+00.719	18:45:11.58	−01:28:08.2	0.9	3.5	12.4	1074	0.27	400	0.32	7.00
G033.331–00.531	18:54:03.20	+00:06:53.4	2.0	6.1	14.3	1065	0.57	600	0.13	1.13
G034.133+00.076	18:53:21.47	+01:06:12.1	1.2	3.8	16.0	579	0.55	700	0.17	1.49
G034.169+00.089	18:53:22.57	+01:08:29.7	1.0	3.8	17.9	596	0.38	300	0.14	1.83
G034.739–00.119	18:55:09.83	+01:33:14.5	1.2	5.3	12.7	2833	0.37	700	0.32	4.69
G036.666–00.114	18:58:39.77	+03:16:16.5	0.9	3.6	13.4	881	0.26	300	0.25	6.00
G305.794–00.096	13:16:33.40	−62:49:42.1	1.3	5.0	16.0	1560	0.32	900	0.58	9.06
G327.116–00.294	15:50:57.18	−54:30:33.6	1.4	3.9	14.3	580	0.39	700	0.30	4.23
G331.372–00.116	16:11:34.10	−51:35:00.1	1.8	5.4	14.0	1640	0.63	1500	0.25	2.07
G332.969–00.029	16:18:31.61	−50:25:03.1	1.1	4.3	12.6	1170	0.59	1100	0.22	1.88
G333.016–00.751	16:21:56.39	−50:53:45.2	2.1	3.7	17.6	690	0.37	300	0.15	2.12
G333.481–00.224	16:21:39.97	−50:11:44.8	1.2	3.5	18.9	593	0.31	400	0.24	4.52
G333.524–00.269	16:22:03.39	−50:11:47.2	1.5	3.5	21.2	2400	0.30	900	0.64	11.10
G337.342–00.119	16:37:21.00	−47:19:25.3	2.8	4.7	14.5	460	0.41	300	0.12	1.52
G337.541–00.082	16:37:58.48	−47:09:05.1	1.1	4.0	12.0	1180	0.42	1200	0.46	5.49
G340.179–00.242	16:48:40.88	−45:16:01.1	1.9	4.1	14.0	1470	0.74	1900	0.23	1.60
G340.222–00.167	16:48:30.83	−45:11:05.8	1.0	4.0	15.0	760	0.36	600	0.29	4.39
G340.232–00.146	16:48:27.56	−45:09:51.9	2.1	3.9	14.0	710	0.47	900	0.26	2.97
G340.398–00.396	16:50:08.85	−45:11:47.9	1.8	3.7	13.5	1690	0.64	2200	0.36	2.86
G341.039–00.114	16:51:14.11	−44:31:27.2	1.1	3.6	14.3	1070	0.47	900	0.28	3.05
G343.489–00.416	17:01:01.19	−42:48:11.0	1.0	2.9	10.3	810	0.41	800	0.32	3.98
G345.114–00.199	17:05:26.26	−41:22:55.4	1.1	2.9	11.2	1350	0.24	300	0.33	7.63

Note. By replacing the G for AGAL, the source name column (1) matches with the ATLASGAL simple names (Schuller et al. 2009; Urquhart et al. 2014, 2018). Column (4) presents the observed velocity dispersion, which was obtained by the fitting of the line profile of C¹⁸O (J = 2 − 1) averaged within the clump with a 1D Gaussian, which was observed by total power (TP). The distance from the Sun in column (5) is from Whitaker et al. (2017), and the dust temperature in column (6) is from Guzmán et al. (2015). Mass in column (7) is cited from Traficante et al. (2015), Contreras et al. (2017) for clumps in the first and fourth quadrants, respectively. Properties in columns (8), (9), (10), and (11) are fitting results of 2D Gaussian for 870 μm continuum images. International Celestial Reference System (ICRS).

A machine-readable version of the table is available.

Download table as:  DataTypeset image

Figure 1 shows the Spitzer and Herschel images for G010.991–00.082, one of the targets. The left panel shows the three-color composite image (3.6 μm in blue, 4.5 μm in green, and 8 μm in red) taken in the GLIMPSE survey (Benjamin et al. 2003). For comparison, the center and right panels display the 24 and 70 μm emission from the MIPSGAL (Carey et al. 2009) and Hi-GAL (Molinari et al. 2010) surveys, respectively, with contours of 870 μm continuum emission (Schuller et al. 2009).

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Molecular cloud surveys suggest as empirical thresholds for high-mass star formation at a surface density >0.05 g cm⁻² (e.g., ATLASGAL Urquhart et al. 2014; He et al. 2015). Another threshold that has been proposed by Kauffmann & Pillai (2010), which after being scaled following Sanhueza et al. (2019), is M > 580 R^1.33 (M and R are the mass and radius in units of M_⊙ and parsecs, respectively).

The mass and radius of clumps depend on the definition used in each study. Traficante et al. (2015) estimated the clump mass from the spectral energy distribution (SED) fitting of far-infrared wavelengths, while the radius of clumps is defined from the fitting of the 250 μm emission. In the MALT90 survey, Contreras et al. (2017) used the deconvolved radius from the 2D Gaussian fitting as the physical radius, and they estimated the clump mass from the radius and the column density, which was computed from SED fitting. Urquhart et al. (2018) estimated the clump mass using ATLASGAL 870 μm continuum emission. Additionally, the temperature and distances adopted are also different among catalogs.

