FRagmentation and Evolution of Dense Cores Judged by ALMA (FREJA). I. Overview: Inner ∼1000 au Structures of Prestellar/Protostellar Cores in Taurus

Single-dish surveys using bolometer cameras revealed that the core mass function (CMF) in the cluster-forming regions of ρ Ophiuchus resembles the stellar IMF, although their observations lack sufficient samples above 0.5 M_⊙ (Motte et al. 1998). The subsequent unbiased survey using a high-density (∼10⁵ cm⁻³) molecular gas tracer confirmed similar results through their compilation of a much robust number of samples (Onishi et al. 1996, 1998, 2002; Tachihara et al. 2002). Deep submillimeter continuum maps (e.g., Nutter & Ward-Thompson 2007) found that the CMF turns over at ∼1 M_⊙, and the slope of the low-mass side is also consistent with that of the IMF (see also Könyves et al. 2015; Marsh et al. 2016). Such large-scale surveys indicate that the core-to-star formation efficiency is ∼20%–40% (e.g., Alves et al. 2007; André et al. 2010) assuming that the CMF is converted to the IMF by the one-to-one transformation. This efficiency is consistent with that realized by mass loss due to protostellar outflow, as expected from numerical simulations (e.g., Machida & Matsumoto 2012). Such a dense parental core prior to protostar formation, called a prestellar core, is supposed to be gravitationally bound (formerly, pre-protostellar cores; see Ward-Thompson et al. 1994). Note that recent surveys suggested that some starless sources are likely pressure confined (e.g., Pattle et al. 2015; Kirk et al. 2017b). Although the above-mentioned relation between the CMF and IMF may not be simple (see the review by Offner et al. 2014), the current observational indications tell us that the nature of prestellar cores is likely to reflect the properties of forming stars, such as stellar mass, and the multiplicity inside them. It is thus important to characterize their properties as the initial condition for star formation (for reviews see, e.g., Bergin & Tafalla 2007; Ward-Thompson et al. 2007). Note hat such surveys are also vital in the search for rare objects, such as very high-density cores just before/after star formation whose timescale is very short (Mizuno et al. 1994; Onishi et al. 1999).

Early millimeter/submillimeter continuum emission and near-infrared extinction studies toward individual dense cores without any indications of star formation demonstrated that most of the starless cores have inner flat density structures (e.g., Ward-Thompson et al. 1994) and the (column) density profiles in Bok globules are well characterized by a critical Bonnor–Ebert (BE) sphere (Ebert 1955; Bonnor 1956) model (Alves et al. 2001; Kandori et al. 2005). Numerical simulations for the gravitational collapse of a dense core often adopt such a relatively simple geometry as an initial condition (e.g., Machida et al. 2008). However, Kirk et al. (2005) showed that the BE model could not be applied to one-third of the observed dense cores and suggested that they are already collapsing or supported by an additional force, such as the magnetic field. Onishi et al. (2002) found a large number of irregular-shaped cores with an average density of ∼10⁵ cm⁻³ in Taurus. Although their tracer, H¹³CO⁺, possibly traces lower density gas and is affected by molecular depletion (see Caselli et al. 2002a), the observations of N₂H⁺ and its deuterated species, which are less sensitive to this problem, also show similar results for some cores (e.g., Tafalla & Hacar 2015; Punanova et al. 2018). Although virial analysis of these objects shows that they are gravitationally bound objects, the presence of such irregular structures imply that environmental effects such as turbulence are still not negligible in the core dynamics. Numerical simulation by Padoan & Nordlund (2002) claimed that the inner density profile with two-dimensional averaging mimics a BE-like structure even if the core has an irregular shape created by turbulent compression. In any case, the previous single-dish observational studies did not have sufficient angular resolution to resolve the inner ∼1000 au regions of prestellar cores. Therefore, they characterized them as uniform density parts.

Recent observational studies in the early phase of star formation (i.e., class 0/I phases) suggest that most of the stars can be formed as binary/multiple members (e.g., Chen et al. 2013) whose frequency is ∼2/3. The classic idea to explain such a system is fragmentation in gravitationally unstable massive disks (Larson 1987; Boss 2002; Machida et al. 2008) after protostar formation. Some numerical simulations adopting strong turbulence produce local high-density maxima, possibly leading to binary/multiple star formation within a single core (e.g., Offner et al. 2010). Tobin et al. (2015, 2016) suggest that such a turbulent-driven fragmentation can be a promising candidate for the origin of wide binary/multiple systems based on their systematic survey, and Pineda et al. (2015) found filamentary clouds, possibly leading to a quadruple star system with a separation of ≳1000 au.

Recent Atacama Large Millimeter/submillimeter Array (ALMA) observations of the protostellar core MC 27/L1521F in Taurus resolved multiple overdense peaks, which cannot be explained by the coherent collapsing motion alone (Tokuda et al. 2014, 2016, 2017). Some ALMA studies (e.g., Williams et al. 2014; Fernández-López et al. 2017; Lee et al. 2017) found binary/multiple protostellar disks whose projected rotational axes are highly misaligned with each other, possibly driven by turbulence. It is crucial to search for fragmented structures at the prestellar collapse phase and investigate their physical properties when we consider the origin of such complex systems. Nevertheless, taking into account the fact that most of the prestellar cores have a flat density profile in the early phase of cloud collapse as suggested by theoretical studies (e.g., Larson 1969) and observations (see Section 1.1), detecting compact emission is a challenging task due to the spatial filtering effect of interferometers.

Early interferometric observations studied millimeter continuum emission (Schnee et al. 2010, 2012; André et al. 2012; Nakamura et al. 2012; Friesen et al. 2014; Ohashi et al. 2018; Tatematsu et al. 2020) and found hidden protostellar objects including the first hydrostatic core (hereafter FHSC, e.g., Larson 1969; Masunaga et al. 1998; Tomida et al. 2013) candidate (e.g., Chen et al. 2010, 2012; Enoch et al. 2010; Pineda et al. 2011; Pezzuto et al. 2012; Hirano & Liu 2014; Karnath et al. 2020) toward infrared-quiescent sources, especially in nearby cluster-forming regions, such as Perseus and ρ Ophiuchus (see the recent ALMA survey by Kirk et al. 2017a). However, these studies cannot clarify how an isolated dense core evolves into protostar(s) without contaminations from surrounding phenomena (e.g., stellar feedback). Investigations toward low-mass star-forming complexes, such as Taurus and Bok Globules, are vital to understanding the process of dense core evolution and possible fragmentation leading to a binary/multiple system inside a single core (see also the introduction in Caselli et al. 2019). The fact that the intrinsic column densities of Taurus dense cores are one order of magnitude lower than those in Perseus (Figure 7 in Ward-Thompson et al. 2007) makes it more difficult for us to find compact/evolved features, which are detectable with interferometers. As one of the most prominent examples, Dunham et al. (2016) could not find any 3 mm continuum emission inside 56 starless sources in Chamaeleon I using the ALMA Main array (12 m array). More recently, Caselli et al. (2019) found a high-density (∼10⁷ cm⁻³) compact peak toward one of the most well-studied prestellar cores, L1544, in Taurus. The critical next step is to reveal universality/diversity regarding the prestellar evolution in a molecular complex, for example, the presence/absence of fragmentation within a single core and their evolution timescale by statistical counting.

