<figure><img src="image_45.png" /><figcaption>**Figure 42.** Same as Figure 13, except for IRAS 16293A and IRAS 16293B. We also added the criterion that $P_F/\sigma_{PF} > 3$ to remove spurious e-vectors at the edges and off source. The dotted blue line segments indicate polarization fractions >10%. IRAS 16293A is located to the south, and IRAS 16293B is located to the north (see Figure 2).</figcaption></figure>

emission from the three-color image of IRAS 16293 from Jørgensen et al. (2016).

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 $3 < P_I/\sigma_{PI} < 4$. 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.

### A.25. Field VLA1623a: VLA 1623 West

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 $M_\odot$ 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 $M_\odot$ Jupiter.

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 ($R \approx 3''$ at
<figure><img src="image_46.png" /><figcaption>Figure 43. Same as Figure 13, except for VLA 1623W.</figcaption></figure>

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".

### A.26. Field VLA1623b: VLA 1623 East

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 ($R \approx 180$ 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 $M_{\text{Jupiter}}$, respectively.

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 ($3 < P_I/\sigma_{P_I} < 4$). 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 $3\sigma$ upper limit of 3.9%. The continuum source is well resolved, with a deconvolved size of 81 au × 37 au and a mass of $8 M_{\text{Jupiter}}$. Kirk et al. (2017) found a much higher mass of 0.071 $M_{\odot}$ (74 $M_{\text{Jupiter}}$) in lower-resolution 3 mm observations, whereas Kawabe et al. (2018) found ~25 $M_{\text{Jupiter}}$ 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.

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
<figure><img src="image_47.png" /><figcaption>**Figure 44.** Same as Figure 13, except for VLA 1623A and VLA 1623B. We used a stricter selection criterion of $I/\sigma_I > 50$ to exclude the noise-like features within the extended emission of the larger VLA 1623-A circumbinary disk, but they are unlikely to be real because they are smaller than the beam.</figcaption></figure>

<figure><img src="image_48.png" /><figcaption>**Figure 45.** Dust continuum map for VLA 1623NE. This source was not detected in polarization.</figcaption></figure>

<caption>**Figure 46.** Dust continuum map for ISO Oph 210. This source was not detected in polarization.</caption>

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 $M_{\text{Jupiter}}$,

we suggest that VLA 1623NE is a Class II source that will form a low-mass star rather than a proto-brown dwarf.

## A.27. Field IRAS 16288: ISO Oph 210

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
<figure><img src="image_49.png" /><figcaption>**Figure 47.** Dust continuum map for ALMA\_J163203.3. This source was not detected in polarization.</figcaption></figure>

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 complementary 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 $3\sigma$ 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 $M_{\text{Jupiter}}$.

Duchêne et al. (2004) also detect a second near-infrared object 7" 8 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 $3\sigma$ 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).

## Appendix B
Off-axis Polarization

In this appendix, we test the on-axis and off-axis polarization observations for IRAS 16293 and VLA 1623. The ALMA Observatory limits reliable polarization measurements to the inner third of the primary beam FWHM, where polarization

<figure><img src="image_50.png" /><figcaption>**Figure 48.** Polarization for IRAS 16293A and IRAS 16293B from the individual fields. Field c2d_1008b (centered on IRAS 16293A) is shown by green line segments, and Field c2d_1008b (centered on IRAS 16293B) is shown by magenta line segments. We also added the criterion that $P_F/\sigma_{PF} > 3$ to remove spurious e-vectors at the edges and off source. IRAS 16293A is located to the south, and IRAS 16293B is located to the north (see Figure 2).</figcaption></figure>

measurements at larger radial extents are considered less reliable. At 1.3 mm, this area corresponds to the inner 4" of the primary beam. Nevertheless, we have overlapping fields that are centered on different sources separated by roughly 5" (IRAS 16293) and 10" (VLA 1623), which puts the phase centers of the two fields outside of the nominal inner third of the primary beam FWHM. We use the independent polarization measurements for both of these cases to determine whether or not we can use the off-axis polarization measurements or mosaic the overlapping fields.

Figure 48 compares the polarization observations for Field c2d_1008a (green line segments, centered on IRAS 16293A) and Field c2d_1008b (purple line segments, centered on IRAS 16293B). We use the same criteria listed in Section 3.2, with the additional criterion that $P_F/\sigma_{PF} > 3$ to avoid spurious e-vectors at the edges of the map (see also Figure 42). The polarization structures from the two maps have excellent agreement, even though the maps are on-axis for one source and slightly off-axis (e.g., positioned outside the inner third of the primary beam FWHM) for the other source.

To quantify the agreement, we compare both fields directly. Figure 49 shows the continuum, polarized intensity, polarization position angle, and polarization fraction from both fields, with c2d_1008a as "Field 1" and c2d_1008b as "Field 2." We only show the data points for the 959 e-vectors given in Figure 48 that have robust detections in both fields. The dashed lines in each panel show a perfect one-to-one relation. We find excellent agreement between the two fields, even though the two fields contain both compact and extended emission and both fields contain emission that extends beyond the inner third of the primary beam FWHM (see Figure 2).

