ALMA High Angular Resolution Polarization Study; An Extremely Young Class 0 Source, OMC-3/MMS 6

TL;DR

This study uses ALMA's high-resolution polarization imaging to reveal detailed magnetic field structures and dust polarization in a very young protostar, MMS 6, providing new insights into early star formation processes.

Contribution

It presents the first high-resolution polarization data of MMS 6, revealing complex magnetic field structures and comparing observations with MHD simulations to understand polarization origins.

Findings

Detection of a ring-like polarization structure at 80 AU radius.

Identification of arm-like polarized structures extending to 1000 AU.

Partial agreement of observations with MHD simulations, but some polarization features remain unexplained.

Abstract

Using the $\approx$15km ALMA long baselines, we imaged the Stokes $I$ emission and linearly polarized intensity ($PI$) in the 1.1-mm continuum band of a very young intermediate-mass protostellar source, MMS 6, in the Orion Molecular Cloud-3. The achieved angular resolution, $0''.02{\times}0''.03$ ($\approx$10 AU), shows for the first time a wealth of data on the dust emission polarization in the central 200 AU of a protostar. The $PI$ peak is offset to the south-west (SW) by $\approx$20 AU with respect to the Stokes $I$ peak. Its polarization degree is 11 % with its $E$-vector orientation of P.A.${\approx}135^{\circ}$. A partial ring-like structure with a radius of $\approx$80 AU is detected in $PI$ but not in the Stokes $I$. NW (north-west) and SE (south-east) parts of the ring are bright with a high polarization degree of $\gtrsim$10 %, and their $E$-vector orientations are roughly orthogonal to those observed near the center. We also detected arm-like polarized structures, extending to 1000 AU scale to the north, with the $E$-vectors aligned along the minor axis of the structures. We explored possible origins of the polarized emission comparing with magnetohydrodynamical (MHD) simulations of the toroidal wrapping of the magnetic field. The simulations are consistent with the $PI$ emission in the ring-like and the extended arm-like structures observed with ALMA. However, the current simulations do not completely reproduce observed polarization characteristics in the central 50 AU. Although the self-scattering model can explain the polarization pattern and positional offset between the Stokes $I$ and $PI$, this model is not able to reproduce the observed high degree of polarization.

Figures

a), there is no significant missing Stokes $I$ flux. Therefore the derived $D_{\rm frac}$ is not overestimated and shows most likely the intrinsic value. In contrast, for the central $2^{\prime\prime}.0$, comparison with low resolution maps suggests that about 25% is missing in the Stokes $I$ emission. The relatively high $D_{\rm frac}$ (7–25%) derived for the extended structure, in the NE side with respect to the center in Figure 5(b), may be somewhat overestimated.

b). The position angle of the $E$-vectors changes in the “ring-like structure”; i.e., the peaks of the P.A. distribution are 25*∘* and 40*∘* for the SE and NW components, respectively, while the peak of the P.A. distribution is 135*∘* at the “centrally concentrated component”. Significant changes in the P.A. of 90*∘* – 105*∘*, occur in the central $0^{\prime\prime}.5$ region. The P.A. within the NW and SE components varies slightly with respect to the overall $E$-vector orientation. This implies that our data not only reveal the bulk structure, but also the small scale $E$-vector changes, whic

A). In this model, the direction of the (uniform) interstellar magnetic field is given by the direction of the $B$-vector. Thus, the magnetic field projected onto the celestial plane is obtained as the perpendicular direction to the observed $E$-vectors as presented in Figure 5(c). In the “centrally concentrated component”, the interstellar magnetic field seems to run parallel to the major axis. The P.A. is measured to be 45*∘*, which is consistent with the orientation of the large-scale magnetic field (Matthews & Wilson, [2000](#bib.bib44); Matthews et al., [2001](#bib.bib45), [2005](#bib.bib

b), which likely originated from the foreground fields associated with the cloud or envelope.. The observational result does not support the scenario expected by Gold ([1952](#bib.bib19)), while the result is more consistent with a scenario proposed by Lazarian & Hoang ([2007](#bib.bib36)), involving an alternative mechanical alignment of helical dust grains. In this scenario, the helical dust grains align with the minor axis being parallel to the gaseous flow (both supersonic and subsonic cases). This results in $E$-vector that are perpendicular to the gas outflow. However, the magnetic align

b). We see local peaks within the ring-like structure due to the effect of integrating polarized emission along the line of sight. The magnetic field vectors in the ring-like structure are aligned more or less along the minor axis of the structure with some fluctuation. In this simulation, while the $PI$ shows a ring-like emission distribution, the column density (reflects Stokes $I$) increases toward the center. Moreover, within the ring-like structure, we can see $PI$ variation (local peaks). $B$-vector orientations in the “ring-like structure” are also aligned along the minor axis of the st