The previous study by Dunham et al. (2016) was a pilot survey to search for extremely high-density objects whose densities are ≳10⁸ cm⁻³, possibly in the FHSC stage. Onishi et al. (2002) implied that the threshold density for the dynamical collapse of cores is ∼10⁶ cm⁻³, and thus investigations of the properties of prestellar cores with a density of 10⁵–10⁶ cm⁻³ is crucial in order to understand the condition for the onset of star formation. The Jeans length (λ_J = $\sqrt{\pi {c}_{{\rm{s}}}/G{\rho }_{0}}$, where G is the gravitational constant, ρ₀ is the mean density, and c_s is the sound speed of 0.2 km s⁻¹ at 10 K) of 10⁶ cm⁻³ gas is ∼2000 au, which corresponds to ∼14'' at nearby star-forming regions, such as Taurus, Ophiuchus-North, Lupus, and Chamaeleon, whose distances are ∼150 pc (e.g., Schlafly et al. 2014). Such a scale is similar to the beam size of the single-dish telescopes, and the ALMA 12 m array may fail to detect the relatively extended emission due to the filtering-out effect (Onishi 2013). The Atacama Compact Array (ACA, a.k.a Morita Array), which includes short-spacing baselines, is the best tool to explore the innermost part of a dense core without a serious missing flux problem compared to the 12 m array alone. We demonstrated the capability of the ACA by discovering a candidate of the prestellar core, possibly leading to brown dwarf or very low-mass star formation (Tokuda et al. 2019). The work was the pilot study of the present project.

We present a survey in 1.3 mm continuum and molecular lines toward 39 dense cores (7 protostellar + 32 prestellar cores) in Taurus using the ACA. We name this project "FRagmentation and Evolution of dense cores Judged by ALMA (FREJA)," which is composed of multiple ALMA campaigns (see Section 2). Our primary strategy is (1) to find evolved features inside prestellar cores and perform statistical analysis to constrain theories of dense core evolution using the ACA stand-alone mode, and (2) to carry out follow-up observations with the 12 m array to further characterize the initial condition of low-mass star formation. In this paper (Paper I), we describe the survey design of this project with the ACA stand-alone mode and especially the early results revealed by the 1.3 mm continuum observations. Fujishiro et al. (2020; hereafter Paper II) investigate the nature of a possible FHSC candidate in L1535NE/MC 35.

2.1.1. Target Selection

We observed a large number of dense cores (32 prestellar core + 7 protostellar cores in total) in Taurus to investigate their inner structures with the ACA stand-alone mode in ALMA Cycles 4 and 6. Although our primary targets are prestellar cores, we included protostellar cores associated with young stellar objects (YSOs) for comparison purposes. In the Cycle 4 program (P.I., K. Tachihara, #2016.1.00928.S, hereafter PROJ4), we targeted 16 dense cores located at several nearby (D ∼ 150 pc) low-mass, star-forming regions—Taurus, Ophiuchus-North, Chamaeleon, and Lupus—based on available continuum data obtained by single-dish telescopes (see the description in Tokuda et al. 2019). Because we have confirmed the ∼50% detection rate in the millimeter continuum emission from prestellar sources, we planned to observe more objects to search for evolved sources and perform statistical analyses.

To obtain a large sample that is as unbiased as possible, we targeted the Taurus molecular cloud as the observation region in the Cycle 6 program (P.I., K. Tachihara, #2018.1.00756.S, hereafter PROJ6). The Nagoya 4 m telescope with ∼3' resolution performed an unbiased survey in ¹³CO(J = 1–0) across the Taurus complex (Mizuno et al. 1995), and the subsequent C¹⁸O(J = 1–0) observations revealed distributions of dense (∼10⁴ cm⁻³) filamentary molecular clouds (Onishi et al. 1996, 1998). Based on the large-scale mapping, high-resolution H¹³CO⁺ (1–0) observations using the Nobeyama 45 m telescope (Onishi et al. 2002) discovered 44 prestellar cores with a density of ≳10⁵ cm⁻³ toward high-column density (>10²² cm⁻²) regions in Taurus. Such cores detectable in high-density gas tracers are gravitationally bound, and thus they are considered to be prestellar cores (Ward-Thompson et al. 1994, 2007; see also Marsh et al. 2014 for the Taurus L1495 region). H¹³CO⁺ sometimes cannot trace the column density peak, possibly due to the depletion effect onto dust grains in cold/dense environments (e.g., Caselli et al. 2002a). Because this problem happens over a single-dish beam-size-scale even in an optically thin case, the confirmation of another molecular line tracer, such as a N-bearing species, is used to select evolved prestellar cores robustly. We investigated the N₂H⁺ detection toward the Onishi et al. (2002) catalog in the literature (Tatematsu et al. 2004; Tafalla et al. 2004, 2006; Tafalla & Hacar 2015; Punanova et al. 2018) and our independent measurements obtained with the Nobeyama 45 m telescope (Y. Miyamoto et al., in preparation; see also Tokuda et al. 2019). Note that the recent large-scale surveys in the B213/L1495 and B18 regions with the Green Bank Telescope (Seo et al. 2015, 2019; Friesen et al. 2017) also detected NH₃ emission toward our selected samples.

We selected the observation coordinates to the peak positions of the millimeter/submillimeter continuum emission obtained by the IRAM 30 m, the James Clerk Maxwell telescope (JCMT) 15 m, and the Herschel telescope (Kauffmann et al. 2008; Palmeirim et al. 2013; Marsh et al. 2016; Ward-Thompson et al. 2016; Tokuda et al. 2019). We set the selection criteria in H₂ column density as ≳10²² cm⁻², which is higher than the column density threshold for prestellar cores (André et al. 2010). If there are two local peaks in the continuum emission on a single core cataloged by Onishi et al. (2002), we targeted two fields to observe each peak. These targets are MC 5N/S, MC 7N/S, MC 13a/W, MC 25E/W, and MC 33bN/S. Note that there are two targets (B10 and L1521E; see Hirota et al. 2002; Hacar et al. 2013; Tafalla & Hacar 2015) that were not included in the Onishi et al. (2002) catalog. The total number of observed fields is 32 as prestellar sources. We included seven protostellar cores, whose evolutionary stages are mostly class 0/I phases, to investigate differences between pre-/protostellar cores. We previously performed a case study toward the MC 27/L1521F class 0 Very Low-Luminosity Object (VeLLO) system using a similar frequency setting (Tokuda et al. 2017, 2018). We include the data set (hereafter, PROJ-MC27) in this paper. Table 1 and Figure 1 give the properties of the targeted objects and their positions on the large-scale Herschel dust continuum image, respectively.