We also have two overlapping fields of VLA 1623, with one field centered on VLA 1623A and VLA 1623B and the other field centered on VLA 1623W. The VLA 1623A/B and VLA 1623W field centers are separated by a larger distance (~10")
<figure><img src="image_51.png" /><figcaption>**Figure 49.** Comparison between fields c2d_1008a (Field 1) and c2d_1008b (Field 2) in (a) Stokes *I* continuum, (b) debiased polarized intensity, (c) polarization position angle, and (d) polarization fraction. The data points only correspond to e-vectors that are measured in both fields in Figure 48. Dashed lines show a one-to-one relation.</figcaption></figure>

<figure><img src="image_52.png" /><figcaption>**Figure 50.** Dust polarization maps for VLA 1623A/B (left) and VLA 1623W (right). In both panels, the on-axis e-vectors are shown in green and the off-axis e-vectors are shown in purple. We show only those e-vectors that match the same criteria as in Figures 44 and 43, respectively.</figcaption></figure>
<figure><img src="image_53.png" /></figure>

<figure><img src="image_54.png" /></figure>

<figure><img src="image_55.png" /></figure>

<figure><img src="image_56.png" /></figure>

**Figure 51.** Comparison between VLA 1623A/B from the on-axis field and off-axis field in (a) Stokes *I* continuum, (b) debiased polarized intensity, (c) polarization position angle, and (d) polarization fraction. The data points only correspond to e-vectors that are measured in both fields in Figure 50. Dashed lines show a one-to-one relation. The dotted line in panel (b) shows a linear least-squares fit to the observations, with a slope of 0.90 ± 0.01.

than the two IRAS 16293 fields (5") and extend over an area beyond the inner half of the primary beam (see Figure 2). Thus, the off-axis uncertainties may be more significant for this region.

Figure 50 compares the polarization observations from the two fields containing VLA 1623. In both cases, the green line segments show the on-axis polarization results, and the purple line segments show the off-axis results using the same criteria listed in Section 3.2, with the additional criterion that $I/σ_I > 50$ to avoid spurious e-vectors at the edges of the disk in VLA 1623A (see also Figure 44). As with IRAS 16293, we find good agreement between the on-axis and off-axis polarization structure, suggesting that the off-axis data are reliable.

Figure 51 compares the polarization measurements for VLA 1623A/B in the on-axis (Field VLA1623b) data and the off-axis (Field VLA1623a) data. This figure contains data points for only the 93 e-vectors given in Figure 50 that have robust detections in both fields. In general, we find broad agreement between the on-axis and off-axis measurements, with near one-to-one relations for the Stokes *I* continuum and polarization position angle. The polarization intensity, however, appears to be slightly underestimated in the off-axis map over the on-axis map at the high-intensity end and overestimated at the low-intensity end. The dotted line in

Figure 51(b) shows a best-fit linear least-squares relation with a slope of 0.90 ± 0.01. As a consequence, the polarization fractions can vary by roughly a factor of two between the on-axis and off-axis measurements.

Figure 52 shows the corresponding results for VLA 1623W. VLA 1623W is considerably fainter and smaller than VLA 1623A/B, resulting in only 10 matching e-vectors between the on-axis and off-axis maps. With such small numbers, it is difficult to draw any conclusions about the reliability of the off-axis observations. We use the on-axis and off-axis results for VLA 1623A/B instead and include this figure for completeness.

The IRAS 16293 fields are separated by 5", whereas the VLA 1623 fields are separated by 10". Thus, we can expect the off-axis VLA 1623A/B sources to be more susceptible to uncertainties in the polarization calibration than the off-axis IRAS 16293 observations. The strong agreement in Figure 49 suggests that our polarization measurements should be considered robust within roughly the inner half of the primary beam FWHM (e.g., a radius of 6"). While the polarization measurements are less reliable with larger separations, we note that a 10" offset from the phase center still produces good polarization position angles. These results indicate that we can reliably mosaic the two IRAS 16293 fields, but we do not attempt to mosaic the two VLA 1623 fields.
<figure><img src="image_57.png" /><figcaption>Figure 52. Same as Figure 51, but for VLA 1623W.</figcaption></figure>

<figure><img src="image_58.png" /></figure>

## Appendix C
### Disk Optical Depth

In this appendix, we calculate the spectral index, $\alpha$, for the disks with multiple continuum wavelengths in the literature as a proxy for the disk optical depth. We use optical depth to help determine why some disks are undetected in polarization and to also investigate the polarization mechanism for those disks that are detected. For simplicity, we infer optical depths from the dust opacity index, $\beta$, assuming $\beta \to 0$ as the dust emission becomes optically thick (e.g., the dust emits like a perfect blackbody). We note that $\beta$ is only a proxy for optical depth. It can also vary from changes in dust grain size, shape, composition, and structure (e.g., Ossenkopf & Henning 1994; Ormel et al. 2011). In addition, a temperature gradient in the disk can broaden the SED and flatten $\beta$ (e.g., Shetty et al. 2009). Thus, a true characterization of dust opacity for these disks will require detailed modeling of their intensity profiles and geometry over multiple wavelengths, which is beyond the scope of the current paper.

We measure $\beta$ by combining our 233 GHz fluxes with complementary fluxes in the literature. We only consider emission $> 10$ GHz from our 233 GHz observations to ensure that there is a large enough lever arm to constrain the spectral index and $\beta$. We also require comparable resolution $\lesssim 0''5$ to our ALMA observations so that the data cover spatial scales similar to our 233 GHz data. This last criterion is necessary, as most of our disks are embedded in dense envelopes.

Lower-resolution observations may therefore be biased toward the envelope emission and have elevated fluxes.

Table 10 lists the disks where we found complementary, high-resolution observations in the literature. Column (2) lists our 233 GHz flux density from Table 3. Columns (3) and (4) give the frequency and total flux density from the literature (reference in the fifth column). The fluxes are similarly obtained from Gaussian fits. If the reference did not quote an error for their source fluxes, we assume 10%. Columns (6) and (7) give our estimated values of $\alpha$ and $\beta$ from combining our 233 GHz fluxes with the literature values and Column (8) gives our assessment of the optical depth. We measure $\beta$ using the flux density spectral index, $S_{\nu} \sim \nu^{\alpha}$, where $\alpha = \beta + 2$ (e.g., Beckwith & Sargent 1991) for dust emission along the Rayleigh-Jeans tail of the SED.