The clump size is difficult to define because clumps are sometimes adjoining, and their borders are unclear. The definition and the measuring method are different from reference to reference. Typically, the clump mass is estimated from the column density obtained from SED fitting or from the ATLASGAL continuum flux with temperature information. One of the caveats for using the column density from the Herschel SED fitting is the low resolution of 35'' at 500 μm, which barely resolves clumps. Therefore, we decide to estimate the clump mass and radius using the ATLASGAL continuum emission, which has an angular resolution of 182. We measured flux density (F_ν ) and the radius of clumps (R_cl) from a 2D Gaussian fitting of 870 μm ATLASGAL continuum images using CASA viewer (McMullin et al. 2007). The radius corresponds to half of the full width at half maximum of the best-fit Gaussian deconvolved with the beam size, estimated by using the CASA task imfit. Using the flux density of 870 μm continuum emission from the ATLASGAL survey, the clump mass can be estimated assuming optically thin conditions as follows:

$$\begin{eqnarray}&&{M}_{\mathrm{cl}}={\mathbb{R}}\displaystyle \frac{{d}^{2}{F}_{\nu }}{{\kappa }_{\nu }{B}_{\nu }({T}_{\mathrm{dust}})},\end{eqnarray} \tag{ 1 }$$

where ${\mathbb{R}}\,=\,$100 is the gas-to-dust mass ratio, κ_{0.87 mm} = 1.72 cm² g⁻¹ is the dust absorption coefficient, d is the distance to the source, and B_ν is the Planck function for a dust temperature T_dust. The dust absorption coefficient (κ_{0.87 mm}) is calculated from κ_{1.3 mm} assuming a dust emissivity spectral index (β) of 1.5, where κ_{1.3 mm} = 0.9 cm² g⁻¹ is from Ossenkopf & Henning (1994; see Section 4.3). As for the dust temperature, we adopted the temperatures (T_cl ∼ 10–20 K) from the SED fitting between 160 and 870 μm from Hi-GAL and ATLASGAL survey at the continuum peak position (Guzmán et al. 2015). We adopted the distances of clumps from Whitaker et al. (2017), ranging from 2.4 to 6 kpc. The different assumption that can be made on ${\mathbb{R}}$ is that it varies depending on the galactocentric distance. Comparing the variation of ${\mathbb{R}}$ with its uncertainties and with what is found in Sabatini et al. (2022), ${\mathbb{R}}=100$ is a reasonable approximation. The uniformly recalculated clumps' properties, mass (M_cl), radius (R_cl), surface density (${{\rm{\Sigma }}}_{\mathrm{cl}}={M}_{\mathrm{cl}}/(\pi {R}_{\mathrm{cl}}^{2})$), and volume density ($n{({{\rm{H}}}_{2})}_{\mathrm{cl}}={M}_{\mathrm{cl}}/{\bar{m}}_{{{\rm{H}}}_{2}}(4\pi {R}_{\mathrm{cl}}^{3}/3)$), are summarized in Table 1. Here, ${\bar{m}}_{{{\rm{H}}}_{2}}$ is the mean molecular mass per hydrogen molecule, and we adopt ${\bar{m}}_{{{\rm{H}}}_{2}}=2.8\,{m}_{{\rm{H}}}$ (Kauffmann et al. 2008). Throughout this work, these are the clump properties that will be used in the analysis.

Figure 2 shows the mass as a function of clump radius colored by dust temperature. We overlaid the widely adopted thresholds for high-mass star formation as black lines. The solid one shows the high-mass star formation relation proposed by Kauffmann & Pillai (2010), as described above. The dashed line represents Σ_cl > 0.05 g cm⁻² suggested by Urquhart et al. (2014), He et al. (2015). All targets from the ASHES sample satisfy these thresholds and are therefore thought to be capable of forming high-mass stars.

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Additionally, we can estimate a possible maximum stellar mass formed in a clump using the clump mass following Sanhueza et al. (2017, 2019). Larson (2003) obtained an empirical relation between the total stellar mass of a cluster (M_cluster) and the maximum stellar mass in the cluster (${m}_{\max }^{* }$) as

$$\begin{eqnarray}&&{m}_{\max }^{* }=1.2{\left(\displaystyle \frac{{M}_{\mathrm{cluster}}}{{M}_{\odot }}\right)}^{0.45}\,{M}_{\odot }\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&=\,15.6{\left(\displaystyle \frac{{M}_{\mathrm{clump}}}{{10}^{3}\,{M}_{\odot }}\displaystyle \frac{{\varepsilon }_{\mathrm{SFE}}}{0.3}\right)}^{0.45}\,{M}_{\odot },\end{eqnarray} \tag{ 3 }$$

where the star formation efficienty (_SFE) is evaluated as ε_SFE = 0.1–0.3 for nearby embedded clusters (Lada & Lada 2003). More recently, Sanhueza et al. (2019) derive another relation for the maximum stellar mass that could be formed in a clump following the Kroupa's initial mass function (Kroupa 2001) as

$$\begin{eqnarray}&&{m}_{\max }^{* }={\left(\displaystyle \frac{0.3}{{\varepsilon }_{\mathrm{SFE}}}\displaystyle \frac{21.0}{{M}_{\mathrm{clump}}/{M}_{\odot }}+1.5\times {10}^{-3}\right)}^{-0.77}\,{M}_{\odot }.\end{eqnarray} \tag{ 4 }$$

Here we assumed that the relation of M_cluster = ε_SFE M_clump, with M_clump = M_cl from Table 1. The calculated maximum stellar masses are in the range of ∼8–53 M_⊙, with an assumption of ε_SFE = 0.3 for Equations (3) and (4).

