Protostellar Evolution in Serpens Main: Possible Origin of Disk-size Diversity

Figure 2(a) shows 1.3 mm continuum images of the Group 1 members. All of the Group 1 members show components as large as ∼1000 au or more extended in the 1.3 mm continuum. The peak brightness temperatures T_b of the 1.3 mm continuum emission range from ∼2 to ∼20 K. The highest T_b, ∼20 K, is measured in SMM4A. This value is as high as a gas temperature estimated from CARMA observations at a spatial resolution of 3000 au (Lee et al. 2014). This indicates that the 1.3 mm emission is optically thick in SMM4A. Peak positions were determined by 2D Gaussian fittings to the continuum images. The deconvolved FWHMs listed in Table 3 were also derived from the Gaussian fittings. The peak intensity ${I}_{1.3\mathrm{mm}}^{\mathrm{peak}}$ and total flux density F_1.3mm were measured within the 3σ contours enclosing each source after primary-beam correction. For the spatially resolved emission, the uncertainty of each flux density was calculated from the rms noise level of intensity σ_i in the unit of Jy beam⁻¹ and the integrated area Ω in the unit of beam as ${\sigma }_{i}\sqrt{4{\rm{\Omega }}}$, where the factor 4 is due to the Nyquist sampling. The measured parameters are listed in Table 3. S68N was identified as a Class 0 protostar by Spitzer observations (Dunham et al. 2015). SMM11, SMM4A, and SMM4B were also reported as Class 0 protostars in previous observational studies using ALMA (Aso et al. 2017a, 2018). S68Nb1 and S68Nc1 are also identified as Class 0 protostars based on their SEDs, as inspected in Section 3.4.

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Table 3.  Intensities, Fluxes, and Sizes of the 1.3 mm Sources Detected with Our ALMA Observations

	${I}_{1.3\mathrm{mm}}^{\mathrm{peak}}$	${F}_{1.3\mathrm{mm}}$	1.3 mm Deconvolved FWHM		${I}_{{{\rm{C}}}^{18}{\rm{O}}}$	${F}_{{{\rm{C}}}^{18}{\rm{O}}}$	Group in
	($\mathrm{mJy}\,{\mathrm{beam}}^{-1}$)	($\mathrm{mJy}$)	(au × au) (P.A.)	error	($\mathrm{Jy}\,{\mathrm{beam}}^{-1}\,\mathrm{km}\,{{\rm{s}}}^{-1}$)	($\mathrm{Jy}\,\mathrm{km}\,{{\rm{s}}}^{-1}$)	this paper
SMM4A	196.4 ± 0.1	492 ± 1	322 × 196 (145°)	5 × 5 (2°)	absorption	absorption	1
SMM4B	29.1 ± 0.1	173 ± 2	300 × 229 (95°)	26 × 19 (16°	0.307 ± 0.007	4.99 ± 0.13	1
S68N	40.4 ± 0.1	208 ± 2	314×217 (38°)	19 × 20 (9°)	0.154 ± 0.006	1.59 ± 0.07	1
S68Nc1	25.6 ± 0.1	114 ± 2	516 × 238 (87°)	25 × 13 (2°)	0.098 ± 0.008	1.01 ± 0.09	1
S68Nb1	60.2 ± 0.2	108 ± 2	160 × 143 (86°)	6 × 4 (17°)	<0.027	<0.027	1
SMM11	93.3 ± 0.1	167 ± 1	160 × 134 (80°)	6 × 5 (10°)	0.037 ± 0.004	0.17 ± 0.02	1
S68Nc2	5.5 ± 0.1	9.9 ± 0.7	203 × 122 (19°)	25 × 39 (19°)	<0.009	<0.009	2
S68Nc3	12.3 ± 0.1	52.3 ± 0.9	567 × 280 (90°)	34 × 18 (3°)	0.010 ± 0.003	0.047 ± 0.003	2
S68Nc4	3.3 ± 0.1	11.4 ± 0.6	497 × 253 (88°)	137 × 82 (22°)	<0.009	<0.009	2
S68Nc5	2.8 ± 0.1	17.5 ± 0.9	892 × 471 (63°)	99 × 56 (7°)	0.037 ± 0.003	0.062 ± 0.003	2
S68Nb2	18.0 ± 0.2	18.0 ± 0.2	30 × 26 (98°)	12 × 16 (76°)	<0.024	<0.024	3
SMM2A	3.8 ± 0.1	4.1 ± 0.1	<55 × 41	⋯	0.027 ± 0.007	0.16 ± 0.04	3
SMM2B	3.5 ± 0.1	3.5 ± 0.1	point	⋯	0.028 ± 0.006	1.78 ± 0.08	3
SMM2C	3.1 ± 0.2	3.6 ± 0.2	121 × 31 (33°)	27 × 58 (25°)	<0.039	<0.039	3
SMM11B	25.5 ± 0.4	26.9 ± 0.4	68 × 22 (95°)	3 × 6 (3°)	<0.042	<0.042	3
SMM11C	8.0 ± 0.4	8.6 ± 0.4	<99 × 51	⋯	<0.042	<0.042	3

Note. The intensities fluxes, and their uncertainties are primary-beam-corrected, and the upper limits of them are the 3σ level. ${I}_{{{\rm{C}}}^{18}{\rm{O}}}$ is the integrated intensity at the continuum peak position. ${F}_{{{\rm{C}}}^{18}{\rm{O}}}$ is the total flux of the C¹⁸O line.

