Dust Polarization toward Embedded Protostars in Ophiuchus with ALMA. III. Survey Overview

We selected 26 protostellar systems (Class 0 and Class I) from the surveys of Enoch et al. (2009), Evans et al. (2009), and Connelley & Greene (2010). Table 1 lists the sources in our sample. Column (1) gives the field name based on their numerical identification in the cores to disks (c2d) survey (Evans et al. 2009) or in common literature. Since VLA 1623 and IRAS 16293-2422 have bright companions at ≳5'' separation, we observed both sources with separated pointings so that we could detect their polarization within the inner third of the primary beam (as required by ALMA specifications for polarization data). These are denoted with "a" and "b" in the field name. Column (2) gives other common names of the sources from the literature. Columns (3) and (4) give the phase center for each field, and Column (5) gives the region of Ophiuchus in which the source is found following the boundaries in Young et al. (2006) and Pattle et al. (2015). Column (6) lists the classification of the source from the literature. Finally, Column (7) lists other known young stellar objects (YSOs) that are detected in each field.

This sample includes all the known Class 0 objects and the embedded Class I sources in Ophiuchus. Source classifications were determined using the standard definitions of the infrared spectral index, α_IR, and the bolometric temperature as summarized in Evans et al. (2009). For the Class I sources, we selected all the stars that had unambiguous envelope detections based on previous single-dish observations (e.g., Enoch et al. 2009) to ensure that the stars are young and still embedded. Three YSOs (c2d_839, c2d_914, c2d_922) have "envelope" designations (Enoch et al. 2009) but appear more evolved with α_IR < 0.3 and T_bol ≳ 600 K (Evans et al. 2009; Dunham et al. 2015). We excluded these sources from our sample. We also added ISO Oph 210 (IRAS 16266-2450E¹³ ) to our source list. This object was not featured in the "c2d" catalog but is listed as a YSO in Hsieh & Lai (2013).

We note, however, that the original classifications for the YSOs in Ophiuchus have come under considerable question (e.g., McClure et al. 2010). In particular, McClure et al. (2010) found that 16/26 "embedded" objects in Ophiuchus were at more evolved stages using infrared spectroscopy. They attributed the difference to substantial foreground extinctions such that measurements of the infrared spectral index are unreliable for Ophiuchus. In Appendix A, we revisit the source classifications for the targets in our sample using archival data to help inform their evolutionary stages.

Figure 1 shows the position of each of our 28 fields on a SCUBA-2 850 μm from Pattle et al. (2015). The SCUBA-2 data are part of data release 3 (DR3), with details on the reduction and imaging given in Kirk et al. (2018). The full Ophiuchus data set has been cropped to focus on L1688, L1689, and L1709. The pointings are color-coded by the regions given in Table 1.

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The 28 pointings were observed at 1.3 mm in full polarization on 2017 May 20, July 11, and July 14 on shared tracks as part of the Cycle 3 program 2015.1.01112.S.¹⁴ The baselines ranged from 15.1 to 1124.3 m for the May observations and 16.7–2647.3 m for the July observations. The precipitable water vapor ranged from 0.38 mm on July 11, 0.94 mm on May 20, and 1.22 mm on July 14. There were 46 antennas on May 20, 43 antennas on July 11, and 42 antennas on July 14. The correlator was configured to the standard full polarization setting for Band 6, with each baseband set to 1.875 GHz bandwidth and 64 channels, centered at 224, 226, 240, and 252 GHz.

For all tracks, J1517-2422 was used for bandpass calibration, J1625-2527 was the calibrator for complex gain and phase, and J1549+0237 was the polarization leakage calibrator. J1517-2422 was also used for absolute flux calibration on the May 20 and July 14 executions, with J1733-1304 as the absolute flux calibration on July 11. To ensure sufficient parallactic angle coverage with J1549+0237, each track was observed over 3–4.5 hr, using two or three consecutive sessions. Typically, all the sessions contained observations of each calibrator. The third session from July 11 did not include the bandpass and flux calibrators and instead used the bandpass solutions from the second session and the complex gain calibrator for absolute flux calibration. The total time spent on each target field is ≈7 minutes.

The observations were manually calibrated using CASA 4.7.2 by the observatory. The standard calibrations (bandpass, flux, gain) were applied first, followed by the final polarization calibration that was performed on each session separately. The expected flux uncertainty for the final observations is ∼10%. We examined the observed flux for the bandpass and leakage calibrators against the expected flux for the date of observations (using analysis utilities task getALMAflux in CASA) and found that they agreed within 10%. The complex gain calibrator had larger uncertainties of ≲20%, but this source is monitored less frequently with only one detection between our observation epochs and a single detection several months before our observations. Hereafter, we quote statistical uncertainties unless stated otherwise.

We imaged each field interactively using clean. Many of the fields have peak Stokes I signal-to-noise ratio (S/N) > 100 and allowed self-calibration. We tested phase-only self-calibration to the Stokes I data for all the observations with S/N > 20 and only applied the ones with good gain solutions based on a visual inspection. The Stokes Q, U, and V data did not benefit from self-calibration. We ran self-calibration iteratively with decreasing solution intervals until the Stokes I noise did not improve. Table 2 summarizes the self-calibration iterations for each of the fields. For most sources one or two rounds of phase-only self-calibration were necessary to reach a consistent noise level. The first round of self-calibration used solution intervals equivalent to the entire scan length, and the second round used solution intervals of 30.25 s, which corresponds to roughly half a scan. For c2d_989, VLA1623a, and VLA1623b, we applied a third round of phase-only self-calibration with a solution interval of 15 s, or five integrations. Additional iterations with shorter solution intervals did not improve the map noise. For c2d1008a and c2d1008b, we applied for the third round an amplitude and phase self-calibration with a solution interval equal to the scan length (see also Paper I; Paper II). In all self-calibration rounds, we visually inspected the data after applying the solutions to ensure that the noise was dropping with each iteration.

Table 2.  Imaging Summary

Field	Self Cala	σIb	σQb	σUb	${\sigma }_{{ \mathcal P }I}$ c	Beamd
		(μJy beam−1)				(arcsec)
c2d_811	2p	32	25	27	26	0.27 × 0.21
c2d_822	1p	34	25	25	25	0.27 × 0.21
c2d_831	2p	34	28	27	27	0.29 × 0.24
c2d_857	1p	30	26	26	26	0.27 × 0.20
c2d_862	2p	35	28	28	28	0.28 × 0.24
c2d_867	2p	34	27	28	27	0.27 × 0.21
c2d_871	2p	31	27	27	27	0.26 × 0.20
c2d_885	1p	30	28	28	28	0.28 × 0.24
c2d_890	1p	30	28	27	28	0.27 × 0.21
c2d_892	None	26	26	26	26	0.27 × 0.21
c2d_894	1p	31	27	27	27	0.27 × 0.21
c2d_899	1p	30	26	26	26	0.27 × 0.21
c2d_901	1p	29	25	25	25	0.27 × 0.21
c2d_902	None	29	26	26	26	0.27 × 0.21
c2d_904	1p	29	26	26	26	0.27 × 0.21
c2d_954	2p	30	26	26	26	0.27 × 0.21
c2d_963	None	29	26	26	26	0.27 × 0.21
c2d_989	3p	71	27	27	27	0.27 × 0.20
c2d_990	1p	31	27	26	27	0.28 × 0.23
c2d_991	1p	31	26	27	27	0.27 × 0.20
c2d_996	None	31	27	27	27	0.27 × 0.20
c2d_998	none	30	26	26	26	0.27 × 0.20
c2d_1003	2p	48	28	28	28	0.26 × 0.20
c2d_1008a	2p,1ap	280	28	30	29	0.28 × 0.24
c2d_1008b	2p,1ap	250	29	29	29	0.28 × 0.23
c2d_1008e	2p,1ap	280	25	25	25	0.28 × 0.23
VLA1623a	3p	56	27	27	27	0.27 × 0.21
VLA1623b	3p	71	27	27	27	0.27 × 0.21
IRAS 16288	None	32	26	26	26	0.27 × 0.21

Notes.

^aSuccessive self-calibration iterations with phase (p) or amplitude and phase (ap). Sources that were not self-calibrated have "none." ^bMap sensitivity at the phase center. ^cThe sensitivity in polarized intensity is estimated from the average of σ_Q and σ_U. ^dBeam size of the field in the final images. ^eFor the mosaic map of fields c2d_1008a and c2d_1008b.

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For each round of self-calibration and for the final deep map, we applied clean with Briggs weighting and a robust parameter of 0.5 and a UV taper of 01. The UV taper was applied to better recover extended emission. We used interactive clean for all the Stokes I maps and noninteractive clean for Stokes Q and U. Interactive clean was necessary for the Stokes I maps, as some fields contained faint, diffuse extended emission. We also used the multiscale option during the Stokes I clean for those sources with substantial extended emission. Table 2 gives the map sensitivities for the Stokes I, Q, and U maps. We exclude the Stokes V data because they cannot be calibrated. The typical map sensitivity is 27 μJy beam⁻¹, although several fields are dynamic range limited and have substantially higher rms values. The map resolution for each field is typically 027 × 021, and the maximum recoverable scale is ∼26, which means that we are sensitive to physical scales in the range of ∼33–360 au (assuming a distance of 140 pc).

For the c2d_1008a and c2d_1008b fields, we performed a final deep clean on the self-calibrated data with both fields to produce a mosaic. The emissions detected in both fields overlap within the inner half of their primary beams, and the individual fields gave consistent Stokes maps (see Appendix B). For the mosaic field, we use clean with the same robust, multiscale, and UV taper values as the individual fields. The map sensitivities for the mosaicked Stokes Q and U maps improved by ∼14%, but we found a similar map sensitivity for mosaic Stokes I, as the map is still limited by dynamic range. Hereafter, we use the field name "c2d_1008" for the mosaic maps.

Polarization is measured from the quadrature sum of Stokes Q and U (${{ \mathcal P }}_{\mathrm{obs}}=\sqrt{{Q}^{2}+{U}^{2}}$), which always yields positive values. The quadrature sum subsequently biases the measured polarized intensity to higher values. This effect is most pronounced for weak Stokes Q or U data (e.g., ${{ \mathcal P }}_{I}$/${\sigma }_{{ \mathcal P }I}$ < 4), where noise will more significantly boost the inferred polarized signal (e.g., Vaillancourt 2006).

We follow Hull & Plambeck (2015) and calculate the debiased polarization intensities using a probability density function. Briefly, this method computes the probability that the observed, uncorrected polarization ${{{ \mathcal P }}_{I}}_{,{obs}}$ has a true, debiased polarization ${{ \mathcal P }}_{I}$ with

$$\begin{eqnarray}&&\begin{array}{l}\mathrm{PDF}({{ \mathcal P }}_{I}| {{ \mathcal P }}_{\mathrm{obs}},{\sigma }_{{ \mathcal P }I})\\ \quad \ =\ \displaystyle \frac{{{ \mathcal P }}_{\mathrm{obs}}}{{\sigma }_{{ \mathcal P }I}^{2}}{I}_{0}(x)\exp \left[-\displaystyle \frac{({{ \mathcal P }}_{\mathrm{obs}}^{2}+{{ \mathcal P }}_{I}^{2})}{2{\sigma }_{{ \mathcal P }I}^{2}}\right],\end{array}\end{eqnarray} \tag{ 1 }$$

where ${\sigma }_{{ \mathcal P }I}$ is the sensitivity of the polarization data and I₀(x) is the Bessel function for the Bessel parameter, x  =  ${{ \mathcal P }}_{\mathrm{obs}}$ ${{ \mathcal P }}_{I}$/${\sigma }_{{ \mathcal P }I}^{2}$. The statistically most likely debiased polarization (${{ \mathcal P }}_{I}$) will produce a peak in Equation (1). Thus, we measured ${{ \mathcal P }}_{I}$ by taking the minimum of $-\mathrm{PDF}({{ \mathcal P }}_{I}| {{ \mathcal P }}_{\mathrm{obs}},{\sigma }_{{ \mathcal P }I})$ using the routine tnmin¹⁵ in IDL for each pixel with S/N < 9; above this threshold, we used the standard maximum likelihood calculation (Vaillancourt 2006),

$$\begin{eqnarray}&&{{{ \mathcal P }}_{I}}_{,\mathrm{bright}}=\sqrt{{Q}^{2}+{U}^{2}-{\sigma }_{{ \mathcal P }I}^{2}},\end{eqnarray} \tag{ 2 }$$

as the two debiasing methods are identical for such bright emission. For ${\sigma }_{{ \mathcal P }I}$, we use the mean rms from the Stokes Q and U observations, taking into account that the map sensitivities vary across the primary beam.

The polarization position angle, θ, and its uncertainty σ_θ are given by (e.g., Coudé et al. 2019)

$$\begin{eqnarray}&&\theta =\displaystyle \frac{1}{2}{\tan }^{-1}\displaystyle \frac{U}{Q}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{\sigma }_{\theta }=\displaystyle \frac{1}{2}\displaystyle \frac{\sqrt{{\left(U{\sigma }_{Q}\right)}^{2}+{\left(Q{\sigma }_{U}\right)}^{2}}}{{Q}^{2}+{U}^{2}}.\end{eqnarray} \tag{ 4 }$$

The polarization position angles are defined from −90° to 90°, north to east. The polarization fraction, ${{ \mathcal P }}_{F}$, and its uncertainty, ${\sigma }_{{ \mathcal P }F}$, are defined by

$$\begin{eqnarray}&&{{ \mathcal P }}_{F}=\displaystyle \frac{{{ \mathcal P }}_{I}}{I}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{\sigma }_{{ \mathcal P }F}={{ \mathcal P }}_{F}\sqrt{{\left(\displaystyle \frac{{\sigma }_{{ \mathcal P }I}}{{{ \mathcal P }}_{I}}\right)}^{2}+{\left(\displaystyle \frac{{\sigma }_{I}}{{I}_{}}\right)}^{2}}.\end{eqnarray} \tag{ 6 }$$

We calculate σ_θ and ${\sigma }_{{ \mathcal P }F}$ for each pixel to account for the changing map sensitivity across the primary beam. We note that the ALMA Technical Handbook for Cycle 6 gives a 1σ instrumental polarization error of 0.03% for compact sources and a 1σ error of 0.1% for extended sources within the inner third of the primary beam FWHM. This instrument polarization error is not included in ${\sigma }_{{ \mathcal P }F}$.

Hereafter, we use the term "e-vector" to correspond to the observed polarization position angles (e.g., no rotation has been applied) and the term "b-vector" when the position angles are rotated by 90° to show the inferred field direction. We note, however, that the position angles are not full vectors because we cannot determine the true direction.

In Stokes I emission, we identify 41 distinct compact sources in the 27 fields. Table 3 lists the coordinates and broad properties of each detected Stokes I object. Column (1) gives the field name, and Column (2) gives the source identification based on a common name in the literature (see Table 1). For multiple sources in the field, the sources are ordered by their distance from the phase center. Columns (3) and (4) give the coordinates of the peak emission. Column (5) gives the source classification adopted for this study (see Appendix A), where Class 0 sources and Class I sources are protostars accreting material from dense envelopes, Class II sources are pre-main-sequence stars that are no longer accreting, and flat-spectrum sources are the transition stage between Class I and Class II when the envelope is being cleared out (e.g., see Evans et al. 2009, for more details). Columns (6) and (7) give the peak flux density and its corresponding error, σ_peak, which we take as the Stokes I uncertainty at the position of the source. For sources near the phase center, this value is equivalent to σ_I given in Table 2. Columns (8)–(11) give the total flux, size, and position angle from simple Gaussian fits to the sources in the image plane using imfit in CASA. We use Gaussian fits to approximate the source properties, but note that some objects may be disks, envelopes, or a combination of both.