Thus, the ASHES clumps fulfill known conditions for high-mass star formation, and they are therefore considered high-mass prestellar clump candidates in this work.

The left panels of Figure 3 present the 1.3 mm continuum images for G010.991–00.082 and G014.492–00.139. We overlaid the single-dish 870 μm continuum emission obtained by ATLASGAL observations as black-dashed contours. Compared with the ATLASGAL observations, ALMA observations succeeded in resolving the area around the emission peak of massive clumps. As reported by the pilot survey (Sanhueza et al. 2019), we confirmed that the internal structures of these clumps vary from region to region: some are filamentary (e.g., G023.47 and G025.16), and some are clumpy (e.g., G014.49 and G333.52). We also resolved some clumps (e.g., G024.01 and G024.52) in networks of hub-filaments (see Section 5.2.4).

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We combined the 12 m array and the 7 m array data to mitigate the missing flux. Indeed, the combined data have ∼1.7 times more flux than the 12 m only data for the entire FOV. To estimate how much flux is recovered in the combined images, we have scaled the 870 μm emission assuming a dust emissivity spectral index (β) of 1.5 as F_recov = F_{1.3 mm,ALMA}/${F}_{1.3\,\mathrm{mm},\exp }$, where F_{1.3 mm,ALMA} is the 1.3 mm flux density obtained by ALMA in the FOV, and ${F}_{1.3\,\mathrm{mm},\exp }$ is estimated as ${F}_{1.3\,\mathrm{mm},\exp }={F}_{0.87\,\mathrm{mm}}{(1.3/0.87)}^{-(1.5+2)}$. F_{0.87 mm} was measured within the area corresponding to the ALMA FOV (blue contours in Figures 3). We integrated pixels where the intensity is more than twice the rms noise level to calculate F_{1.3 mm, ALMA}. The estimated recoverable flux was between 7% and 45%. The estimated values (F_12m+7m/F_12m and F_recov) are summarized in Table 2. These are consistent with SMA and ALMA observations in other IRDC studies (e.g., Sanhueza et al. 2017; Liu et al. 2018).

We identified cores using the obtained 1.3 mm continuum images. In this paper, following the definitions of Sanhueza et al. (2019), we use the term "core" to describe a compact, dense object within a clump with a size of ∼0.01–0.1 pc, a mass of ∼10⁻¹–10² M_⊙, and a volume density of ∼10⁵ cm⁻³ that will likely form a single star or a small multiple system. We adopt the dendrogram technique (Rosolowsky et al. 2008) to extract cores, which is implemented in the Astrodendro Python package. The dendrogram technique classifies the hierarchical structure. The principal parameters are F_min, δ, and S_min. F_min sets the minimum value above which we define structures, and δ sets a minimum significance to separate them. S_min is the minimum number of pixels to be contained in the smallest individual structure (defined as a leaf in the dendrogram technique). The dendrogram algorithm classifies the hierarchical structures as leaf, branch, and trunk. A leaf is a structure that has no substructure, and a trunk is the largest structure. The remaining structure is branch, which has leaves as internal structures.

We set F_min, δ, and S_min as 2.5σ, 1.0σ, and the half-pixel numbers of the beam area following the pilot survey (Sanhueza et al. 2019). Since these parameters are optimistic values, we applied the additional constraint to the flux density to exclude suspicious structures. We have excluded the cores with a flux density smaller than 3.5σ. Additionally, we eliminated the cores at the edge of FOV. As a result of the dendrogram technique, 839 leaf structures were identified in total. The identified leaf structures are indicated as magenta contours in the left panels of Figure 3. We define a leaf as a core. The number of cores in each region ranges from 8 to 39 (median of 20). We named cores ALMA1, ALMA2, ... in order of the peak intensity. Table 3 gives peak position, size (major and minor FWHM), peak intensity, and flux density of cores identified by the dendrogram algorithm (the properties for all cores are summarized in a machine-readable table). As an example, the right panels in Figure 3 show the identified cores in G010.991–00.082 and G014.492–00.139 as circles. Each circle position corresponds to each core's continuum peak position, and the digits on the right panel show the core ID, indicating the order of the peak intensity in each region.

We confirmed only a weak correlation between the number of detected cores and the sensitivity, and between the number of detected cores and the clump distance with Spearman's rank coefficient of r_s = −0.15 and −0.22, and p–value is 0.36 and 0.17, respectively. Although the spatial resolution differs among the different clumps in the sample, this effect seems weak for the core identification.

Core masses can be estimated from the dust continuum emission, assuming the dust emission is optically thin, using Equation (1) following previous ASHES papers (Sanhueza et al. 2019; Morii et al. 2021). We adopt a gas-to-dust mass ratio of 100, and a dust opacity, κ_{1.3 mm} = 0.9 cm² g⁻¹ computed by Ossenkopf & Henning (1994) for the dust grains with the ice mantles at a volume density of 10⁶ cm⁻³. For the mass estimation, the fluxes obtained from dendrograms were used, without removing any additional background emission other than the inherently removed by the interferometer. In the case where the background emission is important, the core masses could be considered to be upper limits. For cores in eleven ASHES clumps, we used the rotational temperatures derived from NH₃ observations at ∼5'' (Li et al. 2022; D. Allingham et al. 2023, in preparation). For the remaining twenty-eight clumps, we adopted the clump temperature for the core mass calculation. Column (3) in Table 4 shows the temperature used for each core in the mass estimation. We confirmed that the dust emission is optically thin by using Equation (B.2) from Pouteau et al. (2022). We find that 99% of cores have an optical depth smaller than 0.04, and the maximum value is ∼0.1.