We note, however, that if the dust emission is cold (e.g., $\lesssim 10$ K), even the 1.3 mm emission may not be on the Rayleigh-Jeans tail, such that spectral index will appear flatter. We require an estimate of the dust temperature to properly correct the SED, however. Since we do not have accurate dust temperatures, we use the spectral index slope alone to give a first-order estimate of $\beta$. The spectral index may also appear steeper or flatter (or negative) from dust scattering (Liu 2019; Zhu et al. 2019), which can increase or decrease $\alpha$ depending on the albedo of the dust grains, the grain size distribution, and whether or not the dust emission is optically thick. Since several disks show polarization signatures consistent with dust self-scattering, we expect the dust scattering to also affect the SED slope. Nevertheless, correcting for dust scattering in the
<table><caption>**Table 10**
Dust Opacity Estimations</caption><thead><tr><th>Source</th><th>S<sub>1.3</sub><br>(mJy)</th><th>ν<sup>a</sup><br>(GHz)</th><th>S<sub>ν</sub><sup>a</sup><br>(mJy)</th><th>Ref<sup>a</sup></th><th>α</th><th>β</th><th>Comments</th></tr></thead><tbody><tr><td>GSS 30 IRS 1</td><td>13.4 ± 0.13</td><td>349.6</td><td>31.1 ± 0.2</td><td>1</td><td>2.12 ± 0.04</td><td>0.12 ± 0.04</td><td>Appears optically thick</td></tr><tr><td>GSS 30 IRS 3</td><td>158.5 ± 1.7</td><td>349.6</td><td>379.3 ± 3.6</td><td>1</td><td>2.19 ± 0.05</td><td>0.19 ± 0.05</td><td>Appears optically thick</td></tr><tr><td>Oph-emb-9</td><td>45.0 ± 0.2</td><td>343.8</td><td>105.0 ± 0.5</td><td>2</td><td>2.18 ± 0.03</td><td>0.18 ± 0.03</td><td>Appears optically thick</td></tr><tr><td>GY 91</td><td>88.8 ± 6.5</td><td>348.6</td><td>258 ± 26</td><td>3</td><td>2.64 ± 0.44</td><td>0.64 ± 0.44</td><td>Not optically thick</td></tr><tr><td>Oph-emb-6</td><td>53.1 ± 0.3</td><td>348.6</td><td>128.3 ± 0.6</td><td>2</td><td>2.27 ± 0.03</td><td>0.27 ± 0.03</td><td>Appears optically thick</td></tr><tr><td>WL 17</td><td>51.26 ± 0.83</td><td>349.6</td><td>130 ± 0.5</td><td>1</td><td>2.29 ± 0.05</td><td>0.29 ± 0.05</td><td>Appears optically thick</td></tr><tr><td>Elias 29</td><td>17.2 ± 0.2</td><td>348.6</td><td>41.2 ± 0.6</td><td>2</td><td>2.25 ± 0.06</td><td>0.25 ± 0.06</td><td>Appears optically thick</td></tr><tr><td>IRS 43-A</td><td>15.08 ± 0.33</td><td>252</td><td>18.5 ± 1.9</td><td>4</td><td>2.61 ± 1.5</td><td>0.61 ± 1.5</td><td>Not optically thick</td></tr><tr><td>...</td><td>15.08 ± 0.33</td><td>348.6</td><td>41.6 ± 1.9</td><td>2</td><td>2.61 ± 0.17</td><td>0.61 ± 0.17</td><td>Not optically thick</td></tr><tr><td>IRS 43-B</td><td>1.92 ± 0.07</td><td>348.6</td><td>7.5 ± 1.0</td><td>2</td><td>3.5 ± 0.4</td><td>1.5 ± 0.4</td><td>Not optically thick</td></tr><tr><td>IRS 44</td><td>12.0 ± 0.3</td><td>348.6</td><td>38.6 ± 1.2</td><td>2</td><td>3.00 ± 0.15</td><td>1.00 ± 0.15</td><td>Not optically thick</td></tr><tr><td>Oph-emb-1</td><td>12.5 ± 0.13</td><td>217.24</td><td>10.1 ± 0.4</td><td>5</td><td>3.04 ± 0.72</td><td>1.04 ± 0.72</td><td>Not optically thick</td></tr><tr><td>...</td><td>12.5 ± 0.13</td><td>344.6</td><td>36.7 ± 1.9</td><td>5</td><td>2.75 ± 0.16</td><td>0.75 ± 0.16</td><td>Not optically thick</td></tr><tr><td>...</td><td>12.5 ± 0.13</td><td>348.6</td><td>39.8 ± 0.7</td><td>2</td><td>2.98 ± 0.06</td><td>0.98 ± 0.06</td><td>Not optically thick</td></tr><tr><td>IRS 63</td><td>312.2 ± 8.8</td><td>343.48</td><td>776 ± 35</td><td>6</td><td>2.35 ± 0.19</td><td>0.35 ± 0.19</td><td>Appears optically thick</td></tr><tr><td>Oph-emb-15</td><td>3.7 ± 0.1</td><td>343.8</td><td>11.3 ± 0.3</td><td>2</td><td>2.87 ± 0.13</td><td>0.87 ± 0.13</td><td>Not optically thick</td></tr><tr><td>IRS 67-A</td><td>8.59 ± 0.2</td><td>343.8</td><td>35.7 ± 7</td><td>2</td><td>3.66 ± 0.64</td><td>1.66 ± 0.64</td><td>Not optically thick</td></tr><tr><td>IRS 67-B</td><td>53.4 ± 0.4</td><td>343.8</td><td>155.5 ± 4</td><td>2</td><td>2.74 ± 0.09</td><td>0.74 ± 0.09</td><td>Not optically thick</td></tr><tr><td>VLA 1623W</td><td>65.5 ± 1.2</td><td>343.8</td><td>159 ± 5</td><td>7</td><td>2.28 ± 0.13</td><td>0.28 ± 0.13</td><td>Appears optically thick</td></tr><tr><td>VLA 1623B</td><td>123.7 ± 5</td><td>343.8</td><td>324 ± 5</td><td>7</td><td>2.48 ± 0.08</td><td>0.48 ± 0.08</td><td>Appears optically thick</td></tr><tr><td>VLA 1623A</td><td>141.8 ± 5.9</td><td>343.8</td><td>368 ± 26</td><td>7</td><td>2.45 ± 0.29</td><td>0.45 ± 0.29</td><td>Appears optically thick</td></tr></tbody></table>