Table 4 summarizes the detection properties for each field. Column (2) gives the number of sources detected in each field, and Column (3) indicates whether or not extended emission is seen in the field. We define extended emission as noncompact or non-Gaussian flux either connected to a compact source or found between sources. In most cases, the extended emission, when detected, is spatially filtered such that we do not recover all the flux. Column (4) gives notes on previous detections from the literature, where "identified disk" indicates that the source emission was previously attributed to a disk and "potential disk" indicates that the previous disk classification was ambiguous. Note that not all "identified disks" have been confirmed with Keplerian rotation.

Figure 2 shows a wide view of the 12 fields that had either multiple sources or extended dust emission. Eleven fields have multiplicity, and eight fields have extended emission. Most of the fields with extended emission also had multiple sources detected. Field c2d_871 was the only field to have a single detection and also extended emission. The multiplicity statistics will be discussed in Section 5.6, and the extended emission will be discussed with their corresponding source in Appendix A.

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In this section, we give a brief overview of the polarization detection statistics for the entire sample. We consider a source to have a robust polarization detection if its detection meets the following specific selection criteria:

• 1.  
  I/σ_I > 3;
• 2.  
  ${{ \mathcal P }}_{I}$/${\sigma }_{{ \mathcal P }I}$ > 3;
• 3.  
  σ_θ < 10°.

These criteria select bright emission above the noise in both Stokes I and polarized intensity. Of the 41 detected continuum sources, only 14 have polarization measurements that satisfy the above criteria.

Figure 3 shows images of the 14 sources with detected polarization. The background images show the Stokes I continuum maps, and the black line segments show normalized polarization e-vectors. Maps with scaled polarization e-vectors are given in Appendix A. The blue and red arrows indicate the direction of the blueshifted and redshifted outflow lobes, if known (see Table 8 for the associated outflow angles and references), and the gray bars illustrate the source position angle (e.g., see Table 3). For most sources, the outflows are perpendicular to the continuum long axis. This orientation indicates that the dust emission likely originates from a disk or flattened envelope.

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Table 5 gives the debiased polarized intensity and the polarization fraction for each of the 14 well-detected sources as measured at the position of their Stokes I peak. For GY 91, however, the detected polarized emission is off the source peak and relatively weak (<4σ). We report its results instead at the position of its peak polarized intensity and hereafter consider GY 91 to be marginally detected. Several sources have low polarization fractions with values <0.5% at their emission peak, but higher fractions at larger radial extents.

Table 5.  Polarization Detection Results

Field	Source	${{ \mathcal P }}_{I}$peaka	${{ \mathcal P }}_{F}$peakb
		(μJy beam−1)	(%)
c2d_811	GSS 30 IRS 1	471 ± 26	3.7 ± 0.2
	GSS 30 IRS 3‡	760 ± 62	1.4 ± 0.1
c2d_822	Oph-emb-9	145 ± 25	0.5 ± 0.09
c2d_831	GY 91c	115 ± 27	12 ± 3
c2d_862	Oph-emb-6	260 ± 28	1.0 ± 0.1
c2d_885	IRS 37-A	169 ± 28	1.7 ± 0.3
c2d_954	Oph-emb-1	122 ± 26	1.1 ± 0.2
c2d_989	IRS 63	1329 ± 27	1.5 ± 0.03
c2d_1003	IRS 67-B	120 ± 28	0.3 ± 0.06
c2d_1008	IRAS 16293B	2460 ± 26	0.5 ± 0.01
	IRAS 16293A	895 ± 27	0.5 ± 0.01
VLA1623a	VLA 16239W	233 ± 27	1.4 ± 0.2
VLA1623b	VLA 1623B	1285 ± 27	2.0 ± 0.04
	VLA 1623A	1185 ± 27	2.1 ± 0.04

Notes.

^aDebiased polarized intensity at the peak Stokes I position (see Table 3). Errors correspond to ${\sigma }_{{ \mathcal P }I}$ for the field scaled by the primary beam correction at the position of the source. Sources with ‡ are outside of the inner third of the primary beam. ^bThe corresponding polarization fraction at the same position. Errors corresponds to the statistical error described in Section 3.2 and do not include the instrument polarization. ^cThe values for polarized intensity and polarization fraction for GY 91 are from the position of the peak polarized intensity.

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Table 6 lists the 28 compact sources that were undetected in polarization. This table gives the uncertainty in polarized intensity at each source position and the 3σ upper limit to the polarization fraction for the nondetection. Of the 28 undetected sources, half (14) have 3σ upper limits ≲2% and 8 have 3σ upper limits of <1%, indicating that many of the nondetected sources have significantly low polarization fractions. Sources labeled with a double dagger are outside of the inner third of the primary beam. We note that the upper limits to the polarization fractions for sources outside of the inner third of the primary beam FWHM may be less reliable (see Appendix B for details).

Table 6.  Nondetection Upper Limits

Field	Source	${\sigma }_{{{ \mathcal P }}_{I}}$ a	${{{ \mathcal P }}_{F}}_{,\mathrm{limit}}$ b
		(μJy beam−1)	(%)
c2d_857	WL 16	26	1.8
c2d_862	ALMA_J162705.5	30	26
c2d_867	WL 17	27.3	0.3
c2d_871	Elias 29	26.5	0.5
c2d_885	IRS 37-B	27.5	9.3
	IRS 37-C	28	10
	ALMA_J162717.7	29	32
	IRS 39‡	83.3	33
c2d_890	IRS 42	27.5	0.7
c2d_892	Oph-emb-5c	26	⋯
c2d_894	Oph-emb-12	26.5	1.8
c2d_899	IRS 43-A	25.5	0.6
	IRS 43-B	25.5	4.8
	GY 263‡	30.2	1.3
c2d_901	IRS 44	25	0.7
c2d_902	IRS 45	26.3	3.9
	VSSG 18 B‡	43	13
c2d_904	IRS 47	26	1.1
	ALMA_J162729.7‡	37	21
c2d_963	Oph-emb-18	25.8	4.1
c2d_990	Oph-emb-4	26.5	0.9
c2d_991	Oph-emb-25	26.5	0.9
c2d_996	Oph-emb-7	26.8	21
c2d_998	Oph-emb-15	26	2.4
c2d_1003	IRS 67-A	28	1.0
VLA1623b	VLA 1623NE‡	149	3.9
IRAS 16288	ISO Oph 210	26	2.0
	ALMA_J163203.3‡	68.4	33

Notes.

^aThe error in the polarized intensity at the position of the source. Sources with ‡ are outside of the inner third of the primary beam. ^bThe 3σ upper limit polarization fraction for a nondetection. ^cOph-emb-5 was not detected in Stokes I continuum.

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Figure 4 compares histograms of log peak Stokes I flux densities for the sources with well-detected polarization and those without polarization detections or with marginal detections. Unsurprisingly, the sources that are well detected in polarization tend to be the brightest objects, as these sources have higher sensitivity to low polarization fractions. The seven sources with I_peak > 32 mJy beam⁻¹ have well-detected polarized intensities, whereas the detection rate drops to 50% (6/12) for the sources with I_peak in the range of 10–32 mJy beam⁻¹ and to 9% (1/11) of sources with I_peak in the range of 3–10 mJy beam⁻¹.

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Table 7 gives a summary of the polarization statistics by region in Ophiuchus and by source classification, using the updated classifications in Table 3. These numbers exclude the five objects that were identified as either galaxies or background stars (see Section 5.5 and Appendix A). Since the younger YSOs in the sample are brighter, they have a higher polarization detection rate than the more evolved objects. All Class 0 sources are detected in polarization, and no flat-spectrum or Class II objects are detected (excluding the marginal detection for GY 91). This result is also in agreement with a number of studies that show higher polarization fractions toward younger sources (e.g., Beckford et al. 2008; Hull et al. 2014).

With this publication, we release the full data products. These products include the self-calibrated maps of the Stokes I, Q, U observations and the maps of debiased polarized intensities, polarization position angles, and polarization fraction for each source. These maps are all primary beam corrected. We also include their associated error maps and a map of the primary beam. The Stokes I, Q, U, and polarized intensity errors correspond to the map error at the phase center (see Table 2) scaled by the primary beam correction. The error maps for the polarization position angles and polarization fraction are calculated by propagating the individual errors in the associated maps pixel by pixel.

The data products are available at Dataverse¹⁶ for individual fields or for the entire sample. The maps are provided as FITS files with the form FIELD_TYPE_233GHz.fits, where FIELD is the name of the field in Table 2 and TYPE indicates whether the map is one of the Stokes parameters (StokesI, StokesQ, StokesU), polarized intensity (POLI), polarization position angle (POLA), polarization fraction (POLF), or the field primary beam (pbeam). Error maps are appended with "err." We also include separate maps for the mosaic of c2d_1008a and c2d_1008b used here; these data use the field name of "c2d_1008."

In Section 3.2, we show images of the 14 YSOs that are detected in polarization. By eye, we see a variety of polarization structures, with some sources showing homogenous polarization position angles, whereas others have circular or complex polarization position angles. Here, we describe the general polarization e-vector morphology of each source and also the orientation of the e-vectors relative to the Stokes I continuum emission.

Table 8 summarizes the polarization morphological description for each source. We include a separate entry for the large circumbinary disk around VLA 1623A separately from its smaller compact disk, as the two show distinct polarization structures that likely arise from different mechanisms (see Paper I). Columns (1) and (2) give the source name and classification from Table 3. Column (3) gives the inclination (i), estimated from the ratio of the minor to major axis (cos i = b/a) from our Gaussian fits (see Table 3), assuming that the dust emission is tracing geometrically thin disks. Column (4) gives the position angle (ϕ) of the semiminor axis. Column (5) gives the weighted average polarization position angle ($\langle {\theta }_{P}\rangle$).¹⁷ The reported error for $\langle {\theta }_{P}\rangle$ corresponds to the weighted standard deviation. Column (6) gives the angle difference, Δ, between the weighted average polarization position angle and semiminor axis, ${\rm{\Delta }}=| \phi \ -\langle {\theta }_{P}\rangle |$. Column (7) describes the overall polarization morphology, where "U" is uniform, "A" is azimuthal, and "C" is complex (see below). Column (8) indicates whether the polarization is aligned with major or minor axes of the Stokes I continuum source. Column (9) gives the dust opacity index, β (see Appendix C and Section 4.2), and Column (10) gives the outflow orientation (θ_out) if known. Since IRAS 16293A and IRAS 16293B are confused with the dense envelope around the stars, we instead fit a Gaussian to their brightest emission defined by an area of I ≳ 100 m Jy beam⁻¹ to get their general geometries and weighted average polarization angles.

Table 8.  Polarization and Disk Orientations

Source	Class	i	ϕ	$\langle {\theta }_{P}\rangle$	Δa	Morphb	Alignb	βc	θoutd
		(deg)	(deg)	(deg)	(deg)				(deg)
GSS 30 IRS 1	I	74.5 ± 10	27.0 ± 6.8	28.5 ± 6.3	1.5 ± 9.0	U	Minor	0.12 ± 0.04	22 (1*)
GSS 30 IRS 3	I	70.8 ± 0.6	19.6 ± 0.4	15.7 ± 4.9	3.9 ± 4.9	U	Minor	0.19 ± 0.05	20 (1*)
Oph-emb-9	I	67.0 ± 0.9	−62.2 ± 0.9	−64 ± 15	1.8 ± 15	C	Minor	0.18 ± 0.03	−65 (2*)
GY 91	F	33.6 ± 9	65 ± 29	69 ± 46	⋯	A	⋯	0.64 ± 0.44	⋯
Oph-emb-6	I	76.0 ± 0.5	78.6 ± 0.1	74.6 ± 4.6	4.0 ± 4.6	U	Minor	0.27 ± 0.03	80 (3*)
IRS 37-A	I	69 ± 8	−82.5 ± 3.9	−86.9 ± 4.1	4.4 ± 5.7	U	Minor	⋯	60 (4*)
Oph-emb-1	0	68.9 ± 2.5	25.2 ± 2.0	85.5 ± 3.7	60.3 ± 4.2	U	None	0.98 ± 0.06	22 (5)
IRS 63	I	47.2 ± 1.6	58.4 ± 2	61 ± 12	2.6 ± 12.2	A	Minor	0.35 ± 0.19	50–64 (6)
IRS 67-B	I	54.2 ± 4	0.5 ± 5.9	87.3 ± 7.9	87 ± 10	U	Major	0.74 ± 0.09	⋯
IRAS 16293A	0	57.3 ± 3	−37 ± 2.9	63 ± 21	100 ± 21	C	Major	⋯	90, −45 (7)
IRAS 16293B	0	20.7 ± 6	35 ± 42	62 ± 48	⋯	A	⋯	⋯	⋯
VLA 1623W	0	81.4 ± 1.0	−79.9 ± 0.5	−81.1 ± 6.3	1.2 ± 6.3	U	Minor	0.28 ± 0.13	⋯
VLA 1623B	0	70.9 ± 2.8	−47.4 ± 1.8	−46.6 ± 2.3	0.8 ± 2.9	U	Minor	0.48 ± 0.08	−55 (8)
VLA 1623A (compact)e	0	64.1 ± 3	−51.8 ± 3.5	−53.7 ± 4.0	1.9 ± 5.3	U	Minor	0.45 ± 0.29	−55 (8)
VLA 1623A (extended)e	0	54.8	−60	26 ± 30	⋯	A	⋯	0.6 ± 0.7	−55 (8)

Notes.

^aSources without values have unconstrained values (errors ≳30°) for ϕ and $\langle \theta \rangle$. ^bMorphological description of the polarization and alignment relative to the major or minor continuum axis. "U" indicates that the polarization is uniform, "A" indicates that the polarization is azimuthal, and "C" indicates that the morphology is complex. Multiple entries mean that more than one morphology is present. ^cEstimated dust opacity index using archival data, if applicable. See Appendix C. ^dEstimated outflow position angle in the literature with reference if applicable (see Figure 3). For VLA 1623A and VLA 1623B, we give the same outflow orientation for both because only one outflow is seen for both sources. Numbers in parentheses indicate the reference for the outflow orientation, and stars indicate that the literature reference did state the position angle, and as such, we estimated the outflow position angle by eye from integrated intensity maps. References are: (1) Friesen et al. (2018); (2) Kamazaki et al. (2003); (3) Bussmann et al. (2007); (4) van der Marel et al. (2013); (5) Yen et al. (2017); (6) Visser et al. (2002); (7) van der Wiel et al. (2019); (8) Santangelo et al. (2015). ^eVLA 1623A is split into two entries, one for the compact disk with uniform polarization and one from the extended disk with azimuthal polarization. Values for i and ϕ are based on a by-eye fit to the continuum data as reported in Paper I. The dust opacity index for the extended emission is estimated from setting nterms = 2 in clean to estimate the spectral index, α, for β = α − 2.