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Table 1.  Target Objects

Name	RA	Decl.	nave(H2)a	Tkb	Distancec	Staged	Other Name	Region	Project
	(J2000.0)	(J2000.0)	(105 cm−3)	(K)	(pc)
MC 1	4h04m480	+26°19'220	⋯	10.0	126.6	Pre	L1489-NH3e,f	L1489	PROJ6
MC 2	4h10m523	+25°10'040	0.8	⋯	126.6	Pre	L1498e	L1498	PROJ6
MC 4	4h14m110	+28°09'120	1.1	⋯	129.5	Pre	L1495SEe	L1495	PROJ6
MC 5N	4h17m420	+28°08'430	1.9	9.3	129.5	Pre	⋯	L1495	PROJ4,PROJ6
MC 5S	4h17m430	+28°06'010	1.9	9.7	129.5	Pre	⋯	L1495	PROJ6
MC 6	4h17m533	+28°13'150	1.2	9.5	129.5	Pre	⋯	L1495	PROJ4
MC 7N	4h18m035	+28°22'570	1.9	9.7	129.5	Pre	⋯	L1495	PROJ6
MC 7S	4h18m029	+28°22'180	1.9	9.7	129.5	Pre	⋯	L1495	PROJ6
MC 8	4h18m075	+28°05'140	1.0	9.3	129.5	Pre	⋯	L1495	PROJ4
MC 11	4h18m399	+28°23'180	0.5	10.3	129.5	Pre	⋯	L1495	PROJ6
B10	4h17m500	+27°56'070	⋯	9.3	129.5	Pre	⋯	L1495	PROJ6
MC 13W	4h19m237	+27°14'505	1.4	9.2	158.1	Pre	⋯	B213	PROJ6
MC 13a	4h19m375	+27°15'230	1.4	9.7	158.1	Pre	⋯	B213	PROJ6
MC 13b	4h19m425	+27°13'320	3.1	10.4	158.1	Class 0/I	⋯	B213	PROJ6
MC 14N	4h19m510	+27°11'340	⋯	9.1	158.1	Pre	04169-NWf	B213	PROJ6
MC 14S	4h19m585	+27°11'595	5.0	10.3	158.1	Class 0/I	⋯	B213	PROJ6
MC 16E	4h21m210	+26°59'470	2.5	9.5	158.1	Pre	L1521Dg	B213	PROJ6
MC 16W	4h20m530	+27°02'490	1.8	9.9	158.1	Pre	L1521Dg	B213	PROJ6
MC 19	4h23m435	+25°04'130	0.7	⋯	126.6	Pre	⋯	L1506	PROJ6
MC 22	4h24m216	+26°36'340	2.1	⋯	140	Pre	L1521Be	L1521	PROJ6
MC 23	4h26m370	+24°36'525	0.7	⋯	126.6	Pre	⋯	B18	PROJ6
MC 24	4h26m355	+24°41'440	2.4	10.7	126.6	Pre	⋯	B18	PROJ6
MC 25E	4h28m095	+26°20'435	1.2	⋯	140	Pre	B217e	L1521	PROJ6
MC 25W	4h27m480	+26°18'020	1.2	⋯	140	Pre	B217e	L1521	PROJ6
MC 26a	4h27m574	+26°19'190	⋯	⋯	140	Class I	⋯	L1521	PROJ6
MC 27	4h28m390	+26°51'399	1.6	9.1	140	VeLLO	L1521Fg	L1521	PROJ-MC27
L1521E	4h29m140	+26°14'000	⋯	⋯	140	Pre	⋯	L1521	PROJ6
MC 28	4h29m229	+24°33'095	1.3	11.0	126.6	Class I	⋯	B18	PROJ6
MC 29	4h30m070	+24°25'520	0.8	9.4	126.6	Pre	⋯	B18	PROJ6
MC 31	4h31m555	+24°32'550	1.2	8.6	126.6	Pre	TMC-2Ae	B18	PROJ4,PROJ6
MC 33bS	4h32m431	+24°23'090	1.5	9.2	126.6	Pre	TMC-2h	B18	PROJ4,PROJ6
MC 33bN	4h32m473	+24°25'266	1.5	9.1	126.6	Pre	TMC-2h	B18	PROJ6
MC 34	4h33m277	+22°42'091	0.6	⋯	162.7	Pre	L1536e	L1536	PROJ6
MC 35	4h35m375	+24°09'170	4.0	10.0	126.6	Pre	L1535NEi	B18	PROJ6
MC 37	4h39m178	+25°52'231	1.1	11.2	137.0	Pre	⋯	HCL2	PROJ6
MC 38	4h39m310	+25°48'050	0.6	⋯	137.0	Pre	⋯	HCL2	PROJ6
MC 39	4h39m347	+25°41'340	1.0	⋯	137.0	Class I	⋯	HCL2	PROJ6
MC 41	4h39m550	+25°45'030	1.1	⋯	137.0	Class II	⋯	HCL2	PROJ6
MC 44	4h41m392	+26°00'150	0.7	9.9	137.0	Pre	TMC-1Ce	HCL2	PROJ4

Notes.

^aAverage number H₂ density estimated from H¹³CO⁺ observations (Onishi et al. 2002). ^bKinematic temperature derived from NH₃ observations (Benson & Myers 1989; Codella et al. 1997; Seo et al. 2015; Fehér et al. 2016; Friesen et al. 2017). ^cDistance measurements toward individual clouds in Taurus by Galli et al. (2018). Because there is no available data for the L1521 region in their study, we used 140 pc (e.g., Elias 1978) for it. ^d"Pre" means prestellar cores. The other sources are protostellar cores containing VeLLO (Bourke et al. 2006), class 0/I (Motte & André, 2001), class I (Kenyon et al. 1993a, 1993b), and class II (Hillenbrand et al. 2012). ^e-iBenson & Myers (1989), Motte & André (2001), Codella et al. (1997), Myers et al. (1979), Hogerheijde & Sandell (2000), respectively.

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2.1.2. Frequency Setting

Detailed data reduction processes and qualities in PROJ4 and PROJ-MC27 were presented in Tokuda et al. (2019) and Tokuda et al. (2018), respectively. We summarize the observation settings and data qualities in Table 2 and describe PROJ6 as follows. We performed the ACA (the 7 m array and the TP (Total Power) array) observations toward the Taurus dense cores (Section 2.1) between 2018 October and 2019 March. The covered uv range of the 7 m array was 5.4–29 kλ. There were three pointings per target with the same pattern (see also Figure 2). The integration time (on-source time) per pointing was ∼8.5 minutes. The bandpass and flux calibrator was the quasar J0423–0120. We observed J0510+1800 or J0336+3218 as phase calibrators once every ∼8 minutes during the observations. There were four spectral windows for molecular line observations with a bandwidth of 62.5 MHz and a spectral resolution of 61.0 kHz, targeting N₂D⁺, ¹²CO, ¹³CO, and C¹⁸O (Section 2.1.2). We used two spectral windows, whose bandwidth and resolution were 2000 MHz and 15.6 MHz, respectively, to obtain continuum images. The central frequencies of the two bands were 218.0 and 232.5 GHz. We individually processed the two bands of two targets, MC 1 and MC 35, following the procedure described in the next paragraph, as a preliminary analysis. After we confirmed that the two bands reproduce almost the same result (see Section A.1 in Appendix A), we combined the two bands to enhance the image sensitivity. The effective frequency of the final processed continuum images is 225.3 GHz (∼1.3 mm).

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Table 2.  Observation Settings and Qualities

Project name	Code	Continuum	Molecular lines	Beam size	Continuum rms	Line rmsb
PROJ4a	2016.1.00928.S	1.2 mm	H13CO+, H13CN(3–2)	74 × 52	∼0.6 mJy beam−1	∼0.07 K
PROJ6a	2018.1.00756.S	1.3 mm	12CO, 13CO, C18O(2–1), N2D+ (3–2)	68 × 63	∼0.4 mJy beam−1	∼0.05 K
PROJ-MC27	2015.1.00340.S	1.3 mm	13CO, C18O(2–1), N2D+ (3–2)	72 × 58	∼0.3 mJy beam−1	∼0.03 K

Notes.

^aThe beam size and rms are the average values among the observed targets. Table A1 in Appendix A gives the individual ones. ^bThe velocity resolution is ∼0.1 km s⁻¹.

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We performed the data reduction using the Common Astronomy Software Application (CASA) package (McMullin et al. 2007) version 5.6.0. In the imaging process, we used the tclean task with the multi-scale deconvolver (Kepley et al. 2020) to recover the extended emission. The imaging grid was set to have square pixels of 10 width, and the scales of the multi-scale clean are 0, 6, and 18 pixels. The weighting scheme was "Natural." We manually selected the emission mask (clean box) and continued the deconvolution process until the intensity of the residual image reached the ∼1σ noise level. We did not apply the self-calibration process, because the continuum emission of the prestellar sources is quite weak. Note that we applied the same method and parameters to the two other different data sets (PROJ4 and PROJ-MC27). Three targets (MC 5N, MC 31, and MC 33bS) were observed in both PROJ4 and PROJ6 and had confirmed continuum detection in the two bands, but we used the PROJ6 (1.3 mm) data alone throughout the analyses in this manuscript. We manually selected emission-free pixels from each continuum image to estimate their rms noise levels. Table 2 summarizes the resultant beam sizes and sensitivities (see also the individual properties of each target in Table A1 in Appendix A).