**Note.**

<sup>a</sup> Frequency and flux for select disks in the literature. We assume 10% errors on flux if the errors are not reported. We exclude IRS 43-B because it was too faint to robustly measure its source flux relative to its larger circumbinary disk. References correspond to (1) P. Sheehan (2019, private communication); (2) Artur de la Villarmois et al. (2019); (3) van der Marel et al. (2019); (4) Brinch et al. (2016); (5) Hsieh et al. (2019b); (6) Cox et al. (2017); (7) Harris et al. (2018).

SED would require extensive multiwavelength observations and radiative transfer modeling, which is beyond the scope of this paper and beyond the current data sets available for most sources. We therefore assume that the effects of dust scattering on α (and β) are negligible in our analysis.

Eighteen disks have complementary high-resolution data in the literature for at least one alternative wavelength. Oph-emb-1 and IRS 43-A have several complementary data sets in the literature, and we report the values of α and β for each of them separately. Fifteen of the sampled disks (83%) have $β < 1$ ($α < 3$), and 10 (56%) have $β < 0.5$ ($α < 2.5$). IRS 43-B, IRS 44, Oph-emb-1, and IRS 67-A are the only two disks with $β \gtrsim 1$. Oph-emb-1, however, has a slightly shallower value of $β \sim 0.75$ using 344.6 GHz data from Hsieh et al. (2019b). For simplicity, we report the median slope of $0.98 \pm 0.06$ for Oph-emb-1 in Section 4.1. Finally, we note that IRAS 16293B has a known spectral index of $α \approx 2$ down to radio frequencies (e.g., Chandler et al. 2005), which indicate that $β \approx 0$ for this object. We do not include this measurement in Table 10, as we do not have a reliable measurement of the 1.3 mm flux density for its disk.

The disks with uniform polarization aligned with their minor axes have $β < 0.5$ ($α < 2.5$). If $β < 0.5$ indicates that these disks are optically thick, then the polarization morphology should be dominated by self-scattering processes over grain alignment. Polarization from grain alignment with a magnetic field is suppressed relative to dust self-scattering if the emission is optically thick (Yang et al. 2017). When dust grains are aligned in a specific direction (e.g., with a magnetic field), their thermal emission is expected to be preferentially aligned with the long axis and will appear polarized (e.g., Hildebrand et al. 2000; Cho & Lazarian 2007). If the emission originates from an isothermal slab (a rough approximation of a disk midplane), we

can expect to detect emission both parallel to and perpendicular to the dust grain long axis as the optical depth increases. These two contributions will then become equal in the optically thick ($τ \gg 1$) case, and their resulting emission will appear unpolarized (Yang et al. 2017). As a result, one will not detect any polarization from grain alignment in the optically thick limit, but polarization from self-scattering can be detected.

To first order, we consider disks with $β < 0.5$ to be optically thick sources, whereas the sources with $β > 0.5$ do not appear to be optically thick. Sources with $β > 0.5$ also do not show clear signatures of dust self-scattering, even if they are highly inclined. In particular, Oph-emb-1 and IRS 67-B are inconsistent with dust self-scattering for inclined, optically thick disks (see Section 4). We note that there are several optically thick disks ($β < 0.5$) that are not detected in polarization (e.g., WL 17). We discuss these sources in more detail in Section 5.4.

**ORCID iDs**

Sarah I. Sadavoy https://orcid.org/0000-0001-7474-6874
Ian W. Stephens https://orcid.org/0000-0003-3017-4418
Philip C. Myers https://orcid.org/0000-0002-2885-1806
Leslie Looney https://orcid.org/0000-0002-4540-6587
John Tobin https://orcid.org/0000-0002-6195-0152
Woojin Kwon https://orcid.org/0000-0003-4022-4132
Dominique Segura-Cox https://orcid.org/0000-0003-3172-6763

**References**

Alves, F. O., Girart, J. M., Caselli, P., et al. 2017, A&A, 603, L3
Alves, F. O., Girart, J. M., Padovani, M., et al. 2018, A&A, 616, A56
Andersen, B. C., Stephens, I. W., Dunham, M. M., et al. 2019, ApJ, 873, 54
Andersson, B.-G., Lazarian, A., & Vaillancourt, J. E. 2015, ARA&A, 53, 501
Andre, P., Martin-Pintado, J., Despois, D., & Montmerle, T. 1990, A&A, 236, 180

André, P., & Montmerle, T. 1994, ApJ, 420, 837

André, P., Ward-Thompson, D., & Barsony, M. 1993, ApJ, 406, 122

Andrews, S. M., Rosenfeld, K. A., Kraus, A. L., & Wilner, D. J. 2013, ApJ, 771, 129