The core mass (M_core) given in column (4) of Table 4 ranges from 0.05 to 81 M_⊙. In the right panels in Figure 3, the size of circles indicates the core mass. More than half (∼55%) of the cores have a mass smaller than 1 M_⊙, and only 3.5% (29/839) of cores have ${M}_{\mathrm{core}}\gtrsim 10\,{M}_{\odot }$. Assuming a core-to-star formation efficiency (hereafter SFE) of 30%, ∼27 M_⊙ of core masses is necessary to form a high-mass star. In total, seven cores satisfy this mass threshold. Compared with the pilot survey, we revealed six additional high-mass cores thanks to the larger number of clumps. More discussion about core masses will be presented in Section 5.

By summing over the mass of all cores in each clump, we can estimate the core formation efficiency (CFE). We define the CFE as the ratio of the sum of core masses to the clump mass, M_cl (e.g., Louvet et al. 2014). It ranges from 0.6% to 16%, indicating that most of the clump mass has not been assembled into cores at the early phase traced in these 70 μm dark IRDCs. Table 5 summarize the core properties in each clump such as the total number of cores identified in each clump (N(core)), the maximum core mass (M_max), the median of core mass (M_med), and the minimum core mass (M_min) as well as the CFE. Table 5 also shows M_3.5σ , the mass sensitivity in each clump, which corresponds to the mass when F_{1.3 mm} is 3.5σ.

The major source of uncertainty in the mass calculation is the gas-to-dust mass ratio and the dust opacity. Assuming that all possible values of ${\mathbb{R}}$ and κ_{1.3 mm} are distributed uniformly between the extreme values, $70\lt {\mathbb{R}}\lt 150$ and 0.7 < κ_{1.3 mm} < 1.05 (e.g., Devereux & Young 1990; Ossenkopf & Henning 1994; Vuong et al. 2003; Sabatini et al. 2019, 2022), the standard deviation can be estimated (Sanhueza et al. 2017). We adopt the uncertainties derived by Sanhueza et al. (2017) of 23% for the gas-to-dust mass ratio and 28% for the dust opacity, for the adopted values of 100 and 0.9 cm² g⁻¹, respectively. In addition, considering an absolute flux uncertainty of 10% for ALMA observations in Band 6, a temperature uncertainty of ∼20%, and a distance uncertainty of ∼10%, we estimate the uncertainties of core mass, volume density, and a surface density of ∼50% (see Sanhueza et al. 2017, 2019, for more details). For the protostellar cores, the actual dust temperature can be higher than the value derived at a coarser angular resolution using single-dish observations (Li et al. 2021; Morii et al. 2021). However, we confirm that the NH₃ kinetic temperatures derived at core scales in ASHES clumps with available NH₃ observations are lower than 23 K (Lu et al. 2015; Li et al. 2022). A similar range of NH₃ temperatures was also reported in other IRDC cores (Wang et al. 2014).

The core radius was defined as half of the geometric mean of the FWHM (Table 1) provided by Astrodendro; see additional details in the Astrodendro website. ¹⁶ The core radius ranges from ∼5 × 10⁻³ to ∼5 × 10⁻² pc, corresponding to ∼10³–10⁴ au, and its median is 2680 au. The core size is only ≲5% of the maximum recoverable scale, and the missing flux contribution for core mass estimation is expected to be small. The surface density, Σ, and the molecular volume density, n(H₂), were estimated assuming a spherical core as follows: ${\rm{\Sigma }}={M}_{\mathrm{core}}/\pi {r}_{\mathrm{core}}^{2}$, and $n({{\rm{H}}}_{2})={M}_{\mathrm{core}}/{\bar{m}}_{{{\rm{H}}}_{2}}(4\pi {r}_{\mathrm{core}}^{3}/3)$, where r_core is the core radius. Figure 4 shows the estimated radius and densities of cores. The orange lines are the cumulative histogram, indicating which percent of cores have higher density than a certain value. The estimated surface density ranges from ∼0.05 to 10 g cm⁻², and the volume density ranges from ∼10⁵ to 3 × 10⁷ cm⁻³. We found that ∼10% of cores (91/839) have a surface density higher than unity, which is the condition suggested by Krumholz & McKee (2008) as a threshold for high-mass star formation. They concluded that 1 g cm⁻² is the minimum necessary to halt excessive fragmentation and allow formation of high-mass stars. Actually, all seven high-mass cores (${M}_{\mathrm{core}}\gt 27\,{M}_{\odot }$) have a surface density higher than this threshold.

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The peak column density, N_peak(H₂), was derived from

$$\begin{eqnarray}&&{N}_{\mathrm{peak}}({{\rm{H}}}_{2})={\mathbb{R}}\,\displaystyle \frac{{I}_{1.3\,\mathrm{mm},\ \mathrm{peak}}}{{\rm{\Omega }}\,{\bar{m}}_{{{\rm{H}}}_{2}}\,{\kappa }_{1.3\,\mathrm{mm}}\,{B}_{1.3\,\mathrm{mm}}({T}_{\mathrm{dust}})},\end{eqnarray} \tag{ 5 }$$

where I_{1.3 mm, peak} is the peak intensity measured at the continuum peak, and Ω is the beam solid angle. In the top right panel of Figure 4, the histogram of the peak column density is shown. It ranges from 10²² to 10²⁴ cm⁻² with a peak around 3 × 10²² cm⁻². The orange line indicates less than 20% of cores have a peak column density higher than 10²³ cm⁻². The physical parameters of the cores are summarized in Table 4 (the full table can be accessed in machine-readable form).