In the present paper, we normally did not use the TP molecular line data to focus on compact features revealed by the 7 m array continuum observation alone and to keep the spatial frequency range of both the line and continuum data similar. Only in Section 4.2, we used the combined 7 m and TP array images obtained by the feather task in CASA to further obtain evidence for realistic substructures within two prestellar cores, MC 1 and MC 7.

Figure 2 shows the 7 m array observations in 1.2/1.3 mm continuum toward all of the observed sources. We could not detect significant (>3σ) emission in 20 prestellar cores (MC 2, MC 4, MC 6, MC 8, MC 11, MC 13a, MC 13W, MC 14N, MC 16W, MC 19, MC 22, MC 23, MC 25E, MC 25W, MC 29, MC 33bN, MC 34, MC 38, MC 44, and L1521E). On the contrary, we confirmed continuum detection toward 12 prestellar cores (MC 1, MC 5N, MC 5S, MC 7N, MC 7S, MC 16E, MC 24, MC 31, MC 33bS, MC 35, MC 37, and B10). The detection rate is about one-third of the observed prestellar cores, which is quite high compared to previous unbiased surveys with a successful detection of zero or one sources toward Chamaeleon I and ρ Ophiuchus using the ALMA 12 m array alone (Dunham et al. 2016; Kirk et al. 2017a), because the larger beam and recovering scales in our observations enable us to be more sensitive to the lower-density regions of the cores (see also discussions in Section 4.3). The peak (F_peak) and total continuum flux (F_ν) within the observed field are 2–5 mJy beam⁻¹ and 5–63 mJy, respectively, as summarized in Table 3. We performed 2D Gaussian fittings to the observed continuum distributions in the image plane after the primary beam correction to derive the central coordinate, major/minor axis (FWHM), and position angle. Note that, in the observed field, there is a large amount of missing flux, more than 80%, with respect to the total flux obtained by single-dish telescopes (see the MC 5N case in Tokuda et al. 2019).

Table 3.  1.3 mm Continuum Properties of Prestellar Cores

Name	RA	Decl.	Major	Minor	P.A.	Fpeak	Fν	Mass	n(H2)	Category	N2D+
	(J2000.0)	(J2000.0)	(arcsec.)	(arcsec.)	(deg)	(mJy beam−1)	(mJy)	(×10−2 M⊙)	(×105 cm−3)
MC 1	04h04m477	+26°09'158	32.4	16.8	161.8	3.3	20.5	3.5	3.3	II	Y
MC 2	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 4	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 5N	04h17m420	+28°08'447	38.9	17.5	173.1	5.4	63.4	12.8	8.1	III	Y
MC 5S	04h17m426	+28°06'002	31.0	13.0	88.9	3.9	26.7	5.0	7.0	III	Y
MC 6	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	⋯
MC 7N	04h18m041	+28°22'567	21.8	14.8	18.0	2.5	14.0	2.6	5.1	II	Y
MC 7S	04h18m030	+28°22'210	35.7	8.6	134.2	3.2	21.2	4.0	8.4	III	Y
MC 8	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	⋯
MC 11	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	Y
B10	04h17m502	+27°56'107	22.5	10.7	24.5	2.0	5.2	1.1	3.1	II	Y
MC 13W	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 13a	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 14N	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 16E	04h21m212	+26°59'435	36.7	13.2	165.7	2.5	17.8	5.1	3.0	II	Y
MC 16W	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 19	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 22	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 23	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 24	04h26m354	+24°41'444	26.3	8.8	9.2	2.7	12.5	3.0	5.2	II	N
MC 25E	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	Y
MC 25W	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 28NW	04h29m228	+24°33'150	21.8	4.3	2.7	4.3	23.1	3.4	44.6	⋯a	N
MC 28SW	04h29m220	+24°33'535	11.6	10.5	58.0	4.6	10.4	1.5	13.5	⋯a	N
MC 29	⋯	⋯	⋯	⋯	⋯	⋯	⋯			I	N
MC 31	04h31m553	+24°32'484	25.8	14.6	4.3	3.5	24.3	5.4	8.8	III	Y
MC 33bS	04h32m436	+24°23'151	39.5	12.6	123.0	2.8	16.8	3.3	3.6	II	N
MC 33bN	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	Y
MC 34	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 35	04h35m379	+24°09'200	12.2	10.1	169.0	2.8	7.8	1.3	11.6	⋯b	Y
MC 37	04h39m180	+25°52'341	23.9	9.2	153.7	2.4	9.2	1.6	4.4	II	N
MC 38	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N
MC 44	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	⋯
L1521E	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	⋯	I	N

Notes.

^aWe did not categorize the starless peaks in the MC 28 protostellar core. ^bAn FHSC candidate (see Paper II).

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We derived the mass of the central regions traced by the 7 m array continuum observations using the following equation,

$$\begin{eqnarray}&&M=\displaystyle \frac{{D}^{2}{F}_{1.3\mathrm{mm}}}{{\kappa }_{1.3\mathrm{mm}}B({T}_{{\rm{d}}})},\end{eqnarray} \tag{ 1 }$$

where D is the distance to the sources, κ_1.3mm is the dust opacity at 1.3 mm, and B(T_d) is the Planck function at a dust temperature T_d. We applied recent distance measurements depending on the region (Galli et al. 2018) and κ_1.3mm = 0.005 cm² g⁻¹ for prestellar cores (Ossenkopf & Henning 1994; Preibisch et al. 1993). We used gas kinematic temperatures derived from early NH₃ observations (see Table 1), T_d, assuming that the temperatures of gas and dust are well coupled in the dense regions and a uniform temperature distribution inside the 7 m array observation fields. Table 3 gives the derived mass. The uncertainty of the mass estimation mainly arises from the assumption of κ_1.3mm due to the grain growth at the central regions of the cores. However, Bracco et al. (2017) reported that the dust emissivity index, β, does not change too much across core radii down to 1000 au at the prestellar cores in the Taurus B213 filament. Although Chacón-Tanarro et al. (2017) suggested that the opacity can increase by a factor of ∼2, which is likely traced by ALMA's resolution, such effect is limited to a small radius, a few hundred astronomical units. The grain growth thus does not strongly affect the mass estimation with the 7 m array beam size.

The estimated masses (M_obs) are ∼10⁻²–10⁻¹ M_⊙ (see Table 3), indicating that the 7 m array observations likely trace compact/dense materials at the center of the cores, but show only small fractions of the entire cores themselves whose total masses are ∼1–10 M_⊙. We estimated the average H₂ number densities using the following equation: n(H₂) = 3M_obs/4πμm_HR_obs³, where μ is the molecular weight per hydrogen (2.8), m_H is the H atom mass, and R_obs is the observed radius (=$\sqrt{\mathrm{Major}\ * \mathrm{Minor}}$/2) adopting each distance (Table 1). The derived densities are ∼(3–10) × 10⁵ cm⁻³ (see Table 3). The identification of the high-density part in the molecular clouds based on millimeter continuum emission alone is sometimes risky, because there may be possible contaminations from unrelated objects, such as distant galaxies (e.g., Tamura et al. 2015; Tokuda et al. 2016). Examining the presence or absence of detection of high-density gas tracers allows us to confirm whether the continuum emission is indeed arising from deeply embedded parts in dense cores. We confirmed C¹⁸O emission toward all of the PROJ6 targets, and most of the continuum peaks have N₂D⁺ emission at more than the 3σ level (see Table 3). We thus conclude that the observed 1.3 mm continuum is arising from the cold high-density parts of the cores. Note that we found an additional source with a flux of 19.3 mJy at the edge of the observed field in MC 4. The position corresponds to a known YSO candidate, J041412.29+280837.0 (Gutermuth et al. 2009; Rebull et al. 2011).