Andrews, S. M., & Williams, J. P. 2007, ApJ, 659, 705

Andrews, S. M., Wilner, D. J., Hughes, A. M., Qi, C., & Dullemond, C. P. 2009, ApJ, 700, 1502

Ansdell, M., Williams, J. P., Manara, C. F., et al. 2017, AJ, 153, 240

Ansdell, M., Williams, J. P., van der Marel, N., et al. 2016, ApJ, 828, 46

Antoniucci, S., Giannini, T., Li Causi, G., & Lorenzetti, D. 2014, ApJ, 782, 51

Artur de la Villarmois, E., Jørgensen, J. K., Kristensen, L. E., et al. 2019, A&A, 626, A71

Artur de la Villarmois, E., Kristensen, L. E., Jørgensen, J. K., et al. 2018, A&A, 614, A26

Aso, Y., Ohashi, N., Saigo, K., et al. 2015, ApJ, 812, 27

Bacciotti, F., Girart, J. M., Padovani, M., et al. 2018, ApJL, 865, L12

Balbus, S. A., & Hawley, J. F. 1998, RvMP, 70, 1

Barsony, M., Ressler, M. E., & Marsh, K. A. 2005, ApJ, 630, 381

Barsony, M., Wolf-Chase, G. A., Ciardi, D. R., & O'Linger, J. 2010, ApJ, 720, 64

Beckford, A. F., Lucas, P. W., Chrysostomou, A. C., & Gledhill, T. M. 2008, MNRAS, 384, 907

Beckwith, S. V. W., & Sargent, A. I. 1991, ApJ, 381, 250

Bertrang, G. H. M., Flock, M., & Wolf, S. 2017, MNRAS, 464, L61

Birnstiel, T., Dullemond, C. P., & Brauer, F. 2010, A&A, 513, A79

Blandford, R. D., & Payne, D. G. 1982, MNRAS, 199, 883

Bontemps, S., & Andre, P. 1997, in IAU Symp. 182, Herbig-Haro Flows and the Birth of Stars, ed. B. Reipurth & C. Bertout (Cambridge: Cambridge Univ. Press), 63

Bontemps, S., André, P., Kaas, A. A., et al. 2001, A&A, 372, 173

Bontemps, S., Andre, P., Terebey, S., & Cabrit, S. 1996, A&A, 311, 858

Brandner, W., Sheppard, S., Zinnecker, H., et al. 2000, A&A, 364, L13

Brauer, F., Dullemond, C. P., & Henning, T. 2008, A&A, 480, 859

Brauer, R., Wolf, S., & Flock, M. 2017, A&A, 607, A104

Brinch, C., & Jørgensen, J. K. 2013, A&A, 559, A82

Brinch, C., Jørgensen, J. K., Hogerheijde, M. R., Nelson, R. P., & Gressel, O. 2016, ApJL, 830, L16

Bussmann, R. S., Wong, T. W., Hedden, A. S., Kulesa, C. A., & Walker, C. K. 2007, ApJ, 657, L33

Calcutt, H., Jørgensen, J. K., Müller, H. S. P., et al. 2018, A&A, 616, A90

Carniani, S., Maiolino, R., De Zotti, G., et al. 2015, A&A, 584, A78

Casey, C. M., Narayanan, D., & Cooray, A. 2014, PhR, 541, 45

Chandler, C. J., Brogan, C. L., Shirley, Y. L., & Loinard, L. 2005, ApJ, 632, 371

Chen, X., Arce, H. G., Zhang, Q., et al. 2013, ApJ, 768, 110

Chen, Y.-C., & Hirano, N. 2018, ApJ, 868, 80

Cho, J., & Lazarian, A. 2007, ApJ, 669, 1085

Cieza, L. A., Ruíz-Rodríguez, D., Hales, A., et al. 2019, MNRAS, 482, 698

Connelley, M. S., & Greene, T. P. 2010, AJ, 140, L124

Connelley, M. S., Reipurth, B., & Tokunaga, A. T. 2008, AJ, 135, 2496

Coudé, S., Bastien, P., Houde, M., et al. 2019, ApJ, 877, 88

Cox, E. G., Harris, R. J., Looney, L. W., et al. 2017, ApJ, 851, 83

Cox, E. G., Harris, R. J., Looney, L. W., et al. 2018, ApJ, 855, 92

Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, yCat, 2246

Dent, W. R. F., Pinte, C., Cortes, P. C., et al. 2019, MNRAS, 482, L29

Doppmann, G. W., Greene, T. P., Covey, K. R., & Lada, C. J. 2005, AJ, 130, 1145

Dotson, J. L., Vaillancourt, J. E., Kirby, L., et al. 2010, ApJS, 186, 406

Duchêne, G., Bouvier, J., Bontemps, S., André, P., & Motte, F. 2004, A&A, 427, 651

Dunham, M. M., Allen, L. E., Evans, N. J., II, et al. 2015, ApJS, 220, 11

Dunham, M. M., Crapsi, A., Evans, N. J., II, et al. 2008, ApJS, 179, 249

Dunham, M. M., Stutz, A. M., Allen, L. E., et al. 2014, in Protostars and Planets VI, ed. H. Beuther et al. (Tucson, AZ: Univ. Arizona Press), 195