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Figure 2(b) shows integrated intensity (moment 0) and mean velocity (moment 1) maps of the ¹²CO J = 2 − 1 line in the Group 1 members. The ¹²CO emission exhibits elongated or fan-shaped morphologies originating from the continuum sources. The ¹²CO emission can be interpreted as an outflow associated with each source. The apparent lengths at the 3σ level of these outflows range from ∼1000 to ∼6000 au. S68Nb1 and SMM4A have monopolar outflows, whereas the other four sources have bipolar outflows consisting of blueshifted and redshifted lobes. Interestingly, the outflows in S68Nc1 and SMM11 are extending roughly parallel to the major axes of their continuum emission (P.A. in Table 3). The morphology and velocity structures of the outflows in the six sources will be investigated in detail in Section 4.1.

Figure 2(c) shows images of the SO line, which is detected at 6σ levels in all the members of Group 1. SO emission traces various parts of protostellar systems in other star-forming regions: for example, a ring between a disk and an envelope in L1527 IRS (Ohashi et al. 2014), a ring in a disk in L1489 IRS (Yen et al. 2014), a jet in HH212 (Lee et al. 2007), a disk wind in HH211-mms (Lee et al. 2018), ambient gas in Barnard 1 (Fuente et al. 2016). In the case of Group 1, the SO emission traces outflows as seen in Figure 2(c). Note that the SO emission from SMM4A and that from SMM4B in Figure 2(c) (i) are distinct from each other because of the different velocity ranges (Aso et al. 2018). The SO emission appears to surround the ¹²CO outflows or lies in the outer parts of the ¹²CO outflow in SMM4A, SMM4B, S68N, and S68Nc1, suggesting that SO traces cavity walls of these ¹²CO outflows. However, the SO in S68Nb and SMM11 is stronger in the inner parts of the ¹²CO outflows. In addition to the outflows, the SO emission was also detected at the central protostellar positions of SMM4B, S68N, and S68Nc1.

Figure 2(d) shows images of the C¹⁸O line. Emission was detected in SMM4B, S68N, S68Nc1, and SMM11. SMM4A shows absorption due to its optically thick continuum emission. It was not detected in S68Nb1, despite extended C¹⁸O J = 1 − 0 emission in IRAM 30 m observations (Duarte-Cabral et al. 2010).

The C¹⁸O emission in S68Nc1 and SMM11 is elongated in the directions of their ¹²CO outflow axes, and velocity gradients of their C¹⁸O emission are also similar to those of their ¹²CO outflows. The C¹⁸O emission in S68N consists of three components, one centered at the continuum peak position, another in the southwest, and the other in the northeast. The central and southwestern components are much stronger than the northeastern component. The C¹⁸O emission is elongated in the associated outflow direction at lower contour levels (<12σ) around the central component, with its velocity gradient similar to that of the ¹²CO outflow.

The peak-integrated intensity and the total flux of the C¹⁸O line in each source were measured inside the 3σ contour enclosing each source after primary-beam correction. The uncertainties of the integrated intensities and the total fluxes are estimated in the same manner as those of the continuum intensities and the continuum flux densities, respectively. When the C¹⁸O emission is not detected, the 3σ upper limits were calculated. Those intensities, fluxes, and upper limits are listed in Table 3.

Figure 3 shows maps of the 1.3 mm continuum and the ¹²CO, SO, and C¹⁸O lines for the Group 2 members. Gaussian fits and flux measurements were performed in the same manner as those for Group 1, and the results are summarized in Table 3. For the cases of S68Nc3 and S68Nc4, the fitting was simultaneously done using a double-component 2D Gaussian function. S68Nc3, S68Nc4, S68Nc5, and possibly S68Nc2 as well, are associated with filaments ≳6000 au in length. This filamentary structure was excluded in the Gaussian fittings for Group 2. None of the Group 2 members were identified by Spitzer observations (Dunham et al. 2015).