Tables

Table 1. Table 1: ALMA Observing Parameters for the Full Polarization Experiments

Parameters	X1aa2 & X269f	X368f, X435c, & X4b9d	X336 & X3d1d
Observing date (YYYY-MM-DD)	2015-10-29	2016-10-09	2016-10-11
Number of antennas	38	42	44
Primary beam size (arcsec)	21	21	21
PWV (mm)	1.3 –1.9	0.44 – 0.90	0.44 – 0.57
Phase stability rms (degree)aaAntenna-based phase differences measured on the bandpass calibrator.	16–23	16 – 56	10 –15
Polarization calibrator	J0522-3627	J0522-3627	J0522-3627
Bandpass calibrators	J0423-0120	J0510+1800	J0510+1800
Flux calibrator	J0423-0120	J0423-0120	J0423-0120
Phase calibrators (separation from the target)bbThe phase calibrator was observed every 1 min. and 8 min. for the high angular and low angular resolution observations, respectively.	J0541-0541 (1.7∘)	J0532-0307 (2.1∘)	J0541-0541 (1.7∘)
Central frequency USB/LSB (GHz)	257 / 273	257 / 273	257 / 273
Total continuum bandwidth; USB+LSB (GHz)	7.5	7.5	7.5
Projected baseline ranges (k$\lambda$)	76 –14700	16 – 3200	16 – 3200
Maximum recoverable size (arcsec)ccOur observations were insensitive to emission more extended than this size scale structure at the 10% level (Wilner & Welch 1994).	0.22	1.0	1.0
On-source time (minutes)	41	12.5	13
Synthesized beam size (arcsec)ddThe natural weighting and the Briggs weighting (robust parameter of 0.5) are used for the high and low angular resolution imaging, respectively.	$0^{\prime \prime }.03\times 0^{\prime \prime }.02$ (P.A.=43∘)	$0^{\prime \prime }.15\times 0^{\prime \prime }.14$ (P.A.=80∘)
RMS noise level of Stokes $I$eeStokes $I$ images are dynamic range limited., $Q$, and $U$ ($\mu$Jy beam-1)	63, 21, and 21	130, 20, and 20

Table 2. Table 2: Multiple Gaussian Fitting Results

	R.A.	Decl.	Deconvolved Size, P.A.	Peak Intensity	Flux Density
	(J2000)	(J2000)	(milli-arcsec, deg)	(mJy beam-1)	(mJy)
(i) Extended component	05 35 23.4220	-05 01 30.532	$321\pm 4\times 312\pm 4$, 134$\pm 18$	5.5$\pm$0.1	724$\pm$8
(ii) Elongated component	05 35 23.4182	-05 01 30.553	$314\pm 37\times 55\pm 6$, 39$\pm$2	1.1$\pm$0.1	28$\pm$3
(iii) Compact component	05 35 23.4201	-05 01 30.515	$54\pm 32\times 13\pm 15$, $72\pm 46$	0.7$\pm$0.2	1.5$\pm$0.8

Table 3. Table 3: Physical Properties of Fitted Components

Component	Source Size	$M_{H_2}$	$n_{H_2}$	$n_{H_2}$
	(AU)	($M_{\odot }$)	(cm-2)	(cm-3)
(i) Extended component	$133\left(\pm 1\right)\times 129\left(\pm 1\right)$	9.5e-01 ($\pm$1.0e-02)	6.4e+25 ($\pm$6.9e+23)	4.3e+10 ($\pm$4.7e+08)
(ii) Elongated component	$130\left(\pm 15\right)\times 23\left(\pm 3\right)$	3.3e-03 ($\pm$3.7e-04)	4.4e+24 ($\pm$4.9e+23)	4.2e+09 ($\pm$4.7e+08)
(iii) Compact component	$22\left(\pm 13\right)\times 5\left(\pm 6\right)$	1.3e-04 ($\pm$6.6e-05)	5.6e+24 ($\pm$2.9e+24)	3.1e+10 ($\pm$1.6e+10)

Table 4. Table 4: Comparisons of Three Proposed Polarization Mechanism at the Central 200 AU a a ○ ○ \bigcirc : Result can be reproduced by the existing models, △ △ \vartriangle : Result could be explained by the proposed model qualitatively, but no clear cases are reported as publication before. × \times : Result cannot be explained by the existing models.