Elias, J. H. 1978, ApJ, 224, 453

Enoch, M. L., Evans, N. J., II, Sargent, A. I., & Glenn, J. 2009, ApJ, 692, 973

Espaillat, C., Calvet, N., D'Alessio, P., et al. 2007, ApJL, 670, L135

Evans, N. J., Di Francesco, J., Lee, J.-E., et al. 2015, ApJ, 814, 22

Evans, N. J., II, Dunham, M. M., Jørgensen, J. K., et al. 2009, ApJS, 181, 321

Fernández-López, M., Stephens, I. W., Girart, J. M., et al. 2016, ApJ, 832, 200

Friesen, R. K., Pon, A., Bourke, T. L., et al. 2018, ApJ, 869, 158

Gagné, M., Skinner, S. L., & Daniel, K. J. 2004, ApJ, 613, 393

Galametz, M., Maury, A., Girart, J. M., et al. 2018, A&A, 616, A139

Galli, D., & Shu, F. H. 1993, ApJ, 417, 220

Geers, V. C., van Dishoeck, E. F., Visser, R., et al. 2007, A&A, 476, 279

Girart, J. M., Curiel, S., Rodríguez, L. F., et al. 2004, AJ, 127, 2969

Girart, J. M., Rodríguez, L. F., & Curiel, S. 2000, ApJL, 544, L153

Gold, T. 1952, MNRAS, 112, 215

Goodman, A. A., Bastien, P., Menard, F., & Myers, P. C. 1990, ApJ, 359, 363

Gray, W. J., McKee, C. F., & Klein, R. I. 2018, MNRAS, 473, 2124

Greene, T. P., & Young, E. T. 1992, ApJ, 395, 516

Günther, H. M., Cody, A. M., Covey, K. R., et al. 2014, AJ, 148, 122

Germuth, R. A., Megeath, S. T., Myers, P. C., et al. 2009, ApJS, 184, 18

Harris, R. J., Cox, E. G., Looney, L. W., et al. 2018, ApJ, 861, 91

Harrison, R. E., Looney, L. W., Stephens, I. W., et al. 2019, ApJL, 877, L2

Hatsukade, B., Kohno, K., Yamaguchi, Y., et al. 2018, PASJ, 70, 105

Hayashi, C. 1981, PThPS, 70, 35

Hayward, C. C., Behroozi, P. S., Somerville, R. S., et al. 2013, MNRAS, 434, 2572

Hennebelle, P., & Ciardi, A. 2009, A&A, 506, L29

Hennebelle, P., & Fromang, S. 2008a, A&A, 477, 9

Hennebelle, P., & Teyssier, R. 2008b, A&A, 477, 25

Herbig, G. H. 2008, AJ, 135, 637

Hildebrand, R. H., Davidson, J. A., Dotson, J. L., et al. 2000, PASP, 112, 1215

Hoang, T., Cho, J., & Lazarian, A. 2018, ApJ, 852, 129

Hsieh, C.-H., Lai, S.-P., Cheong, P.-I., et al. 2019a, arXiv:1904.00133

Hsieh, T.-H., Hirano, N., Belloche, A., et al. 2019b, ApJ, 871, 100

Hsieh, T.-H., Lai, S.-P. 2013, ApJS, 205, 5

Hsieh, T.-H., Lai, S.-P., & Belloche, A. 2017, AJ, 153, 173

Hughes, A. M., Hull, C. L. H., Wilner, D. J., & Plambeck, R. L. 2013, AJ, 145, 115

Hull, C. L. H., & Plambeck, R. L. 2015, JAI, 4, 1550005

Hull, C. L. H., Plambeck, R. L., Kwon, W., et al. 2014, ApJS, 213, L15

Hull, C. L. H., Yang, H., Li, Z.-Y., et al. 2018, ApJ, 860, 82

Imai, M., Oya, Y., Sakai, N., et al. 2019, ApJL, 873, L21

Imanishi, K., Nakajima, H., Tsujimoto, M., Koyama, K., & Tsuboi, Y. 2003, PASJ, 55, 653

Jacobsen, S. K., Jørgensen, J. K., van der Wiel, M. H. D., et al. 2018, A&A, 612, A72

Joos, M., Hennebelle, P., & Ciardi, A. 2012, A&A, 543, A128

Jørgensen, J. K., Bourke, T. L., Nguyen Luong, Q., & Takakuwa, S. 2011, A&A, 534, A100

Jørgensen, J. K., Johnstone, D., Kirk, H., et al. 2008, ApJ, 683, 822

Jørgensen, J. K., van der Wiel, M. H. D., Coutens, A., et al. 2016, A&A, 595, A117

Jørgensen, J. K., van Dishoeck, E. F., Visser, R., et al. 2009, A&A, 507, 861

Kamazaki, T., Nakamura, F., Kawabe, R., et al. 2019, ApJ, 871, 86

Kamazaki, T., Saito, M., Hirano, N., Umemoto, T., & Kawabe, R. 2003, ApJ, 584, 357

Kataoka, A., Machida, M. N., & Tomisaka, K. 2012, ApJ, 761, 40

Kataoka, A., Muto, T., Momose, M., Tsukagoshi, T., & Dullemond, C. P. 2016a, ApJ, 820, 54

Kataoka, A., Muto, T., Momose, M., et al. 2015, ApJ, 809, 78

Kataoka, A., Okuzumi, S., & Tazaki, R. 2019, ApJL, 874, L6

Kataoka, A., Tsukagoshi, T., Momose, M., et al. 2016b, ApJL, 831, L12

Kataoka, A., Tsukagoshi, T., Pohl, A., et al. 2017, ApJL, 844, L5

Kauffmann, J., Bertoldi, F., Bourke, T. L., Evans, N. J., II, & Lee, C. W. 2008, A&A, 487, 993