The spatial distributions of the 1.3 mm continuum are diverse: some cores show single peaks while others contain multiple local peaks. For the first time, we have revealed such a complex substructure toward a large fraction of the sample in Taurus prestellar cores. However, Caselli et al. (2019) cautioned that the interferometric artifacts cause fake substructures even if we observe a smoothed distribution. We discuss this possibility in Section 4.1 further.

We observed seven protostellar cores (MC 13b, MC 14S, MC 26a, MC 27, MC 28, MC 39, and MC 41) with the 7 m array. We detected 1.3 mm continuum emission in all targets. The observed total and peak fluxes are 62–225 mJy and ∼14–202 mJy beam⁻¹, respectively (Table 4), which are about an order of magnitude higher than those in the prestellar sources. Although the early single-dish observations also confirmed this trend (e.g., Motte & André 2001), the filtering-out effect, due to the interferometric observation, enhanced the intensity contrast between the two evolutionary stages. For example, the early study in MC 14S/N provided just a factor of 3 difference in the peak 1.3 mm intensities between the two sources (Bracco et al. 2017). However, our new observations could not detect continuum emission in the prestellar source. We compiled higher-resolution interferometric observations at the same frequency from the literature for all protostellar sources (Table 4) to determine the disk contamination. The much longer baseline observations enable us to reveal further compact emission, which is mostly arising from the protostellar disk. Although the fraction of protostellar disk contribution (F_disk) to the total flux covered by the 7 m array depends from source to source, most of the flux is dominated by F_disk with a range of 35%–90% except for MC 27.

Table 4.  1.3 mm Continuum Properties of Protostellar Cores

Name	Infrared Sourcea	R.A.	Decl.	Major	Minor	P.A.	Fpeak	Fν	Fdisk	N2D+
		(J2000.0)	(J2000.0)	(arcsec.)	(arcsec.)	(deg)	(mJy beam−1)	(mJy)	(mJy)
MC 13b	IRAS 04166+2706	04h19m425	+27°13'361	8.8	7.8	78.0	97	187	66b	Y
MC 14S	IRAS 04169+2702	04h19m585	+27°09'568	7.6	7.4	72.0	92	147	88c	Y
MC 26a	IRAS 04248+2612	04h27m570	+26°19'184	21.5	12.7	122.1	14	62	⋯	N
MC 27	L1521F-IRS	04h28m391	+26°51'328	19.4	13.5	143.4	15	78	1d	Y
MC 28	IRAS 04263+2426	04h29m238	+24°33'003	7.3	6.8	121.4	76	93	84e	N
MC 39	IRAS 04365+2535	04h39m352	+25°41'443	7.2	6.4	102.0	202	225	180f	N
MC 41	IRAS 04369+2539	04h39m558	+25°45'015	7.1	6.3	109.1	179	201	⋯	N

Notes.

^aKenyon et al. (1990) for IRAS sources, Bourke et al. (2006) for L1521F-IRS. ^bCombined Array for Research in Millimeter-wave Astronomy (CARMA) observations with angular resolution of 103 × 090 by Eisner (2012). ^cSubmillimeter Array (SMA) observations with an angular resolution of 176 × 150 by Takakuwa et al. (2018). ^dALMA observations with an angular resolution of 13 × 08 by Tokuda et al. (2016). ^eCARMA observations with an angular resolution of 1'' by Sheehan & Eisner (2014). Note that we combined individual fluxes from the binary source (∼44 mJy for source N and ∼40 mJy for source S). ^fALMA observations with an angular resolution of 101 × 087 by Aso et al. (2015).

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MC 27 is a unique source in our sample containing a class 0 VeLLO (Bourke et al. 2006; Terebey et al. 2009) in the L1521 region (Figure 1). Note that there is another VeLLO, IRAM 04191–1522 (see André et al. 1999; Dunham et al. 2006), which is located outside of the Taurus main cloud. Among the observed protostellar cores, MC 27 shows the weakest peak flux, and the contribution from the protostellar disk is ∼1 mJy (see also the 12 m array observations in Tokuda et al. 2014, 2016).

In MC 28, we found two starless peaks (MC 28 NW/SW) within the >50% sensitivity field, and their locations are away from the class I binary source, IRAS 04263+2426 (Chandler et al. 1998; Roccatagliata et al. 2011). The continuum peaks have C¹⁸O emission with a central velocity of ∼6 km s⁻¹, which is similar to that of the binary source, indicating that these sources belong to the same system.

Revealing the fragmentation/coalescence process of molecular cloud cores just before the onset of star formation is critical toward understanding the origin of binary/multiple star formation and determining the final stellar mass. For example, turbulent perturbations (e.g., Offner et al. 2010) may create a few hundred astronomical unit scale overdense regions locally. However, some of the magnetohydrodynamic simulations (Matsumoto & Hanawa 2011) suggest that the gravitational collapse smoothed out the complex substructures that originated from turbulence. In this case, observations should show that prestellar cores do not have complex substructures (i.e., fragments), possibly leading to multiple objects. The exploration of such a spatial scale in low-mass dense cores is still incomplete (see Section 1.2). The present ACA observations enable us to obtain crucial hints to understanding the mechanism of fragmentation and the evolution of the prestellar collapse phase.

The 7 m array measurements obtained indications of multiple local peaks with an intensity of a few mJy beam⁻¹ toward MC 1, MC 7N, MC 7S, MC 16E, MC 31, MC 33bS, and MC 37. The typical separation among the peaks within a core is similar to the present beam size of ∼900 au. The size scale is much smaller than the Jeans length with a density of ∼10⁶ cm⁻³. If the substructures are real features, the Jeans instability is unlikely to form such fragments. However, we need careful treatments to interpret the substructures obtained by interferometers. Caselli et al. (2019) cautioned that the incomplete cancellation of Fourier components could produce artificial substructures with a low-level contrast among the local peaks even if the real core has a constant-density profile at the center.

We evaluate the spatial distributions of what the 7 m array observations are looking at the core centers and how realistic the multiple peaks are, by comparing the synthetic observations using CASA. We generated smoothed core models with a Plummer-like function as input models for the simulated observations. The formula of column density profile as a function of r, distance from the core center, is as follows:

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}_{2}}(r)=\displaystyle \frac{{N}_{\mathrm{peak}}}{{\left(1+{\left(r/{R}_{\mathrm{flat}}\right)}^{2}\right)}^{\tfrac{p-1}{2}}}.\end{eqnarray} \tag{ 2 }$$

There are three free parameters: peak H₂ column density (N_peak), flattening radius (R_flat), and asymptotic power index (p). Based on the Herschel/SPIRE measurements (e.g., Marsh et al. 2016) toward the 1.3 mm continuum-detected objects with the 7 m array (see Section 4), we adapted a fixed p of 2 and measured ${N}_{{{\rm{H}}}_{2}}$ at a radius of r = 6000 au to determine N_peak using Equation (2). We prepared three sequences with different ${N}_{{{\rm{H}}}_{2}}$ (r = 6000 au), maximum = 3 × 10²² cm⁻², average = 1 × 10²² cm⁻², and minimum = 7 × 10²¹ cm⁻² to mimic the observed sample. For each column density set, the input R_flat are 8000 au, 2500 au, 1500 au, 900 au, and 300 au, which roughly corresponds to the Jeans length (see the definition in Section 1.2) of 10⁵ cm⁻³, 10⁶ cm⁻³, 3 × 10⁶ cm⁻³, 10⁷ cm⁻³, and 10⁸ cm⁻³ gas, respectively. Note that we assumed κ_1.3mm = 0.005 cm² g⁻¹ and T_d = 10 K to convert H₂ column densities to 1.3 mm continuum fluxes (see also the justifications in Section 3.1). In order to investigate the geometric effect of the simulated profiles, we considered parametric models with aspect ratios (see Equation (5) in Caselli et al. 2019). We adapted two aspect ratios of 1.0 and 1.8. The former is called the fixed model. The latter is a parametric model, which mimics the observed aspect ratio of MC 31. In the CASA simulator, we used the simobserve task to generate simulated visibilities at a central frequency of 225 GHz and a similar integration time of our real observations (see Section 2) with the same 7 m array configuration in Cycle 6. The central sky coordinate was the same as that of MC 27, which is close to the central position of the Taurus main cloud (see Figure 1). We made the simulated images using the tclean task with the same parameters that we applied to the real observations (see Section 2.2).