	Magnetic Field	Self-scattering	Anisotropic radiation
(i) Spatial distribution difference between Stokes $I$ and $PI$	$○$	$△$	$\times$
(ii) Peak positional offset between the Stoke $I$ and $PI$	$△$	$○$	$△$
(iii) ring-like depolarized region (ring-like gap)	$○$	$△$	$\times$
(iv) Change of the $E$-vector orientations across the ring-like gap	$○$	$○$	$△$
(v) High polarization percentage of $\gtrsim$10%	$△$	$\times$	$△$

Full text

polarization – starts:individual(OMC-3/ MMS 6) – stars: formation – ISM: jets and outflows

1 Introduction

Magnetic fields are one of the key elements that regulate star formation (Shu et al., 1987; Crutcher, 2012), and organized magnetic fields are often observed in parsec-scale dense molecular clouds and cores. Even when the Lorentz force is insufficient to balance the gravity and to prevent contraction of the core (Crutcher, 2012), the magnetic fields are still important in the star formation process. For instance, in a large scales, the magnetic field seems to produce disk-like structure, which is called “pseudo disk” (Shu et al. 1987; Nakano 1988; Galli & Shu 1993). In the vicinity of the protostar, the Lorentz force plays a critical role for launching outflows and jets (Tomisaka, 2002; Banerjee & Pudritz, 2006; Machida et al., 2008; Commerçon et al., 2010; Tomida et al., 2010), which are commonly observed in the star forming regions (e.g., Arce et al. 2007 and references therein). A strong magnetic field removes the angular momentum from the disk via magnetic braking (e.g., Mellon & Li 2008) and produce outflows (e.g., Machida et al. 2008; Tomisaka 2011), while the Ohmic dissipation promotes the disk formation and growth (e.g., Machida et al. 2011). These effects determine the properties of a rotationally supported disk in the early stage of the protostellar evolution.

A method to study the magnetic field structures in the protostellar core is to observe the linearly polarized thermal emission from magnetically aligned dust grains (e.g., Spitzer & Tukey 1949; Davis & Greenstein 1951; Hildebrand 1988; Lazarian 2007; Rao et al. 1998, 2009, 2014; Lai et al. 2003; Hull et al. 2014, 2017; Girart et al. 2006, 2009, 2013; Tang et al. 2013; Zhang et al. 2014; Cortes et al. 2016; Koch et al. 2018; Maury et al. 2018; Girart et al. 2018; Alves et al. 2018; Lee et al. 2018 and references therein). Since the degree of linear polarization observed in the star forming cores is typically $\lesssim$5%, only a sensitive array such as ALMA can image dust polarization for faint sources and in their most internal parts ($\lesssim$ a few $\times$100 AU). With the ALMA sensitivity and its angular resolution that enables to probe nearby protostars at 10 AU scales, magnetic field structures can be traced in detail and measured magnetic field structures can be directly compared with magnetohydrodynamical (MHD) simulations (e.g., Machida et al. 2008; Tomisaka 2011; Li et al. 2014). Such observations are key to study the formation processes of rotationally supported disks and the launching mechanism of the jet and outflow.

At small scales ($\lesssim$ a few$\times$ 100 AU), dust polarization is not always associated with the magnetic field and could also be related to other mechanisms such as the self-scattering (Kataoka et al., 2015; Yang et al., 2016) and dust grain alignment due to the anisotropic radiation (Tazaki et al., 2017). Each mechanism produces different orientations of the polarization vectors and different dependence of the degree of linear polarization in frequency.

We observed the brightest Class 0 intermediate-mass (IM) protostellar core, MMS 6, located in the Orion Molecular Cloud-3 region (OMC-3; $d$=414 pc by Menten et al. 2007 or $d=$388 pc by Kounkel et al. 2017) 111In this paper, the distance to the object, $d$=414 pc, is adopted.. MMS 6 has a bolometric luminosity of $L_{\rm{bol}}<$ 60 $L_{\odot}$ and a core mass of $M_{\rm{core}}=$30 $M_{\odot}$ (Chini et al., 1997). Takahashi et al. (2012) detected a massive gas envelope (0.29 $M_{\odot}$), the presence of hot gas ($\gtrsim$52 K), and extremely high column density ($N_{\rm{H_{2}}}=$2.1$\times$1025 cm*-2*), in the central 120 AU. In addition, Takahashi & Ho (2012) detected an extremely compact ($\approx$1000 AU) and collimated molecular outflow associated with MMS 6. These results imply that MMS 6 is one of the youngest IM core. MMS 6 is a bright source and relatively close, so it is a unique target to observe the polarized emission at the ALMA highest angular resolutions.