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Extended ¹²CO emission was detected around the Group 2 members, with the exception of S68Nc5. The lack of a systematic velocity gradient suggests that this is ambient gas. The ¹²CO emission has a mean velocity of ∼12 $\mathrm{km}\,{{\rm{s}}}^{-1}$, which is redshifted by ∼3 $\mathrm{km}\,{{\rm{s}}}^{-1}$ from velocities derived in JCMT, IRAM 30 m, and CARMA observations with 1000s au spatial resolutions in this region (Duarte-Cabral et al. 2010; Lee et al. 2014). The SO line was not detected toward any of the Group 2 sources. The C¹⁸O line was clearly detected only in S68Nc5, with marginal detection in S68Nc3. No C¹⁸O line was detected in the other Group 2 members, although extended C¹⁸O J = 1 − 0 line emission was detected in this region in IRAM 30 m observations (Duarte-Cabral et al. 2010).

Figure 4 shows maps of the 1.3 mm continuum and the ¹²CO, SO, and C¹⁸O lines in the Group 3 members. Gaussian fittings and flux measurements were performed in the same manner as those for Group 1, and the results are summarized in Table 3. The continuum emission of the Group 3 members arises from regions having deconvolved sizes smaller than half of the beam (∼120 au). All of the Group 3 members were identified as Class 0 or I protostars by Spitzer observations (Dunham et al. 2015).

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S68Nb2, SMM2C, SMM11B, and SMM11C are associated with compact ¹²CO emission within 1000 au of the continuum peaks. The ¹²CO emission in SMM2A and SMM2B shows more complex structures, although showing a clumpy local peak as well at ∼1'' southeast of SMM2B. These clumpy ¹²CO components of the Group 3 members show spatial offset (≳200 au) from the continuum peak positions or velocity offset (≳3 $\mathrm{km}\,{{\rm{s}}}^{-1}$) from the systemic velocity of Serpens Main (8–9 $\mathrm{km}\,{{\rm{s}}}^{-1}$). Hence, their compact ¹²CO emission can be interpreted as small outflows. The SO line was detected in S68Nb2 at an LSR velocity of ∼9 $\mathrm{km}\,{{\rm{s}}}^{-1}$, which is blueshifted by ∼6 $\mathrm{km}\,{{\rm{s}}}^{-1}$ from the mean velocity of the associated ¹²CO emission. Compact C¹⁸O emission was detected in SMM2A, while extended C¹⁸O emission was detected in SMM2B. No C¹⁸O line was detected in the other Group 3 members, although extended C¹⁸O J = 1 − 0 line emission was detected toward regions around all the Group 3 sources with IRAM 30 m observations (Duarte-Cabral et al. 2010).

The presence of the ¹²CO outflows (Figure 2(b)) indicates star formation activities in the Group 1 members. In fact, those except S68Nb1 and S68Nc1 are identified as Class 0 protostars from their SEDs (Dunham et al. 2015; Aso et al. 2017a, 2018). Hence, the SEDs of S68Nb1 and S68Nc1 are examined to reveal their evolutionary stages in this subsection. Figure 5 shows the SEDs, bolometric temperature T_bol, bolometric luminosity L_bol, and submillimeter luminosity L_smm of S68Nb1 and S68Nc1. The SEDs were constructed from archival data of Spitzer IRAC (3.6, 4.5, 5.8, and 8.0 μm), Spitzer MIPS 24 μm, Herschel PACS 70 μm, CSO SHARK-II 350 μm, and JCMT SCUBA-2 (450 and 850 μm), as well as our ALMA data. In addition, the SEDs also include the 3 mm flux densities of S68Nb and S68Nc measured with CARMA (Lee et al. 2014). Our method to derive fluxes and upper limits, and then calculate T_bol, L_bol, and L_smm, is explained by Aso et al. (2018) in more detail. The uncertainties for the detected flux densities were derived in the same way as those for the 1.3 mm flux densities. The flux densities used in the SEDs are listed in Table 4 with their uncertainties. Here, we emphasize that the measured fluxes in S68Nc1 and particularly in S68Nb1 include contamination from the neighboring Class I protostar S68Nb2 from mid-infrared to submillimeter wavelengths. Even with such contamination, their upper limits of T_bol ≲ 60 K and luminosity ratio L_bol/L_smm ≲ 13 indicate that both S68Nb1 and S68Nc1 are Class 0 protostars (Andre et al. 1993; Chen et al. 1995), as the other members of Group 1.