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We consider three morphological descriptions for the polarization e-vectors: "uniform," "azimuthal," or "complex." While many sources show multiple polarization morphologies, we only report the most dominant one. The source morphologies are defined as follows:

• 1.  
  Uniform Polarization: Uncertainty on the weighted average polarization position angle is <10°.
• 2.  
  Azimuthal Polarization: Polarization e-vectors follow an idealized elliptical pattern (e.g., Mori et al. 2019). For simplicity, we assume that the idealized elliptical pattern traces the same dimensions as the continuum source (e.g., using the geometry given in Table 3).
• 3.  
  Complex Polarization: The polarization morphology is neither uniform nor azimuthal.

From the above definitions, we find that nine YSOs have uniform polarization angles. These systems are GSS 30 IRS 1, GSS 30 IRS 3, Oph-emb-6, IRS 37-A, Oph-emb-1, IRS 67-B, VLA 1623W, VLA 1623B, and VLA 1623A (compact). In most of these systems, the polarization angles are also well aligned with the minor axis, with the exception of IRS 67-B, which is aligned with the major axis, and Oph-emb-1, which is aligned with neither axis. We consider the polarization aligned with the minor axis if the angle difference, Δ, is consistent with zero within ∼1σ (or aligned with the major axis if Δ is consistent with 90° within ∼1σ). We do not calculate Δ for sources with errors ≳30° for either their semiminor axis or weighted average polarization angle, as the individual position angles are too unconstrained to measure a meaningful angle difference.

There are four cases of azimuthal polarization angles. These sources are GY 91, IRS 63, IRAS 16293B, and VLA 1623A (extended). We note, however, that none of these sources showed pure circular or elliptical polarization. Figure 5 compares the observed polarization (purple line segments) of these four YSOs to their idealized elliptical polarization (green line segments), assuming that the idealized elliptical pattern traces the same dimensions as the Stokes I source. For IRS 63, IRAS 16293B, and VLA 1623A (extended), we see substantial deviations from the elliptical pattern that may be indicative of other polarization mechanisms or changes in optical depth (see Section 4.2). As such, we cannot quantify the azimuthal structure using the distribution of angular deviations to measure the agreement as in Mori et al. (2019). Instead, we require that the polarization morphology must be dominated by an elliptical component for the system to be considered azimuthal. We therefore define azimuthal polarization when at least half of the e-vectors have an angular deviation of <25° with the idealized elliptical pattern.

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Finally, there are two YSOs, Oph-emb-9 and IRAS 16293A, that have complex polarization (see Figure 3). Both sources appear to have a mix of azimuthal and uniform polarization, but neither morphology dominates. Nevertheless, its polarization is well aligned with the minor axis. The polarization of IRAS 16293A is mostly aligned with the major axis but shows substantial curvature at larger radial extents that result in larger uncertainties on its weighted average polarization position angle (20°). Thus, neither object is well fit with a uniform or elliptical morphology.

In this section, we determine the likely polarization mechanism for the YSOs using the morphological description of the previous section and the physical properties of the source. Several different mechanisms can cause polarization in disks. These mechanisms include dust self-scattering processes and grain alignment from either magnetic fields, RATs or k-RATs, mechanical torques, or aerodynamic alignment (e.g., Tazaki et al. 2017; Hoang et al. 2018; Kataoka et al. 2019; Yang et al. 2019). For this analysis, we use morphological arguments to support or reject specific polarization mechanisms. In particular, we focus on polarization from dust self-scattering and magnetic fields, as the theoretical frameworks for these two mechanisms are better established.

4.2.1. Polarization from Dust Self-scattering

4.2.2. Polarization from Magnetic Fields

In this section, we briefly discuss other polarization mechanisms that can affect disk scales. These mechanisms include aerodynamic grain alignment, mechanical torques, and radiative grain alignment (e.g., Tazaki et al. 2017; Kataoka et al. 2019; Yang et al. 2019). Each of these mechanisms can produce radial or azimuthal polarization patterns depending on gas flow and grain properties and inclination. These mechanisms can, however, produce uniform polarization if the system is very highly inclined (e.g., near edge-on). VLA 1623W is our most highly inclined disk detected in polarization at 81°, which makes it near edge-on. Nevertheless, VLA 1623W has relatively high optical depth (see Appendix C), and polarization from grain alignment is suppressed when dust emission is optically thick (Yang et al. 2017). In addition, Harris et al. (2018) found identical dust polarization position angles at 872 μm, and we expect the dust emission to be more optically thick at shorter wavelengths. Based on this analysis, we do not favor any of these alternative polarization mechanisms for our sources with uniform polarization angles. We instead focus on those sources with azimuthal or complex polarization angles.

While the theoretical framework for these mechanisms is still being developed, we cannot rule out k-RAT alignment, aerodynamic alignment, or mechanical torques for Oph-emb-9, GY 91, IRS 63, IRAS 16293B, and VLA 1623A (extended). In the case of GY 91, deeper observations are necessary to confirm the polarization structure hinted at in these data. Ultimately, we lack sufficient sensitivity to properly analyze the polarization for this complicated disk. For Oph-emb-9, IRS 63, IRAS 16293B, and VLA 1623A (extended), we have a better sampling of their polarization. These sources also show substantial deviations from idealized elliptical polarization (see Section 4.1), which could imply that multiple mechanisms are contributing the observed polarized structure.

To determine whether or not these alternative mechanisms are contributed to the observed polarization signatures, we need multiwavelength dust polarization observations to trace out the polarization structure for different dust grain populations. Previous multiwavelength observations of HL Tau have shown a significant change in polarized structure with wavelength that is attributed to different polarization mechanisms. Stephens et al. (2017) found that the polarization morphology of HL Tau transitions from uniform at 870 μm to circular at 3 mm (see also Harrison et al. 2019), with the 1.3 mm polarization representing a hybrid of the two patterns. The uniform polarization at 870 μm is well matched by dust self-scattering models (Kataoka et al. 2015), whereas the circular polarization at 3 mm is likely due to a different mechanism (see Section 4.3). Initial studies suggested that the circular polarization was from k-RAT alignment (Kataoka et al. 2017; Stephens et al. 2017; Tazaki et al. 2017), but more recent studies suggest that the signature is inconsistent with that mechanism (Yang et al. 2019). Other mechanisms that may need to be considered are aerodynamic grain alignment (Yang et al. 2019) or mechanical torques (Kataoka et al. 2019). IRS 63 in particular closely resembles HL Tau at 1.3 mm in both polarization intensity and polarization morphology. Thus, the polarization we see toward IRS 63 may not be solely due to dust self-scattering. Oph-emb-9 also shows some similarities to HL Tau and could be another source with multiple mechanisms.

The initial goal of this survey was to conduct an unbiased study of dust polarization on ≲100 au scales to determine to what extent magnetic fields influence disk formation and fragmentation. Our study, however, finds that the majority of sources have polarization measurements consistent with dust self-scattering processes rather than magnetic fields. Out of 37 YSOs detected in continuum emission, only 5 (14%) of them have polarization morphologies that appear inconsistent with dust self-scattering. We note, however, that two of these sources also show a mix of dust self-scattering toward the most compact emission, making the detections of magnetic fields down to disk scales more complex.

Our unbiased survey shows that dust polarization does not appear to be a good tracer of magnetic fields on ≲100 au scales on average (see also Cox et al. 2018). This result is in stark contrast to previous studies of polarization in protostellar cores and envelopes on >500 au scales, which find that nearly all sources are polarized (e.g., Hull et al. 2014; Galametz et al. 2018). We note, however, that dust polarization may not be a good tracer of magnetic fields in disks. For example, larger dust grains from grain growth may be less efficiently aligned with the field (e.g., Andersson et al. 2015), or polarization from the magnetic field may be obscured owing to dust polarization from competing processes (see Sections 4.2 and 4.3). Therefore, we cannot conclude that the undetected disks have no magnetic fields. Their magnetic fields may instead be better detected by other tracers, such as molecular line polarization (e.g., Brauer et al. 2017; G. Bertrang & S. Cortes 2019, in preparation).

5.1.1. Field Morphologies

In this section, we focus on the five sources with polarization morphologies that are inconsistent with expectations from dust self-scattering. These sources are Oph-emb-1, IRS 67-B, VLA 1623A (extended), IRAS 16293A, and IRAS 16293B. (We exclude GY 91, as this source has only a few marginal polarization detections.) Assuming that their dust polarization is attributed to magnetic fields, Figure 6 shows their inferred magnetic field orientation obtained from rotating the polarization e-vectors by 90° (b-vectors). The line segments in Figure 6 are normalized to highlight the broad field morphology. We also mask out the bright compact disks for VLA 1623A and VLA 1623B and the bright inner 1'' of IRAS 16293B, as these e-vectors appear to be associated with dust self-scattering rather than magnetic fields (see Section 4.2).

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As outlined in Section 4.2.2, the polarization around IRAS 16293A and IRAS 16293B mainly traces the inner envelope around the stars and not disks. The field morphology is also quite different between the two protostars (see Paper II, for more details). The field around IRAS 16293A shows hints of a pinched morphology but has a fair degree of disorder that may be attributed to turbulence. The pinched, hourglass-shaped field is more prominent in lower-resolution polarization data from the SMA (Rao et al. 2009, 2014), suggesting that gas motions are affecting the field structure only on small scales. IRAS 16293B also shows hints of a pinched structure at larger radial extents from the protostar, but this morphology may be confused with substantial polarization detected in the dust bridge between the stars. The dust bridge has relatively uniform polarization where the inferred magnetic field is parallel to the filamentary structure. In Paper II, we suggest that the filamentary structures could be magnetized accretion channels.

For Oph-emb-1, IRS 67-B, and VLA 1623A (extended) the inferred magnetic field is more confined to a compact disk structure. The inferred fields for IRS 67-B and VLA 1623A (extended) are mainly perpendicular to their disk long axes, whereas the inferred field for Oph-emb-1 is about 60° offset from the long axis. Both Oph-emb-1 and IRS 67-B have highly uniform field orientations (see also Table 8). VLA 1623A (extended) shows more structure. Its inferred field morphology is broadly radial with signatures of a pinch. Paper I found largely good agreement between the observed field structure and a poloidal, hourglass magnetic field model, although there were some deviations.

Overall, these protostars have magnetic fields that are primarily poloidal on <100 au scales, and some of them also have pinched, hourglass-shaped structures. Such morphologies are generally expected in gravitationally dominated systems where the field is flux-frozen to the gas and dragged inward with the contraction (e.g., Mestel 1966; Mestel & Strittmatter 1967; Galli & Shu 1993). Indeed, each of these sources shows evidence of infall or accretion (e.g., Mardones et al. 1997; Pineda et al. 2012; Evans et al. 2015; Mottram et al. 2017; Hsieh et al. 2019b), which suggests that their larger cores and envelopes are collapsing. Poloidal fields are important for driving jets and outflows (e.g., Hennebelle & Ciardi 2009; Tomisaka 2011), but they can also remove angular momentum through magnetic braking and suppress the formation of disks or companion stars (e.g., Machida et al. 2005; Price & Bate 2007; Hennebelle & Fromang 2008a; Li et al. 2011).

To first order, we expect magnetic fields in disks to be mainly toroidal, as field lines are wrapped up by rotation (Hennebelle & Ciardi 2009; Tomisaka 2011; Kataoka et al. 2012). This toroidal field is important to stabilize the disk and to promote accretion onto the star (e.g., Blandford & Payne 1982; Balbus & Hawley 1998; Hennebelle & Teyssier 2008b). Nevertheless, we see no evidence that the magnetic field is dominated by a toroidal component toward these four sources even though all them have signatures of (Keplerian) rotation (e.g., Murillo et al. 2013; Artur de la Villarmois et al. 2018; Calcutt et al. 2018). The inferred magnetic field morphology for a toroidal field would be circular or spiral shaped (e.g., Kataoka et al. 2012, 2017), whereas the observations show primarily radial or linear field structures. If there is a significant toroidal component within these disks, then our observations suggest that dust polarization may not trace such field morphologies well.

5.1.2. Comparison with Other Protostars

In this section, we compare our high-resolution ALMA data to the magnetic field measurements in Ophiuchus on clump scales. For simplicity, we focus on far-infrared and submillimeter polarization that resolves the Ophiuchus clumps from the James Clerk Maxwell Telescope (JCMT) and the Stratospheric Observatory for Infrared Astronomy (SOFIA) polarimeters. To first order, we also assume that far-infrared and submillimeter polarization on clump scales is generally attributed to grain alignment from a magnetic field.

The ρ Oph A clump has been observed in dust polarization at 89 μm and 154 μm with SOFIA/HAWC+ (Santos et al. 2019) and at 850 μm with JCMT/POL-2 (Kwon et al. 2018), and the Oph B and C clumps have been observed at 850 μm (Soam et al. 2018; Liu et al. 2019). For Oph A, the 214–850 μm data show largely consistent, well-ordered polarization across Oph A such that the inferred magnetic field appears to be mostly uniform. At 89 μm, there is still broad agreement with the longer-wavelength data, but the far-infrared observations include additional polarization structure east of the main dense clump that is not seen at the longer wavelengths. This eastern region may be tracing smaller dust grains and cannot be compared to our millimeter observations. For Oph B and C, the polarization structures and inferred magnetic fields for these two regions are more disordered than what is seen in Oph A, and their field strengths are lower than what was obtained for Oph A (Liu et al. 2019).

Eight of our sources lie within Oph A, and six of these are well detected in dust polarization (note that GY 91 lies outside of the polarization maps in the aforementioned studies). By contrast, three of our sources are in Oph B, with none of them being detected in polarization, and Oph C is starless. We therefore focus our large-scale comparison on the six sources in Oph A. In general, we find that the large-scale polarization and small-scale polarization morphologies are inconsistent. Some of these differences may be explained by different polarization mechanisms at small scales from magnetic fields on large scales. Indeed, we find that GSS 30 IRS 1, GSS 30 IRS 3, Oph-emb-6, and the three VLA 1623 circumstellar disks show polarization consistent with dust self-scattering rather than magnetic fields. Dust self-scattering is unlikely to have the same polarization structure as the inferred magnetic field.

For the VLA 1623 region, however, Kwon et al. (2018) find an inferred magnetic field direction that is roughly perpendicular to the inferred magnetic field axis from the hourglass model in Paper I. While the dust scattering signatures toward the circumstellar disks can dominate over an hourglass field signature when both components are unresolved (e.g., see the 3'' polarization map from Hull et al. 2014), these contributions will be localized to VLA 1623A/B and VLA 1623W, whereas the lower-resolution POL-2 observations show uniform polarization well off of these sources across the ≳0.05 pc area of Oph A. This uniform field structure is in agreement with the slightly higher resolution (7.8–136) data from SOFIA (Santos et al. 2019), but the far-infrared data also show hints of a pinched magnetic field in the vicinity of VLA 1623, although at a different orientation. If the SOFIA, JCMT, and ALMA observations are each tracing pinched, hourglass-shaped magnetic fields, then the orientation of that field appears to change from the clump scale to the disk scale. This change suggests that either the polarization in the extended disk of VLA 1623A does not trace a magnetic field or the magnetic field toward VLA 1623A may be affected by dynamical processes, such as rotation or outflows, that alter its orientation on small scales.