In addition to the compact structures (cores), the continuum emission also resolved clumps in a network of filaments, some of which consist of hub-filament systems. A hub is the convergence of multiple filaments and recently caught more attention as the possible birthplace of high-mass stars (e.g., Motte et al. 2018).

We applied the publicly available filament finding package FilFinder (Koch & Rosolowsky 2015) to the ASHES continuum images to identify filamentary structures. It first creates a mask of a filamentary structure by adopting an intensity threshold, and each structure within the identified mask is reduced to a skeleton. These skeletonized structures are pruned by imposing thresholds for their lengths or sizes prior to obtaining the extracted filaments. We exclude very short structures and identified the prominent ones (see Appendix for more details).

Filamentary structures are identified in almost all clumps (36/39), ¹⁷ some of which contain hub-filament systems. The identified skeletons are highlighted as orange lines in Figure 5, for example. In this figure, the convergence point is a hub. We have identified 31 hubs in 17 ASHES clumps. We will discuss whether the MMCs or high-mass cores are preferentially located at such hub positions later (see Section 5.2). For this work, we focus on the dust continuum emission, and the detailed analysis of filaments and hubs is beyond the scope of this paper.

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View figure set (3 panels)

Tarball of figure set images

The top panel of Figure 6 shows the core mass and the corresponding surface density of the natal clump. Red circles represent the MMCs in each clump, blue triangles represent mass sensitivity for each clump corresponding to the integrated intensity of 3.5σ. We find a moderate correlation between clump surface density and the maximum core mass with a Spearman's rank correlation coefficient of r_s = 0.39, and p–value = 0.01. The bottom panel of Figure 6 displays the differential core mass function (CMF) sharing the horizontal axis of the top panel. The core mass distribution peaks at around 0.6 M_⊙ (close to the worst mass sensitivity in the sample), and rapidly decreases toward the high-mass end. The detailed analysis for the CMF will be addressed in a dedicated paper under preparation (K. Morii et al. 2023, in preparation).

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As described in Section 2, at least one high-mass star is expected to be formed from each ASHES clump. In this section, we focus on the MMCs found in each clump (hereafter MMCs), those with ${M}_{\mathrm{core}}={M}_{\max }$.

5.2.1. Correlation between the Maximum Core Mass and Clump Surface Density

In stellar clusters, higher-mass stars are found in higher-mass clusters (Larson 2003). In a similar fashion, it may be expected that higher-mass cores should form in higher-mass clumps. Here, to minimize the effect of having different spatial resolutions, we have limited the sample for this discussion. We have excluded the clumps that locate too close (<3.5 kpc) and too far (>5.5 kpc), and two more with the worst mass sensitivity (>0.45M_⊙). As a result, the 30 clumps remaining are located between 3.5 and 5.5 kpc and have a mass sensitivity between 0.086 and 0.41 M_⊙. Figure 7 shows the scatter plots of the maximum core mass (M_max) versus clump surface density, clump mass, distance, and clump surface density within a certain area. As seen in Figure 7, the clump surface density correlates with M_max, having a Spearman's rank correlation coefficient r_s = 0.55, and p–value = 0.0016. On the other hand, M_max and clump mass weakly correlate with a Spearman's rank correlation coefficient of r_s = 0.27, and a p–value = 0.15. It indicates that the maximum core mass in each clump is not determined by the natal clump mass at least in the very early stages traced in the ASHES survey. Considering the relation between the cluster mass (clump mass) and the maximum stellar mass empirically derived by Larson (2003; see Equation (3) used earlier), the weak correlation implies the final stellar mass is not determined from the initial core mass. The left panel in Figure 7 would rather indicate that more massive cores form in clumps with higher surface density. We confirmed that the stronger correlation between the maximum core mass and the clump surface density does not result from the codependence on the distance as shown in the right two panels of Figure 7. We recalculated the clump surface density within a circle with a radius of 0.45 pc centered on the mean positions of cores, (Σ_{cl,0.45 pc}) to reduce the dependence on distance. The circle almost corresponds to the FOV of the closest clump (3.5 kpc). A moderate correlation is present with a Spearman's rank correlation coefficient of r_s = 0.43, and p–value = 0.017.

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5.2.2. The Lack of High-mass Prestellar Cores

We revealed 839 dense cores, among which about 55% are low-mass (<1 M_⊙). Although seven high-mass cores (≳27 M_⊙) are identified thanks to a large sample, more than half of the ASHES clumps (23/39) host only cores with masses smaller than 10 M_⊙. We compared the maximum core mass with the expected maximum stellar mass in Figure 8. Clumps are sorted in order of their masses, and the clump mass (and the expected maximum stellar mass) increases from left to right. The expected maximum stellar mass is estimated from the clump mass in two different ways, using Equations (3) and (4) (plotted as blue and green star symbols, respectively). We overplotted M_max multiplied by 0.3 as red circles, assuming a core-to-star formation efficiency of 30%.