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The Group 1 members show clear outflows in the ¹²CO line as seen in Figure 2(b). To quantitatively examine these outflows, we first measure the intensity-weighted orientation angles (i.e., P.A.), lengths r_flow, and opening angles ${\theta }_{\mathrm{flow}}^{{\prime} }$ projected onto the plane of the sky using ¹²CO moment 0 maps. Concretely, these orientation angles and lengths are calculated as the intensity-weighted mean, i.e., $\langle x\rangle \equiv {\sum }_{{ij}}{I}_{{ij}}{x}_{{ij}}/{\sum }_{{ij}}{I}_{{ij}}$, where I_ij and x_ij are intensity and the quantity of interest at the pixel (i, j). The uncertainty of the quantity of interest can be calculated from that of the intensity through propagation of uncertainty; the uncertainty of $\langle x\rangle$ is estimated from ${({\rm{\Delta }}\langle x\rangle )}^{2}={({\rm{\Delta }}I)}^{2}{\sum }_{{ij}}{({x}_{{ij}}-\langle x\rangle )}^{2}/{({\sum }_{{ij}}{I}_{{ij}})}^{2}$, where ΔI is the uncertainty of the intensity. The derived values are listed in Table 5. The outflow opening angles are shown with green lines in Figure 2(b) as well. In Table 5, the outflow direction P.A. is $\langle \theta \rangle$, and the outflow length r_flow is $\langle r\rangle$ in the r–θ plane, while the outflow opening angles are calculated as two times intensity-weighted standard deviation ${\theta }_{\mathrm{flow}}^{{\prime} }=2\sqrt{\langle {\theta }^{2}\rangle -\langle \theta {\rangle }^{2}}$. Note that, in order to avoid overestimating the opening angles due to beam convolution, the ¹²CO moment 0 maps were deconvolved in the way of CLEAN: finding peaks in a moment 0 map, recording the peaks as "CLEAN components", subtracting beam (Gaussian) functions from the moment 0 map, and then repeating these down to a 5σ cutoff. Then, the derived CLEAN components (not the CLEAN components derived from dirty maps in Section 2) were adopted as the intensity for weighting.

Table 5.  Properties of the ¹²CO Outflows in Group 1

	P.A.	rflow	${\theta }_{\mathrm{flow}}^{{\prime} }$	${v}_{\mathrm{blow}}$	${\tau }_{\mathrm{dyn}}^{{\prime} }$	i
	(deg)	(au)	(deg)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)	(year)	(deg)
SMM4A (blue)	14.1 ± 1.7	2030 ± 40	67.8 ± 3.7	5.5 ± 0.3	1750 ± 100	${65.1}_{-2.6}^{+0.3}$
SMM4B (blue)	6.1 ± 0.9	1900 ± 60	23.9 ± 3.9	13.4 ± 0.2	670 ± 20	${36}_{-3}^{+3}$
- (red)	146.0 ± 1.2	2000 ± 110	25.4 ± 5.4	9.5 ± 0.2	1000 ± 60	${70}_{-2}^{+2}$
S68N (blue)	−51.0 ± 0.4	2940 ± 20	35.6 ± 1.4	5.8 ± 0.4	2400 ± 170	${72.0}_{-0.3}^{+0.1}$
- (red)	133.0 ± 0.5	4280 ± 60	32.1 ± 0.2	6.0 ± 0.5	3380 ± 290	${83.4}_{-0.5}^{+0.1}$
S68Nc1 (blue)	109.6 ± 0.5	2250 ± 90	11.0 ± 1.3	14.7 ± 0.3	730 ± 30	${84.8}_{-0.1}^{+0.1}$
- (red)	−71.8 ± 0.6	1780 ± 70	16.9 ± 3.0	9.2 ± 0.4	920 ± 50	${82.3}_{-0.1}^{+0.1}$
S68Nb1 (red)	−111.9 ± 1.3	640 ± 20	21.8 ± 6.6	5.6 ± 0.6	540 ± 60	${76.4}_{-0.5}^{+1.5}$
SMM11 (blue)	82.4 ± 0.2	4020 ± 60	11.1 ± 0.5	5.9 ± 0.3	3230 ± 170	${81.0}_{-0.3}^{+0.1}$
- (red)	−109.1 ± 0.2	4430 ± 50	9.6 ± 0.3	4.2 ± 0.4	5000 ± 480	${88.0}_{-0.2}^{+0.1}$

Note. The inclination angle i is measured from the line of sight (i = 0° is pole-on). The sixth column is dynamical time calculated as ${\tau }_{\mathrm{dyn}}^{{\prime} }={r}_{\mathrm{flow}}/{v}_{\mathrm{flow}}$. r_flow, ${\theta }_{\mathrm{flow}}^{{\prime} }$, ${v}_{\mathrm{flow}}$, and ${\tau }_{\mathrm{dyn}}^{{\prime} }$ in this table are not inclination-corrected.