We find 37 continuum sources associated with YSOs. In Appendix A, we give the source size and mass assuming that the compact emission can be fitted with a Gaussian (see also Table 3). We assume that these continuum detections are tracing thin disks with smooth density distributions, e.g., most of the continuum sources are compact and ellipsoidal in shape. We caution, however, that both the Gaussian fits and the mass measurements should be considered approximations since (1) many of these sources are known to have complex disk structure, (2) their dust emission may include flux from the disk and inner envelope, and (3) we adopt the same temperature and opacity for each object. Nevertheless, applying the same approach to all sources allows us to conduct a broad comparison between them such that the statistical results are still robust.

Figure 7 shows the distribution of the inferred disk masses in our sample in order of increasing mass. For simplicity, we exclude IRAS 16293A and IRAS 16293B because their dust continuum is significantly confused with envelope emission and their Gaussian fits are unreliable. We also exclude the circumbinary disk around VLA 1623A (estimated mass of 0.1 M_⊙) and focus instead on the compact circumstellar emission around VLA 1623A and VLA 1623B that can be fitted with a single Gaussian (Paper I). We show sources detected in polarization as filled red symbols and the undetected sources as open black symbols. For GY 91, we use an open red symbol to represent the marginal detection.

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Most of the disks in Ophiuchus have relatively low masses. Roughly 83% (29/35) have masses <10 ${M}_{\mathrm{Jupiter}}$ (0.01 M_⊙), which corresponds to the minimum mass solar nebula (MMSN; Weidenschilling 1977; Hayashi 1981), and roughly 34% (12/35) have masses ≲1 ${M}_{\mathrm{Jupiter}}$. Similar low-mass disks were also seen in T Tauri stars in Orion (Ansdell et al. 2017), Lupus (Ansdell et al. 2016), and Chameleon (Long et al. 2018). Our disk masses, however, assume ${{ \mathcal R }}_{{GD}}$ = 100, whereas observations of T Tauri stars generally find ${{ \mathcal R }}_{{GD}}$ < 100 (e.g., Ansdell et al. 2016; Long et al. 2017; Miotello et al. 2017). We adopt the typical interstellar medium ratio, as most of our targets are in the protostellar (Class I) stage and therefore may still be gas-rich.

The more massive disks tend to be detected in polarization. This result matches the detection summary in Section 3.2, where the brightest sources also tended to be detected in polarization. All sources above 10 ${M}_{\mathrm{Jupiter}}$ are detected in polarization (or marginally detected), although disks with masses down to 2 ${M}_{\mathrm{Jupiter}}$ are also detected. Of the 20 sources with masses >2 ${M}_{\mathrm{Jupiter}}$, 8 are not detected in polarization, and 7 of these nondetections have robust 3σ upper limits to their polarization fraction of ≲1%, which indicates that these sources have significantly low polarization. We discuss these nondetections in more detail in Section 5.4.

Figure 8 compares source mass and size (major-axis FWHM) that we measure from the Gaussian fits. Unresolved sources are plotted as upper limits with a fixed size equal to roughly 1/4 of the beam (8.7 au). The sources are also separated by their classification, with Class 0 in red, Class I in yellow, flat spectrum in cyan, and Class II in black. For clarity, we do not plot mass error bars, as the masses are uncertain within factors of a few.¹⁹ Therefore, we only consider broad properties for the continuum detections, assuming that they are tracing disks.

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Overall, we find that disk mass and size are correlated. The dashed line shows the best-fit weighted linear least-squares relation to the full sample of resolved disks. The slope of this relation is 1.13 ± 0.01. We note that this linear least-squares fit is heavily biased by the more massive disks, as they tend to be brighter and have lower fitting errors. An unweighted linear least-squares fit is steeper with a slope of 1.41 ± 0.24. Assuming that Σ ∝ M/R², we find that Σ ∼ R^{−(0.6–0.9)} using both the weighted and unweighted linear least-squares fits. Andrews et al. (2009) found a similar surface density of Σ ∝ r^−0.9 for nine protoplanetary disks in the Ophiuchus based on SMA observations and radiative transfer models to determine the disk profiles. This agreement suggests that protostellar disks and protoplanetary disks have similar dust surface densities even though processes such as planet formation, grain growth, and gas depletion may be different. More detailed disk modeling, however, is necessary to produce more accurate disk masses and test the relationship between disk surface densities as a function of source evolution.

There is no strong correlation between YSO class and disk size, although we note that our statistics for the flat-spectrum sources and Class II sources are incomplete. Segura-Cox et al. (2018) found that Class 0 and Class I disks in Perseus had comparable sizes and masses (see also Andersen et al. 2019), whereas Maury et al. (2019) found that Class 0 disks appear smaller than Class I disks. With only four Class 0 protostars in the Ophiuchus cloud, there are too few sources to support either study. In general, Cieza et al. (2019) found that the majority of Class II disks in Ophiuchus have diameters <30 au, which is comparable to what we see for most objects. Combining our results with those of Cieza et al., we find that most disks in Ophiuchus have sizes <30 au (FWHM) between Class I and Class II, with hints that the Class 0 disks may be larger on average, although we require a larger sample to verify this claim.

The majority of our disks are undetected in polarization. Table 6 lists these systems with their 3σ upper limits to their undetected polarization. Roughly half (13/23) of the nondetected disks have 3σ upper limit polarization fractions ≲2%, and 7 of these disks have 3σ upper limits of <1%. Since previous observations of polarization on envelope scales found typical polarization fractions of ≳2% for YSOs (e.g., Hull et al. 2014; Cox et al. 2018), many of the disks undetected in polarization have significantly low polarization fractions.

Indeed, many disks may have very low polarization fractions in general. Hughes et al. (2013) observed three protoplanetary disks in polarization with the SMA and CARMA and found that all were undetected with 3σ upper limits of <1%. Subsequent ALMA observations of one disk, DG Tau, found that these had uniform polarization consistent with dust self-scattering at low polarization fractions of ∼0.4% (e.g., Bacciotti et al. 2018). Similarly, Harrison et al. (2019) detected very low polarization fractions <1% toward a small sample of protoplanetary disks with ALMA in 3 mm dust polarization. They also found that two of their six disks remained undetected with 3σ upper limits <1% with ALMA. Since the four detected disks show polarization attributed to self-scattering processes or radiative grain alignment, Harrison et al. suggested that the nondetected disks may lack a population of large dust grains, which are needed to produce these polarization signatures. Deeper observations, however, are necessary.

Low polarization fractions may arise if the grains cannot be efficiently aligned (e.g., they lack paramagnetic material necessary to align with the magnetic field) or if the grains are too small to produce a dust self-scattering signature. Kataoka et al. (2015) found that dust grains with sizes of ≈λ/2π are most efficient at producing polarization from self-scattering processes. At 1.3 mm, this size corresponds to 200 μm, but a small range in dust grain sizes (e.g., ∼50–250 μm) can produce a polarization signature at 1.3 mm from self-scattering. Simulations of dust grain growth suggest that grains with sizes of ∼100 μm can form quickly in the inner radii of disks, where the surface densities are high (e.g., Brauer et al. 2008; Birnstiel et al. 2010). We see no evidence of unusually low surface densities in our disks to suggest that they cannot form large dust grains (see Section 5.3).

Alternatively, these disks may have unresolved polarization structure that appears depolarized at our resolution. In Sections 4.2 and 4.2.2, we outline how disk geometry can affect the observed polarization signatures. Figure 9 compares histograms of disk inclination for the resolved sources that are detected in polarization (solid) with those that are undetected (dashed). For simplicity, we exclude IRAS 16293A and IRAS 16293B, as these sources do not have clear disks with which to measure their inclination, and GY 91, because it is only marginally detected in polarization. To help improve the statistics, we include two values for VLA 1623A, one for the compact circumstellar material around the unresolved binary and a second entry for the extended circumbinary disk (see Figure 44). We can treat these two components separately because they show different polarization structures attributed to different mechanisms (see Section 4).

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Figure 9 shows that the disks detected in polarization tend to have inclinations of >60°, whereas the undetected disks have shallower inclinations of <60°. Using an Anderson–Darling test, we find that the two distributions are inconsistent at the 2.5% level. We note, however, that disk inclinations as measured from cos i = b/a are only robust if the disk is well resolved (e.g., over two beams along the minor axis) and geometrically thin. Since most of our disks are compact (<2 beams), we may be biased to steeper inclinations. Nevertheless, higher-resolution observations of WL 17, Oph-emb-1, and VLA 1623B (Sheehan & Eisner 2017; Harris et al. 2018; Hsieh et al. 2019b) give consistent inclinations within 5° of our estimate, which suggests that our inclinations are broadly reliable.

Figure 10 compares disk inclination with peak intensity (top) and deconvolved major-axis size (bottom) for the sources with uniform polarization (red diamonds), azimuthal polarization (blue diamonds), and undetected sources (open diamonds). For simplicity, we only show the undetected sources with 3σ upper limits <2%. We find that disks with inclinations >60° tend to have uniform dust polarization morphologies. Since disks with higher inclinations will be observed through higher columns of dust, we should expect these disks to have higher optical depths on average. In these cases, we would expect the dust polarization signature to be dominated by self-scattering and the signature to be uniform and along the minor axis owing to the high inclination (e.g., Kataoka et al. 2016a, 2017; Yang et al. 2016, 2017).

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Figure 10 also shows that sources with azimuthal polarization tend to have lower inclinations (<50°) and very large sizes. Sources of comparable inclination but smaller size may therefore appear unpolarized owing to unresolved azimuthal structure. For example, WL 17 is the brightest source in our sample that is undetected in dust polarization. It has a low dust opacity index of β < 0.3 (see Appendix C), such that we would expect it to be detected in polarization from self-scattering processes. Based on its moderate inclination of 38° and central cavity (Sheehan & Eisner 2017), the expected polarization pattern from self-scattering should be azimuthal (e.g., Pohl et al. 2016; Ohashi et al. 2018). Indeed, GY 91 and IRS 63 also have moderate inclinations and are dominated by an azimuthal polarization structure. WL 17, by contrast, is marginally resolved compared to GY 91 and IRS 63, and an azimuthal pattern would be depolarized within the beam (e.g., see the 3 mm observations of HL Tau in Kataoka et al. 2017). We note that smaller and fainter disks than WL 17, e.g., GSS 30 IRS 1 and IRS 37-A, are well detected in polarization likely because they have high inclinations (≳70°) such that their polarization pattern from self-scattering is uniform and can be recovered even if the disk is only marginally resolved.

There are three larger sources (≳02) with high inclinations (>70°) that are also not detected in polarization with 3σ upper limits of ∼1%. These sources are GY 263, IRS 47, and Oph-emb-4. Based on their inclinations, we would expect these objects to have uniform polarization aligned with their minor axis due to dust self-scattering. Since other disks in this study and in the literature show very low polarization fractions of <1% (e.g., like HL Tau or DG Tau; Stephens et al. 2017; Bacciotti et al. 2018), we may need deeper observations to detect the polarization for GY 263, IRS 47, and Oph-emb-4. Alternatively, the very low polarization fractions may indicate that these disks lack large dust grains or high optical depths necessary to produce a dust self-scattering signature, as seen for similarly inclined but brighter disks like GSS 30 IRS 1 and IRS 37-A.

Several of our new detections are faint, point-like objects that are also undetected at near-infrared and mid-infrared wavelengths with Spitzer and WISE (see Appendix A). Since these objects are undetected in the infrared, they are unlikely to be YSOs. We therefore consider the possibility that they are external galaxies. Several recent surveys have estimated the background galaxy source counts as a function of brightness using the SMA (e.g., Hayward et al. 2013) and ALMA (Carniani et al. 2015; Hatsukade et al. 2018). These studies typically estimate >10⁴ galaxies with intensities >0.15 mJy per square degree at ∼1 mm. Within the ALMA primary beam, these source counts amount to a non-negligible probability of detecting a galaxy in each field.

The likelihood of detecting a background galaxy is a strong function of its brightness and where it falls in the primary beam. To estimate the probability of detecting a background galaxy in our observations, we calculate the likelihood of finding a galaxy above a threshold across the primary beam. For the galaxy number counts, we use the 1.3 mm results of Carniani et al. (2015) based on ALMA observations. They give a Schechter function of the differential galaxy numbers of

$$\begin{eqnarray}&&\displaystyle \frac{{dN}}{{dS}}=1800\ {{\rm{\deg }}}^{-2}{\left(\displaystyle \frac{S}{{S}_{0}}\right)}^{-2.08}\exp \left(-\displaystyle \frac{S}{{S}_{0}}\right),\end{eqnarray} \tag{ 7 }$$

where N is the number of galaxies with intensity S, and S₀ = 1.7 mJy. For simplicity, we adopt three galaxy intensity thresholds of 5σ(r), 10σ(r), and 20σ(r), where σ(r) is the map sensitivity as a function of position in the primary beam. We adopt σ = 0.03 mJy at the phase center and allow σ(r) to increase at larger radial extents according to the primary beam correction. Since the threshold varies across the primary beam, we calculate the probability of detecting a galaxy at each threshold in annuli separated by ∼03, or roughly the synthesized beamwidth.

Figure 11 shows the probability of detecting a galaxy in these annuli as a function of radial extent in the primary beam. In all three cases presented, we find that the probability differential functions peak near the halfway point between the phase center and the primary beam FWHM. As outlined above, there are two competing factors to the probability of detecting a galaxy across the primary beam. The search area increases with radius, but the sensitivity to the galaxy decreases with radius. The distributions peak at slightly different locations for each of the thresholds. We find a peak probability at 93 for the 5σ threshold, 88 for the 10σ threshold, and 81 for the 20σ threshold.

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Figure 12 shows the cumulative probability functions for a galaxy detection for each threshold. These curves are measured from the annuli functions by taking the product of the probability of a nondetection in each annulus, Π (1 − P_i). We find that the probability of detecting a galaxy within the primary beam is 66% for the 5σ threshold, 31% at 10σ, and 10% at 20σ.

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We consider galaxy contamination to be most significant for sources with S/N < 20 in our observations based on the probability curves in Figure 12. Only 6/41 (15%) of our continuum source have fluxes <20σ. These objects are ALMA_J162705, ALMA_J162717.7, IRS 39, ALMA_J162729.7, Oph-emb-7, and ALMA_J162729.7. Using the source S/N value and their positions within the primary beam, we estimate the probability that these objects are galaxies. The probabilities are 5%, 5%, 35%, 14%, <1%, and 42%, respectively. Of these faint detections, Oph-emb-7 has a very low probability (<1%) of being a galaxy and is likely a true YSO. We also consider IRS 39 to be a YSO, even though it has a high probability (35%) of being a galaxy, because it is also detected at infrared wavelengths (e.g., Evans et al. 2009). High-redshift galaxies detected in the (sub)millimeter have spectral energy distributions (SEDs) that peak at far-infrared wavelengths (e.g., Casey et al. 2014) and would not be detected at near-infrared or mid-infrared wavelengths.

Thus, we classify four continuum sources as extragalactic objects. Based on our analysis, the probability of detecting a galaxy at ∼10σ in any given field should be ∼30%. Excluding those fields with σ ≳ 50 μJy beam⁻¹ at the phase center (e.g., those that are dynamic range limited), we estimate that an extragalactic source should be detected at 10σ in roughly six fields, which is comparable to the observed number. We note, however, that our probabilities assume that galaxies are distributed randomly in the primary beam, whereas galaxies tend to cluster (Hatsukade et al. 2018). These probabilities should therefore be taken as a first-order estimate.