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We again find no strong correlation between the maximum core mass and clump mass as mentioned in the previous section. Moreover, most red circles (30% of core mass) show lower masses than those of the blue and green stars (expected stellar masses). The majority of the ASHES clumps (35/39) have currently the MMCs with insufficient mass to form high-mass stars with the expected mass. This plot highlights that most cores in such a very early phase do not have sufficient mass to form high-mass stars without additional mass feeding, as predicted by clump-fed scenarios, such as competitive accretion, hierarchical collapse, and the inertial-inflow model. The MMCs in only four regions could form a high-mass star and have a mass near to the expected maximum stellar mass, assuming an SFE of 30% (G024.01, G028.56, G033.33, and G340.23). Even if we assume a higher SFE of 50%, only two additional clumps (G023.47 and G025.16) are added. We should note that these high-mass cores are associated with outflows traced by CO (J = 2–1) and also warm line emission such as H₂CO and CH₃OH (E_u > 45 K), implying that these high-mass cores present star formation signatures and are not prestellar (results that will be presented in a forthcoming paper).

The MMCs are generally intermediate-mass cores, more massive than the thermal Jeans mass of the host clump (e.g., 1–5 M_⊙). As an initial condition, the competitive accretion scenario predicts that clumps fragment into low-mass cores, comparable to the Jeans mass. It does not entirely match our observations in terms of core mass, although some of the maximum core masses may have been initially low-mass but have already grown by accreting gas from the surrounding medium. Contreras et al. (2018) estimated a core infall rate of 2 × 10⁻³ M_⊙ yr⁻¹ in one core of the ASHES sample. Assuming that gas accretion with this infall rate continues for ∼2.0×10⁴ yr, the mean freefall time of the 39 MMCs (${t}_{{ff}}=\sqrt{3\pi /(32G\rho )}$), the cores can gain the additional mass of ∼40 M_⊙. Sabatini et al. (2021) estimated a duration of 5 × 10⁴ yr for the 70 μm dark phase from 110 massive clumps at different evolutionary stages. This timescale, longer than the mean freefall time for the 39 more massive cores, suggests that the cores initially of a Jeans mass have sufficient time to accrete and grow before becoming bright at IR wavelengths. In the following subsection, we will investigate whether MMCs are located at the position where efficient mass feeding is expected.

Using mosaic observations at high sensitivity, we have therefore revealed a large number of low-mass cores and the lack of high-mass prestellar cores, in dense, massive 70 μm dark clumps. Considering the large number of cores detected in this study (839 in 39 clumps), following Sanhueza et al. (2019), we can say with more confidence that high-mass prestellar cores do not exist, or, if they do, they should form later when environmental conditions are appropriate for their formation.

5.2.3. Weak Mass Segregation and Strong Density Segregation

Mass feeding scenarios, such as the competitive accretion model, expect high-mass cores to be formed from low-mass cores located near the bottom of the gravitational potential or (hub-)filaments where cores acquire mass more efficiently. The different spatial distribution of massive objects with respect to lower-mass objects is called mass segregation (e.g., Allison et al. 2009; Parker & Goodwin 2015). The segregation caused by two-body relaxation is called dynamical mass segregation (von Hoerner 1960; Meylan 2000), while the segregation found in young clusters, believed to be inherited from the initial fragmentation, is called primordial mass segregation (e.g., Alfaro & Román-Zúñiga 2018). The Herschel Gould Belt Survey (André et al. 2010) has found mass segregation in some star-forming region such as Aquila, Corona Australis, and W43-MM1 (Dib & Henning 2019), Orion A (Román-Zúñiga et al. 2019), Orion B (Parker 2018; Könyves et al. 2020), NGC6334 (Sadaghiani & Sánchez-Monge 2020), and NGC2264 (Nony et al. 2021) at ∼0.01–0.1 pc scale. Dib & Henning (2019) indicates regions with more active star formation present centrally clustering core distributions and significant mass segregation. Our sample is expected to be in the very early phase of high-mass star and cluster formation without IR-bright sources and be the best target to investigate if there is primordial mass segregation in the very early phase.

Following the pilot survey (Sanhueza et al. 2019), we first studied mass segregation ratios (MSRs), Λ_MSR (Allison et al. 2009) and Γ_MSR (Olczak et al. 2011), based on the minimum spanning tree (MST) method developed by Barrow et al. (1985). MST connects cores (in this case), minimizing the sum of the length and determining a set of straight lines. Black line segments on the right panel in Figure 3 show an example of the outcome from MST. Λ_MSR compares the sum of the edge length of the MST (l_MST) of random cores with that of the same number of massive cores:

$$\begin{eqnarray}&&{{\rm{\Lambda }}}_{\mathrm{MSR}}({N}_{\mathrm{MST}})=\displaystyle \frac{\langle {l}_{\mathrm{MST}}^{\mathrm{random}}\rangle }{{l}_{\mathrm{MST}}^{\mathrm{massive}}}\pm \displaystyle \frac{{\sigma }_{\mathrm{random}}}{{l}_{\mathrm{MST}}^{\mathrm{massive}}},\end{eqnarray} \tag{ 6 }$$

where $\langle {l}_{\mathrm{MST}}^{\mathrm{random}}\rangle$ is the sum of the edge length of N_MST random cores averaged by 1000 trial, and ${l}_{\mathrm{MST}}^{\mathrm{massive}}$ is that of N_MST MMCs. σ_random is the standard deviation associated with estimating the average value $\langle {l}_{\mathrm{MST}}^{\mathrm{random}}\rangle$. If massive cores are distributed similarly to random cores (i.e., no mass segregation), Λ_MSR would be close to unity. If massive cores are concentrated, and their distribution is different from the lower-mass cores (mass segregation), Λ_MSR becomes larger than unity. In turn, Λ_MSR < 1 implies massive cores are spread out compared to others (inverse-mass segregation). We calculated Λ_MSR(N_MST) varying N_MST from two to the total number of cores in each clump, $N(\mathrm{core})$. The second method (Γ_MSR) uses the geometric mean of the edges (γ_MST), not the sum of the edges (l_MST)