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The intensity-weighted mean velocities v_flow (absolute values) were also measured from the ¹²CO data cube using the equation ${v}_{\mathrm{flow}}\equiv | {\sum }_{k}{F}_{k}({v}_{k}-{v}_{\mathrm{sys}})/{\sum }_{k}{F}_{k}|$, where F_k is the total flux of ¹²CO emission associated with each outflow lobe at each velocity channel, v_k, and v_sys is the systemic velocity. This definition provides an uncertainty of each mean velocity calculated from the uncertainty of the velocity at each channel (i.e., velocity resolution) through propagation of uncertainty, ${({\rm{\Delta }}{v}_{\mathrm{flow}})}^{2}={({\rm{\Delta }}v)}^{2}\,{\sum }_{k}{F}_{k}^{2}/{({\sum }_{k}{F}_{k})}^{2}$, where Δv is the velocity resolution. This requires a systemic velocity of each source. The systemic velocities of SMM4A, SMM4B, and SMM11 were determined from Gaussian fittings to their line profiles in C¹⁸O J = 2 − 1 (Aso et al. 2017a, 2018) to be 7.5, 7.9, and 9.1 $\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively. Similarly, the systemic velocities of S68N and S68Nc1 were determined to be 9.3 and 7.6 $\mathrm{km}\,{{\rm{s}}}^{-1}$, respectively, by Gaussian fittings to their C¹⁸O line profiles. The systemic velocity of S68Nb1 was assumed to be the same as that of S68Nc1 since the C¹⁸O line is not detected in S68Nb1. Dynamical time of the outflows ${\tau }_{\mathrm{dyn}}^{{\prime} }$, without inclination-correction, was also calculated from v_flow and r_flow. Its uncertainty was calculated from those of v_flow and r_flow through propagation of uncertainty. The derived v_flow and ${\tau }_{\mathrm{dyn}}^{{\prime} }$ are also listed in Table 5.

An important uncertainty regarding outflows is their inclination angles i. To estimate i of the Group 1 outflows, the ¹²CO moment 0 maps and ¹²CO position–velocity (PV) diagrams are fitted with the wind-driven-shell model (Shu et al. 1991; Lee et al. 2000), which adopts a parabolic shape and a radially expanding velocity field. We follow the method described in Appendix A of Yen et al. (2017): the ¹²CO moment 0 maps (Figure 2(b)) are used to constrain the morphology, while the velocity and the inclination angle are constrained by fitting PV diagrams along the outflow axes. To simplify the fitting procedure, the intensities at the image pixels with the emission stronger than the 5σ level are all replaced with unity, and those weaker than 5σ are replaced with zero. The low velocity ranges are filled by emission (i.e., unity) to compensate for the effect of missing flux: 6–10 $\mathrm{km}\,{{\rm{s}}}^{-1}$ in S68N, 4–9 $\mathrm{km}\,{{\rm{s}}}^{-1}$ in S68Nb1, 4–9 $\mathrm{km}\,{{\rm{s}}}^{-1}$ in S68Nc1, 7–9 $\mathrm{km}\,{{\rm{s}}}^{-1}$ in SMM4A, and 7–9 $\mathrm{km}\,{{\rm{s}}}^{-1}$ in SMM11. The Markov chain Monte Carlo method is used through an open source, emcee (Foreman-Mackey et al. 2013). The log likelihood is $-{\chi }^{2}/2$, where χ² is the sum of squared differences between the model and the observations (i.e., unity or zero). The uncertainty of the inclination angles are calculated from the 5th and 95th percentiles. The outflow in SMM4B exhibits the signature of episodic mass ejection (Aso et al. 2018), which consists of multiple Hubble-law patterns. Our single shell model is not appropriate to fit such a complex velocity structure. For this reason, SMM4B is excluded for this fitting, and i and its uncertainty of the SMM4B outflow are adopted from Aso et al. (2018), which was estimated by assuming equal momentum ejection between the blueshifted and redshifted lobes of the SMM4B outflow. Figure 6 shows the best-fit model curves overlapped with the moment 0 maps and PV diagrams in the ¹²CO line. The best-fit i is listed in Table 5.

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The intensity-weighted values are corrected using the inclination angles derived from the fitting. Figure 7 shows the relation between inclination-corrected τ_flow and θ_flow. The inclination-corrected values τ_dyn and θ_flow are defined as ${\tau }_{\mathrm{dyn}}={\tau }_{\mathrm{dyn}}^{{\prime} }/\tan i$ and $\tan ({\theta }_{\mathrm{flow}}/2)=\sin i\,\tan ({\theta }_{\mathrm{flow}}^{{\prime} }/2)$ using the quantities in Table 5. Figure 7 shows the mean values for the outflows having both blueshifted and redshifted lobes. The errors in this figure are calculated from those of ${\tau }_{\mathrm{dyn}}^{{\prime} }$, ${\theta }_{\mathrm{flow}}^{{\prime} }$, and i through propagation of uncertainty. Although the number of the sampling points is small, the points in Figure 7 seem to show a hint of trend.