We here report on new ALMA high angular resolution observations of the polarization of the dust continuum emission in the protostellar core MMS 6 at sub-arc ($0^{\prime\prime}.02{\times}0^{\prime\prime}.03$) resolution corresponding to 10 AU for the adopted distance of MMS 6. Previous studies indicate that MMS 6 is a clear case of a magnetically dominated region. The large-scale magnetic field orientations in the northern part of OMC-3, where MMS 6 is located, show an organized magnetic field structure that is smoothly connected between the size scale of filamentary cloud, core, and envelope (Matthews & Wilson, 2000; Matthews et al., 2001, 2005; Poidevin et al., 2010; Hull et al., 2014).

In different star forming regions, ALMA polarization observations toward protoplanetary disks have been extensively performed enabling detailed discussions of the origin of their emission (e.g., Kataoka et al. 2016; Hull et al. 2018; Bacciotti et al. 2018; Ohashi et al. 2018; Dent et al. 2019). For the earlier evolutionary stage (i.e., Class I/0), many observational results are also available today (Stephens et al. 2017; Kataoka et al. 2017; Hull et al. 2017; Maury et al. 2018; Cox et al. 2018; Alves et al. 2018; Kwon et al. 2018; Lee et al. 2018; Sadavoy et al. 2018; Harris et al. 2018; Girart et al. 2018), showing a high degree in variations in the origin of the polarized emission and displaying complex morphologies.

The new ALMA data allow us to study the polarization and magnetic field structures at the center of a protostellar core, MMS 6/OMC-3 at the highest angular resolution as possible with current ALMA at the observed frequency, and to better understand the origin(s) of the dust polarized emission, characterize its nature, and compare the results with other Class 0/I sources.

The paper is organized as follows. The dust polarization observations and the molecular outflow observations are described in Section 2. The total intensity and the polarized intensity distributions, from 10 AU to a few $\times$1000 AU scales, are shown and described in Section 3. Origins of the ALMA dust polarized emission in MMS 6 and comparisons with the MHD simulation are discussed in Section 4. Finally, concluding remarks as well as future prospects are given in Section 5.

2 OBSERVATIONS AND DATA REDUCTION

2.1 The 1.1 mm Continuum Polarimetric Observations

The ALMA observations of MMS 6 were obtained through the science project 2015.1.00341.S (P.I. S. Takahashi) using two different configurations. The high angular resolution observations were made in Cycle 3 on 2015 October 29 with the 16-km ALMA configuration in two consecutive observing blocks, and the lower angular resolution observations were made in Cycle 4 on 2016 October 9 and 11 with the 3.6-km ALMA configuration in five observing blocks. The phase center of all of the observations were R.A. (J2000) = 5h35m23s.4200, decl. (J2000) =−05*∘01′30′′*.350. Observing parameters associated with the three observations are listed in Table 1. Both high and low angular resolution observations had about 40 minutes on-source time with about forty 12-m diameter antennas. The low and high angular resolution data sets cover projected baselines between 16 k$\lambda$ and 3200 k$\lambda$ and between 76 k$\lambda$ and 14700 k$\lambda$, respectively. The two data sets are respectively insensitive to structures more extended than $1^{\prime\prime}.0$ and $0^{\prime\prime}.22$ at the 10% level (Wilner & Welch, 1994). Four spectral windows (SPWs) with 1.875 GHz bandwidth, centered at 256, 258, 272, and 274 GHz are allocated with the time division mode for this polarization experiment, giving a total continuum bandwidth of 7.5 GHz.

The Common Astronomy Software Application (CASA; McMullin et al. 2007) version 4.5.0 was used for the standard ALMA data reduction. The calibration scripts were provided by the observatory. The calibration steps include (1) correcting the gains associated with the variable receiver and sky noise and phases associated with the water vapor along the line of site, (2) providing the flux density scale with an observation of calibrator of known flux density, (3) removing the amplitude and phase frequency dependence (bandpass) for each SPW, (4) removing the amplitude and phase temporal dependence using a phase calibrator within a few degrees of MMS 6, (5) removing instrumental polarization using a bright polarized calibrator, J0522-3627, which was observed every 25 minutes during each execution, and (6) making appropriate data flagging as calibrations progress. The calibrated data from the two 16-km high resolution experiments were combined into the high resolution data set. The data from the five 3.6-km low resolution experiments were combined into the low resolution data set. The data points in the combinations were weighted by their theoretical SNR which gives best theoretical SNR in the combined data sets.