$$\begin{eqnarray}&&{\gamma }_{\mathrm{MST}}={\left(\displaystyle \prod _{i=1}^{N(\mathrm{core})-1}{L}_{i}\right)}^{1/(N(\mathrm{core})-1)},\end{eqnarray} \tag{ 7 }$$

and defined by

$$\begin{eqnarray}&&{{\rm{\Gamma }}}_{\mathrm{MSR}}({N}_{\mathrm{MST}})=\displaystyle \frac{{\gamma }_{\mathrm{MST}}^{\mathrm{random}}}{{\gamma }_{\mathrm{MST}}^{\mathrm{massive}}}{\left(d{\gamma }_{\mathrm{random}}\right)}^{\pm 1},\end{eqnarray} \tag{ 8 }$$

where d γ_random is the geometric standard deviation given by

$$\begin{eqnarray}&&d\gamma =\exp \left(\sqrt{\displaystyle \frac{{{\rm{\Sigma }}}_{i=1}^{N(\mathrm{core})-1}{\left(\mathrm{ln}\,{L}_{i}-\mathrm{ln}\,{\gamma }_{\mathrm{MST}}\right)}^{2}}{N(\mathrm{core})-1}}\right),\end{eqnarray} \tag{ 9 }$$

where L_i is the ith MST edge. The term ${\gamma }_{\mathrm{MST}}^{\mathrm{random}}$ is the geometric mean of the edges for N_MST random cores, and ${\gamma }_{\mathrm{MST}}^{\mathrm{massive}}$ is that for the N_MST massive cores. These two different MSRs (Λ_MSR and Γ_MSR) are thought to behave in the same way, but Olczak et al. (2011) proposed that Γ_MSR is more sensitive to finding weak mass segregation.

Figure 9 shows the MSRs as Γ_MSR and Λ_MSR with changing N_MST from 2 to $N(\mathrm{core})$. We display regions with relatively high MSR (max(MSR) > 2 at N_MST > 3) or low MSR (max(MSR) < 0.5 at N_MST > 3). For the remaining regions, Γ_MSR and Λ_MSR are consistent with unity (i.e., no mass segregation) for N_MST > 3. The MSRs at N_MST = 3 in six clumps is higher than 2, but MSRs' values gradually decrease for larger N_MST values. Only G034.73 shows a tentative detection of mass segregation with MSR of ∼3 at N_MST = 5. Compared with the pilot survey (Sanhueza et al. 2019), in which no evidence of mass segregation was found, this larger sample reveals weak detections of mass segregation in G018.80, G023.47, G024.01, G024.52, G028.92, and G034.73. We note that most of these clumps host no high-mass cores except for G024.01 (${M}_{\max }=38.4{M}_{\odot }$), and there is no strong correlation between the maximum core mass and the MSR. Thus, the weak mass segregation found in the ASHES sample implies that the relatively high-mass cores (e.g., MMCs) form similarly to the lower-mass cores at the initial phase traced by the studied 70 μm dark IRDCs.

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However, a caveat to keep in mind for this discussion is the small core sample used for estimating MSRs. Although the previous studies such as Dib & Henning (2019) treat about 100 objects, the sample here contains 40 at most.

If we replace ${l}_{\mathrm{MST}}^{\mathrm{massive}}$ in Equation (6) by ${l}_{\mathrm{MST}}^{\mathrm{dense}}$, an edge length of the N_MST densest cores instead of the MMCs, we can investigate whether denser cores are distributed differently from relatively less dense cores. We refer to this as density segregation. Figure 10 shows the segregation ratios Λ(N_MST) calculated by sorting by core volume density, n(H₂) (top panels), and core surface density, Σ (bottom panels), instead of core mass. Using the same threshold as Figure 9, we only plot the clumps that show a high or low segregation ratio (Λ > 2 or <0.5, respectively). As the figures clearly show, contrary to mass segregation, the segregation by density was confirmed in about half of our sample, and their Λ values are generally higher than Λ_MSR, implying a stronger segregation. We note that all six clumps with signs of mass segregation show density segregation as well. By carefully checking core positions, core masses, and densities, we found that mass segregation and density segregation occur around the same part within these clumps. To highlight the density segregation in Figure 3, we colored in orange the cores that are denser than the median of the surface density of all cores in the clump.

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The density segregation may trace a segregation resulting from the different evolutionary stages of cores within a given clump. One may expect that cores become denser as they evolve. Thus, the density segregation observed may indicate that more evolved cores are segregated. Another possibility is that such denser cores are formed from the fragmentation of denser parts within clumps. We found a strong correlation between the clump surface density and the median of cores' surface density with a Spearman's rank correlation coefficient of r_s = 0.53, and a p–value = 4.8 × 10⁻⁴. Assuming that these correlations hold even at a smaller scale (i.e., within the clump), a denser region within a nonuniform clump would produce denser cores than a less dense part, resulting in density segregation. Therefore, the initial spatial distribution of cores would be dictated by density.

Alfaro & Román-Zúñiga (2018), Román-Zúñiga et al. (2019) also reported a spatial segregation by volume density stronger than the segregation by mass in the Pipe Nebula and Orion A. They concluded that density controls the clumpy spatial distribution of prestellar cores at the very early phase.