In this section, we briefly discuss the multiplicity statistics for the Class 0 and Class I systems only. We exclude the flat-spectrum and Class II statistics because those populations statistics are incomplete (e.g., we detect flat-spectrum and Class II sources only if they were within our field of view or if a Class I source was previously misclassified). For simplicity, we consider two sources to be companions if they are within the same primary beam and they are at the same evolutionary stage. Table 3 lists the adopted evolutionary stages of each YSO based on ancillary data that probe the star SED, outflows, surrounding envelope, disk structure, and chemistry (see Appendix A).

We find a total of six multiple systems in the Class 0 and Class I populations of the Ophiuchus molecular cloud and 10 single systems. For the multiple systems, four are binaries (GSS 30, IRS 43, IRS 67, IRAS 16293), one is a triple-star system (IRS 37), and one system has four stars (VLA 1623). We note that VLA 1623 is identified with four stars using the higher-resolution results from Harris et al. (2018), which separate VLA 1623A into two companions with separations of ∼14 au. For the Class 0 systems, 2/3 (67%) are in multiple systems, whereas for the Class I systems, 4/13 (31%) are in multiple systems. Although we have small numbers, we find a similar decrease in the fraction of multiple systems from the Class 0 to Class I stage to what was seen in previous studies (e.g., Looney et al. 2000; Chen et al. 2013; Tobin et al. 2016).

Tobin et al. (2016) conducted a complete analysis of the Class 0 and Class I multiplicity fraction (MF) and companion star fraction (CSF) for the Perseus molecular cloud using the Karl G. Jansky Very Large Array (VLA). That study is the largest homogeneous analysis of protostellar multiplicity in a single cloud to date. By comparison, Ophiuchus has far fewer Class 0 and Class I objects than Perseus. Tobin et al. (2016) identified ∼60 Class 0 and Class I systems in Perseus (total number depends on how one defines the multiple systems), whereas we find 16 Class 0 and Class I systems in Ophiuchus, and of these, only three are at the Class 0 stage. Thus, we will evaluate the multiplicity of Ophiuchus as a whole rather than separate the Class 0 and Class I sources.

Following Tobin et al. (2016), we calculate MF = (B + T + Q)/(S + B + T + Q) and CSF = (B + 2T + 3Q)/(S + B + T + Q), where S is the number of single systems, B is the number of binaries, T is the number of triple systems, and Q is the number of quadruple systems. Our sample is complete over separation ranges of ∼35–1800 au. There are higher-resolution (∼15 au) observations of VLA 1623A (Harris et al. 2018), but we lack comparable resolution data for our entire sample. On larger separations, we are limited by the primary beam FWHM of ∼25''. While some sources are detected beyond the primary beam FWHM (e.g., see Figure 2), we may not have complete statistics beyond 1800 au separations. Thus, we only calculate MF and CSF for separation ranges between 35 and 1800 au.

For our full sample of Class 0 and Class I systems, we measure MF = 0.29 ± 0.11 and CSF = 0.41 ± 0.12 for multiple separations between 35 and 1800 au. (Errors in the MF and CSF values are derived from binomial statistics following Chen et al. 2013.) Tobin et al. (2016) reported values of MF = 0.27 and CSF = 0.31 for a separation range of 50–2000 au and MF = 0.31 and CSF = 0.35 for a separation range of 15–2000 au. Hence, Ophiuchus and Perseus have broadly consistent multiplicity statistics over similar separation ranges. The Ophiuchus multiples tend to peak at ∼100 and ∼1200 au. The first peak matches what has been seen in Perseus (Tobin et al. 2016, 2018) and in Orion (J. Tobin et al. 2019, in preparation), but the latter peak is roughly 3× smaller than these other clouds. This smaller second peak may be due to our limited sensitivity to detect companions at separations >1800 au or due to the lower number statistics in Ophiuchus compared to Perseus and Orion. We cannot conclude that the differences in the separation peaks are statistically significant.

The c2d_811 field contains two sources, GSS 30 IRS 1 and GSS 30 IRS 3, which are separated by 148 (∼2000 au). Figure 2 shows a wide view of this field with both sources labeled. These objects are associated with the GSS 30 region of L1688 Oph A, a low-mass core with a bipolar reflection nebula. The core also contains GSS 30 IRS 2, a T Tauri star that is likely unrelated to the nebula (Leous et al. 1991; Weintraub et al. 1993) but lies within our primary beam, and GSS 30 IRS 4, an infrared source that lies outside of the main core (Weintraub et al. 1993) and is outside the primary beam. GSS 30 IRS 2 is undetected in our ALMA observations and was similarly undetected in previous millimeter observations (Zhang et al. 1997; Jørgensen et al. 2009; Friesen et al. 2018), although it is bright at 6 cm (Leous et al. 1991). Based on its position in the primary beam, we can put a 3σ upper limit for a point-source 1.3 mm continuum flux of <0.4 mJy.

Both GSS 30 IRS 1 and GSS 30 IRS 3 are embedded objects. GSS 30 IRS 3, however, is considered to be younger because it is the only object in the core detected at both 1.3 and 2.7 mm (André & Montmerle 1994; Zhang et al. 1997). Previous observations from the SMA and ALMA show that it has a bright elongated disk and a bipolar outflow perpendicular to the long axis of the dust emission (Jørgensen et al. 2009; Friesen et al. 2018). GSS 30 IRS 1 is considered slightly more evolved than GSS 30 IRS 3 owing to less envelope emission (Zhang et al. 1997; Jørgensen et al. 2009). Nevertheless, Andre et al. (1990) found 1.3 mm continuum around GSS 30 IRS 1 with the IRAM 30 m telescope, and van Kempen et al. (2009) detected 850 μm and HCO⁺ (4–3) emission around both sources with the JCMT. The single-dish observations suggest that GSS 30 IRS 1 is also embedded and may share a common spherical envelope with the younger GSS 30 IRS 3. Since both sources also appear to drive outflows (White et al. 2015), we consider them to be Class I objects for this study.

Figure 13 shows our ALMA polarization maps for GSS 30 IRS 1. The polarization angles are mainly uniform at ≈29°, and they are aligned with the minor axis (27°). The disk is very compact with a (deconvolved) size of 12 au × 3 au (FWHM) and a mass of 2.2 ${M}_{\mathrm{Jupiter}}$. We also detect faint diffuse Stokes I continuum that extends from GSS 30 IRS 1 eastward (see Figure 2) that could be associated with an envelope. This extended dust emission is detected at only ∼3σ but is also faintly detected at 1.1 mm with ALMA in Friesen et al. (2018), and it is located in the same direction as the brightest HCO⁺ (4–3) line emission (van Kempen et al. 2009).

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Figure 14 shows the ALMA polarization maps for GSS 30 IRS 3, also commonly called LFAM1 (Leous et al. 1991). This source is located well outside the nominal inner third of the primary beam, and in general, such off-axis polarization is considered less robust. Nevertheless, ALMA commission tests show that off-axis polarization is reliable if the source is strongly polarized (Harris et al. 2018). Indeed, Harris et al. (2018) found excellent agreement between off-axis polarization of VLA 1623W in their data and on-axis polarization of VLA 1623W presented here. In Appendix B, we further test the reliability of off-axis polarization using adjacent fields that detect the same sources. We find excellent agreement between the "on-axis" polarization and "off-axis" polarization for offsets of ≲5'' and good agreement for offsets of ∼10'', indicating that our measurements for GSS 30 IRS 3 can be considered mostly reliable. To still account for the higher degree of uncertainty for an off-axis source, Figure 14 uses more stringent selection criteria for the polarization e-vectors: I/σ_I > 10 and ${{ \mathcal P }}_{I}$/${\sigma }_{{ \mathcal P }I}$ > 5.

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As with Figure 13, GSS 30 IRS 3 shows mainly uniform polarization angles that are along the direction of the minor axis. Here, the polarization position angles are ≈16°, and the minor-axis position angle is 20°. This disk is also quite large. We measure a deconvolved size of 82 au × 27 au (FWHM) and a mass of 25.5 ${M}_{\mathrm{Jupiter}}$. This mass agrees well with the measurement of 0.026 M_⊙ (27 ${M}_{\mathrm{Jupiter}}$) from fitting SMA observations at 1.3 mm with a disk and envelope model in Jørgensen et al. (2009).

This field contains one source, Oph-emb-9. This source appears to be embedded (Enoch et al. 2009; Evans et al. 2009; Dunham et al. 2015), and it has redshifted and blueshifted emission from CO consistent with a bipolar outflow. The outflow, however, is partially confused by a redshifted lobe from VLA 1623 (White et al. 2015). Nevertheless, near-infrared nebulosity around Oph-emb-9 shows an opening angle consistent with the blueshifted emission, indicating that this source is likely driving an outflow with a position angle of roughly −60° to −70° (Kamazaki et al. 2003). We consider Oph-emb-9 to be a Class I object.

Figure 15 shows the polarization results for Oph-emb-9. The Stokes I image of the source is compact and fairly round, whereas the polarized intensity map is peanut shaped with minima along the minor axis. The polarization position angles range from roughly −40° to −80° in an arc-like morphology. From our Gaussian fit to the continuum emission, we find a disk position angle of 28°, which is nearly perpendicular to the position angle of the outflow from Kamazaki et al. (2003) and also perpendicular to the general direction of the polarization. The deconvolved disk size is 32 au × 12.5 au (FWHM), and the mass is 7 ${M}_{\mathrm{Jupiter}}$.

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Field c2d_831 contains GY 91. It has been identified as a Class I source (Evans et al. 2009; Dunham et al. 2015) and a disk object in McClure et al. (2010). It also has a spectral type of an M4 star based on infrared spectroscopy (Doppmann et al. 2005) in spite of being embedded in an envelope (Enoch et al. 2009). Recent high-resolution ALMA observations have shown it to have a very large, slightly inclined disk with multiple rings and gaps. Sheehan & Eisner (2018) observed GY 91 in 3 mm continuum at 005 resolution with ALMA. They found three gaps in the disk, and van der Marel et al. (2019) used the same data to identify a fourth gap. Sheehan & Eisner (2018) measure a slightly larger envelope for GY 91 than HL Tau, suggesting that this source could be younger than HL Tau. Alternatively, van der Marel et al. (2019) find that GY 91 could be as young as or a bit older than HL Tau, although it was the only source in their sample that was optically extincted. We classify GY 91 as a flat-spectrum source for this study.

GY 91 is the only object with a polarization classified as marginal. Figure 16 shows its polarization results. Its polarized intensities are weak (${{ \mathcal P }}_{I}$/${\sigma }_{{ \mathcal P }I}$ < 4) and off the Stokes I intensity peak. Based on the nondetection at the continuum peak, we can put a 3σ upper limit of 0.6%, which suggests that it has significantly low polarization fractions at the peak of the continuum. Nevertheless, the detections are also associated with five independent beams and appear to map out a near-azimuthal morphology.

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GY 91 is one of the largest disks in our sample. We find a deconvolved size of 110 au × 94 au (FWHM) and a mass of 14 ${M}_{\mathrm{Jupiter}}$. These values, however, are only broadly representative because GY 91 has known substructure (e.g., Sheehan & Eisner 2017; van der Marel et al. 2019). More extensive disk modeling that accounts for the gaps is beyond the scope of the current paper.

Field c2d_857 has WL 16. While this source has been identified as an embedded Class I object (Evans et al. 2009; Dunham et al. 2015), it has also been identified as a more evolved Herbig Ae star (Ressler & Barsony 2003; Connelley & Greene 2010). This object has a rising red SED that is saturated in some of the Spitzer bands (Hsieh & Lai 2013), which makes it difficult to classify by its infrared emission. While previous observations of WL 16 found millimeter emission from Bolocam (Enoch et al. 2009), more recent observations have shown that there is no surrounding core detected at 850 μm by SCUBA-2 (Pattle et al. 2015). WL 16 also has only faint CO line wings that may be indicative of a weak outflow (White et al. 2015), and its disk is detected in extended polycyclic aromatic hydrocarbon (PAH) emission that normally traces pre-main-sequence stars (Geers et al. 2007; Seok & Li 2017). Thus, WL 16 may be a more evolved source than a Class I object and located behind and heavily extincted by the Oph E cloud. We reclassify this source as Class II.

Figure 17 shows the Stokes I image of WL 16. This source is undetected in polarization with a 3σ upper limit of 1.8%. Previously, Zhang et al. (2017) found polarization fractions of 1%–3% from spectropolarimetry at 8.7 μm and 10.3 μm toward WL 16. The mid-infrared polarization angles were also fairly uniform at ∼27°–30° toward the inner 2'' of the mid-infrared disk. Zhang et al. (2017), however, attribute their mid-infrared polarization to absorption from the foreground cloud rather than emission from the disk. Their mid-infrared polarization position angles and fractions are consistent with optical and near-infrared polarization of background stars (Sato et al. 1988; Goodman et al. 1990; Beckford et al. 2008) and the expectations that this source is behind the Oph E cloud. By contrast, our ALMA observations are sensitive to polarization from the disk itself.

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The disk is also unresolved in our ALMA 1.3 mm observations, which suggests that it is very small (≲9 au; or 1/4 the beam) with an estimated mass of 0.7 ${M}_{\mathrm{Jupiter}}$. This disk size and mass are much smaller than what were obtained from near-infrared and mid-infrared observations. Ressler & Barsony (2003) measured a disk size of 900 au at mid-infrared wavelengths, which they attributed to very small grains (VSGs) and PAHs. The 1.3 mm ALMA data will instead be sensitive to larger dust grains, which are more likely than small dust grains to move inward owing to radial drift (e.g., Pérez et al. 2012). Thus, we would expect the disk size traced by large dust grains to be more compact than what is traced by small dust grains. WL 16 may also have a limited population of large dust grains. Najita et al. (2015) report a millimeter-detected disk mass of ≲0.16 ${M}_{\mathrm{Jupiter}}$ (scaled by the revised distance to Ophiuchus) using 1.3 mm data in the literature, whereas Ressler & Barsony (2003) find a VSG disk mass of ≲10 ${M}_{\mathrm{Jupiter}}$. This difference indicates that the mass in VSGs may be two orders of magnitude higher than the mass in large dust grains. We note that our estimated disk mass of 0.7 ${M}_{\mathrm{Jupiter}}$ is higher than that of Najita et al. (2015), because we use a fixed temperature of 20 K, whereas Najita et al. scale their dust temperatures by the star luminosity. If we use the same dust temperature as Najita et al. (2015), we get a disk mass of 0.1 ${M}_{\mathrm{Jupiter}}$, in agreement with their upper limit.

Field c2d_862 contains the Class I source Oph-emb-6. This source has a well-established core (Enoch et al. 2009; Pattle et al. 2015) and outflow (White et al. 2015; Hsieh et al. 2017), indicative of a true embedded protostar. The infrared emission, however, is relatively weak, and Oph-emb-6 has been classified as a candidate very low luminosity object in the literature (e.g., Bussmann et al. 2007; Dunham et al. 2008). Figure 2 shows that we identify two compact objects separately by roughly 4'' (560 au). We label these objects as Oph-emb-6 and ALMA_J162705.51-243622.27 (ALMA_J162705.5 for short), where Oph-emb-6 is nearly 80 times brighter than ALMA_J162705.5 in our 1.3 mm data.