Figure 3 shows the results of the 7 m array synthetic observations for the cases of average H₂ column density in the fixed (aspect ratio = 1.0) and parametric (aspect ratio = 1.8) models. We could not detect any significant (above 3σ) emission at the R_flat of 8000 au cases. For the other radii models, the fixed models are close to circularly symmetric shapes as a whole, while the parametric models have elongated distributions in the east–west direction. Although the integrated fluxes, which were measured using the same method we used for our real observations (see Section 3), depend on the absolute column density of the input models as shown in Figure 4(a), the same R_flat models reproduce similar spatial distributions to each other. We then compared the real and synthetic observations. The case of R_flat of 2500 au shown in Figure 3 is very similar to the observed substructures, as shown in Figure 2. This means that the 7 m array measurements can artificially produce multiple peaks whose angular separation is similar to the observed beam size, even if we observe a smooth distribution inside the observed fields (see also Appendix A.3). Therefore, we cannot merely claim that the observed substructure is a substantial piece of evidence of fragmentation of prestellar cores. We further discuss the fidelity of the internal substructures by considering the molecular line emission in Section 4.2.

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Figure 4(b) shows the histogram of the observed 1.3 mm continuum flux at pre-/protostellar cores. We tentatively estimated the central volume density using the N_flat/R_flat of the input models, where N_flat is the H₂ column density at R_flat, as shown in each plot in Figure 4(a). Note that a similar method was also applied to real observations of centrally concentrated prestellar cores (e.g., Ward-Thompson et al. 1999). The simulated 1.3 mm flux of the minimum column density model with R_flat of 2500 au gives us a detection limit of the central density, ∼4 × 10⁵ cm⁻³, which is consistent with our real observations. Only a few cores (MC 5N, MC 5S, MC 7S, and MC 31) have a relatively strong continuum flux more than ∼20 mJy, and their central densities are likely more than 8 × 10⁵ cm⁻³ (see also Table 3), which is higher than the other sources. The 1.3 mm fluxes of the bright prestellar sources are comparable to those in protostellar cores without their disk contributions, as shown in Figure 4(b). This result can be an indirect piece of evidence that the bright cores are more evolved than the other weak cores.

Molecular line observations help us to evaluate the density distribution of dense cores. MC 1 and MC 7S/N have at least two significant peaks with an intensity of ∼3 mJy beam⁻¹ in the 1.3 mm continuum image (Figures 5(a) and 6(a)), although such a low-intensity contrast distribution can be reproduced by the interferometric artifact as discussed in the previous subsection. The molecular gas tracers (C¹⁸O, and N₂D⁺) tell us of further fruitful structures (Figures 5 and 6).

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For MC 1, the N₂D⁺ distribution itself indicates that there is a density/size difference between the two continuum sources (Figures 5(c) and (e)). The southern source has an extended structure, while the size of the northern 1.3 mm peak is close to the beam with a marginal detection in N₂D⁺, indicating that the northern one is much smaller and less dense than the southern one. Another crucial evidence for the presence of density contrast is that the two continuum peaks sandwich the C¹⁸O peak. Although this feature is more apparent in the 7 m array image alone, which filters out the large-scale emission, the combined 7 m + TP array image also reproduces the same trend (Figures 5(b) and (d)). If the innermost part of the dense core has uniform density, but the density is high enough to detect N₂D⁺, CO molecules are considered to be depleted on dust grains and possibly show a ring-like structure surrounding the dusty central part (e.g., Caselli et al. 2002b; Crapsi et al. 2005). The present C¹⁸O distribution in MC 1 indicates that there is a relatively low-density (∼10⁴ cm⁻³) gas in between the overdense continuum peaks.

Another promising candidate having significant substructures is MC 7N/S. The molecular line distribution of C¹⁸O and N₂D⁺ follows a similar manner to that in MC 1, as described above (see also Figure 6). The projected separation between 1.3 mm peaks in each source is approximately 5000 au, which is significantly larger than the flattening radius of the synthetic observation, producing fake substructures in the smoothed core (Figure 3). In addition to this, the positions of each continuum source correspond to local peaks obtained by the early single-dish 0.87 mm continuum observation (Buckle et al. 2015, see also Figure B2 in Appendix B). We thus exclude the interferometric artifact that produces the substructures over a few ×1000 au in this case. In summary, by considering the continuum and molecular line distributions, we confirmed that at least two prestellar sources harbor internal substructures, possibly produced by a fragmentation/coalescence process (see also 4.4).

We observed the center positions of ∼30 prestellar cores in Taurus. The observed targets are carefully selected based on previous single-dish surveys in the dust continuum and molecular lines. The almost-complete sample allows us to statistically estimate the lifetime of high-density (∼10⁶ cm⁻³) peaks at the center of the core. Onishi et al. (2002) discovered 44 prestellar cores with an average density of ≳10⁵ cm⁻³ and derived the timescale of protostar formation inside them, ∼4 × 10⁵ yr, assuming that the timescale of one of ∼100 pre-main-sequence stars in Taurus with ages of ≲10⁶ yr (Kenyon et al. 1990) is ∼10⁴ yr, and their constant evolution speed. They conclude that the lifetime of prestellar cores is several times longer than the freefall timescale of gas with 10⁵ cm⁻³. This result is roughly consistent with both mildly subcritical magnetized cores and models invoking low levels of turbulent support (Ward-Thompson et al. 2007). After their study, several observations additionally found similar density cores in molecular line observations (e.g., Hirota et al. 2002; Hacar et al. 2013; Tafalla & Hacar 2015; Arzoumanian et al. 2018) in Taurus, and our survey includes two of them (B10, L1521E). Our recent independent measurements in H¹³CO⁺ and N₂H⁺ using the Nobeyama 45 m telescope (K. Tokuda et al., in preparation) tell us that, in total, there are at most 10 prestellar cores, which are not present in the Onishi et al. (2002) catalog. Although we can possibly revise the total number of prestellar cores in Taurus and their lifetime to be 54 and ∼5 × 10⁵ yr, respectively, the previous conclusion does not change that much.