Kawabe, R., Hara, C., Nakamura, F., et al. 2018, ApJ, 866, 141

Kirchschlager, F., Bertrang, G. H. M., & Flock, M. 2019, MNRAS, 488, 1211

Kirk, H., Dunham, M. M., Di Francesco, J., et al. 2017, ApJ, 838, 114

Kirk, H., Hatchell, J., Johnstone, D., et al. 2018, ApJS, 238, 8

Kwon, J., Doi, Y., Tamura, M., et al. 2018, ApJ, 859, 4

Kwon, W., Stephens, I. W., Tobin, J. J., et al. 2019, ApJ, 879, 25

Lazarian, A., & Hoang, T. 2007, MNRAS, 378, 910

Lee, C.-F., Kwon, W., Jhan, K.-S., et al. 2019, ApJ, 879, 101

Lee, C.-F., Li, Z.-Y., Ching, T.-C., Lai, S.-P., & Yang, H. 2018, ApJ, 854, 56

Leous, J. A., Feigelson, E. D., Andre, P., & Montmerle, T. 1991, ApJ, 379, 683

Li, Z.-Y., Krasnopolsky, R., & Shang, H. 2011, ApJ, 738, 180

Liu, H. B. 2019, ApJL, 877, L22

Liu, J., Qiu, K., Berry, D., et al. 2019, ApJ, 877, 43

Lommen, D., Jørgensen, J. K., van Dishoeck, E. F., & Crapsi, A. 2008, A&A, 481, 141

Long, F., Herczeg, G. J., Pascucci, I., et al. 2017, ApJ, 844, 99

Long, F., Herczeg, G. J., Pascucci, I., et al. 2018, ApJ, 863, 61

Looney, L. W., Mundy, L. G., & Welch, W. J. 2000, ApJ, 529, 477

Machida, M. N., Matsumoto, T., Tomisaka, K., & Hanawa, T. 2005, MNRAS, 362, 369

Manigand, S., Calcutt, H., Jørgensen, J. K., et al. 2019, A&A, 623, A69

Mardones, D., Myers, P. C., Tafalla, M., et al. 1997, ApJ, 489, 719
Markwardt, C. B. 2009, in ASP Conf. Ser. 411, Astronomical Data Analysis Software and Systems XVIII, ed. D. A. Bohlender, D. Durand, & P. Dowler (San Francisco, CA: ASP), 251

Masson, J., Chabrier, G., Hennebelle, P., Vaytet, N., & Commerçon, B. 2016, A&A, 587, A32

Matthews, B. C., McPhee, C. A., Fissel, L. M., & Curran, R. L. 2009, ApJS, 182, 143

Maury, A., Ohashi, N., & André, P. 2012, A&A, 539, A130

Maury, A. J., André, P., Testi, L., et al. 2019, A&A, 621, A76

Maury, A. J., Girart, J. M., Zhang, Q., et al. 2018, MNRAS, 477, 2760

McClure, M. K., Furlan, E., Manoj, P., et al. 2010, ApJS, 188, 75

Mestel, L. 1966, MNRAS, 133, 265

Mestel, L., & Strittmatter, P. A. 1967, MNRAS, 137, 95

Miotello, A., Testi, L., Lodato, G., et al. 2014, A&A, 567, A32

Miotello, A., van Dishoeck, E. F., Williams, J. P., et al. 2017, A&A, 599, A113

Mori, T., Kataoka, A., Ohashi, S., et al. 2019, ApJ, 883, 16

Mottram, J. C., van Dishoeck, E. F., Kristensen, L. E., et al. 2017, A&A, 600, A99

Murillo, N. M., Harsono, D., McClure, M., Lai, S. P., & Hogerheijde, M. R. 2018, A&A, 615, L14

Murillo, N. M., & Lai, S.-P. 2013, ApJL, 764, L15

Murillo, N. M., Lai, S.-P., Bruderer, S., Harsono, D., & van Dishoeck, E. F. 2013, A&A, 560, A103

Myers, P. C., Basu, S., & Auddy, S. 2018, ApJ, 868, 51

Najita, J. R., Andrews, S. M., & Muzerolle, J. 2015, MNRAS, 450, 3559

Nakamura, F., Kamada, Y., Kamazaki, T., et al. 2011, ApJ, 726, 46

Nisini, B., Santangelo, G., Giannini, T., et al. 2015, ApJ, 801, 121

Ochsenbein, F., Bauer, P., & Marcout, J. 2000, A&AS, 143, 23

Ohashi, S., Kataoka, A., Nagai, H., et al. 2018, ApJ, 864, 81

Ormel, C. W., Min, M., Tielens, A. G. G. M., Dominik, C., & Paszun, D. 2011, A&A, 532, A43

Ortiz-León, G. N., Loinard, L., Dzib, S. A., et al. 2018, ApJL, 869, L33

Ossenkopf, V., & Henning, T. 1994, A&A, 291, 943

Parks, J. R., Plavchan, P., White, R. J., & Gee, A. H. 2014, ApJS, 211, 3

Pattle, K., Ward-Thompson, D., Kirk, J. M., et al. 2015, MNRAS, 450, 1094

Pérez, L. M., Carpenter, J. M., Chandler, C. J., et al. 2012, ApJL, 760, L17

Pineda, J. E., Maury, A. J., Fuller, G. A., et al. 2012, A&A, 544, L7

Pohl, A., Kataoka, A., Pinilla, P., et al. 2016, A&A, 593, A12

Pontoppidan, K. M., Dullemond, C. P., van Dishoeck, E. F., et al. 2005, ApJ, 622, 463

Price, D. J., & Bate, M. R. 2007, MNRAS, 377, 77

Rao, R., Girart, J. M., Lai, S.-P., & Marrone, D. P. 2014, ApJL, 780, L6

Rao, R., Girart, J. M., Marrone, D. P., Lai, S.-P., & Schnee, S. 2009, ApJ, 707, 921