Figure 18 shows the dust polarization results for Oph-emb-6. The Stokes I continuum image is highly elongated, and the polarization is uniform with position angles of ≈75° across the disk with variations of 5° only at the edges. These position angles align well with the disk minor-axis orientation of 79°. The disk deconvolved size is 58 au × 14 au (FWHM), and the mass is 8.6 ${M}_{\mathrm{Jupiter}}$.

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Previous observations of Oph-emb-6 predicted that the protostellar disk would be viewed nearly edge-on based on its outflow cavity. Duchêne et al. (2004) found an east–west hourglass-shaped cavity toward Oph-emb-6 from near-infrared imaging (see also Hsieh et al. 2017). Molecular line observations of the outflow are also east–west with a position angle of roughly 80° north to east (Bussmann et al. 2007; Nakamura et al. 2011). This orientation places the outflow nearly perpendicular to the long axis of the elongated dust emission in Figure 18, consistent with expectations that the continuum emission is tracing a mostly edge-on disk that is perpendicular to the outflow.

Figure 19 shows the Stokes I continuum image of ALMA_J162705.5. This source is not detected in polarization, but it is also very faint. The 1.3 mm continuum peaks at 9σ, resulting in a 3σ upper limit of 26% for polarization. Thus, we do not have the sensitivity to make any conclusions about the polarization of ALMA_J162705.5.

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ALMA_J162705.5 could be a faint binary star companion to Oph-emb-6. This source has no Spitzer counterpart of any classification from the full c2d source catalog, and no object is seen in WISE (Wright et al. 2010) at this source position. With a separation of 4'', ALMA_J162705.5 may be undetected with Spitzer and WISE given its proximity to Oph-emb-6. Nevertheless, Oph-emb-6 is a relatively low luminosity protostar, and as such, the higher-resolution infrared data should have less confusion. Based on its low flux (peak S/N = 9) and galaxy source count statistics (see Section 5.5), we consider ALMA_J162705.5 to be a background galaxy.

Field c2d_867 contains one object, WL 17. There are some uncertainties about its classification in the literature. WL 17 has a rising red SED that peaks at infrared wavelengths (Evans et al. 2009; Dunham et al. 2015) and a possible envelope (McClure et al. 2010) indicative of young, embedded protostars. Nevertheless, WL 17 has only a weak high-velocity CO emission that may trace an outflow, but this emission appears confused by other nearby sources (White et al. 2015). Its disk also appears more evolved. Sheehan & Eisner (2017) observed WL 17 in high-resolution (005) 3 mm continuum with ALMA and found an inner cavity with a radius of 01 (∼14 au). This cavity is consistent with later-stage transition disks (e.g., Espaillat et al. 2007) that are typically associated with more evolved T Tauri stars. We therefore consider WL 17 to be more evolved than the canonical Class I stage.

Figure 20 shows the dust continuum image of WL 17. This source is not detected in polarization in spite of being one of the brightest objects in the entire sample (peak S/N ≈ 800). We measure a 3σ upper limit for the polarization fraction of 0.3%, which is equivalent to a nondetection down to the instrument noise. WL 17 is also fairly compact. It has a deconvolved disk size of 32.5 au × 25.6 au (FWHM) and a mass of 8.3 ${M}_{\mathrm{Jupiter}}$.

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Field c2d_871 contains Elias 29, a well-known embedded object with an outflow (White et al. 2015). It also has evidence of a disk from SMA and ATCA observations (e.g., Lommen et al. 2008; Jørgensen et al. 2009; Miotello et al. 2014), although these studies did not resolve it. Miotello et al. (2014) combined the 1 and 3 mm observations to model the disk and envelope. They found a disk mass of ≳10.5 ${M}_{\mathrm{Jupiter}}$(see also Jørgensen et al. 2009) and evidence that dust grains must have reached millimeter sizes within the disk and in its collapsing envelope. Although McClure et al. (2010) identified Elias 29 as a disk source, we consider it a Class I object based on its envelope and outflow detections.

Figure 21 shows our dust continuum map for Elias 29. This source is compact in dust continuum and undetected in polarization with a 3σ upper limit of 0.5% for the polarization fraction, which is near the instrument noise limit. We find a deconvolved size of 10.5 au × 9 au (FWHM), indicating that this disk is very compact (Miotello et al. 2014). The estimated disk mass is 2.8 ${M}_{\mathrm{Jupiter}}$.

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Our estimated mass is a factor of three lower than the mass estimates from Jørgensen et al. (2009) and Miotello et al. (2014). These studies, however, did not resolve the Elias 29 disk and instead fitted a disk and envelope model to the SMA and ATCA visibilities. We detect substantial extended emission south of the compact disk (see Figure 2) at >5σ. This extended emission matches the north–south concentration of HCO⁺ (3–2) seen in Lommen et al. (2008), which is mainly attributed to envelope emission. They find that Elias 29 has a relatively high M_env/M_disk ratio. Since this envelope emission is well detected at high resolution with ALMA, the envelope itself may contain substructure that will confuse the disk and envelope models. Indeed, Miotello et al. (2014) find that they can fit the Elias 29 data with either a small optically thick disk of radius 15 au or a large optically thin disk with a radius of 50–200 au. Both disks are much larger than the resolved disk size from these ALMA data, suggesting that previously unresolved envelope structure may have inflated the disk size and mass for this source.

Field c2d_885 has IRS 37, a well-known YSO that has been identified as Class I (Evans et al. 2009; Gutermuth et al. 2009). It has a detected outflow (van der Marel et al. 2013; White et al. 2015) and core (Pattle et al. 2015), even though McClure et al. (2010) identified the source as a disk object. Figure 2 shows that the field also contains four additional compact objects, including a more evolved YSO, IRS 39, 15'' southwest of the phase center. Several of the aforementioned compact objects were also detected by Cieza et al. (2019) in their ALMA 1.3 mm emission. We use a similar naming scheme to Cieza et al. (2019) and refer to the four sources near the phase center as IRS 37-A, IRS 37-B, IRS 37-C, and ALMA_J162717.72-242852.84 (hereafter ALMA_J162717.7) in order of their brightness. The faintest object, ALMA_J162717.7, is a new detection.

Figure 22 show the polarization results for IRS 37-A, the only source in the field with a robust polarization detection. The polarization morphology appears fairly uniform with position angles of roughly −87°. These polarization angles are roughly parallel to the disk minor axis, which has an orientation of roughly −82°. The disk is marginally resolved, with a deconvolved size of 17 au × 6 au (FWHM) and a mass of 1.8 ${M}_{\mathrm{Jupiter}}$.

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We note that the source outflow does not appear to be perpendicular to the long axis of the continuum emission. van der Marel et al. (2013) and White et al. (2015) each used single-dish observations to trace CO from outflows throughout L1688. Since neither study reports the outflow position angle, we estimate it by eye using Figure 1 of van der Marel et al. (2013). We determine an approximate outflow position angle of 25°–30°, compared to the disk position angle of 8°. This discrepancy could mean that the continuum source of IRS 37-A is not uniquely tracing a disk but may include emission from an inner envelope. Alternatively, the IRS 37 outflow may not be well defined. Both van der Marel et al. (2013) and White et al. (2015) find the outflow confused with neighboring sources and only identify one lobe.

Figure 23 shows the continuum images for the four sources in the field that are not detected in polarization. These objects are more than an order of magnitude fainter than IRS 37-A, and the 3σ upper limits for their nondetection in polarization range from 9% to 33% (see Section 5.4). IRS 39 is a more evolved YSO. It has an infrared spectral index (α < −1) and bolometric temperature (T_bol > 1000 K) consistent with a pre-main-sequence star (Evans et al. 2009; Gutermuth et al. 2009). IRS 37-B, IRS 37-C, and ALMA_J162717.7 have no Spitzer or WISE counterpart, but such emission is likely lost in the point-spread function wings of the brighter IRS 37-A source. IRS 37-B and IRS 37-C each have peak 1.3 mm fluxes >20σ. With such high S/N, these two sources have low probabilities of being extragalactic sources (see Section 5.5). Moreover, IRS 37-A, IRS 37-B, and IRS 37-C roughly align with the long axis of their larger host core (Pattle et al. 2015), and this orientation is often seen for wide binary pairs (Sadavoy & Stahler 2017). Thus, we consider IRS 37-B and IRS 37-C to be companions to IRS 37-A. ALMA_J162717.7, however, is much fainter (peak S/N is 8.5σ). Since it has a non-negligible probability of being a background galaxy (see Section 5.5) and it does not align with the host core long axis like the other three sources, we consider it to be an extragalactic object.

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We estimate disk masses of 0.16 ${M}_{\mathrm{Jupiter}}$ for IRS 37-B, 0.15 ${M}_{\mathrm{Jupiter}}$ for IRS 37-C, and 0.12 ${M}_{\mathrm{Jupiter}}$ for IRS 39. IRS 37-B is compact, with a deconvolved size of 14 au × 12.6 au (FWHM), whereas IRS 37-C and IRS 39 are unresolved in our observations.

Field c2d_890 contains a single source, IRS 42. IRS 42 is on the edge of the Oph F core outside the main clump. It has been classified as a Class I object (Evans et al. 2009; Dunham et al. 2015) and a Class II object (Gutermuth et al. 2009) based on its SED. van Kempen et al. (2009) detected only weak HCO⁺ emission, and they found no obvious compact core at 850 μm (see also Pattle et al. 2015). IRS 42 also shows only a marginal outflow detection (White et al. 2015), suggesting that it is perhaps more evolved. We consider this object a Class II source in our analysis.

IRS 42 is not detected in polarization. Figure 24 shows its Stokes I continuum image. Based on the peak intensity, we have a 3σ upper limit of 0.7%, which suggests that this source has very low polarization. The continuum source is unresolved, however, indicating that the central disk must be compact (≲9 au, 1/4 the beam). We estimate a disk mass of 2 ${M}_{\mathrm{Jupiter}}$.

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Field c2d_892 contains Oph-emb-5, a source identified as a Class I YSO in Enoch et al. (2009) based on Bolocam and Spitzer detections. By contrast, Gutermuth et al. (2009) classified the Spitzer infrared object as a transition disk candidate with an infrared spectral index of α = −0.93, and Sadavoy et al. (2010) classified the Spitzer source as an asymptotic giant branch (AGB) star. Subsequent observations indicate that Oph-emb-5 is unlikely to be an embedded YSO. Pattle et al. (2015) found no evidence of a dense core at the position of the Spitzer source in SCUBA-2 observations, and there is no molecular line emission from dense gas tracers showing an envelope or from CO tracing an outflow (White et al. 2015; Kamazaki et al. 2019).

We do not detect Oph-emb-5 in Stokes I continuum. Figure 25 shows the noise map at the position of the Spitzer infrared source, J162721.82-242727.6. This is the only object that was completely undetected in our sample. Cieza et al. (2019) and Kamazaki et al. (2019) also found no continuum object with 1.3 mm ALMA observations. In particular, the observations from Kamazaki et al. (2019) include both the main ALMA array and the compact array and show that there is no disk or envelope structure at the position of the Spitzer source. Our observations have a point-source sensitivity of 26 μJy, which is nearly a factor of 20 better than Kamazaki et al. (2019) and a factor of 6 better than Cieza et al. (2019).

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Kamazaki et al. (2019) argued that the nondetection in their continuum data was consistent with low masses in T Tauri disks. Ansdell et al. (2017) and Long et al. (2018) surveyed T Tauri disks in Orion and Chamaeleon with ALMA and found masses down to M_d ≳ 1.5 × 10⁻⁴ M_⊙ (assuming a gas-to-dust ratio of 100). With our sensitivity, we measure a 3σ upper limit mass of 10⁻⁵ M_⊙ (0.01 ${M}_{\mathrm{Jupiter}}$) with our assumed temperature and opacity. This upper limit is roughly an order of magnitude lower than the masses in Ansdell et al. (2017) and Long et al. (2018). Even if we adopt a more conservative dust opacity of κ_d = 1.1 ${\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$ from the relation κ_d = (10 ${\mathrm{cm}}^{2}\,{{\rm{g}}}^{-1}$)(ν/1000 THz)^β and β = 1.5, which is used in Kamazaki et al. (2019), our 3σ mass limit is still considerably lower than the typical dust masses in T Tauri disks.

With an unclear host core and no detected envelope or disk, Oph-emb-5 is unlikely to be an YSO. Based on its infrared colors matching an extincted AGB star (Sadavoy et al. 2010), we consider this source to be a star that is background to the Ophiuchus cloud.

Field c2d_894 contains a single source, Oph-emb-12. This source is an embedded YSO based on its infrared SED shape (Evans et al. 2009; McClure et al. 2010) and its proximity to a dense core (Evans et al. 2009; Pattle et al. 2015), although the infrared source is offset from the core continuum peak (van Kempen et al. 2009). It also has a compact bipolar nebula at near-infrared wavelengths that is indicative of a nearly edge-on disk (Brandner et al. 2000). It has a marginal outflow detection (White et al. 2015), such that we consider Oph-emb-12 to be a Class I object. Using near- and mid-infrared spectroscopy, Pontoppidan et al. (2005) conducted radiative transfer models for the disk. They estimated a disk mass of 1.6 ${M}_{\mathrm{Jupiter}}$, radius of 90 au, and inclination of 69°.

Figure 26 shows the continuum image of Oph-emb-12. It is undetected in polarization with a 3σ upper limit of 1.8%. The disk is very compact and unresolved. We estimate a disk mass of 0.7 ${M}_{\mathrm{Jupiter}}$ with a disk size of ≲9 au (1/4 the beam). Cieza et al. (2019) similarly did not resolve Oph-emb-12 in their ALMA data at slightly higher resolution.

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Field c2d_899 contains IRS 43, a well-studied protobinary system. Girart et al. (2000) first identified two sources (VLA1 and VLA2) separated by 06 using the VLA. We refer to these sources as IRS 43-A and IRS 43-B, respectively. The IRS 43 system contains embedded protostars. Evans et al. (2009) measured an infrared spectral index and bolometric temperature consistent with deeply embedded Class I protostars, and the stars have a clear outflow and envelope (e.g., McClure et al. 2010; Pattle et al. 2015; White et al. 2015). Girart et al. (2004) proposed that the system was in transition between Class 0 and Class I based on nondetections at near-infrared wavelengths, but subsequent deep near-infrared observations detect this source (e.g., Parks et al. 2014). For this study, we consider the IRS 43 system to be at the Class I stage.

Figure 27 shows the continuum image of IRS 43. We do not detect polarization toward either object in the protobinary. The 3σ upper limits for the nondetections are 0.6% for IRS 43-A and 4.8% for IRS 43-B. Thus, we can only conclude that IRS 43-A has significantly low polarization. Both sources are compact in our observations. We find deconvolved sizes of 16 au × 9 au (FWHM) for IRS 43-A and 15 au × 13 au (FWHM) for IRS 43-B. The inferred masses are 2.4 ${M}_{\mathrm{Jupiter}}$ and 0.3 ${M}_{\mathrm{Jupiter}}$, respectively. These masses agree with the measurements from Brinch et al. (2016) for both sources from 1.1 mm ALMA observations at slightly higher resolution.