The present 7 m array observations confirmed 1.3 mm dust continuum emission toward 10 sources (see Section 3.1). Note that if there are multiple local peaks from single observations (e.g., MC 5, MC 7, MC 33), with at least one of them detected by the 7 m array, we count it as one source. The total number of continuum-detected objects is significantly higher than that in the previous surveys, with zero or one successfully detected object by Dunham et al. (2016) and Kirk et al. (2017a). This discrepancy is a quite reasonable result because they targeted much higher density (≳10⁷ cm⁻³) objects. They evaluated the detectability in continuum emission toward overdense regions within starless cores using the following equation,

$$\begin{eqnarray}&&\mathrm{Detection}\gt \displaystyle \frac{3}{2}\times {N}_{\mathrm{total}}\times {\left(\displaystyle \frac{{n}_{\mathrm{Detectable}}}{{n}_{\mathrm{Limit}}}\right)}^{-1},\end{eqnarray} \tag{ 3 }$$

where N_total is the number of observed cores, n_Detectable is the central density threshold for detection, and n_Limit is the observed lower limit for the central number densities of the cores. With N_total = 30, n_Detectable = ∼3 × 10⁵ cm⁻³ (Section 4.1), and n_Limit = ∼1 × 10⁵ cm⁻³, Equation (3) tells us that the expected total number of detections is ∼11, which is consistent with our present observations.

Our study gives us an observational constraint for the lifetime of the innermost parts of prestellar cores on the verge of star formation. Based on our 7 m array 1.2/1.3 mm continuum measurements, we divided the 54 prestellar sources, whose lifetime is ∼5 × 10⁵ yr, in Taurus (see the first paragraph in this subsection) into three categories: (I) cores without continuum, (II) cores with weak continuum, and (III) cores with strong continuum (see Table 3). We tentatively set a flux criterion of 21 mJy, whose density is ≳8 × 10⁵ cm⁻³, to separate II and III. The total numbers in categories I, II, and III are 45, 6, and 3, respectively. We assumed that the unobserved cores in this study are categorized under I, because even single-dish observations indicate a less evolved feature than our selected target (see the Introduction). If a single core has two peaks with different categories (e.g., MC 7N/S and MC 33bS/N), we counted the core as the latter stage. The central density ranges of each category are roughly ≲3 × 10⁵ cm⁻³ (I), (3–8) × 10⁵ cm⁻³ (II), and ≳8 × 10⁵ cm⁻³ (III). If we adopt the lifetime of prestellar cores, ∼5 × 10⁵ yr, the timescale of each stage can be divided into ∼3 × 10⁵ yr (I), ∼6 × 10⁴ yr (II), and ∼3 × 10⁴ yr (III). We exhibit the estimated lifetimes in Figure 7, which is similar to the "JWT plot" (after Jessop & Ward-Thompson 2000; see also Figure 2 in Ward-Thompson et al. 2007) with a density range of 10³–10⁵ cm⁻³. For the less dense cores (category I), the lifetime is several or a few times longer than the freefall time of the gas density. This means that supporting forces, such as the magnetic field and turbulence, still play a role in preventing freefall collapse. On the other hand, in the further high-density regime, the timescale approaches freefall time (see also Könyves et al. 2015). We thus propose that the density threshold is ∼10⁶ cm⁻³ when self-gravity becomes the dominant force regulating the core dynamics. Infalling motions may be detectable in the latest stage. However, if the collapsing radius is smaller than the beam sizes of single-dish telescopes, detecting blue asymmetric profile emission is difficult (see the discussion for MC 5N, one of the category III objects, by Tokuda et al. 2019). Interferometric observations with high-J transitions of optically thick tracers are possible methods to further confirm the internal core dynamics (see also Section 6).

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We briefly mention the lifetime of the possible candidate for the FHSC in MC 35. From the dust peak, we found a bipolar outflow, whose dynamical age is less than 10⁴ yr. Paper II described the observed nature of MC 35 to be consistent with the theoretical properties of the FHSC (e.g., Machida et al. 2008). Finding only one candidate out of the dozen starless targets indicates that the lifetime is less than 10⁴ yr (=5 × 10⁵ yr ∗ 1/54). This is marginally consistent with that from theoretical predictions, ∼10³ yr (e.g., Larson 1969). We further discussed the lifetime of the FHSC candidate and the comparison between our observations and some numerical simulations in Paper II.

Most of the dense cores, including our present targets in Taurus, lie in filamentary clouds, suggesting that dense core formation is deeply related to the kinematics of filamentary gas, such as fragmentation and collapse as suggested by previous studies (Onishi et al. 1998, 2002; see the general review by André et al. 2014). Our present study features the subsequent fate after the dense core formation with a ∼1000 au spatial resolution.

Early single-dish observations revealed the diversity of shapes of prestellar sources: for example, nearly spherical, prolate/oblate structure, and highly irregular morphology based on the dust continuum and molecular line observations (e.g., Onishi et al. 2002; Caselli et al. 2002b; Kauffmann et al. 2008). The large-scale structures of category III objects have relatively axisymmetric shapes in their strong intensity levels (e.g., more than the FWHM contour; see Tokuda et al. 2019 for MC 5N/S, and Kauffmann et al. 2008 for MC 31). This fact is consistent with our suggestion that self-gravity is eventually responsible for the dynamics of prestellar cores whose central density exceeds more than 10⁶ cm⁻³.

For category II, some of the parental cores show a highly irregular shape (e.g., MC 33, see Onishi et al. 2002; Caselli et al. 2002a; Kauffmann et al. 2008). In this stage, in addition than self-gravity, magnetic field and turbulence may also play an essential role in forming high-density maxima, which are detectable with interferometers. In addition to this, our measurements discovered at least two promising candidates whose internal substructures have a size scale of ∼1000 au. Although their actual origin and whether or not the substructures may harbor or go on to form protostars individually remain to be studied, the new findings suggest that the molecular cloud cores are not necessarily isolated objects, and there mass has a time dependence during the fragmentation/coalescence processes.

Intriguingly, the cores with possible substructures belong to category II. We suggest that substructure formation may occur before self-gravity controls their fate. Theoretical studies do not prohibit coalescence among multiple cores after the fragmentation of their parental filamentary cloud, depending on the actual perturbation in the filament (e.g., Inutsuka & Miyama 1997; Masunaga & Inutsuka 1999; Inutsuka 2001). If we assume an initial core separation of ∼0.1 pc and the velocity of the core motion is similar to the isothermal sound speed, ∼0.2 km s⁻¹, for a gas temperature of 10 K, the expected timescale of the coalescence is ∼5 × 10⁵ yr (=0.1 pc/0.2 km s⁻¹). This timescale is close to the statistical lifetime of the Taurus dense core with a density of ∼10⁵ cm⁻³ (see Section 4.3), indicating that coalescence of dense cores can occur within their lifetime.

Regarding fragmentation processes, Nakamura & Hanawa (1997) demonstrated that core-forming clouds become unstable to bar mode after magnetically supercritical core formation (see also Machida et al. 2005; Nakamura & Li 2002). The two overdense regions in MC 7 are distributed along the major axis of the parental core (see Figure B2 in Appendix B). Although bar-mode fragmentation is plausible in this case, MC 1 shows the opposite trend (see the single-dish continuum observation by Motte & André 2001). These diversities imply that there are several mechanisms that promote fragmentation/coalescence processes.

We made continuum images with two individual spectral windows whose central frequencies are 218.0 and 232.5 GHz (see Section 2.1.2). As representative examples, we performed the imaging of MC 1, which is one of the promising candidates with internal substructures (see Section 4.1), and MC 35, the first core candidate (see Paper II). Figure A1 shows that the two frequency images reproduce almost the same result.

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Table A1 gives the beam sizes and rms sensitivities of each continuum map. The average angular resolution is 68 × 62, and the geometric mean is 65. We quote this value as the representative angular resolution in the abstract and summary.

Figure A2 illustrates the comparison between the real and synthetic observations of MC 31 as a representative example. We adopted an aspect ratio of 1.8 and a position angle of 4° estimated from the real observation (Table 3) as input parameters of the parametric model. The synthetic core with an R_flat of 2500 au and ${N}_{{{\rm{H}}}_{2}}$ (r = 6000 au) = 1 × 10²² cm⁻² reproduces total and peak fluxes similar to the real observation. The residual image does not show large differences between the real and synthetic observations. This result demonstrates that the synthetic model is reasonable to fit the observed image and that interferometric observations can artificially produce fake substructures even if the core has a smooth distribution in nature.