Reissl, S., Wolf, S., & Seifried, D. 2014, A&A, 566, A65

Ressler, M. E., & Barsony, M. 2003, ApJ, 584, 832

Riaz, B., Thi, W. F., & Caselli, P. 2018, MNRAS, 481, 4662

Ridge, N. A., Di Francesco, J., Kirk, H., et al. 2006, AJ, 131, 2921

Sadavoy, S. I., Di Francesco, J., Bontemps, S., et al. 2010, ApJ, 710, 1247

Sadavoy, S. I., Myers, P. C., Stephens, I. W., et al. 2018a, ApJ, 859, 165

Sadavoy, S. I., Myers, P. C., Stephens, I. W., et al. 2018b, ApJ, 869, 115

Sadavoy, S. I., & Stahler, S. W. 2017, MNRAS, 469, 3881

Santangelo, G., Murillo, N. M., Nisini, B., et al. 2015, A&A, 581, A91

Santos, F. P., Chuss, D. T., Dowell, C. D., et al. 2019, ApJ, 882, 113

Sato, S., Tamura, M., Nagata, T., et al. 1988, MNRAS, 230, 321

Schöier, F. L., Jørgensen, J. K., van Dishoeck, E. F., & Blake, G. A. 2002, A&A, 390, 1001

Segura-Cox, D. M., Looney, L. W., Stephens, I. W., et al. 2015, ApJL, 798, L2

Segura-Cox, D. M., Looney, L. W., Tobin, J. J., et al. 2018, ApJ, 866, 161

Seifried, D., Banerjee, R., Pudritz, R. E., & Klessen, R. S. 2013, MNRAS, 432, 3320

Seok, J. Y., & Li, A. 2017, ApJ, 835, 291

Sheehan, P. D., & Eisner, J. A. 2017, ApJL, 840, L12

Sheehan, P. D., & Eisner, J. A. 2018, ApJ, 857, 18

Shetty, R., Kauffmann, J., Schnee, S., Goodman, A. A., & Ercolano, B. 2009, ApJ, 696, 2234

Shirono, C., Itho, Y., & Oasa, Y. 2011, PASJ, 63, 1071

Soam, A., Pattle, K., Ward-Thompson, D., et al. 2018, ApJ, 861, 65

Stanke, T., Smith, M. D., Gredel, R., & Khanzadyan, T. 2006, A&A, 447, 609

Stephens, I. W., Looney, L. W., Kwon, W., et al. 2014, Natur, 514, 597

Stephens, I. W., Yang, H., Li, Z.-Y., et al. 2017, ApJ, 851, 55

Tazaki, R., Lazarian, A., & Nomura, H. 2017, ApJ, 839, 56

Tobin, J. J., Hartmann, L., Chiang, H.-F., et al. 2011, ApJ, 740, 45

Tobin, J. J., Hartmann, L., Looney, L. W., & Chiang, H.-F. 2010, ApJ, 712, 1010

Tobin, J. J., Looney, L. W., Li, Z.-Y., et al. 2016, ApJ, 818, 73

Tobin, J. J., Looney, L. W., Li, Z.-Y., et al. 2018, ApJ, 867, 43

Tomida, K., Okuzumi, S., & Machida, M. N. 2015, ApJ, 801, 117

Tomisaka, K. 2011, PASJ, 63, 147

Vaillancourt, J. E. 2006, PASP, 118, 1340

van der Marel, N., Dong, R., di Francesco, J., Williams, J. P., & Tobin, J. 2019, ApJ, 872, L12

van der Marel, N., Kristensen, L. E., Visser, R., et al. 2013, A&A, 556, A76

van der Marel, N., Verhaar, B. W., van Terwisga, S., et al. 2016, A&A, 592, A126

van der Wiel, M. H. D., Jacobsen, S. K., Jørgensen, J. K., et al. 2019, A&A, 626, A93

van Kempen, T. A., van Dishoeck, E. F., Salter, D. M., et al. 2009, A&A, 498, 167

Vaytet, N., Commerçon, B., Masson, J., González, M., & Chabrier, G. 2018, A&A, 615, A5

Visser, A. E., Richer, J. S., & Chandler, C. J. 2002, AJ, 124, 2756

Weidenschilling, S. J. 1977, MNRAS, 180, 57

Weintraub, D. A., Kastner, J. H., Griffith, L. L., & Campins, H. 1993, AJ, 105, 271

Wenger, M., Ochsenbein, F., Egret, D., et al. 2000, A&AS, 143, 9

Whelan, E. T., Riaz, B., & Rouzé, B. 2018, A&A, 610, L19

White, G. J., Drabek-Maunder, E., Rosolowsky, E., et al. 2015, MNRAS, 447, 1996

Wilking, B. A., Gagne, M., & Allen, L. E. 2008, yCat, 5, 351

Wilking, B. A., & Lada, C. J. 1983, ApJ, 274, 698

Wilking, B. A., Lada, C. J., & Young, E. T. 1989, ApJ, 340, 823

Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868

Yang, H., Li, Z.-Y., Looney, L. W., & Stephens, I. W. 2016, MNRAS, 456, 2794

Yang, H., Li, Z.-Y., Looney, L. W., Girart, J. M., & Stephens, I. W. 2017, MNRAS, 472, 373

Yang, H., Li, Z.-Y., Stephens, I. W., Kataoka, A., & Looney, L. 2019, MNRAS, 483, 2371

Yen, H.-W., Koch, P. M., Takakuwa, S., et al. 2017, ApJ, 834, 178

Young, K. E., Enoch, M. L., Evans, N. J., II, et al. 2006, ApJ, 644, 326

Zhang, H., Telesco, C. M., Pantin, E., et al. 2017, MNRAS, 465, 2983

Zhang, Q., Wootten, A., & Ho, P. T. P. 1997, ApJ, 475, 713

Zhu, Z., Zhang, S., Jiang, Y.-F., et al. 2019, ApJL, 877, L18