Then CLEANed images were made using the CASA task “clean”. The Briggs weighting with robust parameter of 0.5, and natural weighting were used for the high and low angular resolution final images, respectively. In order to reduce residual phase errors and improve the dynamic range of the images, self-calibrations have been applied for the low angular resolution image. This process improved the maximum dynamic range by a factor of 1.8. The resulting synthesized beam sizes are 0*′′.03 $\times$ 0′′.02 (P.A.= 43∘) and 0′′.15 $\times$ 0′′.14 (P.A.= $-80^{\circ}$) for the high angular resolution and low angular resolution images, respectively. The achieved rms noise level (1 $\sigma$) for the high angular resolution and low angular resolution images (for Stokes $I$, $Q$, and $U$) are 63, 21, 21$\mu$Jy beam-1* and 130, 20, 20 $\mu$Jy beam*-1*, respectively. The Stokes $Q$ and $U$ image rms is near the expected thermal noise level. However, the Stokes $I$ image is limited by small residual phase errors that could not be calibrated using phase referencing. Still, a peak sensitivity at high resolution of 7 mJy is more than 100 times the rms level. Figure 1 presents the low and high angular resolution Stokes $I$, $Q$, and $U$ images at the central ${\approx}1.^{\prime\prime}0$ region.

The derived polarization intensity ($PI$) image is given by the quadrature sum of the $Q$ and $U$ images, $PI=\sqrt{Q^{2}+U^{2}}$. The polarization angle in degrees is given by $E_{\rm{PA}}=(1/2)\times\arctan(U/Q)$. $PI$ and $E_{\rm PA}$ were calculated using a CASA task “immath”. Debiasing level of 5$\sigma$ in Stokes $Q$ and $U$ was used in order to derive $PI$. The estimated error of the polarized intensity is, $\Delta PI\approx\sqrt{\Delta Q^{2}+\Delta U^{2}+(0.002*I)^{2}}$ which is the quadrature sum of the $Q$ and $U$ errors plus the nominal polarization calibration error. The estimated error of the polarization angle in degrees is $\Delta E_{PA}\approx(1/2)\Delta PI/PI$. There is a lower limit of $\Delta E_{PA}$ of $\approx 1^{\circ}$ related to the uncertainty of the position angle determination of the polarization calibrator and antenna feed orientation. The degree of polarization is $D_{\rm{frac}}=PI/I$. Because of non-linearities in the parameters, only those pixels that contain both more than 5$\sigma$ signal level in the $PI$ maps and 3$\sigma$ signal level in the Stokes $I$ maps, were used for calculating $D_{\rm frac}$. In this paper, we use the term “$E$-vector” to refer to the observed polarization vector, and “$B$-vector” to refer to the observed polarization vector after rotating 90*∘*.

2.2 The Molecular Line Observations

In addition to the 1.1 mm polarization observations, we also performed observations in the CO (2–1) and SiO (4–3) line emission from the same science project in order to trace the molecular outflow associated with MMS 6. These observations were done separately, but the data were obtained in a similar period as the lower resolution polarization observations. Two SPWs were allocated to measure CO (2–1) and SiO (4–3) using the frequency division mode resulting in a the velocity resolution of $\approx$0.06 km s*-1*. The standard data reduction script provided from the observatory was used to calibrate the data sets using CASA. The Briggs weighting with robust parameter of 0.5 was used for CLEAN binning with the velocity width to 3 km s*-1*. The resulting synthesized beam sizes of the CO (2–1) and SiO (4–3) images are $0^{\prime\prime}.18{\times}0^{\prime\prime}.15$ (P.A.=$-16.5^{\circ}$) and $0^{\prime\prime}.22{\times}0^{\prime\prime}.17$ (P.A.=$-27.7^{\circ}$), respectively. The achieved rms noise levels of the CO (2–1) and SiO (4–3) images are 3.6 mJy beam*-1* km s*-1* and 2.7 mJy beam*-1* km s*-1*, respectively. The mean velocity maps (Figures 3 and 7) are produced from the data cube using a CASA task “immoment” with the clip levels of 3${\sigma}$ for CO (2–1) and 10${\sigma}$ for SiO (5–4). Details for the line data sets including both the analysis and interpretation will be presented in a forthcoming paper (Takahashi et al. 2019 in preparation).

3 Results

3.1 Morphology and Polarization Vectors at Several 1000 AU Scale

In Figure 2, we present the spatial distribution of the linearly polarized emission, Stokes $I$ emission, and $E$-vectors obtained from the 1.1 mm low angular resolution image. The image shows that the $PI$ peak is closely associated with the Stokes $I$ peak, while showing clumpy substructures. These substructures (central 200AU) will be described in $\S$ 3.2. In addition to the centrally concentrated substructures, we also detect extended emission both in Stokes $I$ and polarized emission. The emission is extended on 3000 AU scale and shows substructures. The most prominent feature is an “arm-like structure”, detected in the northern part as denoted by the orange line in Figure 2. The arm-like structure is particularly clear in the $PI$ map, and also detected in the Stokes $I$ at a 5–15$\sigma$ level. The $E$-vectors are aligned with the minor axis of the “arm-like structure”, and their orientations change smoothly along them. To the north of the arm-like structure, we find another faint component that is elongated north-south. This component was detected at a 5$\sigma$ level in the polarized emission, and a part of the structure was marginally detected in Stokes $I$ at a 3$\sigma$ level.

