PLANCK COLD CLUMPS IN THE λ ORIONIS COMPLEX. I. DISCOVERY OF AN EXTREMELY YOUNG CLASS 0 PROTOSTELLAR OBJECT AND A PROTO-BROWN DWARF CANDIDATE IN THE BRIGHT-RIMMED CLUMP PGCC G192.32–11.88

The observations toward PGCC G192.32–11.88 in the ¹²CO (1–0), ¹³CO (1–0), and C¹⁸O (1–0) lines were carried out with the PMO 13.7 m radio telescope in 2011 May. The new nine-beam array receiver system in single-sideband mode was used as the front end (Shan et al. 2012). FFTS spectrometers were used as back ends, which have a total bandwidth of 1 GHz and 16,384 channels, corresponding to a velocity resolution of 0.16 km s⁻¹ for the ¹²CO (1–0) and 0.17 km s⁻¹ for the ¹³CO (1–0) and the C¹⁸O (1–0). The ¹²CO (1–0) was observed in the upper sideband (USB), while the ¹³CO (1–0) and the C¹⁸O (1–0) were observed simultaneously in the lower sideband (LSB). The half-power beam width (HPBW) is 56'', and the main-beam efficiency is ∼0.45. The pointing accuracy of the telescope was better than 4''. The typical system temperatures (T_sys) are around 130 K for LSB and 220 K for USB, which vary about 10% among the nine beams. The on-the-fly (OTF) observing mode was utilized. The antenna continuously scanned a region of $22^{\prime} \times 22^{\prime}$ centered on the Planck cold clumps with a scan speed of 20'' s⁻¹. However, the edges of the OTF maps have a much higher noise level, and thus only the central $14^{\prime} \times 14^{\prime}$ regions are selected to be further analyzed. The typical rms noise level per channel was 0.3 K in ${T}_{A}^{*}$ for the ¹²CO (1–0) and 0.2 K for the ¹³CO (1–0) and the C¹⁸O (1–0).

Observations of "Clump-S" in the ¹²CO (2–1), ¹³CO (2–1), and C¹⁸O (2–1) lines were carried out with the Caltech Submillimeter Observatory (CSO) 10 m radio telescope in 2014 January. We used the Sidecab receiver and the FFTS2 spectrometer. The spectral resolution is ∼0.35 km s⁻¹. The weather was good during observations with a system temperature of 244 K. The beam size and beam efficiency of the CSO telescope at 230 GHz are ∼34'' and 0.76, respectively. The map size is $5^{\prime} \times 5^{\prime}$, with a spacing of 10''. The typical rms noise level per channel is 0.2 K in ${T}_{A}^{*}.$

Using the GILDAS software package including CLASS and GREG (Guilloteau et al. 2000), the OTF data of CO isotopologues were converted to 3D cube data. Baseline subtraction was performed by fitting linear or sinusoidal functions. Then the data were exported to MIRIAD (Sault et al. 1995) and CASA for further analysis.

We also observed "Clump-S" in the J = 1–0 transitions of HCO${}^{+},$ H¹³CO⁺, and N₂H⁺, as well as HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) and o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$), with the Korean VLBI Network (KVN) 21 m telescope at Yonsei station in single-dish mode (Kim et al. 2011). The observations were carried out in 2015 February. The spectral resolution and system temperature for the J = 1–0 of HCO${}^{+},$ H¹³CO⁺, and N₂H⁺ (1–0) are ∼0.052 km s⁻¹ and 230 K, respectively. The spectral resolution and system temperature for HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) and o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) are ∼0.034 km s⁻¹ and 453 K, respectively. We did single-pointing observations with an rms level per channel of ${T}_{A}^{*}\lt 0.1$ K. The beam size and beam efficiency of the KVN telescope at 86 GHz band are ∼32'' and 0.41, respectively. The beam size and beam efficiency of the KVN telescope in the 129 GHz band are ∼24'' and 0.40, respectively. The data were reduced using the GILDAS software package.

The observations of "Clump-S" with James Clerk Maxwell Telescope (JCMT) SCUBA-2 were conducted in 2015 April. We used the "CV Daisy" mapping mode, which is suitable for point sources. The 225 GHz opacity during observations ranges from 0.088 to 0.11. Therefore, we only obtained 850 μm continuum data. The data were reduced using SMURF in the STARLINK package. The FOV of SCUBA-2 at 850 μm is 8'. The mapping area is about 12' × 12'. The beam size of SCUBA-2 at 850 μm is ∼14''. The rms level in the central 3' area of the map is around 8 mJy beam⁻¹.

The observations of "Clump-S" with the Submillimeter Array (SMA)²⁶ were carried out in 2014 November in its compact configuration. The phase reference center was R.A. (J2000) = 05^h29^m5432 and decl. (J2000) = $12^\circ 16^{\prime} 40\buildrel{\prime\prime}\over{.} 50$. In observations, QSOs 0530 + 135 and 0510 + 180 were observed for gain and phase correction. QSO 3c 279 was used for bandpass calibration. Uranus was applied for flux-density calibration. The channel spacing across the 8 GHz spectral band is 0.812 MHz, or ∼1.1 km s⁻¹. The visibility data were calibrated with the IDL superset MIR package and imaged with the MIRIAD and CASA packages. The 1.3 mm continuum data were acquired by averaging all the line-free channels over both the upper and lower spectral bands. The synthesized beam size and 1σ rms of the continuum emission are 34 × 23 (PA = −59°) and ∼1 mJy beam⁻¹, respectively. The 1σ rms for lines is ∼50 mJy beam⁻¹ per channel. We detect strong ¹²CO (2–1) emission and weak ¹³CO (2–1) emission above the 3σ signal-to-noise level in the SMA observations. To recover the missing flux in the SMA ¹²CO (2–1) and ¹³CO (2–1) emission, we combined the SMA data with the CSO data following a procedure outlined in Zhang et al. (1995). The combined SMA+CSO data for ¹²CO (2–1) and ¹³CO (2–1) emissions were convolved with the same beam size of 52 × 38 (PA = −53°) to derive the ¹³CO column density. The 1σ rms for lines is ∼300 mJy beam⁻¹ per channel in the SMA+CSO combined data. We use primary-beam-corrected continuum and line data in further analysis.

We also used Spitzer MIPS and IRAC archival data.

3.1.1. Moment Maps

The integrated intensity of ¹³CO (1–0) is shown as contours overlayed on its Moment 1 color image in panel (a) of Figure 2. Two large clumps ("Clump-N" and "Clump-S") are revealed in ¹³CO (1–0) emission. The integrated intensity of ¹³CO (2–1) of "Clump-S" is shown as contours overlayed on its Moment 1 color image in panel (b) of Figure 2. From the Moment 1 maps, a clear velocity gradient is seen along the southwest to northeast direction, indicating that the cloud might be externally compressed. We derived the systemic velocities of ¹³CO (1–0) and ¹³CO (2–1) from Gaussian fits of the spectra along the dashed lines in panels (a) and (b) and plotted the position–velocity diagrams in panels (c) and (d), respectively. The velocities linearly decrease from the southwest to northeast. The direction of the velocity gradient is inconsistent with the elongation of the cloud. We notice that the B-type star HD 36104 is at the southwest edge of "Clump-S." Therefore, the velocity gradient may be caused by the joint effect of the radiation pressure from the giant H ii region and HD 36104. From linear fits, we found that the velocity gradient of the cloud is 1.6–1.8 km s⁻¹ pc⁻¹.

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In Figure 3, we present the Moment 2 maps of ¹³CO (1–0) and ¹³CO (2–1) emission. The velocity dispersions become larger toward the clump centers, suggesting that the line widths might be broadened by feedback of star formation activity (e.g., outflows) inside the clumps.

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3.1.2. Line Intensity Ratios

The integrated intensity ratios of ¹²CO J = 2–1 to J = 1–0 (R_12CO) and ¹³CO J = 2–1 to J = 1–0 (R_13CO) were calculated by convolving the ¹²CO (2–1) and ¹³CO (2–1) data with the beam of PMO 13.7 m. The two ratios are shown in color images in panels (a) and (b) of Figure 4. The ratios become larger from clump center to clump edge. The integrated intensity ratios of ¹²CO (1–0) to ¹³CO (1–0) (R${}_{12\mathrm{CO}/13\mathrm{CO}}^{10}$) and ¹²CO (2–1) to ¹³CO (2–1) (R${}_{12\mathrm{CO}/13\mathrm{CO}}^{21}$) were also derived and displayed in panels (c) and (d), respectively. Smaller ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{10}$ and ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{21}$ ratios indicate higher optical depths for CO emission. The optical depth of CO emission decreases from clump center to clump edge. In Table 1, we present statistical results of these ratios and integrated intensity of ¹³CO and C¹⁸O within a 50% contour (region 1), 20% contour of C¹⁸O (1–0) (region 2), and 20% contour of ¹³CO (1–0) (region 3), respectively. These statistical results are not artificial owing to low signal-to-noise level because the minimum value of ¹³CO (2–1) integrated intensity within its 20% contour is 1.21 K km s⁻¹, which is larger than 6σ ($\sigma \sim 0.2$ K km s⁻¹). In general, the average density from region 1 to region 3 decreases, while the mean or maximum values of different ratios generally increase with decreasing average density, which quantitatively indicates that the CO emission at the clump edge is less optically thick and more highly excited than that at the clump center.