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Figures B1 shows 1.2/1.3 mm continuum distributions toward the B213 filamentary cloud. We observed three prestellar and two protostellar cores in this region. The line mass of the filament is larger than the critical line mass, M_line,crit = $2{c}_{{\rm{s}}}^{2}$/G (e.g., Stodólkiewicz 1963; Ostriker 1964; Inutsuka & Miyama 1992), where c_s ∼ 0.2 km s⁻¹ is the isothermal sound speed for a gas temperature of ∼10 K. It means that the filament is unstable against fragmentation and collapse. In this region, several prestellar and prestellar cores alternate with a separation of ∼0.1 pc (e.g., Onishi et al. 2002; Hacar et al. 2013 see also Figure B1). There is no other star-forming filament showing such a regular distribution in Taurus. The present 7 m array observations could not find the 1.3 mm continuum emission toward all of the prestellar sources in the B213 filament (Figure B1(a)), suggesting that they are not sufficiently centrally concentrated. The onset of dynamical collapse is one option to get that configuration, i.e., detection of continuum emission with the 7 m array.

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Previous studies suggested that a large-scale colliding accretion flow created the B213 filament (Palmeirim et al. 2013; Shimajiri et al. 2019). If the filament initially has a uniform density with a 0.1 pc width, which is a quasi-universal value in nearby molecular clouds (Arzoumanian et al. 2011, 2019), we cannot explain such an evolutionary difference unless there was a density fluctuation in this system at the formation phase. In MC 14S and MC 13b, the fluctuation of the filament formed overdense regions, and then it might have collapsed into the protostar faster than the other cores. In this case, the alternating distribution of pre-/protostellar cores itself is a coincidence rather than having some inherent physical meanings.

The present frequency setting allows us to investigate the outflow distribution in ¹²CO. Figures B1(b) and (c) show the directions of the ¹²CO outflows, which are consistent with the early interferometric measurements (Takakuwa et al. 2018, for MC14; Tafalla et al. 2010, 2017, for MC 13b). The outflow axis seems to be perpendicular to the parental filament elongation, but not in the case of MC 14S. This feature means that the large-scale kinematics not only determines the rotation axis of the protostellar disk that originated from the filament fragmentation, but also local phenomena within the dense core. Takakuwa et al. (2018) found a counterrotation between the disk and protostellar envelope in MC 14S. They interpreted that the magnetic field may affect the formation of such a complex system.

A previous single-dish study found a remarkable filamentary complex in the L1495 region. We observed seven prestellar cores in Figure B2(a). In this region, more than 10 dense cores are clustering without any indication of star formation. As shown by early molecular line observations in ¹³CO and C¹⁸O (Mizuno et al. 1995; Hacar et al. 2013), several filamentary structures are entangled with each other toward this region, indicating that the surrounding filamentary gas accreted onto the primary dense filaments and then they fragmented into several cores (Tafalla & Hacar 2015). Our 7 m array continuum observations found internal structures toward the prestellar cores except for MC 6 and MC 8, suggesting that these cores may be highly evolved and collapse into protostars soon.

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Tokuda et al. (2019) reported that MC 5N has a high-density (∼10⁶ cm⁻³) peak at the center of the core, and it is a promising candidate of a brown dwarf prestellar core based on its small parental core mass, ∼0.2–0.4 M_⊙. We predicted that another subcore, MC 5S, also has a similar density enhancement, if they were formed by a common mechanism, which is the fragmentation of a filamentary cloud after radial collapse (Inutsuka & Miyama 1992, 1997). The detection of 1.3 mm continuum and N₂D⁺ in MC 5S indicate that there is a high-density peak, and it is consistent with our prediction. Although the early single-dish study already confirmed the two local peaks of the core (Buckle et al. 2015; Ward-Thompson et al. 2016), we also found 1.3 mm continuum detection with the 7 m array at the positions of MC 7N and MC 7S. A crucial difference between MC 5 and MC 7 is the length of each separation within their system; the projected distance of two subcores in MC 5 is as long as ∼0.1 pc, while that in MC 7 is much shorter, ∼0.02 pc.

The B18 cloud is at the southern part of the Taurus (Figure 1), and star formation is more active there than at the western side, the L1531 region (e.g., Mizuno et al. 1995). Although the overall distribution roughly shows a filamentary structure, the individual dense cores have highly complex morphologies. The separation between the cores is sparse compared to that in the other subregion, e.g., B213/L1495. The recent survey using the Green Bank Telescope (Friesen et al. 2017) detected ammonia emission toward the bright regions in the Herschel dust continuum observations (Figure 1). There are only three prestellar sources without 1.3 mm continuum emission from the 7 m observation. The detection rate is similar to that in L1495.

In this region, there are some intriguing sources in terms of the early phases of star formation. As mentioned in Section 3.1, MC 35 is a possible candidate for the FHSC, because the source has no bright infrared sources and the CO observations found a possible compact bipolar outflow. In MC 24, we also detect a redshifted high-velocity wing. Because the high-velocity component is not connected to the dust continuum peak, we cannot exclude the possibility that the high-velocity component is part of the large-scale outflow from a nearby protostellar source, IRAS 04239+2436 (Narayanan et al. 2012). We thus suppose that the probability of a protostellar object being contained in MC 24 seems to be lower than that of MC 35.

We observed two positions in MC 33; one has a dust continuum peak (MC 33bS) in the single-dish observation (Kauffmann et al. 2008), and the other shows the N₂H⁺, N₂D⁺, and NH₃ peak (Caselli et al. 2002a; Crapsi et al. 2005). If we accept that the N-bearing species are tracers of chemically evolved regions, current observations suggest that MC 33bS is a physically evolved peak with a high column density, while MC 33bN is a more chemically evolved part. Our 7 m array observations also detected 1.3 mm continuum emission in MC 33bS, not MC 33bN. This result is consistent with previous studies. MC 33 is a vital target for examining the inhomogeneity between a mass distribution and its chemical composition.

MC 28 is an interesting target harboring both the protostellar source IRAS 04263+2426 and two starless peaks. As mentioned in Section 3.2, they share almost the same systemic velocity. This fact indicates that the fragmentation process of the parental core or the protostellar feedback produced the dense starless blobs. This system can be an excellent candidate to study the formation of a wide binary/multiple.

The HCL2 (Heiles cloud 2) region (Heiles 1968) has ring-like or filamentary structures observed by dense gas tracers and dust continuum emission (e.g., Onishi et al. 1996; Fehér et al. 2016, see also Figure 1). Fehér et al. (2016) estimated the gas temperature from the NH₃ observations. The Mt. Fuji telescope found a C i peak, whose position is away from the dense material, in the eastern part of the region (Maezawa et al. 1999). This result indicates that the region is a chemically young region where C i has not yet been fully converted into CO and the evolutionary sequence propagates from the eastern to western side. The absence of the 1.3 mm continuum emission in MC 44 in our measurement means that the core is in a relatively young phase before the dynamical collapse and follows the global evolutionary sequence of this region. On the western side, there are several famous star-forming cores, such as L1527 and MC 39(=TMC-1A). As shown in Table 4, the F_disk/F_ν in MC 39 is higher than that in other cores harboring class 0/I protostars (MC 13b, MC 14S). This result indicates that the extended gas in MC 39 has been accreted onto the protostar and protostellar disk, which is consistent with the prediction that the protostar is in a late class I phase (Aso et al. 2015).

MC 37 is a prestellar core with weak continuum emission in our survey, although the complex distribution itself possibly arises from the interferometric artifact (see Section 4.3).