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The Group 2 members are located in the filamentary structure in the S68Nc region (Figure 3(a)), and have 1.3 mm continuum fluxes several times lower than the Group 1 protostars (Table 3). None of them shows a signature of a ¹²CO outflow or a Spitzer source (Dunham et al. 2015), which suggests that Group 2 members are starless. The gravitational stability of the Group 2 cores is assessed through a Jeans analysis. Central densities are calculated from the 1.3 mm continuum intensities in Table 3. First, the peak intensity is converted to a column density of molecular hydrogen within the ∼05 (∼210 au) beam. We adopt a dust opacity coefficient of $\kappa (850\,\mu {\rm{m}})=0.035\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ (Andrews & Williams 2005), an opacity index, β = 1, and a temperature of 10 K because the Group 2 members have no central heating sources. Second, the H₂ column density is converted to the central number density ${n}_{{{\rm{H}}}_{2}}$ by assuming a Gaussian density profile along the line of sight with an FWHM of the geometrical mean of the deconvolved sizes along the major and minor axes listed in Table 3. Then, the Jeans length λ_Jeans is calculated as ${\lambda }_{J}={c}_{s}\sqrt{\pi /(G\mu {m}_{{\rm{H}}}{n}_{{{\rm{H}}}_{2}})}$, where c_s, G, μ, m_H are the sound speed at 10 K, the gravitational constant, the mean molecular weight (=2.37), and the mass of atomic hydrogen.

Figure 8 shows the relation between ${n}_{{{\rm{H}}}_{2}}$ and the ratio FWHM/λ_Jeans for Group 2. The errors in this figures are calculated from those of the peak intensity, major axis, and minor axis through propagation of uncertainty. In addition, if the dust opacity index β is close to the interstellar value ∼2, the central H₂ density is ∼50% higher, and the ratio FWHM/λ_Jeans is ∼20% higher. If the dust is more evolved (β ∼ 0), these quantities are lower by the same factor. If the temperature is relatively high as prestellar sources, ∼15 K, the density is two times lower, and the ratio is ∼40% lower. The absolute flux error ∼10% also causes uncertainties of ∼10% and ∼3% for the density and the ratio, respectively. The ratios are around unity within the total uncertainty of a few 10%, implying that the Group 2 sources are marginally Jeans stable/unstable. The central densities of the Group 2 members are typically ∼10⁸ cm⁻³, which is similar to that of a prestellar Bonner–Ebert sphere on the spatial scale of our angular resolution, ∼200 au (e.g., Aikawa et al. 2008). For these reasons, we interpret the Group 2 members as prestellar sources.

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The fractional abundance of C¹⁸O relative to H₂ is calculated from the 1.3 mm continuum intensity and the C¹⁸O integrated intensity at the continuum peak position, assuming both are optically thin. The temperature is assumed to be 20 K for the protostellar sources (Group 1 and 3) (Lee et al. 2014) and 10 K for the prestellar sources (Group 2), and local thermodynamic equilibrium is assumed. SMM4A is excluded from this estimation because the C¹⁸O line is detected as absorption in this source due to its optically thick continuum emission. Figure 9 shows the derived C¹⁸O abundance. The abscissa, central concentration degree, is plotted merely to distinguish the sources. The errors in this figure are calculated from those of the continuum peak intensity, continuum flux density, and C¹⁸O integrated intensities through propagation of uncertainty. The optical depths in SMM11 and S68Nb1 are estimated to be ∼0.8 and ∼0.4, and lower for the other sources. When these optical depths are considered, the estimated $X({{\rm{C}}}^{18}{\rm{O}})$ is higher by a factor of $({e}^{{\tau }_{c}}-1)/{\tau }_{c}$, ∼1.5 and ∼1.2 for SMM11 and S68Nb1 respectively, where τ_c is the optical depth of continuum emission. These factors, however, do not change overall trends of data points in Figure 9.

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Compared to the C¹⁸O abundance in Serpens Main of (6–9) × 10⁻⁸ at ∼15'' (∼6400 au) scales based on JCMT and IRAM 30 m observations (Duarte-Cabral et al. 2010), the calculated abundances of the prestellar and protostellar cores are 10–100 times lower. Figure 9 shows that the C¹⁸O abundance varies by an order of magnitude even in each of Group 1, 2, and 3. This variation will be discussed in the context of evolution in Section 5.1.2.

All of the Group 1 members are classified as Class 0 sources. Nevertheless, our previous study (Aso et al. 2018) on three of them, SMM11, SMM4A, and SMM4B revealed that each have distinct evolutionary characteristics. Specifically, SMM4A has the largest disk and the widest outflow opening angle; SMM4B has an unresolved disk, whereas SMM11 does not show presence of a disk in the uv domain; C¹⁸O is more abundant in SMM4 than in SMM11. This picture is consistent with the classical scenario of star formation (e.g., Terebey et al. 1984; Basu 1998), in which disks grow steadily to the sizes of r ∼ 100 au, as in the case of SMM4A. Our discovery of Group 3 sources with small disks, however, requires that the classical disk growth scenario should be modified to consider a range of final disk radii. Currently none of the Group 1 sources except SMM4A has a large disk. These members, therefore, could evolve to become Group 3-like objects (Section 5.2). In order to avoid the bias toward the classical disk growth scenario, we exclude SMM4A in this subsection. The relation between SMM4A and the other Group 1 members will be discussed in Section 5.2. We use a simple scoring system to assess evolutionary trends in the other Group 1 members here, and summarize our conclusions in Table 6.