In addition, the Stokes $I$ shows an extended faint (3–6$\sigma$) emission in the south-east part of the core. Unlike the northern arm-like structure, this component is not bright in the $PI$. Overall, $E$-vector orientations from the extended emission are aligned in the NW to SE direction, which is consistent with the large-scale orientation presented by Hull et al. (2014).

Figure 3 shows the Stokes $I$ image from a large squared region in Figure 2, and it is compared with the mean velocity map from the CO molecular outflow 222The CO outflow results will be presented in a separate paper (Takahashi et al. 2019 in prep.).. The Stokes $I$ emission associated with the central compact component shows an elongated structure in the north-south direction with an extension of 3*′′* (1200 AU). The spatial distribution of the extended continuum emission shows enhancements on both edges of the CO molecular outflow. A depression in the Stokes $I$ emission is seen along the outflow, both in the north and the south. This implies that the interaction between the outflow and the surrounding material likely created the outflow cavity wall. The Stokes $I$ emission is not only detected from the area perpendicular to the molecular outflow where we normally expect infalling material to a pseudo disk, but is also detected in the direction of the outflow where material may be swept up by the outflow.

The $E$-vectors associated with this outflow interacting area, especially in the southern component (highlighted in yellow lines in Figure 2 particularly at the south), show a different P.A. as compared to the global $E$-vector orientations, and seems to follow the interacting surface of the outflow.

3.2 Morphology and polarization vectors in the central 200 AU

Figures 4(a) and 4(b) show the images of the central 200 AU region obtained in the low and high angular resolutions, respectively. The angular resolution of the image in Figure 4(b) of $0^{\prime\prime}.02{\times}0^{\prime\prime}.03$ is close to the highest angular resolution currently available with ALMA at 1.1 mm, and corresponds to a linear size scale of ${\approx}8{\times}12$ AU at the distance of MMS 6. Our high angular resolution images show that the MMS 6 continuum emission is very well resolved both in Stokes $I$ and in the polarized flux displaying a series of intricate structures. The source size (FWHM) measured in Stokes $I$, is ${\approx}$165 synthesized beams. Furthermore, comparison of the high and low angular resolution Stokes $I$ images indicates that we are recovering 96% of Stokes $I$ flux in the central 200 AU (i.e., central $0^{\prime\prime}.5$, the region denoted in the dashed circle in Figure 1a). This shows that nearly little or none of the emission in the central region is contained in a large, resolved-out, component.

Both the Stokes $I$ and $PI$ emissions show a peak around the center. However, the $PI$ peak is offset to the south-west (SW) by $0^{\prime\prime}.05$ ($\approx$20 AU) with respect to the Stokes $I$ peak. Hereafter we will refer to this concentrated $PI$ structure as the “centrally concentrated component” (Figure 4c). The emissions of both Stokes $I$ and $PI$ are elongated along the NE to SW direction with P.A.${\approx}45^{\circ}$. The associated $E$-vectors are aligned to the minor axis of the elongated structure (P.A.$\approx$135*∘*). Around this central structure, there are three more components called “NW”, “SE” and “West” components (identified in Figure 4c), each displaying substructures, that, together, define an approximate ring surrounding the central component. Hereafter, we call this the “ring-like structure” (Figure 4c). The substructures seen within the “ring-like structure”, are particularly clear within the SE component, with a size scale as small as the synthesized beam size ($\approx$10 AU).

The $E$-vectors associated with the NW and SE components are more or less azimuthally aligned (Figure 4b). The position angle of the $E$-vectors changes in the “ring-like structure”; i.e., the peaks of the P.A. distribution are 25*∘* and 40*∘* for the SE and NW components, respectively, while the peak of the P.A. distribution is 135*∘* at the “centrally concentrated component”. Significant changes in the P.A. of 90*∘* – 105*∘*, occur in the central $0^{\prime\prime}.5$ region. The P.A. within the NW and SE components varies slightly with respect to the overall $E$-vector orientation. This implies that our data not only reveal the bulk structure, but also the small scale $E$-vector changes, which may be related to small scale variations in the magnetic field, due to local structural changes, dust property changes, or dynamics.

Finally, there is a clear polarization gap between the “centrally concentrated component” and the “ring-like structure”. The width of the gap is significantly larger than the beam size, and is therefore not caused by the beam dilution. This gap implies that either the $PI$ is intrinsically low or that the $E$-vector orientations originating from the centrally concentrated component and the ring-like structure are approximately orthogonal along the line of sight.