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Table 1.  Statistics of Integrated Intensities and Intensity Ratios

Transitions	Meana	Stda	Mina	Maxa
	Within 50% Contour of C18O (1–0)
CO/13CO (1–0)	2.80	0.31	2.49	3.28
CO/13CO (2–1)	2.33	0.19	1.96	2.79
C18O (2–1)/(1–0)	1.51	0.23	1.24	1.87
CO (2–1)/(1–0)	0.91	0.04	0.85	0.96
13CO (2–1)/(1–0)	1.04	0.13	0.91	1.26
C18O (1–0)b	1.39	0.27	1.10	1.88
13CO (1–0)b	9.45	1.20	7.59	10.8
13CO (2–1)b	10.3	1.59	7.38	13.0
C18O (2–1)b	2.25	0.61	1.18	3.42
N${}_{{{\rm{H}}}_{2}}$c	1.05 × 1022	1.78 × 1021	8.07 × 1021	1.22 × 1022
Tex c	18.84	0.79	17.66	19.89
	Within 20% Contour of C18O (1–0)
CO/13CO (1–0)	3.14	0.56	2.37	4.59
CO/13CO (2–1)	2.75	0.56	1.77	4.53
C18O (2–1)/(1–0)	1.79	0.52	1.00	3.30
CO (2–1)/(1–0)	0.90	0.07	0.79	1.06
13CO (2–1)/(1–0)	1.04	0.21	0.77	1.56
C18O (1–0)	0.92	0.40	0.41	1.88
13CO (1–0)	7.74	1.95	3.04	10.83
13CO (2–1)	8.15	2.06	4.61	13.0
C18O (2–1)	1.58	0.70	0.30	3.42
	Within 20% Contour of 13CO (1–0)
CO/13CO (1–0)	4.14	1.40	2.37	8.14
CO/13CO (2–1)	3.50	1.20	1.77	10.10
CO (2–1)/(1–0)	0.90	0.08	0.77	1.14
13CO (2–1)/(1–0)	1.11	0.29	0.72	2.27
13CO (1–0)	6.23	2.35	1.79	10.83
13CO (2–1)	6.62	2.41	1.21	13.0

Note.

^aWe get statistical results from pixel values after beam convolution. ^bUnits of K km s⁻¹. ^cUnits of K.

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3.1.3. Clump Properties from Local Thermodynamic Equilibrium (LTE) Analysis

We first calculated the excitation temperature of ¹²CO (1–0) and column density of ¹³CO assuming LTE. The details of the LTE analysis are described in Appendix A.

The mean peak brightness temperature ratio of ¹²CO (1–0) to ¹³CO (1–0) within the 20% contour of ¹³CO (1–0) integrated intensity is ∼4, corresponding to an optical depth of 17 for ¹²CO (1–0) emission. Thus, ¹²CO (1–0) emission is apparently optically thick in PGCC G192.32–11.88. The excitation temperature of ¹²CO (1–0) is shown as a color image in Figure 5. It can be seen that the excitation temperature (T${}_{\mathrm{ex}}\sim 21$ K) at the western edge is higher than that (∼15 K) at the eastern edge of the cloud, indicating that the cloud might be externally heated. The mean excitation temperatures of "Clump-S" and "Clump-N" are 18.1 ± 0.3 and 18.0 ± 0.2 K, respectively, which are consistent with the dust temperature (17.3 ± 6.0 K) of the cold component in Planck observations (Planck Collaboration et al. 2015).

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The column density of H₂ was obtained by adopting typical abundance ratios [H₂]/[¹²CO] = 10⁴ and [¹²CO]/[¹³CO] = 60 in the ISM (Deharveng et al. 2008). The column density of H₂ is shown as contours in Figure 5. The mean column densities of "Clump-S" and "Clump-N" are (6.5 $\pm 0.4)\times {10}^{21}$ and (6.3 $\pm 0.2)\times {10}^{21}$ cm⁻², respectively.

The radii of the clumps are defined as $R=\sqrt{a\cdot b},$ where a and b are the FWHM deconvolved sizes of the major and minor axes, respectively. The radii of "Clump-S" and "Clump-N" are 0.33 and 0.47 pc, respectively. The LTE masses of the clumps are estimated as ${M}_{\mathrm{LTE}}=\pi {R}^{2}\cdot \bar{N}\cdot {m}_{{\rm{H}}}\cdot {\mu }_{{\rm{g}}},$ where $\bar{N}$ is the mean column density, m_H is the mass of atomic hydrogen, and ${\mu }_{{\rm{g}}}$ = 2.8 is the mean molecular weight of the gas. The LTE masses of "Clump-S" and "Clump-N" are 49 ± 3 and 99 ± 3 ${M}_{\odot },$ respectively. In calculating masses, we only considered the errors in flux measurement. Other uncertainties such as distance, abundance, and calibration were not taken into account. These systematic uncertainties can have an effect that is much greater than the random noise in the data on mass measurement. For example, the various distance determinations have uncertainties of approximately 10%. If the distance was actually 10% higher, then the LTE mass determination would be increased by ∼20%. Additionally, as discussed in Section 3.3.1, CO gas may be depleted in the central region. Therefore, the abundance we adopted here might be larger than the real value. If we adopt an abundance two times smaller than the present value, the corresponding LTE masses will increase by a factor of 2. To study the gravitational stability of these two clumps, we also estimated their virial masses. The virial mass considering turbulent support can be derived as $\frac{{M}_{\mathrm{vir}}}{{M}_{\odot }}=210{(\frac{R}{\mathrm{pc}})(\frac{{\rm{\Delta }}V}{\mathrm{km}{{\rm{s}}}^{-1}})}^{2}$(Zhang et al. 2015), where ${\rm{\Delta }}V$ is the line width of C¹⁸O (1–0). We used the C¹⁸O (1–0) line rather than the ¹³CO (1–0) line to derive virial masses because the C¹⁸O (1–0) line emission is more optically thin than the ¹³CO (1–0) line emission and therefore a better tracer for turbulence. From Gaussian fits toward the spectra at clump centers, the line widths of C¹⁸O (1–0) of "Clump-S" and "Clump-N" are 0.93 ± 0.09 and 0.86 ± 0.11 km s⁻¹, respectively. Thus, the virial masses of "Clump-S" and "Clump-N" are 59 ± 10 and 74 ± 19 ${M}_{\odot },$ respectively. The virial masses of the two clumps are consistent with their LTE masses, indicating that these two gas clumps are gravitationally bound.

3.1.4. CO Gas Excitation from Non-LTE Analysis

In Figure 6, we applied RADEX (Van der Tak et al. 2007), a one-dimensional non-LTE radiative transfer code, to investigate the excitation of CO isotopologues within the 50% contour of C¹⁸O (1–0) in "Clump-S" by exploring parameter ranges of H₂ volume density in [1 $\times \quad {10}^{3},$ $5\times {10}^{4}{\rm{]}}$ cm⁻³, kinetic temperature in [15, 30] K, and column density of ¹²CO in [1 $\times \quad {10}^{17},$ $5\times {10}^{18}{\rm{]}}$ cm⁻². The modeled values, which are consistent with observed mean values within 1σ, are adopted. For example, the blue boxes in Figure 6 represent the solutions in which modeled ${R}_{13\mathrm{CO}}$ is consistent with the observed value 1.04 ± 0.13. The best solutions should satisfy the criteria that all the modeled ratios (R${}_{12\mathrm{CO}},$ ${R}_{13\mathrm{CO}},$ ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{10},$ ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{21}$) are consistent with the observed values. The kinetic temperature, volume density, and CO column density in the overlapped regions are 18.9 K, 3.2 × 10³ cm⁻³, and $1.05\times {10}^{18}$ cm⁻², respectively, which are the best solutions. The kinetic temperature (18.9 K) is consistent with the average excitation temperature (18.84 ± 0.79 K) of ¹²CO (1–0) in the LTE analysis, as listed in Table 1. Assuming an abundance ratio of [H₂]/[¹²CO] = 10⁴, the H₂ column density calculated with RADEX is $1.05\times {10}^{22}$ cm⁻², which is the same as the value ($(1.05\pm 0.18)\times {10}^{22}$ cm⁻²) obtained from the LTE analysis, suggesting that the central part of the southern clump satisfies the LTE condition very well. The thickness (h) of  "Clump-S" can be estimated as $h=\frac{\bar{{N}_{{{\rm{H}}}_{2}}}}{\bar{{n}_{{{\rm{H}}}_{2}}}},$where $\bar{{N}_{{{\rm{H}}}_{2}}}$ and $\bar{{n}_{{{\rm{H}}}_{2}}}$ are the average column density and volume density, respectively. The thickness of the clump is ∼0.95 pc, which is about 1.5 times larger than the diameter (0.66 pc) of the southern clump.

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In Figure 7, we investigate integrated intensity ratios versus kinetic temperature in three groups of volume density and column density. Roughly speaking, for a given density, integrated intensity ratios increase with kinetic temperature except for ${R}_{12\mathrm{CO}}$ in the lowest-density group (n${}_{{{\rm{H}}}_{2}}=1.6\times {10}^{3}$ cm⁻³). For a given kinetic temperature, ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{10}$ and ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{21}$ decrease with increasing density, indicating that in high-density regions CO is more optically thick. As shown in panels (c) and (d), extremely high ratios of ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{10}$ and ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{21}$ indicate much higher temperature and lower density. As shown in Table 1, the maximum values of ${R}_{12\mathrm{CO}},$ ${R}_{13\mathrm{CO}},$ ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{10}$, and ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{21}$ within the 20% contour of ¹³CO (1–0) are 1.14, 2.27, 8.14, and 10.10, respectively. Such high ratios are larger than the maximum ratios we calculated with RADEX, as marked with black solid lines in Figure 7, indicating that the kinetic temperature should be larger than 50 K close to the clump edge. However, the J = 1 and 2 levels of CO are only at 5.53 K and 16.60 K above ground level, respectively, indicating that we could not reveal such high-temperature (T${}_{k}\;\gt$ 50 K) conditions accurately with the present data. Observations of higher J transitions of CO are needed to reveal the exact excitation condition at the clump edge. As shown in panels (c) and (d), to achieve extremely high ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{10}$ and ${R}_{12\mathrm{CO}/13\mathrm{CO}}^{21},$ not only higher temperatures but also lower densities are needed, indicating that the clump might be surrounded by a hot and low-density envelope.