5.2.4. Spatial Distribution of MMCs: Hub-filament System

In addition to the weak mass segregation, we also found no significant difference in the spatial distribution between MMCs and the lower-mass cores. Since we have no information on the gravitational potentials of clumps, we assume that they are around the continuum peak of the single-dish observations. Figure 11 displays the plot of core mass versus separation from the continuum peak of each clump (hereafter clump peak position) obtained by single-dish observations (i.e., ATLASGAL survey). The MMCs in each clump are highlighted as orange, and the other cores are shown in blue circles. Above the worst mass sensitivity (∼0.58 M_⊙), we cannot reject the null hypothesis at a 5% level that the separation distributions of MMCs (orange) and the other cores (blue) are identical since the estimated p–value is 0.47 from the Kolmogorov–Smirnov (KS) test. It implies that there is no significant difference. We note that this lack of difference in spatial distribution is confirmed when the clump peak positions are replaced with the mean position of cores identified by ALMA.

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Alternatively, another preferred location for the MMCs could be a hub-filament system. Our observations resolve 70 μm dark massive clumps, revealing cores and filamentary structures within clumps. We revealed prominent hub-filament systems in some clumps, such as G024.524–00.139 and G025.163–00.304, as identified in Section 4.4. This motivates us to study whether there is correlation between the position of the MMCs and the hub-filament systems. Assuming that cores at hub positions can efficiently accumulate gas, more massive cores are expected to form at hub positions. We overlaid the MMCs and second MMCs as red and cyan circles, respectively, in Figure 5. Most of the MMCs are not located at such hub positions. Indeed, only eight (20%) MMCs are found at hubs. Even after considering the second MMC in each clump, only eleven cores in total are located in hubs (11/(39 × 2) = 14%). Considering projection effects, the real percentage would be lower. If we focus on high-mass cores (>27 M_⊙), only a single clump hosts high-mass cores at hub positions among the 17 hub-hosting clumps. Our observations imply that the hub-filament systems within massive clumps at very early evolutionary stages are not yet efficiently contributing to core accretion. This is also in agreement with the finding that MMCs are similarly distributed to lower-mass cores at early stages, as we have discussed so far. Line emission, such as N₂H⁺, would trace more extended emission, which may reveal more filaments or hub-filament systems.

However, half of the high-mass cores are located within filaments, implying that high-mass cores may form by acquiring gas along filaments, adding further support to previous studies (e.g., Henshaw et al. 2014; Peretto et al. 2014; Lu et al. 2018; Williams et al. 2018; Chen et al. 2019; Sanhueza et al. 2021; Zhou et al. 2022). Recently, Redaelli et al. (2022) revealed an accretion flow seen in N₂H⁺ (J=1–0) in a target of the ASHES sample, G014.492-00.139, and estimated an accretion rate of 2 × 10⁻⁴ M_⊙ yr⁻¹. Assuming that this gas accretion feeds a core for its freefall time (∼2 × 10⁴ yr), the core can acquire an additional mass of 4 M_⊙. There are an additional two MMCs in the whole 39 MMCs that can grow into high-mass cores (≳27 M_⊙) with this assumed accretion rate. However, we note that, with either a longer accretion time (e.g., 1.5 × t_ff ) or higher SFE (e.g., 50%), accretion through filaments would be substantial and key for the formation of high-mass stars. The study of gas dynamics around the whole population of ASHES cores would make clearer the role of accretion along filaments in the formation of high-mass stars.

Using ALMA observations toward 70 μm dark massive clumps, we have revealed the properties of hundreds of cores in the very early phases of high-mass star formation. The majority of the identified MMCs have insufficient mass to form high-mass stars following the core accretion scenario. In addition, no high-mass prestellar cores were detected. We only found a weak correlation between the maximum core mass and the natal clump mass, in contrast to the correlation between the maximum stellar mass and the cluster's mass (i.e., Larson's relation Equation (3)), implying that the initial core mass does not have to be correlated with the final stellar mass (e.g., Smith et al. 2009; Pelkonen et al. 2021). These conditions found in the ASHES sample support clump-fed accretion scenarios, such as competitive accretion, global hierarchical collapse, and the inertial-inflow model.

In spite of infall rate estimations being so far rare in IRDCs, the few examples available (Contreras et al. 2018; Chen et al. 2019; Redaelli et al. 2022) suggest that cores with masses as those found in ASHES cores can grow significantly in mass in a core freefall time (as discussed in two ASHES clumps; Contreras et al. 2018; Redaelli et al. 2022). Some ASHES cores have the conditions to become massive as hot cores and form high-mass stars. We note that we cannot completely rule out the core accretion picture. However, if high-mass prestellar cores exist, we constrain their formation to later times, once the conditions for their formation may be adequate (e.g., a denser or warmer environment, or under the presence of a more turbulent medium or stronger magnetic field).

The high-resolution ALMA observations also reveal that 45% of the ASHES targets (18/39) have developed hub-filament systems. However, our analysis suggests that, at the moment, hub-filament systems do not efficiently contribute to the formation of high-mass stars (picture that can change at later evolutionary stages). As discussed in Section 5.2.4, only one clump (2.5%) hosts high-mass cores, and eight (20%) host their MMCs at a hub-position. Such low probability implies that the high-mass cores or the MMCs are not preferentially formed at hub-filament systems, but rather it implies that cores originally formed in hub-systems eventually evolved to become massive at later stages (Liu et al. (2023).