3.3 Polarization Degree

In Figures 5(a) and (b), we present the degree of the polarization, $D_{\rm frac}$, as derived from the low angular resolution image. We find that $D_{\rm frac}$ in the arm-like structure shown in Figure 5(a), has a relatively high value of 15-20%. For the central region in Figure 5(b), $D_{\rm frac}$ is less than 3% for most of the area, but there are local peaks with $D_{\rm frac}$ up to ${\approx}$8%. The locations of the peaks in $D_{\rm{frac}}$ coincide with the local maxima of $PI$.

The distribution of $D_{\rm frac}$ obtained with the high angular resolution image is presented in Figure 5(c) and the comparison of this central region between the low and high resolution images in $I$, $Q$ and $U$ is shown in Figure 1. The internal structures within the central 200 AU are spatially resolved and show the following components: (i) the “centrally concentrated component”, showing the peak in $PI$ with $D_{\rm frac}$ of 11%, and (ii) the partial “ring-like structure” with $D_{\rm frac}$ up to 19%. $D_{\rm frac}$ is particularly high within the SE component. The locations of all the local maxima of $D_{\rm frac}$, coincide well with the local peaks in $PI$.

Considering the central $0^{\prime\prime}.5$ region (denoted by the dashed circle in Figure 1a), there is no significant missing Stokes $I$ flux. Therefore the derived $D_{\rm frac}$ is not overestimated and shows most likely the intrinsic value. In contrast, for the central $2^{\prime\prime}.0$, comparison with low resolution maps suggests that about 25% is missing in the Stokes $I$ emission. The relatively high $D_{\rm frac}$ (7–25%) derived for the extended structure, in the NE side with respect to the center in Figure 5(b), may be somewhat overestimated.

Finally, note that a comparison between the low and high resolution images presented in Figure 5(b) and 5(c) clearly shows that $D_{\rm frac}$ becomes higher for the high angular resolution image toward local substructures. Those substructures contain highly organized $E$-vectors as small as a few $\times$10 AU scale, while they are diluted by the beam and show considerably less $D_{\rm frac}$ in the low resolution map.

3.4 Origin and Physical Properties of the 1.1mm Continuum Emission

The total flux of the 1.1 mm continuum emission is measured to be 0.9 Jy using the area where the SNR is greater than 5 from the high angular resolution image. This flux includes the possible contribution of the free-free emission from the ionized jet from the protostar. The free-free emission can be extrapolated from the centimeter observations, with an assumption of the frequency dependence of $F({\nu}){\propto}{\nu}^{0.6}$ (Anglada et al., 1998; Reynolds, 1986). Takahashi et al. (2009) measured a 3$\sigma$ upper limit of 0.09 mJy in the 3.6 cm continuum band. Adopting this number as the upper flux limit attributed to the free-free jet, the free-free contribution at the 1.1 mm band is at most 0.7 mJy, which is $\lessapprox$0.8% of the total Stoke $I$ flux 333No significant time variation in the free-free emission is assumed.. This indicates that the thermal dust emission is dominating in the 1.1 mm continuum band, and that the contribution from the free-free emission of the ionized jet is within the measurement errors.

In order to characterize the internal structures and their physical parameters from the Stokes $I$ high angular resolution image, we used a two-dimensional Gaussian fit with multiple components. The fitting results are summarized in Table 2 and show that with three Gaussian components; (i) an extended component, (ii) an elongated component, and (iii) a compact component, The observed structures are well reproduced. The residual level of the fitting result is less than 1.5% with respect to the observed peak flux (i.e., the residual level is less than SNR${\leq}1.7$). Note that the fitting region includes the NW, SE, West components. However, those components are only bright in the $PI$ image. Hence Stokes $I$ fitting results are not affected by those substructures, but rather based on the total material distribution.

The extended component shows structure sizes of ${\approx}0^{\prime\prime}.3$ ($\approx$120 AU) in FWHM. This size is comparable to the maximum recoverable size of the experiments. For a component that is more extended, flux will be missed by the lack of short antenna spacings. The elongated component has a fitted size of $0^{\prime\prime}.3{\times}0^{\prime\prime}.05$ (120 AU $\times$ 20 AU), with an aspect ratio of 5.8 with P.A.=39*∘*. Finally, a compact component of $0^{\prime\prime}.05{\times}0^{\prime\prime}.01$ (20 AU $\times$ 4 AU) is necessary in order to explain additional flux seen at the center. This compact component is barely resolved with respect to the synthesized beam.