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As shown in the left panel of Figure 8, "Clump-S" fragments into two dense cores in the 850 μm continuum from JCMT/SCUBA-2 observations. The southern and northern cores are hereafter denoted as G192S and G192N, respectively. The two dense cores are located in a low-density halo with a mean flux density of ∼0.12 Jy beam⁻¹. After subtracting a local background flux density of 0.12 Jy beam⁻¹, the two dense cores can be fitted with two Gaussian components, as shown in the middle panel. The two dense cores were unresolved by JCMT/SCUBA-2. Assuming that the dust emission is optically thin and the dust temperature equals the kinetic temperature (18.9 K) derived from CO isotopologues, the masses of the two cores can be obtained with the formula $M={S}_{\nu }{D}^{2}/{\kappa }_{\nu }{B}_{\nu }({T}_{d})$ (Planck Collaboration et al. 2015), where ${S}_{\nu }$ is the flux of the dust emission at 850 $\mu {\rm{m}},$  D is the distance, and ${B}_{\nu }({T}_{d})$ is the Planck function. Here the ratio of gas to dust is taken as 100. The dust opacity ${\kappa }_{\nu }={\kappa }_{0}{(\frac{\nu }{{\nu }_{0}})}^{\beta }$ = 0.018 cm² g⁻¹, where β = 1.4 is the dust opacity index obtained from PGCC catalog and ${\kappa }_{0}=0.01$ cm² g⁻¹ is the dust opacity at 230 GHz derived from Ossenkopf & Henning (1994). The fluxes of G192N and G192S from two Gaussian component fits are 0.51 ± 0.04 and 0.27 ± 0.03 Jy, corresponding to masses of 0.43 ± 0.03 and 0.23 ± 0.03 ${M}_{\odot },$ respectively. We only considered flux uncertainties in estimating the mass uncertainties. However, other parameters such as dust temperature, dust opacity, and distance should also have a great effect on the mass measurement. For example, if we adopt a dust opacity index of 2, the inferred mass should be reduced by ∼23%. In the right panel of Figure 8, we subtracted the two modeled Gaussian components and presented the residual as a color image. The total flux of the residual within the 10% contour of 850 μm continuum emission is 1.36 ± 0.29 Jy, corresponding to a mass of 1.16 ± 0.25 ${M}_{\odot }.$ The core gas masses of G192N and G912S without subtracting local background are 0.53 ± 0.04 and 0.33 ± 0.03 ${M}_{\odot },$ respectively. The corresponding beam-averaged column densities of G192N and G192S are (1.1 $\pm \;0.1)\times {10}^{22}$ and (6.8 $\pm \;0.6)\times {10}^{21}$ cm⁻², respectively, which are used to calculate the abundances of molecules in each core as below. The beam-averaged column density of G192N is consistent with the column density estimated from CO isotopologues above. G192S has lower density than G192N. The total mass inferred from JCMT/SCUBA-2 850 μm continuum, including both dense cores and a low-density halo, is 1.94 ± 0.32 ${M}_{\odot },$ which is roughly consistent with the mass (3.0 ± 2.4) ${M}_{\odot }.$ inferred from the Planck data, indicating that JCMT/SCUBA-2 traced the same cold component as that of Planck. The SCUBA-2 850 μm continuum band may be contaminated by the ¹²CO (3–2) line (Drabek et al. 2012). From the RADEX calculation, we estimated that the integrated intensities of the ¹²CO (3–2) line are ∼22 and 21 K km s⁻¹ for G192N and G192S, respectively. Adopting a molecular line conversion factor of 0.7 mJy beam⁻¹ per K km s⁻¹ in the grade 3 weather band (Drabek et al. 2012), the contaminations of the ¹²CO (3–2) line at the SCUBA-2 850 μm continuum band are 15.4 and 14.7 mJy beam⁻¹, corresponding to only ∼3% and ∼4% of the 850 μm flux for G192N and G192S, respectively. Therefore, line contamination does not greatly affect the mass calculation above.

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3.3.1. CO Depletion

Figure 9 shows the spectra of J = 2–1 of CO isotopologues from CSO observations. All the spectra are single-peaked. Weak wing emission can be identified in the ¹²CO (2–1) emission. We fitted these spectra with Gaussian profiles and listed the fitted results in Table 2. The brightness temperature ratios of ¹³CO (2–1) to C¹⁸O (2–1) toward G192N and G192S are 3.5 and 2.7, respectively. Assuming a terrestrial abundance ratio of 5.5 for [¹³CO/C¹⁸O], the optical depths of ¹³CO (2–1) toward G192N and G192S are ∼1.3 and ∼2.3, while the optical depths of C¹⁸O (2–1) toward G192N and G192S are $\lt 0.5.$ Compared with ¹²CO (2–1) and ¹³CO (2–1), C¹⁸O (2–1) emission is more optically thin and can reveal the actual CO column density distribution. In Figure 10, we present the integrated intensity of C¹⁸O (2–1) emission in blue contours and JCMT/SCUBA-2 850 μm continuum in black contours. The emission peak of C¹⁸O (2–1) is clearly displaced from continuum emission peaks, indicating that the CO gas may be depleted toward the clump center. Assuming LTE and optically thin for both 850 μm continuum and C¹⁸O (2–1) emission, the ratio of 850 μm continuum to C¹⁸O (2–1) could reflect the CO depletion factor in the clump neglecting any temperature change. We convolved the 850 μm data with the CSO beam and presented the flux ratio of 850 μm continuum to C¹⁸O (2–1) as a color image in Figure 10. The flux ratio toward the clump center is larger than the ratio at the clump edge. In the right panel of Figure 10, we investigated the circularly averaged JCMT/SCUBA-2 850 μm intensity, integrated intensity of C¹⁸O (2–1), and their ratio as a function of radius. JCMT/SCUBA-2 850 μm intensity drops nearly linearly from center to edge. Integrated intensity of C¹⁸O (2–1) peaks at $\sim 15^{\prime\prime}$ from the clump center. The ratio of 850 μm intensity to integrated intensity of C¹⁸O (2–1) changes by a factor of five from center to edge, indicating that CO gas is severely depleted in the clump center. The column densities and abundances of C¹⁸O toward G192N and G192S are presented in Table 3. The C¹⁸O abundance of G192S is about two times larger than that of G192N, indicating that CO gas in G192N is more depleted than in G192S.

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Table 2.  Parameters of Molecular Lines in Single-dish Observations

Lines	G192N					G192S
	Area	Vlsr	FWHM	Tb	rms	Area	Vlsr	FWHM	Tb	rms
	(K km s−1)	(km s−1)	(km s−1)	(K)	(K)	(K km s−1)	(km s−1)	(km s−1)	(K)	(K)
CO (2–1)	29.78 ± 0.46	11.88 ± 0.01	2.17 ± 0.04	12.86	0.33	25.99 ± 0.43	11.59 ± 0.01	2.00 ± 0.04	12.19	0.31
13CO (2–1)	12.11 ± 0.24	11.84 ± 0.01	1.30 ± 0.03	8.74	0.23	11.07 ± 0.33	11.78 ± 0.01	1.13 ± 0.04	9.19	0.23
C18O (2–1)	2.43 ± 0.20	11.88 ± 0.03	0.90 ± 0.09	2.53	0.23	2.72 ± 0.18	11.77 ± 0.02	0.74 ± 0.06	3.43	0.22
HCO+ (1–0)	7.15 ± 0.04	12.48 ± 0.00	1.79 ± 0.01	3.75	0.07	5.95 ± 0.04	12.25 ± 0.01	1.37 ± 0.01	4.06	0.07
H13CO+ (1–0)	1.05 ± 0.03	12.08 ± 0.01	0.80 ± 0.03	1.23	0.08	1.07 ± 0.02	12.10 ± 0.01	0.68 ± 0.02	1.47	0.09
H2CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$)	5.05 ± 0.05	12.50 ± 0.01	2.73 ± 0.03	1.73	0.09	3.46 ± 0.04	12.27 ± 0.01	1.60 ± 0.02	2.02	0.08
HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$)	0.59 ± 0.03	12.04 ± 0.02	0.94 ± 0.05	0.59	0.08	0.51 ± 0.02	12.15 ± 0.01	0.50 ± 0.03	0.96	0.09

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Table 3.  Column Densities and Abundances

Species	Column density (cm−2)	Abundancea
	G192N
H2b	(1.1 ± 0.1) × 1022	⋯
C18O	(2.5 ± 0.2) × 1015	(1.4 ± 0.2) × 10−6
H13CO+	(1.1 ± 0.1) × 1012	(5.2 ± 0.5) × 10−10
N2H+	(4.4 ± 0.6) × 1013	(2.1 ± 0.4) × 10−8
o-H2CO	∼1.5 × 1014	(4.1 ± 0.3) × 10−8
HDCO	(1.9 ± 0.1) × 1012	(5.0 ± 0.6) × 10−10
	G192S
H2b	(6.8 ± 0.2) × 1021	⋯
C18O	(2.8 ± 0.2) × 1015	(2.4 ± 0.2) × 10−6
H13CO+	(1.1 ± 0.1) × 1012	(8.4 ± 1.0) × 10−10
N2H+	(2.3 ± 0.5) × 1013	(1.8 ± 0.4) × 10−8
o-H2CO	∼1.1 × 1014	(2.9 ± 0.3) × 10−8
HDCO	(1.7 ± 0.1) × 1012	(7.3 ± 0.5) × 10−10

Notes.

^a Corrected with the filling factor as described in Section 3.3.2. ^b Derived from SCUBA-2 850 μm continuum as described in Section 3.2.