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The circumbinary emission around the stars has been seen previously in molecular line emission (Brinch & Jørgensen 2013) and in dust (Brinch et al. 2016). Brinch & Jørgensen (2013) found near-Keplerian motions through the circumbinary disk, and they modeled the molecular line emission to find a mass of ∼0.004 M_⊙ (4.2 ${M}_{\mathrm{Jupiter}}$) and an inclination of 70° for the circumbinary material. Brinch et al. (2016) later resolved the compact disks around IRS 43-A and IRS 43-B and estimated their orbital parameters. They found that the stellar orbits (inclined at 30°) are misaligned with the axis of the circumbinary material and proposed that the system orientation formed by either turbulent fragmentation or ejection of a third component.

The field contains a third source, GY 263, which is located roughly 65 northwest from IRS 43 (see Figure 2). Figure 28 shows the continuum emission for this object. It was not detected in polarization at a 3σ upper limit of 1.3%. GY 263 was also detected by Brinch et al. (2016) in their ALMA data, but it has no Spitzer counterpart in the full c2d source catalog. The Two Micron All Sky Survey (2MASS) detection of GY 263 appears to be an extension of the brighter IRS 43 (see also Beckford et al. 2008; Wilking et al. 2008), indicating that any Spitzer emission may have been confused with the much brighter IRS 43 system. For example, Barsony et al. (2005) observed GY 263 at 10.8 μm and 12.5 μm with Keck at ∼025 resolution and detected the source weakly at 10.8 μm only. They subsequently classified GY 263 as a Class II object. We also consider GY 263 to be a Class II object and measure a deconvolved disk size of 54 au × 18 au (FWHM) and a mass of 2.6 ${M}_{\mathrm{Jupiter}}$.

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Field c2d_901 contains IRS 44. IRS 44 is a well-established Class I object based on its infrared SED (e.g., Evans et al. 2009; Gutermuth et al. 2009), embeddedness in a dense core (e.g., van Kempen et al. 2009; McClure et al. 2010; Pattle et al. 2015), and outflows (e.g., White et al. 2015). Nevertheless, IRS 44 does not appear to have any prior observations at high resolution with an interferometer in the literature and no prior estimates of a disk mass or size.

Figure 29 shows our continuum image of IRS 44. The central continuum source is marginally resolved by the beam but is not detected in polarization with a 3σ upper limit of 0.7%. This upper limit indicates that IRS 44 is significantly unpolarized. The continuum source is compact, with a deconvolved size of 16 au × 9 au (FWHM) and a mass of 1.9 ${M}_{\mathrm{Jupiter}}$.

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Field c2d_902 is centered on IRS 45. This source has varied classifications in the past. Using Spitzer observations, Evans et al. (2009) and Gutermuth et al. (2009) both found relatively flat infrared spectral indices for IRS 45 that indicate a flat-spectrum source, and McClure et al. (2010) identified it as a disk object from infrared spectroscopy. Nevertheless, IRS 45 is located on the edge of a dense core (e.g., van Kempen et al. 2009; Pattle et al. 2015), suggestive of an embedded source. Moreover, Kamazaki et al. (2019) observed this source at 1.3 mm with the ALMA main array and the ACA. They detected a compact continuum source toward IRS 45 with red- and blueshifted CO outflow lobes. Thus, we consider IRS 45 to be a Class I object in this study.

Figure 30 shows the continuum image of IRS 45. We do not detect this object in dust polarization, with a 3σ upper limit of 3.9%. The continuum is also very compact and only marginally resolved with a deconvolved size of 14 au × 8 au (FWHM). The source mass is 0.4 ${M}_{\mathrm{Jupiter}}$, making IRS 45 one of the lower-mass disk candidates in our sample.

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This field also contains a second object, VSSG 18 B, which is 11'' northeast of IRS 45 (see Figure 2). Figure 31 shows the continuum image of VSSG 18 B, which is also undetected in polarization with a 3σ upper limit of 13%. This source is listed in the full c2d catalog as a "red" spectrum object, but it was not originally classified as a YSO in Evans et al. (2009). More recently, VSSG 18 B was identified as a flat-spectrum source in the Spitzer YSO variable catalog (SSTYSV J162729.21-242716.9; Günther et al. 2014). Since VSSG 18 B does not have a clear outflow or 70 μm emission (Kamazaki et al. 2019), it is more likely an evolved YSO. Thus, we consider this object to be a Class II object. This source has a deconvolved size of 17 au × 14 au (FWHM) and a mass of 0.2 ${M}_{\mathrm{Jupiter}}$.

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Field c2d_904 is centered on IRS 47. This object has an infrared SED consistent with a flat-spectrum source or Class II object (Evans et al. 2009; Gutermuth et al. 2009), and McClure et al. (2010) identified its infrared SED as being dominated by a disk. Nevertheless, IRS 47 appears to be driving a large outflow (White et al. 2015; Kamazaki et al. 2019), and it is well detected in mid- and far-infrared wavelengths, with hints of a surrounding core structure from single-dish data (Enoch et al. 2009; Kamazaki et al. 2019). Thus, we consider this source to be a Class I object.

Figure 32 shows the continuum image of IRS 47. We do not detect it in polarization with a 3σ upper limit of 1.1%. The source also appears to be highly inclined. The deconvolved size is roughly 32.5 au × ≲ 1.8 au (FWHM), where the minor-axis dimension depends heavily on the elliptical region we use to fit the source with imfit. This minor-axis limit gives a disk inclination of ≳86°. The estimated disk mass is 1.6 ${M}_{\mathrm{Jupiter}}$.

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We also detect a second compact source 10'' northwest of IRS 47. Figure 33 shows the continuum emission for this source, ALMA_J162729.75-242735.83 (hereafter ALMA_J162729.7). It is not detected in polarization with a 3σ upper limit of 21%. ALMA_J162729.7 was not previously detected in the literature, and there is no counterpart in the 2MASS, Spitzer, or WISE catalogs. Moreover, this source was undetected by Kamazaki et al. (2019) in both dust and gas with their ALMA data. With a peak flux of 12.5σ, ALMA_J162729.7 has a non-negligible probability of being a galaxy (see Section 5.5). Thus, we consider it to be an extragalactic object.

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Figure 2 shows that there is substantial extended emission between IRS 47 and ALMA_J162729.7. Kirk et al. (2017) weakly detected similar extended emission at 3 mm in ∼2'' resolution ALMA data, and Kamazaki et al. (2019) strongly detected this structure in 1.3 mm continuum, ¹³CO (2–1), and C¹⁸O (2–1) in their ALMA observations that combine the 12 m main array and the compact ACA. The arc structure curves further around IRS 47 in the two line tracers, forming a near bubble, and the arc also coincides with 70 μm emission from Herschel (Kamazaki et al. 2019). The arc is highly filtered out in our observations, but its shape matches previous data.

Field c2d_954 contains the deeply embedded Class 0 protostar, Oph-emb-1. This object has a low bolometric temperature (Evans et al. 2009) and a bipolar, well-collimated outflow (Stanke et al. 2006). Spitzer observations further show a prominent jet and an extensive outflow cavity in scattered light and shocked H₂ emission that is viewed nearly face-on (Barsony et al. 2010; Hsieh et al. 2017). Oph-emb-1 also has a dense, symmetric, and mostly spheroidal envelope that shows a small gradient normal to the outflow and also traces the outflow cavity (Tobin et al. 2010, 2011). Previous high-resolution observations of Oph-emb-1 (Chen et al. 2013; Yen et al. 2017; Hsieh et al. 2019b) revealed a compact, elongated structure perpendicular to the outflow that is indicative of a disk. Hsieh et al. (2019b) further show that this structure has red- and blueshifted C¹⁸O (2–1) emission indicative of both infall and rotation. They suggest that Oph-emb-1 is likely to form a brown dwarf.

Figure 34 shows the polarization results for Oph-emb-1. The source is very compact with uniform polarization e-vectors. The polarization position angles are ≈85° over the entire compact structure. By comparison, the disk position angle is −65°, which means that the polarization angles are misaligned with both the major axis and minor axis of the disk. Oph-emb-1 is compact with a deconvolved size of 18.8 au × 6.7 au (FWHM). This disk size is a factor of two smaller than the disk size from lower-resolution ALMA data in Yen et al. (2017), which suggests that their two-Gaussian fit to a compact and extended component may have overestimated the size of the compact component. The inferred disk position angle of −65° is nearly perpendicular to the outflow position angle of 20°–25° (Yen et al. 2017). We measure a disk mass of 2 ${M}_{\mathrm{Jupiter}}$.

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Hsieh et al. (2017) proposed that Oph-emb-1 may be a binary system based on its outflow showing an S-shape morphology in scattered light and H₂ emission. Binary systems induce tidal interactions that can change the momentum vector of the outflowing source and cause the outflow to precess. To test for a possible companion, we re-imaged the c2d_954 field with robust = −2 and no UV taper. The resulting map has a resolution of 02 × 011 (28 au × 15 au), but we find no evidence of substructure toward Oph-emb-1 in this higher-resolution map. Therefore, Oph-emb-1 appears to be a single protostar, although we cannot rule out a companion object at <20 au scales.

Field c2d_963 is centered on Oph-emb-18. This object is located on the outskirts of L1688 and has not been well studied in the literature. It is a low-luminosity source with an SED indicative of a Class I protostar (e.g., Evans et al. 2009; Hsieh & Lai 2013). Antoniucci et al. (2014), however, identified it as a candidate for eruptive EXor accretion based on observations from Spitzer and WISE. EXor events are marked by significant IR excess and redder emission when the source is fading and are typically associated with T Tauri stars (Herbig 2008). van Kempen et al. (2009) also classified this object as a later-stage YSO based on the lack of envelope emission in dust and gas. We consider it a Class II object in this study.

Figure 35 shows the continuum image of Oph-emb-18. This is a relatively fainter source that is not detected in polarization. We estimate a 3σ upper limit for the dust polarization of 4.1%. Despite its faint emission, Oph-emb-18 is marginally resolved in our observations. We find a deconvolved size of 20 au × 11.6 au with a mass of 0.4 ${M}_{\mathrm{Jupiter}}$.

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Field c2d_989 contains a very bright, well-known Class I source, IRS 63. This source has an SED consistent with a Class I object (Evans et al. 2009), but its disk emission is significant (McClure et al. 2010). Nevertheless, IRS 63 has a bipolar outflow (Visser et al. 2002; Dunham et al. 2014) and a surrounding dense envelope (van Kempen et al. 2009), which are expected for an embedded protostar. We consider it a Class I object here. IRS 63 has been well studied in the past, in particular for its large disk (Andrews & Williams 2007; Lommen et al. 2008; Miotello et al. 2014). Previous studies using SMA observations estimated a disk size of 165 au and a mass of 100 ${M}_{\mathrm{Jupiter}}$ from radiative transfer models (e.g., Brinch & Jørgensen 2013). These values indicate that IRS 63 has a very high disk mass for a Class I protostar (e.g., Jørgensen et al. 2009; Aso et al. 2015).

Figure 36 shows the polarization results of IRS 63. We detect substantial polarization across the entire disk and a clear change in the polarization structure as a function of radius. Toward the disk center, the polarization position angles are uniform at ≈60°, nearly parallel to the minor axis of the disk (58°). At larger radial extents, however, the polarization transitions to an azimuthal morphology. This morphology is also captured in the polarized intensity map, which looks peanut shaped.

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IRS 63 is one of the best-resolved sources in our sample. We find a deconvolved size of 68 au × 46 au (FWHM) and a mass of 50 ${M}_{\mathrm{Jupiter}}$. More recently, Cox et al. (2017) observed IRS 63 at ∼02 resolution with ALMA in 0.87 mm dust continuum. They find a smaller disk size of 73 au × 50 au (FWHM) and a smaller mass of 47 ${M}_{\mathrm{Jupiter}}$ from a Gaussian fit to the continuum data. These values should only be considered a first-order estimate, however. First, IRS 63 appears to have a relatively high mass, dense disk. The dust emission toward such a disk may be optically thick (see Appendix C). Indeed, we find a higher disk mass at 1.3 mm than Cox et al. at 0.87 mm. Second, higher-resolution observations indicate that this disk has at least one bright ring (D. Segura-Cox et al. 2019, in preparation). If confirmed, IRS 63 may not be well fit with a simple Gaussian profile and will require more complex disk models to determine its size, mass, and geometry.

Field c2d_990 contains a single object, Oph-emb-4, located roughly 3' south of IRS 63 in L1709. The classification of this source is uncertain. Its Spitzer infrared spectral index has rising blue emission, suggesting that it is a Class II object (van der Marel et al. 2016), but it has a bolometric temperature indicative of a Class I object (e.g., Evans et al. 2009). Moreover, this source is faint. Dunham et al. (2008) identified Oph-emb-4 as a candidate low-luminosity embedded object with no known associated high-density material. Riaz et al. (2018) classified it as a proto–brown dwarf based on a low (<0.1 M_⊙) dust mass from SCUBA-2 observations, and van der Marel et al. (2016) identified it as a low-mass (<5 M_Jupiter) transition disk with a small cavity. We consider this source to be a Class II object.

Figure 37 shows the continuum image of Oph-emb-4. The continuum emission is fairly bright and compact, but it is not detected in polarization. We measure a 3σ upper limit of 0.9%, indicating that the continuum source appears significantly unpolarized compared to typical disks. The source also appears highly inclined. Its deconvolved size is 36 au × 8 au (FWHM), resulting in an estimated inclination of 77°. We also find a mass of 2 ${M}_{\mathrm{Jupiter}}$, which is in agreement with the transition disk limit of <5 M_Jupiter from van der Marel et al. (2016).

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Field c2d_991 is centered on Oph-emb-25. It has an infrared spectral index consistent with a flat-spectrum source and a bolometric temperature consistent with a Class I object (Evans et al. 2009). Oph-emb-25 is another proto–brown dwarf candidate (Riaz et al. 2018; Whelan et al. 2018), although Dunham et al. (2008) do not list this object as a candidate low-luminosity source. Whelan et al. (2018) observed a jet and outflow toward this source with near-infrared spectroscopy. They find a relatively narrow (40° opening angle) and high outflow mass, which suggests that the outflow is young. Nevertheless, Pattle et al. (2015) do not detect a core around the infrared source. We therefore consider Oph-emb-25 to be a flat-spectrum object.

Figure 38 shows the continuum image of Oph-emb-25, which we do not detect in polarization. The 3σ upper limit for the nondetection is 0.9%. We find a deconvolved size of 10 au × 4.5 au (FWHM) with a position angle of −38°. Since the outflow position angle is 50°, the major axis is roughly perpendicular to the direction of the outflow, indicating that the compact object is likely tracing a disk. We estimate a disk mass of roughly 1.5 ${M}_{\mathrm{Jupiter}}$.

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Field c2d_996 is centered on Oph-emb-7. Bontemps et al. (2001) first identified this source with mid-infrared observations and classified it as a Class II object. Spitzer observations, however, yield an infrared spectral index and bolometric temperature that is normally associated with a Class I object (e.g., Evans et al. 2009; Dunham et al. 2015). Nevertheless, Jørgensen et al. (2008) identified this source as a candidate edge-on disk, and single-dish (sub)millimeter observations found no clear surrounding core for this object. There is no corresponding SCUBA or SCUBA-2 core (Jørgensen et al. 2008; Pattle et al. 2015) at the position of this source, and the nearest Bolocam source, Bolo 33, is roughly half an arcminute south of the infrared detection (Young et al. 2006; Enoch et al. 2009). Thus, we consider Oph-emb-7 to be a Class II source.