5.1.1. Outflows

5.1.2. C¹⁸O Abundance

5.1.3. Continuum Morphology

Figure 10 shows that the continuum intensity profiles perpendicular to the outflows across the protostellar positions. The profiles of SMM4B, S68N, and S68Nc1 include extended components and central compact components significantly stronger than the extended components. We interpret the extended and compact components as envelopes and unresolved disks, respectively. The extended component of S68Nc1 is elongated along its outflow direction or tracing a cavity wall of the outflow (Figure 2(b) (iii)). S68Nb1 and SMM11 do not show such compact+extended components, although their emission is significantly more extended than the expected emission from a central point source. Their single-peak structures suggest that any central disks are too small to be detected. We score one point to SMM4B, S68N, and S68Nc1, showing unresolved disks, and zero points to the rest, showing no detectable disks.

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S68Nb1 and SMM11 show single compact continuum emission. Furthermore, their continuum emission is close to circular (aspect ratio ∼1.2), and their deconvolved major axes (P.A. in Table 3) are in similar directions to their outflow axes. S68Nc1 also shows continuum emission elongated along its outflow axis. Such morphologies suggest spherical envelopes and outflows, rather than flattened envelopes and disks (Aso et al. 2017a). We thus score one point to SMM4B and S68N and zero point to the rest, based on whether they lack or exhibit continuum elongations along their outflows.

The continuum emission in SMM11 is elongated along the north–south direction at low contour levels in Figure 2(a(v)) (it is more clearly seen in the zoom out version in Figure 1(a) of Aso et al. 2017a). This elongation reflects the structure of the filament passing SMM11 on a sub-pc scale (Lee et al. 2014). Such filamentary structures are interpreted as gas accretion streams in other young protostars, such as L1157 (Looney et al. 2007) and L1521F (Tokuda et al. 2017). The elongated component of the continuum emission in SMM11 is thus consistent with the conclusion that SMM11 is relatively young in Group 1. A similar filamentary structure is seen more clearly around the prestellar sources (Group 2), i.e., even younger sources.

One may wonder why the young members, S68Nc1, S68Nb1, and SMM11, show smaller envelopes in the 1.3 mm continuum than the more evolved members, S68N and SMM4B. Similar results are found in the Barnard 1 region between a typical Class 0 protostar, B1-c, and young Class 0 protostars, B1-bS and B1-bN (Hirano & Liu 2014). B1-c shows 0.9 mm continuum emission extending over ∼4'' (Cox et al. 2018), whereas B1-bS and B1-bN show 0.9 mm continuum emission extending over ∼06 (Gerin et al. 2017). The apparent sizes of the continuum emission are related to density and temperature distributions. The density at a given radius rises when the mass-supplying radius expands outward because outer regions have more volume and thus more mass. The temperature distribution depends on the luminosity of the central protostar. For example, S68N has ${L}_{\mathrm{bol}}=14\,{L}_{\odot }$ (Dunham et al. 2015), whereas the younger members have ${L}_{\mathrm{bol}}\lesssim 2\,{L}_{\odot }$. The ∼7 times larger ${L}_{\mathrm{bol}}$ can cause a $\sqrt{7}=2.6$ times larger isotemperature radius (e.g., Goldreich & Kwan 1974). In addition, the more extended members, SMM4B, S68N, and S68Nc1, show lower 1.3 mm peak intensities, implying lower densities, than the more centrally concentrated members, S68Nb1 and SMM11. Due to this density difference, the central star could heat the envelope more easily in the extended three members than in the compact two members. Although it is not clear only from the present data whether these two mechanisms are due to protostellar evolution or intrinsic differences, the combination of these mechanisms would explain the difference of the apparent envelope sizes in the 1.3 mm continuum among the Group 1 members.