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3.3.2. Molecular Abundances from KVN Observations

Figure 11 shows the spectra of N₂H⁺ (1–0) toward G192N and G192S obtained with the KVN Yonsei 21 m telescope. We fitted the hyperfine structure of N₂H⁺ (1–0) with the pyspeckit package²⁷ assuming LTE. The excitation temperature T_ex(0), optical depth τ(0), systemic velocity v(0), and velocity dispersion of the central component are shown in the upper right corners in each panel. G192N has a lower excitation temperature and a higher optical depth than G192S, indicating that G192N might be colder and denser than G192S.

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Figure 12 shows spectra of other molecular transitions from the KVN single-dish observations. For G192N, both HCO⁺ (1–0) and o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) lines show clear line wing emission. The o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) line has a double-peak profile and larger line width than HCO⁺ (1–0), indicating that the profile of the o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) line is greatly affected by outflows. In contrast, the optically thin lines H¹³CO⁺ (1–0) and HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) have much smaller line widths and seem to be unaffected by outflow activities. Interestingly, HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) also has a double-peak profile, which might be a hint for rotation. The separation of the two peaks is ∼0.6 km s⁻¹, about 8 times larger than the spectral resolution (0.073 km s⁻¹). We will discuss the profile of HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) in Section 5.2. For G192S, both HCO⁺ (1–0) and o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) lines show weak line wings. H¹³CO⁺ (1–0) and HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) are single-peaked and have very narrow line widths. We fitted all the spectra with Gaussian profiles and listed the results in Table 2. In general, molecular lines of G192N have larger line widths than those of G192S. The systemic velocity for both G192N and G192S is 12 km s⁻¹, which is determined from optically thin lines (C¹⁸O (2–1), H¹³CO⁺ (1–0), and HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$)). For a kinetic temperature of 18.9 K, the sound speed is ∼0.24 km s⁻¹. We found that the nonthermal velocity dispersions (0.33–0.39 km s⁻¹) of all optically thin lines C¹⁸O (2–1), H¹³CO⁺ (1–0), and HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) toward G192N are larger than the sound speed. The nonthermal velocity dispersions (0.28–0.31 km s⁻¹) of C¹⁸O (2–1) and H¹³CO⁺ (1–0) toward G192S are also larger than the sound speed. The nonthermal velocity dispersion (0.20 ± 0.01 km s⁻¹) of HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) toward G192S is smaller than the sound speed, indicating that the line width of HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) contains a subsonic turbulent component, probably suggesting turbulence dissipation.

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We calculated the beam-averaged column densities of different molecular species in Appendix B and present them in Table 3. The abundance "X_m" of molecule "m" can be derived as

$$\begin{eqnarray}&&{X}_{{\rm{m}}}=\displaystyle \frac{{N}_{{\rm{m}}}\cdot {\eta }_{{\rm{m}}}}{{N}_{{{\rm{H}}}_{2}}\cdot {\eta }_{{\rm{c}}}},\end{eqnarray} \tag{ 1 }$$

where N_m, ${\eta }_{{\rm{m}}},$ ${N}_{{{\rm{H}}}_{2}}$, and ${\eta }_{{\rm{c}}}$ are the beam-averaged column density of molecule "m," filling factor of molecular line emission, beam-averaged column density of H₂ estimated from SCUBA-2 850 μm continuum, and filling factor of continuum emission, respectively. We remind the reader that our single-dish observations could not resolve the sources. In another Class 0 source, HH 212 located in the Orion complex, the extents of continuum and dense molecular line (e.g., HCO⁺) emissions are about 2''–5'' (Lee et al. 2014), which are much smaller than the beam sizes of JCMT and KVN. We assume that continuum and molecular line emissions have similar source sizes that are much smaller than the beam sizes of JCMT and KVN in G192N and G192S, $\displaystyle \frac{{\eta }_{{\rm{m}}}}{{\eta }_{{\rm{c}}}}\approx \frac{{\theta }_{\mathrm{KVN}}^{2}}{{\theta }_{\mathrm{JCMT}}^{2}},$where ${\theta }_{\mathrm{KVN}}$ and ${\theta }_{\mathrm{JCMT}}$ are the beam sizes of KVN and JCMT, respectively. Then the abundances were derived from Equation (1) and presented in the last column of Table 3. It should be noted that further higher angular resolution observations are needed to resolve the line and continuum emission to determine their source filling factors and to study the chemistry in detail.

G192N and G192S have a similar N₂H⁺ abundance. The H¹³CO⁺ abundance of G192S is about 1.6 times larger than that of G192N, indicating that H¹³CO⁺ in G192N might be as depleted as CO. The HDCO column densities of G192N and G192S are $(1.9\pm 0.1)\times {10}^{12}$ and $(1.7\pm 0.1)\times {10}^{12}$ cm⁻², respectively. The o-H₂CO column densities of G192N and G192S are ∼1.5 × 10¹⁴ and $\sim 1.1\times {10}^{14},$ respectively. Assuming that the ortho/para ratio for H₂CO is the statistical value of 3 (Roberts et al. 2002), the [HDCO]/[H₂CO] ratios of G192N and G192S are $(1.0\pm 0.1)\times {10}^{-2}$ and $(1.1\pm 0.1)\times {10}^{-2},$ respectively.

As shown in the left panel of Figure 13, G192N contains a compact condensation in SMA 1.3 mm continuum, which is marked with a red plus sign. Its peak position is R.A. (J2000) = 05^h29^m5416 and decl. (J2000) = $12^\circ 16^{\prime} 53\buildrel{\prime\prime}\over{.} 08$. Its deconvolved FWHM angular size is $1\buildrel{\prime\prime}\over{.} 26\times 0\buildrel{\prime\prime}\over{.} 36$ with a P.A. of 763, corresponding to a radius of 255 AU at a distance of 380 pc. As marked with a blue plus sign, G192S contains a relatively weak source, which was detected at a level of 9σ. Its peak position is R.A. (J2000) = 05^h29^m5435 and decl. (J2000) = $12^\circ 16^{\prime} 29\buildrel{\prime\prime}\over{.} 68$. That weak source has a deconvolved FWHM angular size of $2\buildrel{\prime\prime}\over{.} 45\times 1\buildrel{\prime\prime}\over{.} 43$ with a P.A. of −421, corresponding to a radius of 710 AU. The total fluxes of G192N and G192S in the 1.3 mm continuum are 0.223 and 0.013 Jy, respectively. The condensations detected in SMA observations are much more compact than the cold envelope traced by 850 μm continuum in JCMT/SCUBA-2 observations. The condensations G192N and G192S may be more affected by heating from protostars or outflows and should have higher dust temperatures. In Section 4.3, we will show evidence that the central region may be heated by outflows up to ∼30 K. Assuming a dust temperature of 30 K, the masses of G192N and G192S are 0.38 and 0.02 ${M}_{\odot },$ respectively. The volume densities of G192N and G192S are $7.2\times {10}^{8}$ and $1.9\times {10}^{6}$ cm⁻³. As shown in the right panel of Figure 13, we found that the emission peaks of SMA 1.3 mm continuum for both G192N and G192S are significantly offset from the emission peaks of the JCMT/SCUBA-2 850 μm continuum. The offsets for G192N and G192S are $\sim 5^{\prime\prime}$ and $\sim 7^{\prime\prime} ,$ respectively. Such offsets are much larger than the pointing error ($\sim 2^{\prime\prime}$) of the JCMT.

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As shown in the right panel of Figure 13, G192N is undetected in the Spitzer/IRAC 4.5 μm band. G192S shows extended 4.5 μm emission. The SMA 1.3 mm continuum emission of G192S coincides with 4.5 μm emission very well. To the west of G192S, another point source, G192SW, is seen in 4.5 μm emission but not in SMA 1.3 mm continuum emission, indicating that it might be a foreground or background star. In Figure 14, we present Spitzer/MIPS 70 and 24 μm emission as color images. G192N is not detected at Spitzer/MIPS 24 μm or IRAC bands but has a large envelope seen in Spitzer/MIPS 70 μm and 1.3 mm continuum from SMA observations. After subtracting a local background flux density of ∼44.9 MJy sr⁻¹, the total flux of G192N at 70 μm is 475 ± 15 mJy, corresponding to an internal luminosity of 0.21 ± 0.01 ${L}_{\odot }$ derived by using an empirical correlation between fluxes at 70 μm and internal luminosities (Dunham et al. 2008). The southern object (G192S) is a point source at Spitzer/MIPS 24 μm and has weak emission in Spitzer/MIPS 70 μm and 1.3 mm continuum. It has a flux of 184 ± 10 mJy at 70 $\mu {\rm{m}},$ corresponding to an internal luminosity of 0.08 ±0.01 ${L}_{\odot }.$ Owing to its low luminosity, we classify it as a very low luminosity object, i.e., a VeLLo (Di Francesco et al. 2007).

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It should be noted that we did not consider systematic effects (e.g., distance, calibration) on the internal luminosities. The uncertainties of internal luminosities caused by calibration uncertainties of fluxes at MIPS 70 μm are ∼20% (Evans 2007; Dunham et al. 2008). Additionally, if the distance was actually 10% higher, the internal luminosities can increase by ∼20%. Therefore, the internal luminosities estimated above have uncertainties of at least 20%.

Figure 15 shows the channel maps of ¹²CO (2–1) emission from the SMA observations. The ¹²CO (2–1) emission in the central channels [10, 14] km s⁻¹ is very clumpy. Blueshifted high-velocity emission associated with G192N is clearly seen from −2 to 9 km s⁻¹, indicating that the maximum outflow velocity can be up to ∼14 km s⁻¹ without correction of the inclination angle. In contrast, the redshifted high-velocity emission is much weaker, which can only be seen in channels from 15 to 17 km s⁻¹. From channel maps, one can also identify weak outflows associated with G192S. The blueshifted high-velocity emission of G192S can be seen from 7 to 9 km s⁻¹, while redshifted high-velocity emission is only apparent in the 15 km s⁻¹ channel. The integrated intensity of the high-velocity ¹²CO (2–1) emission is shown in Figure 16. The outflow associated with G192N is well collimated. As shown in the right panel of Figure 16, the outflow associated with G192S is very compact and its redshifted emission and blueshifted emission overlap. We listed the radius and maximum outflow velocity of each lobe in the second and third columns of Table 4, respectively. The outflow dynamical age (t_dyn) is estimated as ${t}_{\mathrm{dyn}}=2{R}_{\mathrm{lobe}}/{V}_{\mathrm{max}}$ and listed in the fourth column of Table 4. R_lobe is the radius of each outflow lobe.