Figure 39 shows the continuum image of Oph-emb-7. It is the faintest of the main targets in our sample, with a peak flux of only 12σ_peak. We do not detect this source in polarization with a 3σ upper limit of 21%. The continuum emission is unresolved in our data, indicating that the disk is compact (≲9 au; 1/4 the beam). We also find a very low disk mass of 0.05 ${M}_{\mathrm{Jupiter}}$. If we instead calculate the mass in dust only, we find a dust mass of roughly 0.2 M_⊕. Thus, the Oph-emb-7 disk mass appears to be a factor of 9 lower than the lowest-mass Class II disk in Ansdell et al. (2017) for Orion and a factor of 2 lower than the lowest-mass disk in Long et al. (2018) for Chameleon.

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Field c2d_998 contains Oph-emb-15. This source has an uncertain classification. It has been identified as a Class II object (Bontemps et al. 2001) and a Class I object (e.g., Evans et al. 2009; Dunham et al. 2015) based on its SED. We could find no previous outflow observation in the literature for this source, however. Oph-emb-15 appears to have a surrounding core (Jørgensen et al. 2008; Pattle et al. 2015), although the infrared source is located toward the edge of a core (roughly 17'' north of the core peak). This offset is still considered within the core boundary (Sadavoy et al. 2010), and optical observations of Oph-emb-15 show extended nebulosity indicative of a surrounding envelope (Duchêne et al. 2004). Thus, we classify Oph-emb-15 as a Class I source.

Figure 40 shows the continuum image of Oph-emb-15. It is not detected in polarization with a 3σ upper limit of 2.4% for the polarization fraction. The dust emission is compact, however, with a deconvolved size of 16 au × 6 au and a disk mass of 0.6 ${M}_{\mathrm{Jupiter}}$.

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Field c2d_1003 is centered on the well-known Class I system, IRS 67. This object has an established dense core (Young et al. 2006; Pattle et al. 2015), and its infrared emission is consistent with a Class I object (Evans et al. 2009; McClure et al. 2010). It also has signatures of both infall and outflows (Bontemps et al. 1996; Mottram et al. 2017) and strong nebulosity (Duchêne et al. 2004), which signify its youth. Due to its embeddedness, IRS 67 was first identified as a binary system separated by ∼06 through deep infrared observations (McClure et al. 2010). McClure et al. (2010) called the components A and B, where the brighter A source was a disk candidate and the fainter B source was a younger envelope candidate. More recently, Artur de la Villarmois et al. (2018) observed IRS 67 with ALMA in Band 7 at ∼04 resolution. They spatially resolved the A and B components and also detected a circumbinary disk around them in dust and gas emission. The circumbinary structure also shows a clear velocity gradient that is consistent with Keplerian rotation and infall.

Figure 41 shows the polarization results for IRS 67. IRS 67-B is much brighter than IRS 67-A at millimeter wavelengths (see also Artur de la Villarmois et al. 2018), and subsequently, we detect uniform dust polarization only toward IRS 67-B. The polarization is fairly uniform, with typical position angles of 87° that are nearly aligned with the long axis of the disk at 89°. IRS 67-B also has relatively low polarization fractions of ≲1%. IRS 67-A is not detected in dust polarization with a 3σ upper limit of 1%. If IRS 67-A has similar polarization fractions to IRS 67-B, it would be below our sensitivity.

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Both sources are compact. We find a deconvolved disk size of 8 au × 7 au (FWHM) and a mass of 1.4 ${M}_{\mathrm{Jupiter}}$ for IRS 67-A and 15.8 au × 9.3 au (FWHM) and 8.6 ${M}_{\mathrm{Jupiter}}$ for IRS 67-B. We also detect the circumbinary disk around the stars in Stokes I continuum, although the extended dust emission is highly filtered out in our observations.

Field c2d_1008 contains the well-studied Class 0 protostellar system, IRAS 16293-2422 (hereafter IRAS 16293). This is a deeply embedded protostellar system in L1689N containing two main complexes, IRAS 16239A to the south and IRAS 16293B to the north, separated by roughly 5'' (e.g., Chen et al. 2013; Jørgensen et al. 2016). Both sources have been the target of extensive study for their hot core chemistry (e.g., Schöier et al. 2002; Jørgensen et al. 2011; Pineda et al. 2012), including a dedicated ALMA survey to sample the molecular line emission of this source over 40 GHz in Band 7 (e.g., Jørgensen et al. 2016; Manigand et al. 2019, and references therein). The ALMA observations have also revealed an extensive dust bridge between the stars (e.g., Pineda et al. 2012; Jacobsen et al. 2018; van der Wiel et al. 2019).

Figure 42 shows the polarization results for IRAS 16293. These data were previously discussed in Paper II. Briefly, this map shows the most extensive and complex polarization structure of the entire sample. We see distinct and resolved polarization morphologies for IRAS 16293A and IRAS 16293B and polarization in the dust bridge between them, as well as the dust streamers from each of the stars. We also resolve a depolarization zone between the northern streamer from IRAS 16239B and the bridge between the stars (Paper II). This depolarization region also aligns well with the bluer dust emission from the three-color image of IRAS 16293 from Jørgensen et al. (2016).

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We note that Figure 42 shows more polarization e-vectors than Paper II owing to the updated polarization debiasing method (see Section 2.4) that reliably corrects polarization e-vectors with 3 < ${{ \mathcal P }}_{I}$/${\sigma }_{{ \mathcal P }I}$ < 4. Most of the new e-vectors are in the lower emission regions and do not alter the conclusions in Paper II. We also see evidence of very high polarization fractions >10% toward the periphery of IRAS 16293B and the bridge.

The dust emission and dust polarization seen toward IRAS 16293A and IRAS 16293B are likely tracing material from the inner envelope around and between the two stars rather than disks. As such, we use a Gaussian fit to only the brightest emission (>100 mJy beam⁻¹) to estimate the general morphology of each source. Since this emission primarily traces envelopes rather than disks, we do not attempt to estimate their disk masses.

Field VLA1623a is centered on VLA 1623W (see Figure 2), one of the protostellar objects embedded within the VLA 1623.4-2418 core, the canonical Class 0 object (André et al. 1993). Bontemps & Andre (1997) first identified this component in VLA radio emission at 3.6 cm and 6 cm observations and initially called it clump B. The source name changed to VLA 1623 West (or VLA 1623W) in Chen et al. (2013) following the naming contention of VLA 1623A and VLA 1623B for the eastern sources (Looney et al. 2000). VLA 1623A/B are also in the field but will be discussed in Appendix A.26.

The classification of VLA 1623W has been under debate (Maury et al. 2012; Murillo et al. 2018). The SED of the VLA 1623 core indicates that VLA 1623A/B protostars are deeply embedded (e.g., Evans et al. 2009; Gutermuth et al. 2009) with a prominent bipolar outflow (e.g., White et al. 2015), but the SED of VLA 1623W peaks at shorter wavelengths. VLA 1623W also has a lower envelope mass compared to VLA 1623A/B (Murillo & Lai 2013; Murillo et al. 2018), and it has no obvious outflow (Nisini et al. 2015; Santangelo et al. 2015). Nevertheless, we consider this source to be a Class 0 object in this study. First, VLA 1623W appears to be comoving with VLA 1623A/B (Harris et al. 2018) and associated with the same dense core (Pattle et al. 2015). Second, VLA 1623W still has a substantial envelope, although it may be more tenuous than the envelope around VLA 1623A/B. Murillo et al. (2018) note that their ALMA data recover scales out to ∼400 au, whereas the envelope can extend to 1000 au scales. For example, Kirk et al. (2017) measured a more comparable envelope mass of 0.1 M_⊙ for VLA 1623W with 3 mm ALMA data that recover emission out to 3000 au.

Figure 43 shows the polarization results for VLA 1623W. We see uniform polarization structure, with position angles of roughly −81° across the disk that are aligned with the disk minor axis of −80°. The disk also appears to be highly elongated. We measure a disk size of 99 au × 14.7 au (FWHM) and a mass of 10.6 ${M}_{\mathrm{Jupiter}}$.

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The 1.3 mm polarization in Figure 43 is in good agreement with 872 μm polarization from Harris et al. (2018). The average 872 μm polarization position angle was −80° across VLA 1623W. This agreement is significant not only to help identify the polarization mechanism (see Section 4) but also to trust the 872 μm polarization observations of VLA 1623W, which was not located at the phase center of the primary beam. Harris et al. (2018) centered their map between VLA 1623W and VLA 1623A/B, such that each system was roughly 5'' from the phase center. This positioning placed VLA 1623W outside the inner third of the primary beam FWHM (R ≈ 3'' at 345 GHz). Although off-axis polarization is considered less reliable, Harris et al. (2018) argued that the agreement between their off-axis polarization data at 872 μm and the on-axis 1.3 mm polarization data presented here indicates that their measurements are robust. In Appendix B, we test the polarization measurements for adjacent fields and indeed find that the dust polarization is largely consistent for separations ≲10''.

Field VLA1623b is centered on VLA 1623A/B. Both sources are well studied in the literature and are separated by ≈1'' (Chen et al. 2013). We consider these sources to be Class 0 objects (André et al. 1993), as both sources are deeply embedded in a dense core (e.g., Pattle et al. 2015), they have cold SEDs (e.g., Evans et al. 2009; Gutermuth et al. 2009; Murillo et al. 2018), and at least one of them is driving a powerful, bipolar outflow (e.g., Murillo & Lai 2013; White et al. 2015). VLA 1623A further has a large (R ≈ 180 au), massive disk that shows evidence of Keplerian rotation (Murillo et al. 2013; Hsieh et al. 2019a). Harris et al. (2018) used very high resolution data to show that the VLA 1623A source is itself a tight binary system (VLA 1623Aa and VLA 1623Ab) separated by ∼14 au such that the large disk around VLA 1623A is a circumbinary disk. For simplicity, we use VLA 1623A to refer to the unresolved circumstellar material from VLA 1623Aa and VLA 1623Ab. The field also contains VLA 1623W, which we discuss in Appendix A.25.

Figure 44 shows extensive polarization across VLA 1623A/B. These observations were first discussed in Paper I and are consistent with that study. In brief, the polarization structures of VLA 1623A and VLA 1623B show two distinct morphologies. The dust polarizations toward the compact, circumstellar material around VLA 1623A and VLA 1623B are both uniform with angles of ≈−50° that are roughly parallel to the minor axes of the dust emission. In the extended dust emission around VLA 1623A (e.g., toward the larger Keplerian circumbinary disk), the dust polarization is azimuthal. These dual polarization morphologies are also seen at 872 μm by Harris et al. (2018). The deconvolved sizes are 50.5 au × 22 au for the circumstellar material of VLA 1623A (e.g., excluding the extended dust emission) and 44 au × 14.4 au for the circumstellar disk of VLA 1623B (see also Paper I). Their estimated masses are 22 and 20.6 ${M}_{\mathrm{Jupiter}}$, respectively.

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Appendix A.26 also shows several additional polarization e-vectors to Paper I. Since we use a more robust debiasing method (see Section 2.4), we are able to include these polarization e-vectors that have lower S/N (3 < ${{ \mathcal P }}_{I}$/${\sigma }_{{ \mathcal P }I}$ < 4). In particular, there are three e-vectors in the upper left quadrant that were previously below the selection criteria in Paper I. These new e-vectors are consistent with the overall azimuthal polarization structure seen in the circumbinary disk.

This field also contains a fourth object, VLA 1623NE, 19'' northeast of VLA 1623A/B (see Figure 2). Figure 45 shows the continuum emission for this object. It is not detected in polarization with a 3σ upper limit of 3.9%. The continuum source is well resolved, with a deconvolved size of 81 au × 37 au and a mass of 8 ${M}_{\mathrm{Jupiter}}$. Kirk et al. (2017) found a much higher mass of 0.071 M_⊙ (74 ${M}_{\mathrm{Jupiter}}$) in lower-resolution 3 mm observations, whereas Kawabe et al. (2018) found ∼25 ${M}_{\mathrm{Jupiter}}$ using ALMA and VLA observations between 1 mm and 6 cm. As these observations have lower resolution, the dust masses may be affected by envelope emission.

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VLA 1623NE has unclear classification. It is also called VLA 1623N1 (Chen & Hirano 2018) and Source X (Kawabe et al. 2018). It has been previously seen at (sub)millimeter wavelengths (e.g., Kirk et al. 2017; Chen & Hirano 2018) and in X-rays with Chandra (Imanishi et al. 2003; Gagné et al. 2004), but it is not seen in dense gas tracers (Chen & Hirano 2018) or in the infrared (Evans et al. 2009; Gutermuth et al. 2009). There is no corresponding object in the entire c2d catalog at this position, although there is extended mid-infrared emission at its position that could be obscuring a fainter point source. Kawabe et al. (2018) detected high-velocity blueshifted and redshifted CO (2–1) emission near VLA 1623NE, but the emission overlaps northeast of the source and there is no corresponding lobe to the southwest. If this emission is from an outflow, Kawabe et al. (2018) suggest that the outflow axis must be along the plane of the sky and that VLA 1623NE is either a proto–brown dwarf or a very young low-mass protostar. Since VLA 1623NE coincides with X-ray emission but lacks a clear outflow and dense gas, we consider it to be a Class II YSO. Based on our estimated disk mass of 8 ${M}_{\mathrm{Jupiter}}$, we suggest that VLA 1623NE is a Class II source that will form a low-mass star rather than a proto–brown dwarf.

Field IRAS 16288 contains the infrared source ISO Oph 210. This source has not been well studied in the literature. It was first identified in mid-infrared emission with ISO by Bontemps et al. (2001) and subsequently detected in near-infrared emission with 2MASS (Cutri et al. 2003). This source was also detected in Spitzer observations of Ophiuchus but was classified as a star ("star+dust(IR1)") in Evans et al. (2009). Hsieh & Lai (2013) revisited the Spitzer observations and found that this source is consistent with an embedded YSO, and Duchêne et al. (2004) consider this object a flat-spectrum source based on its infrared spectral index. But ISO Oph 210 has no corresponding dense core (e.g., Pattle et al. 2015) and unknown outflow properties. Given its lack of complimentary information, we classify this object as a flat-spectrum source (Duchêne et al. 2004).

Figure 46 shows the continuum source for ISO Oph 210. It is undetected in polarization with a 3σ upper limit of 2%, which is marginally significant given the typical polarization fraction for young stars. The continuum source is also compact. We find a deconvolved source size of 26 au × 14.4 au, with a mass of 0.8 ${M}_{\mathrm{Jupiter}}$.

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Duchêne et al. (2004) also detect a second near-infrared object 78 south of ISO Oph 210. We do not see any object at this position. Instead, we find a new detection roughly 15'' east of the YSO. Figure 47 shows the continuum image of this source, which we call ALMA_J163203.31-245614.43 (hereafter ALMA_J163203.3). This object is much fainter than ISO Oph 210, and it is undetected in polarization with a 3σ upper limit of 33%. We could find no corresponding emission within 5'' of this source position at any other wavelength in a literature search with SIMBAD (Wenger et al. 2000) and Vizier (Ochsenbein et al. 2000). Based on its faint detection (peak Stokes I S/N ≈ 7) and its lack of complementary data, we classify ALMA_J163203.3 as a background galaxy (see Section 5.5).

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