Six 1.3 mm continuum sources are categorized into Group 3 in our sample. Spitzer observations (Dunham et al. 2015) identified four members (SMMb2, SMM2C, SMM11B, and SMM11C) as Class I protostars and two members (SMM2A and SMM2B) as Class 0 protostars (Table 3). Their bolometric luminosities L_bol ≳ 1 ${L}_{\odot }$ indicate that the central objects are massive enough to be classified as protostars rather than proto-brown dwarfs. Their total flux densities of the 1.3 mm continuum emission range from 27 down to $3\,\mathrm{mJy}$. This range corresponds to the gas-mass range from 0.045 down to $0.006\,{M}_{\odot }$, where $\kappa (1.3\,\mathrm{mm})=0.023\,{\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ and ${T}_{\mathrm{dust}}=20$ K are assumed. This is typically >10 times smaller than those of Group 1 ($0.2\mbox{--}0.8\,{M}_{\odot }$). The Group 3 members also show compact, faint outflows in the ¹²CO line. These results, i.e., Spitzer identification, the deficiency of the envelope materials, and the faint outflows, can be explained by a final phase of mass accretion, where most of the envelope materials are being exhausted. The lack of envelope causes outflows to be faint in molecular lines, while making the central protostar bright even at near-IR and mid-IR wavelengths.

The envelope dissipation around the Group 3 members suggests that Group 3 disks will not grow further from their present size, r ≲ 15–60 au (Table 3). In this sense, Group 3 may represent the precursors of small T Tauri disks with radii of tens of astronomical units, identified in recent observational studies (Najita & Bergin 2018; Cieza et al. 2019). In particular, SMM2A and SMM2B show r ≲ 30 au at the Class 0 stage, whereas a large disk (r ∼ 240 au) is identified from a continuum visibility analysis in the Group 1 member SMM4A at the same stage (Aso et al. 2018). These differences imply a diverse evolution from the Class 0 phase, which may be due to local conditions such as multiplicity or magnetic field configurations as discussed in Section 5.3 in more detail, even in the same star-forming region. This diversity in protostellar initial conditions may produce a disk-size diversity over radii of tens to hundreds of astronomical units in the T Tauri phase (Najita & Bergin 2018).

Previous observations also identified Group 3-like objects in other star-forming regions at Class 0 and I stages. For example, SM1-A (Class 0) and Source-X (Class 0) in Oph A (Kawabe et al. 2018), B1-bW (Class I) in Barnard 1 (Hirano & Liu 2014), L1448C(S) (Class I) in Perseus (Hirano et al. 2010; Tobin et al. 2015), and MMS-1 (Class I) in MC27/L1521F (Bourke et al. 2006; Tokuda et al. 2017) show small (≲100 au) and faint (i.e., low-mass $\lesssim 0.05\,{M}_{\odot }$) or no millimeter/submillimeter continuum emission and clumpy ¹²CO outflows. This suggests a similar diversity of protostellar conditions in other star-forming regions as well as Serpens Main.

Theoretical studies provide potential mechanisms for the formation of the Group 3 members. A relatively simple mechanism is star formation in a very low-mass ($\sim 0.1\,{M}_{\odot }$) core (Tomida et al. 2010). In the case of the binary formation, most of the initial angular momentum is converted to the orbital motion, leaving only small angular momentum to form circumstellar disks, as found in a binary system, L1551 NE (Takakuwa et al. 2017); this could be the case for the closest pair of Group 3 members SMM11B and SMM11C with a separation of ∼600 au. Similarly, ejection from multiple systems can make disk masses and disk sizes smaller (Bate 2018). Another potential mechanism is the Hall effect in MHD; magnetic fields parallel to the initial angular momentum vector suppress disk growth, while anti-parallel combination enhances disk growth, resulting in a bimodal distribution of disk sizes (Tsukamoto et al. 2017). In addition to the Hall effect, a low initial ratio of rotational to gravitational energies or low diffusivity in non-ideal MHD can also enhance magnetic breaking, and thus produce smaller disks.

Observational studies provide other potential mechanisms as well. Brown dwarfs tend to have less massive disks than typical low-mass stars (e.g., Scholz et al. 2006), and such disks could appear smaller at a given sensitivity. However, the Group 3 members are not proto-brown dwarfs, and their bolometric luminosities are similar or higher than those of the Group 1 members. The Group 3-like source L1448C(S) is found to be impacted by an outflow from a neighboring protostar, L1448C(N) (Hirano et al. 2010), which could blow off the envelope around L1448C(S), and terminate mass accretion forcibly. The Group 3 members in Serpens Main may be in the same situation because large-scale outflows exist almost everywhere in this region (Davis et al. 1999). The ¹²CO emission in SMM2A and SMM2B shows an elongation in the east–west direction passing SMM2A and a U-shaped structure surrounding SMM2B. These structures show a wide velocity range of ∼10 $\mathrm{km}\,{{\rm{s}}}^{-1}$. The morphology and velocity in the ¹²CO line may suggest effects of large-scale outflows in SMM2A and SMM2B. Such interaction among neighboring protostars should occur more easily in cluster environments than in isolated environments. The recent ODISEA 1.3 mm survey toward the moderately dense Ophiuchus star-forming region also reported that only 23 of 133 Spitzer-selected protoplanetary disks have radii larger than 30 au (Cieza et al. 2019). This result, along with our result in the clusters, may suggest that cluster environments play a role in generating small disks.