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Table 4.  Parameters of CO Outflow in the SMA Observations

Lobesa	Radiusb	Vmax	Age	Mass	${\dot{M}}_{\mathrm{loss}}$	Fflow	${\dot{M}}_{\mathrm{acc}}$	Lacc
	(103 AU)	(km s−1)	(103 yr)	(10−5${M}_{\odot }$)	(10−8${M}_{\odot }\;{\mathrm{yr}}^{-1}$ )	(10−7${M}_{\odot }$ km s−1 yr−1)	(10−8${M}_{\odot }$ yr−1)	(10−5${L}_{\odot }$)
G192N-red	0.9	5	1.7	7.4	4.5	1.8	4.8	4.0
G192N-blue	1.8	14	1.2	45	36	22	58	430
G192S-red	0.8	3	2.6	1.6	0.6	0.2	0.5	0.1
G192S-blue	1.0	4	2.3	5.1	2.2	0.9	2.3	1.3

Notes.

^aOutflow lobes associated with G192N and G192S as shown in the left panel of Figure 16. ^bThe radius of each outflow lobe is defined as $R=\sqrt{a\cdot b},$ where a and b are the FWHM deconvolved sizes of the major and minor axes, respectively.

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The gas mass of the outflow can be estimated following Qiu et al. (2009):

$$\begin{eqnarray}{M}_{\mathrm{out}} & = & 1.39\times {10}^{-6}\mathrm{exp}(\displaystyle \frac{16.59}{{T}_{\mathrm{ex}}})({T}_{\mathrm{ex}}+0.92){D}^{2}\\ & & \times \displaystyle \int \displaystyle \frac{{\tau }_{12}}{1-{e}^{-{\tau }_{12}}}{S}_{v}{dv},\end{eqnarray} \tag{ 2 }$$

where M_out, T_ex, D, ${\tau }_{12}$, and S_v are the outflow gas mass in ${M}_{\odot },$ excitation temperature of ¹²CO (2–1), source distance in kpc, optical depth of ¹²CO (2–1), and line flux in Jy, respectively. The mass of each outflow lobe is presented in the fifth column of Table 4. We sum both redshifted and blueshifted outflow masses to derive total outflow mass. The total outflow masses for G192N and G192S are $\sim 5.3\times {10}^{-4}$ and $\sim 6.7\times {10}^{-5}$ ${M}_{\odot },$ respectively.

The mass-loss rate (${\dot{M}}_{\mathrm{loss}}$) of the outflow can be derived as ${\dot{M}}_{\mathrm{loss}}={M}_{\mathrm{out}}/{t}_{\mathrm{dyn}}.$ The total mass-loss rates of the outflows associated with G192N and G192S are $4.1\times {10}^{-7}$ and $2.8\times {10}^{-8}$ ${M}_{\odot }$ yr⁻¹. Under the assumption that jet energy and wind energy are due to the gravitational energy released by mass accretion onto the protostar, as stated in Bontemps et al. (1996), the outflow force (F_out) is related to the mass accretion rate (${\dot{M}}_{\mathrm{acc}}$) as given in the following equation obtained from the principle of momentum conservation and some manipulation of the equation:

$$\begin{eqnarray}&&{\dot{M}}_{{\rm{acc}}}=\displaystyle \frac{1}{{f}_{{\rm{ent}}}}\;\displaystyle \frac{{\dot{M}}_{{\rm{acc}}}}{{\dot{M}}_{{\rm{w}}}}\displaystyle \frac{1}{{V}_{{\rm{w}}}}\;{F}_{\mathrm{flow}}.\end{eqnarray} \tag{ 3 }$$

We assume a typical jet/wind velocity of ${V}_{{\rm{w}}}\sim 150$ km s⁻¹ (Bontemps et al. 1996). ${\dot{M}}_{{\rm{w}}}$ is the wind/jet mass-loss rate. Models of jet/wind formation predict, on average, ${\dot{M}}_{{\rm{w}}}/{\dot{M}}_{\mathrm{acc}}\quad \sim$ 0.1 (Pelletier & Pudritz 1992; Wardle and Königl 1993; Shu et al. 1994; Bontemps et al. 1996). The entrainment efficiency is typically ${f}_{{\rm{ent}}}\sim 0.1-0.25.$ Here we take 0.25. The outflow force F_flow is calculated as

$$\begin{eqnarray}&&{F}_{\mathrm{flow}}=\displaystyle \frac{{P}_{\mathrm{flow}}}{{t}_{\mathrm{dyn}}}=\displaystyle \frac{{M}_{\mathrm{out}}{V}_{\mathrm{char}}}{{t}_{\mathrm{dyn}}}={\dot{M}}_{\mathrm{out}}{V}_{\mathrm{char}},\end{eqnarray} \tag{ 4 }$$

where V_char is the characteristic outflow velocity, which is estimated from the intensity-weighted velocity. The calculated outflow forces and mass accretion rates are listed in the seventh and eighth columns, respectively. The total mass accretion rate for G192N is $6.3\times {10}^{-7}$ ${M}_{\odot }$ yr⁻¹, while the total mass accretion rate for G192S is $2.8\times {10}^{-8}$ ${M}_{\odot }$ yr⁻¹.

The accretion luminosity was calculated as

$$\begin{eqnarray}&&{L}_{\mathrm{acc}}=\displaystyle \frac{{{GM}}_{{\rm{acc}}}{\dot{M}}_{\mathrm{acc}}}{R}\;\;,\end{eqnarray} \tag{ 5 }$$

where ${M}_{\mathrm{acc}}={\dot{M}}_{\mathrm{acc}}\times {t}_{\mathrm{dyn}}$ is the mass accreted during a dynamical time. We present the accretion luminosity in the last column of Table 4. The total accretion luminosities for G192N and G192S are $4.3\times {10}^{-3}$ and $1.4\times {10}^{-5}$ ${L}_{\odot },$ respectively.

In Figure 17 we present the spectra of CO lines at the emission peak of the blueshifted lobe of G192N. The PMO 13.7 m CO (1–0) and CSO CO (2–1) lines show weak line wings with V_lsr up to 8 km s⁻¹ at the blueshifted side and 16 km s⁻¹ at the redshifted side, respectively. However, the blueshifted high-velocity emission in SMA CO (2–1) covers a much larger velocity range from −2 to 10 km s⁻¹. For comparison, we convolved the SMA data with the CSO beam and found that even for the low-velocity part (8–10 km s⁻¹) the CSO intensity is only 3–5 times larger than the SMA emission, while the blueshifted emission in SMA CO (2–1) is mainly dominated by higher-velocity (${V}_{\mathrm{lsr}}\lt 8$ km s⁻¹) gas. The SMA+CSO CO (2–1) emission recovers most of the missing flux at low velocities. However, the high-velocity outflow emission is not clearly seen in either CSO or SMA+CSO CO (2–1) emission, indicating that the outflow is very compact and its emission is totally diluted by single-dish observations. Therefore, it seems that the missing flux of the SMA is not significant for high-velocity outflow gas. The outflow mass or mass-loss rate should only be underestimated by a factor of <3–5 as a result of missing flux.

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The integrated intensity maps of SMA+CSO ¹²CO (2–1) and ¹³CO (2–1) emissions are shown in panels (a) and (b) of Figure 18, respectively. The ¹²CO (2–1) emission has two emission peaks, which are offset from the 1.3 mm continuum emission. The ¹³CO gas is highly fragmented. All the ¹³CO emission peaks are also away from the 1.3 mm continuum peaks. We derived the excitation temperature of ¹²CO (2–1) emission from Equation (10) assuming that its emission is optically thick. The excitation temperature is shown as a color image in panel (c) of Figure 18. Assuming that ¹³CO (2–1) emission has the same excitation temperature as ¹²CO (2–1) emission under LTE conditions, we derived the column density of H₂ from Equation (9) by adopting typical abundance ratios [H₂]/[¹²CO] = 10⁴ and [¹²CO]/[¹³CO] = 60. The H₂ column density map revealed from SMA+CSO ¹³CO (2–1) emission data is shown in panel (d) of Figure 18. We identified nine fragments from the column density map within its 50% contour, as shown in Figure 19. From Gaussian fits, their peak positions, radii (R), and peak column densities (N${}_{{{\rm{H}}}_{2}}$) are derived and shown in columns (2)–(4) in Table 5. Their volume densities (n${}_{{{\rm{H}}}_{2}}$) and masses (M_LTE) are calculated as ${n}_{{{\rm{H}}}_{2}}=\frac{{N}_{{{\rm{H}}}_{2}}}{2R}$ and ${M}_{\mathrm{LTE}}=\displaystyle \frac{4}{3}\pi {R}^{3}\cdot {n}_{{{\rm{H}}}_{2}}\cdot {m}_{{\rm{H}}}\cdot {\mu }_{{\rm{g}}},$ respectively. The Jeans masses of the fragments are derived following Wang et al. (2014):

$$\begin{eqnarray}&&{M}_{J}=\displaystyle \frac{{\pi }^{5/2}{c}_{s}^{3}}{6\sqrt{{G}^{3}\rho }}=0.877{M}_{\odot }{(\displaystyle \frac{T}{10{\rm{K}}})}^{3/2}{(\displaystyle \frac{n}{{10}^{5}{\mathrm{cm}}^{-3}})}^{-1/2}.\end{eqnarray} \tag{ 6 }$$

We use the mean excitation temperature of ¹²CO (2–1) emission to derive the Jeans mass for each fragment. The M_LTE and M_J are shown in the last two columns of Table 5. We find that the gas fragments have Jeans masses significantly larger than their LTE masses, indicating that the gas fragments will not collapse but will be dispersed eventually.

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Table 5.  Parameters of ¹³CO Fragments in the SMA+CSO Observations

Fragment	Offseta	Radius	N${}_{{{\rm{H}}}_{2}}$	n${}_{{{\rm{H}}}_{2}}$	Tex	MLTE	MJ
	(arcsec, arcsec)	(10−2 pc)	(1021 cm−2)	(104 cm−3)	(K)	(10−1 ${M}_{\odot }$)	(M${}_{\odot }$)
a	(10.13, 8.53)	1.6	8.4	8.5	15	1.0	1.7
b	(9.08, −0.10)	2.3	12.4	8.7	17	3.1	2.1
c	(4.68, −17.82)	1.4	7.8	9.0	12	0.7	1.2
d	(5.80, −27.82)	2.2	9.6	7.1	12	2.2	1.4
e	(−29.19, −12.43)	3.2	9.0	4.6	10	4.3	1.3
f	(−17.28, 3.14)	1.5	4.9	5.3	17	0.5	2.7
g	(−14.55, 12.62)	3.3	9.2	4.5	16	4.7	2.6
h	(7.60, 32.31)	2.2	8.9	6.6	10	2.0	1.1
i	(12.96, 32.92)	<0.8	4.6	9.3	10	0.1	0.9

Note.

^aOffset from phase center R.A. (J2000) = 05^h29^m5432 and decl. (J2000) = $12^\circ 16^{\prime} 40\buildrel{\prime\prime}\over{.} 50$.

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As shown in Figure 18, the two continuum sources G192N and G192S are located in the cavities enclosed by the gas fragments, indicating that the gas distribution may be affected by ongoing star formation. In Figure 20, we plot the outflow emission contours on the excitation temperature of ¹²CO (2–1) emission. Interestingly, we find that the CO gas at the blueshifted outflow lobe has the highest excitation temperature (∼30 K), hinting at outflow heating.

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We integrated SMA ¹²CO (2–1) emission between 10 and 14 km s⁻¹ and present the integrated intensity in Figure 21. We identified eight dense and compact fragments with integrated intensity larger than 30% of the peak value 15.52 Jy beam⁻¹ km s⁻¹. Figure 22 shows the beam-averaged spectra of ¹²CO (2–1) toward each fragment. We fitted the spectra with Gaussian profiles and presented the fitted results in Table 6.

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Table 6.  Parameters of CO Fragments in the SMA Observations

Fragment	Offseta	Area	Vlsr	FWHM	Ipeak	rms
	(arcsec, arcsec)	(Jy beam−1 km s−1)	(km s−1)	(km s−1)	(Jy beam−1)	(mJy beam−1)
G192N	(−2.38, 12.58)	5.06 ± 0.17	9.07 ± 0.04	4.74 ± 0.19	1.00	42.9
	(−2.38, 12.58)	2.99 ± 0.14	15.16 ± 0.07	3.39 ± 0.17	0.83	42.9
G192S	(0.51, −10.82)	6.77 ± 0.11	11.55 ± 0.04	5.02 ± 0.09	1.26	42.1
1	(−11.76, 16.33)	6.32 ± 0.12	13.51 ± 0.02	2.52 ± 0.05	2.35	50.7
2	(4.78, 5.93)	2.74 ± 0.08	0.24 ± 0.09	5.21 ± 0.10	0.49	24.4
	(4.78, 5.93)	3.00 ± 0.01	5.14 ± 0.08	4.30 ± 0.12	0.65	24.4
	(4.78, 5.93)	12.59 ± 0.08	11.26 ± 0.02	5.70 ± 0.03	2.07	24.4
3	(−14.61, 3.52)	5.45 ± 0.05	13.84 ± 0.01	2.88 ± 0.03	1.77	39.3
4	(5.87, −8.75)	7.85 ± 0.10	11.36 ± 0.01	2.85 ± 0.04	2.58	40.8
5	(0.40, −9.19)	19.14 ± 0.10	11.61 ± 0.01	5.14 ± 0.03	3.49	46.3
6	(−4.86, −8.31)	9.16 ± 0.07	14.08 ± 0.01	3.06 ± 0.03	2.81	24.7
7	(8.61, −22.33)	4.22 ± 0.19	11.73 ± 0.06	3.15 ± 0.17	1.25	72.4
8	(−6.50, −23.31)	5.45 ± 0.17	12.23 ± 0.08	4.98 ± 0.18	1.02	50.9

Note.

^aOffset from phase center R.A. (J2000) = 05^h29^m5432 and decl. (J2000) = $12^\circ 16^{\prime} 40\buildrel{\prime\prime}\over{.} 50$.

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Except for G192N, the spectra of ¹²CO (2–1) emission at other positions are all single-peaked. The SMA ¹²CO (2–1) spectrum toward G192N shows a typical "blue profile" with the blueshifted emission peak stronger than the redshifted peak, a signature for infall motions (Zhou et al. 1993). The nondimensional parameter $\delta V=({V}_{\mathrm{thick}}-{V}_{\mathrm{thin}})/{\rm{\Delta }}{V}_{\mathrm{thin}}$ is usually used to quantify the spectral line asymmetries (Mardones et al. 1997). Here V_thick is the peak velocity of the optically thick line; V_thin and ${\rm{\Delta }}{V}_{\mathrm{thin}}$ are the peak velocity and line width of the optically thin line, respectively. Infall candidates will have $\delta V\lt -0.25.$ In the case of G192N, the $\delta V$ derived from the SMA ¹²CO (2–1) line and CSO C¹⁸O (2–1) line is −3.1, much smaller than −0.25, indicating that the SMA ¹²CO (2–1) line toward G192N might trace an infalling envelope. However, such a double-peak profile might also be caused by outflows as shown by the o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) line (Figure 12) or missing flux. We do not see such a double-peak profile in the SMA+CSO combined spectra because the combined data are dominated by large-scale extended emission. Higher angular resolution and higher-sensitivity observations of dense molecular tracers (e.g., HCN, HCO⁺) are needed to resolve the envelope to test the infall scenario.

Fragments 1 and 3 have velocities ∼1.5 and ∼1.8 km s⁻¹, respectively, blueshifted with respect to the systemic velocity (12 km s⁻¹). Fragment 2, which is close to the blueshifted outflow lobe, is greatly affected by the outflow. The ¹²CO (2–1) line of fragment 2 can be fitted with three Gaussian components with velocities at ∼0.2, ∼5.1, and ∼12.6 km s⁻¹, respectively. The components at ∼0.2 and ∼5.1 km s⁻¹ trace outflow gas with different velocities, hinting that the outflow jet might be episodically changing. The line width of the ∼12.6 km s⁻¹ component toward fragment 2 is more than two times larger than that of fragments 1 and 3, indicating that the ¹²CO (2–1) emission at fragment 2 may be broadened by the outflow shocks. Fragments 4, 5, and 6 are connected and located close to G192S. Fragment 6 has a velocity about 2.5 km s⁻¹ redshifted to that of fragment 5, indicating that fragment 6 is impelled by the outflows. G192S itself is about 16 south of fragment 5. The peak intensity of the ¹²CO (2–1) line toward G192S is only about one-third of that of fragment 5. It seems that G192S has moved out of its natal core. Fragments 7 and 8 are located in a filament.

In conclusion, we think that the feedback of star-forming activities (e.g., outflow shocks) in this region can propel, heat, unbind, and disperse the surrounding gas.

As shown in Table 3, the C¹⁸O and H¹³CO⁺ abundances in G192N are smaller than those in G192S, indicating that a larger amount of CO is frozen out in icy mantles, which results in a depletion of HCO⁺ in G192N. As a major destroyer of N₂H${}^{+},$ the absence of CO in the gas phase could enhance the abundance of N₂H${}^{+}.$ Indeed, the N₂H⁺ abundance in G192N is larger than that in G192S. In Figure 23, we compared the N₂H⁺ and H¹³CO⁺ abundances in G192N and G192S with that of other dense cores in the Orion A cloud (Ohashi et al. 2014). In protostellar cores, the N₂H⁺ and H¹³CO⁺ column densities are correlated with each other (Ohashi et al. 2014). The N₂H⁺ and H¹³CO⁺ column densities in G192S follow this correlation well. This behavior has also been observed in a large sample of IRDC clumps (Sanhueza et al. 2012), while G192N seems to have a relatively larger N₂H⁺-to-H¹³CO⁺ abundance ratio than other protostellar cores. In warm regions, CO evaporation could destroy N₂H⁺ and enhance the abundance of HCO⁺ by the following reaction (Lee et al. 2004; Busquet et al. 2011):

$$\begin{eqnarray}&&{{\rm{N}}}_{2}{{\rm{H}}}^{+}+\mathrm{CO}\to {\mathrm{HCO}}^{+}+{{\rm{N}}}_{2}.\end{eqnarray} \tag{ 7 }$$

The larger N₂H⁺-to-H¹³CO⁺ abundance ratio in G192N indicates that G192N is much colder and is thus chemically younger than other protostellar cores, including G192S.

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In a survey of low-mass protostellar cores, Roberts et al. (2002) found that the observed [HDCO]/[H₂CO] abundance ratios are ∼0.05–0.07. These ratios are larger than those of G192N and G192S. Bell et al. (2011) found that turbulent mixing in clouds could reduce the efficiency of deuteration by increasing the ionization fraction and reducing freeze-out of heavy molecules. The low [HDCO]/[H₂CO] ratios (∼1 × 10⁻²) in G192N and G192S could be produced in their chemical models at very early evolutionary stages, i.e., with a chemical age less than $\lt 1\times {10}^{4}$ yr (Bell et al. 2011). As shown in the left panel of Figure 13, we notice that G192N and G192S are surrounded by extended warm dust emission as traced by 70 μm continuum. The 70 μm continuum even shows a bar-like structure close to the southern edge of the cloud, probably indicating the existence of an ionization front (IF). The IF from the H ii region can heat the cloud and increase its ionization fraction, leading to lower abundances of deuterated species in prestellar phase as described in Bell et al. (2011). Therefore, we argue that the chemistry in PGCC G192.32–11.88 might be greatly affected by stellar feedback of the H ii region. However, we notice that the small value of the [HDCO]/[H₂CO] ratio could also be partly attributed to the very different emission regions traced by these two isotopologues. This can be deduced from the very different line widths of the two lines (Figure 12). o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) could have a significant contribution from either outflow regions or a large volume of turbulent clouds, while HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) may come from a compact region, which needs to be confirmed by further higher angular resolution observations in future.

Anyway, G192N and G192S are more chemically evolved than starless cores but might be still at earlier evolutionary stages than most protostellar objects so far observed.

In Figure 24, we compare the infrared properties of G192N with other candidates of young Class 0 protostars (e.g., PACS Bright Red Sources [PBRSs]; Stutz et al. 2013; Tobin et al. 2015), which are deeply embedded in dense envelopes and are also either too faint (m${}_{24}\;\gt$ 7 mag) or undetected in the Spitzer/MIPS 24 μm band. Those PBRSs are very rare, and only 18 were identified in the whole Orion molecular cloud (Stutz et al. 2013). G192N is located in the same region as PBRSs in both the 70 μm flux versus 70-to-24 μm flux ratio plot and the 70-to-24 μm flux ratio versus 870-to-70 μm flux ratio plot, indicating that G192N should have similar properties as PBRSs. As shown in the upper panels of Figure 25, the bolometric temperature and luminosity of PBRSs in the Orion complex are strongly correlated to the flux of 70 μm emission (Stutz et al. 2013). Assuming that G192N also follows these relationships, the bolometric temperature and luminosity of G192N are derived as ∼30 K and ∼0.8 ${L}_{\odot }$, respectively. As shown in the lower panel of Figure 25, G192N is also located in the same region as PBRSs in the T_bol versus L_bol plot. When compared with other Class 0 protostars, PBRSs (including G192N) have relatively low bolometric temperatures. G192N itself has a relatively smaller bolometric luminosity when compared with other PBRSs.

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In a survey of 15 Class 0 protostars, Yıldız et al. (2015) found that the median values of outflow mass and outflow mass-loss rate are $1.7\times {10}^{-2}$ ${M}_{\odot }$ and $3.3\times {10}^{-5}$ ${M}_{\odot }$ yr⁻¹, respectively, which are about two orders of magnitude larger than those values of the outflow associated with G192N. But we should note that the outflow parameters in Table 4 were not corrected with missing flux and inclination angle. As mentioned in Section 4.2, the outflow mass or mass-loss rate could be underestimated by a factor of <3–5 owing to missing flux. Since the blue and red components of the elongated outflow are well separated, neither the very low (pole-on) inclination nor the very high (edge-on) inclination is likely. The outflow mass-loss rate and accretion rate can increase by a factor of ∼1.6 and 2.9, respectively, at the mean angle of 573 of random outflow inclination. Even considering these effects, the outflow mass and outflow mass-loss rate of G192N are still about one order of magnitude smaller than those of other protostars. Therefore, we argue that G192S probably has the outflow with the lowest mass and mass-loss rate among known Class 0 sources.

As mentioned in Section 3.3.2, the HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) line of G192N has a double-peak profile. The line width of HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) is much smaller than that of the o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) line, indicating that its line emission is not affected by outflow activities. The critical density of HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) is much larger than those of other lines (e.g., J = 1–0 of N₂H⁺ and H¹³CO) and therefore could trace the inner envelope or disk. Therefore, the double-peak profile of HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) might be produced by rotation. If that is true, we can estimate a dynamical mass M_dyn by

$$\begin{eqnarray}&&{M}_{\mathrm{dyn}}=\displaystyle \frac{{{Rv}}_{\mathrm{rot}}^{2}}{G},\end{eqnarray} \tag{ 8 }$$

where R is the distance to the object of mass M creating the gravitational field, G is the gravitational constant, and v_rot is the rotational velocity. Taking R of 255 AU as estimated from SMA 1.3 mm continuum and v_rot of 0.3 km s⁻¹, which is half of the velocity separation of the two emission peaks, the dynamical mass is inferred to be ∼0.026 ${M}_{\odot },$ much smaller than that of other Class 0 sources (Yen et al. 2015).

In general, when compared with other young Class 0 sources in the Orion complex, G192N has potentially the smallest stellar mass and lowest bolometric luminosity and accretion rate, indicating that G192N might be at an earlier evolutionary phase than other Class 0 sources. The formation of the central protostar must be preceded by the formation of a larger, less dense, first hydrostatic core (hereafter FHSC; Larson 1969). The FHSC thus represents an intermediate evolutionary stage between the prestellar and protostellar phases. Theoretical works indicate that FHSCs might have a maximum mass of 0.01–0.1 ${M}_{\odot },$ lifetime of 0.5–50 kyr, and internal luminosity of 10⁻⁴-10⁻¹${L}_{\odot }$ (Dunham et al. 2014). Their spectral energy distributions (SEDs) are characterized by emission from 10–30 K dust and no observable emission below ∼20–50 μm (Dunham et al. 2014). As mentioned before, G192N is not visible at 24 μm or shorter wavelength bands. The stellar mass (∼0.026 ${M}_{\odot }$) and lifetime (1.2–1.7 kyr) estimated from outflows of G192N are consistent with the predictions of FHSCs. However, the internal luminosity (0.21 ± 0.01 ${L}_{\odot }$) of G192N is slightly larger than the upper limit of that of FHSCs. Machida et al. (2008) showed that FHSCs drive slow (∼5 km s⁻¹) outflows with wide opening angles, while Price et al. (2012) showed that FHSCs can indeed produce tightly collimated outflows with speeds of ∼2–7 km s⁻¹. The maximum outflow speed (>14 km s⁻¹) of G192N runs against the predictions for FHSCs. However, it should be noted that velocities >9 km s⁻¹ would not be reached in the simulations of Price et al. (2012) owing to the 5 AU size of the central sink particle. When compared with other FHSC candidates (Dunham et al. 2014, and references therein), G192N is more luminous and has a more energetic outflow. Therefore, although G192N shares some similar properties to predicted FHSCs, it might be more evolved than FHSCs. G192N might be among the youngest Class 0 sources, which are slightly more evolved than an FHSC.

To summarize, we could not exclude the possibility that G192N is a relatively more evolved Class 0 object in the low-mass end of the Class 0 type distribution. Considering its low envelope mass, which is 0.35–0.43 ${M}_{\odot }$ from SMA and JCMT/SCUBA-2 observations, G192N may only form a very low mass hydrogen-burning star (M$\leqslant \;0.2$ ${M}_{\odot }$) assuming a typical core-to-star formation efficiency of 30% (Alves et al. 2007; André et al. 2014). However, the dynamical age of the outflow is (1.2–1.7) × 10³ yr, which decreases to (0.8–1.1) × 10³ yr at an outflow inclination angle of 573, indicating that G192N should be at a very early evolutionary phase.

As shown in Figure 26, we fitted the SED of G192S with a YSO SED fitting tool (Robitaille et al. 2006, 2007). The stellar mass, disk mass, and envelope mass of the best-fit model are 0.12 ${M}_{\odot },$ $7.43\times {10}^{-3}$ ${M}_{\odot },$ and 0.27 ${M}_{\odot },$ respectively. The envelope mass is consistent with that estimated from JCMT/SCUBA-2 850 μm continuum emission. The stellar age is $8.2\times {10}^{4}$ yr. The disk and envelope accretion rates are $1.5\times {10}^{-8}$ ${M}_{\odot }$ yr⁻¹ and $1.8\times {10}^{-5}$ ${M}_{\odot }$ yr⁻¹, respectively, indicating that G192S is still at the evolutionary stage 0/I (Robitaille et al. 2006, 2007). G192S also probably has a much smaller stellar mass and envelope mass than the values estimated from SED fitting because (a) the minimum stellar mass in model SEDs of Robitaille et al. (2006, 2007) is 0.1 ${M}_{\odot }$, and thus those model SEDs could not fit stellar masses below 0.1 ${M}_{\odot };$ (b) the modeled 70 μm flux is more than 2 times larger than the observed value, indicating that the stellar mass should be overestimated; (c) as shown in the left panel of Figure 13, the 4.5 μm emission of G192S is offset from the core center in JCMT/SCUBA-2 850 μm emission, indicating that G192S might have a much smaller envelope mass than that estimated from SED modeling or JCMT/SCUBA-2 850 μm continuum emission (d). Its Vega magnitudes at Spitzer/IRAC 3.4 (ch1) and 4.5 (ch2) μm bands are 14.613 ± 0.009 and 12.836 ± 0.001 mag, respectively, which are compliant with the criteria (ch1-ch2 $\geqslant$ 1.5, ch2 $\leqslant \;17.0$ mag) for brown dwarf candidates (Griffith et al. 2012). Therefore, we suggest that G192S is more likely forming a brown dwarf (M$\;\leqslant \;0.075$M${}_{\odot }$).

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The accretion rate and accretion luminosity for G192S are comparable to or orders of magnitude smaller than that of other proto-brown dwarf candidates (Lee et al. 2009; Palau et al. 2014; Morata et al. 2015). For example, the typical proto-brown dwarf L328-IRS has an accretion rate and accretion luminosity of $3.6\times {10}^{-7}$ ${M}_{\odot }$ yr⁻¹ and 0.02 ${L}_{\odot }$ (Lee et al. 2009), which are about one order of magnitude larger than those of G192S. Its extremely low accretion rate (2.8 × 10⁻⁸${M}_{\odot }$ yr⁻¹) also indicates that G192S is indeed likely to form a brown dwarf. Additionally, the 4.5 μm emission and SMA 1.3 mm continuum emission of G192S (Figure 13) are clearly offset from SCUBA-2 850 μm continuum emission and CO gas fragments, indicating that G192S might have moved out of its natal envelope. The total mass estimated from SMA 1.3 mm continuum emission is only 0.02 ${M}_{\odot },$ which is insufficient for accretion to form a low-mass or very low mass star. In conclusion, we argue that G192S is an ideal proto-brown dwarf candidate.

PGCC G192.32–11.88 is a typical bright-rimmed cloud. As shown in Figure 1, it is surrounded by Hα emission from the H ii region. The Spitzer  70 μm continuum emission reveals hot dust inside PGCC G192.32–11.88 and possibly also traces the IF in the south. The velocity and temperature gradients revealed in line emissions of CO isotopologues also indicate that the cloud might be compressed by the H ii region. All this evidence suggests that star formation in PGCC G192.32–11.88 should be affected by the feedback of the H ii region.

The total mass of the dense cores G192N and G192S in Clump-S is 0.63 ± 0.06 ${M}_{\odot }.$ Assuming a typical core-to-star formation efficiency of 30%, the total eventual stellar mass of Clump-S should be about 0.2 ${M}_{\odot }.$ By comparing with the total clump mass (49 ± 3 or 59 ± 10 ${M}_{\odot }$) derived from CO isotopologues or virial analysis, we infer an SFE of ∼0.3%–0.4% in the southern clump of PGCC G192.32–11.88. Such a low SFE is about one order of magnitude lower than that (3%–6%) in nearby GMCs (Evans et al. 2009). We can also calculate a core formation efficiency (CFE), ${M}_{\mathrm{core}}/({M}_{\mathrm{cloud}}+{M}_{\mathrm{core}}).$ The CFE of the southern clump in PGCC G192.32–11.88 is ∼1%. When compared with the CFE in the whole L1641 cloud, which is ∼4% and increases to the dense filaments, which is 12% (Polychroni et al. 2013), the CFE in PGCC G192.32–11.88 is much lower. It seems that star formation in PGCC G192.32–11.88 is greatly suppressed.

Additionally, as mentioned in Section 4.1, we found that G192N and G192S significantly depart from their parent cores along the direction of the velocity/temperature gradient. This offset is more evident for G192S. G192S departs about 7'' from the SCUBA-2 850 μm emission and 16 from the nearest CO clump in SMA observations. It seems that G192N and G192S will move out of their parent cores, or their envelopes will be blown away owing to photo-erosion during their formation. Since G192S is close to the IF, its formation is very similar to the brown dwarf formation model of Whitworth & Zinnecker (2004), in which a prestellar core's growth to a normal star is limited by photo-erosion of the ionizing radiation from a nearby OB star. We need further observations to test this scenario. Additionally, we note that a large population of brown dwarfs has been discovered in the λ Orionis complex (Barrado y Navascués et al. 2004, 2007; Bouy et al. 2009; Bayo et al. 2011, 2012). Those brown dwarfs are not located at the edges of star cluster as the ejection mechanism would predict (Bayo et al. 2011), indicating that other mechanisms (like photo-erosion) may be responsible for the brown dwarf formation in the λ Orionis complex.

At any rate, the stellar feedback seems to have a very negative effect on the star formation in PGCC G192.32–11.88.

The column density of N₂H⁺ is calculated as (Furuya et al. 2006)

$$\begin{eqnarray}{N}_{{{\rm{N}}}_{2}{{\rm{H}}}^{+}} & = & 3.30\times {10}^{11}\displaystyle \frac{{T}_{\mathrm{ex}}+0.75}{1-{e}^{-4.47/{T}_{\mathrm{ex}}}}(\displaystyle \frac{{\tau }_{\mathrm{tot}}}{1.0})\\ & & \times (\displaystyle \frac{{\rm{\Delta }}v}{1.0\;\mathrm{km}\;{{\rm{s}}}^{-1}})\;{\mathrm{cm}}^{-2},\end{eqnarray} \tag{ 14 }$$

where ${\tau }_{\mathrm{tot}}$ and ${\rm{\Delta }}v$ are the total optical depth and line width obtained from the N₂H⁺ spectra through the HFS analysis.

The optical depth of HCO⁺ (1–0) (${\tau }_{12}$) can be derived using Equation (11) from the intensity ratio of HCO⁺ (1–0) to H¹³CO⁺ (1–0). After determining the optical depth of HCO⁺ (1–0), its excitation temperature can be derived from Equation (10) assuming that the filling factor is 1. In Figure 27, the intensity ratio of HCO⁺ (1–0) to H¹³CO⁺ (1–0) and excitation temperature of HCO⁺ (1–0) calculated with Equations (10) and (11) are plotted as a function of optical depth of HCO⁺ (1–0). It can be seen that the excitation temperature of HCO⁺ (1–0) stays constant when optical depths are larger than ∼10. The excitation temperatures of HCO⁺ (1–0) toward G192N and G192S are 6.79 and 7.11 K, respectively. Assuming that H¹³CO⁺ (1–0) has the same excitation temperature as HCO⁺ (1–0), the column density of H¹³CO⁺ can be derived from (Furuya et al. 2006)

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}=2.32\times {10}^{11}\displaystyle \frac{{T}_{\mathrm{ex}}+0.69}{1-{e}^{-4.16/{T}_{\mathrm{ex}}}}(\displaystyle \frac{1}{J({T}_{{\rm{ex}}})-J({T}_{{\rm{bg}}})})\\ &&\times (\displaystyle \frac{\displaystyle \int {T}_{b}{dv}}{1.0\;{\rm{K}}\;\mathrm{km}\;{{\rm{s}}}^{-1}})\;{\mathrm{cm}}^{-2}.\end{eqnarray} \tag{ 15 }$$

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We estimated the column density of o-H₂CO with RADEX. We adopted a kinetic temperature of 18.9 K, as determined from CO isotopologues. We convolved the SCUBA-2 850 μm data with the KVN beam (24''). Then we derived a mean volume density of $2.1\times {10}^{4}$ cm⁻³ from the Gaussian fit toward the continuum source. Since o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) has a much higher critical density than J = 1–0 and 2–1 transitions of CO isotopologues (Shirley 2015), we adopt $2.1\times {10}^{4}$ cm⁻³ in RADEX calculations. From RADEX calculations, we found that the column density and excitation temperature of o-H₂CO found in G192N are ∼1.1 × 10¹⁵ cm⁻² and ∼5.0 K, respectively. For G192S, the column density and excitation temperature of o-H₂CO are ∼7.8 × 10¹⁴ cm⁻² and ∼5.3 K, respectively.

Assuming that HDCO (${2}_{\mathrm{0,2}}-{1}_{\mathrm{0,1}}$) is optically thin and has the same excitation temperature as o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$), the column density of HDCO can be calculated following Roberts et al. (2002):

$$\begin{eqnarray}&&{N}_{\mathrm{TOT}}={N}_{{\rm{u}}}Q({T}_{\mathrm{ex}}){e}^{-{E}_{{\rm{u}}}/{{kT}}_{\mathrm{ex}}}/{g}_{{\rm{u}}},\end{eqnarray} \tag{ 16 }$$

where N_TOT is the total column density, Q(Tex) is the partition fraction, and g_u is the degeneracy factor in the upper energy level. N_u is the column density in the upper level of the transition:

$$\begin{eqnarray}&&{N}_{{\rm{u}}}=\displaystyle \frac{8\pi k{\nu }^{2}}{{A}_{{ul}}{{hc}}^{3}}\int {T}_{{\rm{b}}}{dv}.\end{eqnarray} \tag{ 17 }$$

The HDCO column densities of G192N and G192S are $(1.9\pm 0.1)\times {10}^{12}$ and $(1.7\pm 0.1)\times {10}^{12}$ cm⁻², respectively. Assuming that the ortho/para ratio for H₂CO is the statistical value of 3 (Roberts et al. 2002), the [HDCO]/[H₂CO] ratios of G192N and G192S are $(1.0\pm 0.1)\times {10}^{-2}$ and $(1.1\pm 0.1)\times {10}^{-2},$ respectively.

We can also calculate the o-H₂CO column density with Equation (16). In the optically thin case, the o-H₂CO column densities of G192N and G192S are ∼1.2 × 10¹⁴ and ∼7.1 × 10¹³ cm⁻², respectively. The corresponding [HDCO]/[H₂CO] ratios of G192N and G192S are $\sim 1.6\times {10}^{-2}$ and $\sim 1.4\times {10}^{-2},$ respectively, which are larger than the values obtained from RADEX calculations and should be taken as upper limits. In the optically thick case, the column density of o-H₂CO should be corrected with a factor of $\displaystyle \frac{\tau }{1-{e}^{-\tau }},$ where τ is the optical depth of o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$). The excitation temperatures of o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) toward G192N and G192S derived from RADEX calculations are consistent with the values derived by assuming LTE and that o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) emission is optically thick ($\tau \gt 5$), as shown in the upper panel of Figure 28. In the lower panel of Figure 28, we show the [HDCO]/[H₂CO] ratio as a function of the optical depth of o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$). When compared with the value derived in the optically thin case, the [HDCO]/[H₂CO] ratio decreases by a factor of larger than five if the optical depth of o-H₂CO (${2}_{\mathrm{1,2}}-{1}_{\mathrm{1,1}}$) is larger than 6. Therefore, we argue that [HDCO]/[H₂CO] ratios of G192N and G192S might be even lower than 0.01, which needs to be confirmed by further observations.

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