The measured 1.1 mm peak intensity of 7 mJy beam*-1* corresponds to a brightness temperature of 192 K. Gas temperatures of $\gtrsim$100 K are expected at the radius of $\approx$10 AU from the protostellar source (e.g., Nakazato et al. 2003). Assuming that the measured peak flux mainly comes from the circumstellar materials associated with the central protostar, the estimated high brightness temperature of the dust can be compared to the expected gas temperature at the radius of 10 AU. We conclude that the observed dust emission may become optically thick at radii $\lesssim$10 AU.

On the other hand, the measured peak flux may be attributed to the multiple components integrated along the line of sight. The mean brightness temperatures estimated from the fitted total fluxes listed in Table 2 are 25 K (extended component), 27 K (elongated component), and 36 K (compact component). These are considered as the lower limits of the dust temperatures. From a theoretical approach, Tomida et al. (2017) presented the temperature distribution around the center region of the protostellar core using radiative transfer calculations. They found that the observed temperature integrated along the line of sight is $\approx$20 K in the mid-plane of the pseudo disk at $r{\lesssim}200$ AU due to the optical depth effect. The fitted three components also have similar size structures (${\approx}0^{\prime\prime}.3$ or $\approx$120 AU), thus likely trace emission from the pseudo disk. The observed brightness temperatures are lower than predicted by Tomida et al. (2017). This implies that MMS 6 also has an optically-thick pseudo disk with a relatively low temperature.

Assuming the respective mean dust temperatures of 25, 27, and 36 K for the extended, elongated, and compact components, an optical depth of ${\tau}{\approx}1$, a gas-to-dust ratio of 100, we have estimated the lower limits of the column density ($N_{\rm{H_{2}}}$), the gas mass ($M_{\rm{H_{2}}}$), the number density ($n_{\rm{H_{2}}}$) as listed in Table 3. Here, the brightness temperatures estimated for the elongated and compact components are adopted as the dust temperature. A spherical geometry with the geometric mean of the major and minor axes of the source size is assumed in order to estimate the number densities.

The dust temperature for the extended component is assumed from previous multi-wavelength observations of the large scale structure (Sadavoy et al., 2016). For those estimates, we adopted a dust emissivity index of $\beta$=0.93 from Takahashi et al. (2009), and a dust absorption coefficient of ${\kappa_{\lambda_{\rm{(obs)}}}}$=0.037 cm2 g*-1* (${\lambda_{\rm{obs}}}$/400$\mu$m)-β by Keene et al. (1982) where $\lambda_{\rm{obs}}$ the observed wavelength of 1.1 mm with ${\kappa_{\lambda_{\rm{(1.1mm)}}}}$=0.014 cm2 g*-1*. Note that, for the large-scale emission ($\gtrsim$0.05 pc), $T_{\rm{dust}}$=25 K and $\beta$=1.4 were estimated toward MMS 6 from $Herschel$ and GISMO/IRAM 30m data sets (Sadavoy et al., 2016). Adopting their value of $\beta$, the estimated dust masses increase by a factor of 1.7. Another factor that affects the estimates is the mass absorption coefficient. Sadavoy et al. (2016) adopted $\kappa_{\nu_{\rm{(obs)}}}$=0.1 cm2 g*-1* ($\nu_{\rm{obs}}$/1.0 THz)β based on $Herscel$ results by André et al. (2010). Adopting this number, $\kappa_{\rm{1.1mm}}$ increases by a factor of 2.3, resulting in a corresponding decrease in the estimated dust masses.

The fitted source size of the extended component of ${\approx}0^{\prime\prime}.3$ is consistent with the value reported from previous lower resolution SMA observations of the dust continuum emission at 850$\mu$m (Takahashi et al., 2012). The estimated total mass in this paper, $M_{\rm{H_{2}}}{\approx}1$ $M_{\odot}$, is about three times larger than those in Takahashi et al. (2012) because we have used in this paper a dust temperature that is lower by a factor of 2. Assuming the same dust temperature as used in Takahashi et al. (2012), the derived physical parameters ($M_{\rm{H_{2}}}$, $N_{\rm{H_{2}}}$, and $n_{\rm{H_{2}}}$) in this paper would be more consistent with previous results (e.g., the estimated mass would be agreement within a factor of 1.3).

4 Discussion

As described in $\S$3, the $E$-vectors derived from our ALMA 1.1 mm dust continuum emission data show totally different field patterns as compared with previous interferometric studies such as obtained with BIMA by Matthews et al. (2005) or with CARMA by Hull et al. (2014). One obvious factor is a significant difference in beam sizes, which is a factor of $\approx$10000 in terms of the beam surface area, between the previous experiments and our ALMA high angular resolution data. It is natural to consider that the polarized emissions from the two different spatial scales trace totally different physical structures and phenomena inherent to each spatial scale. Comparison of these different angular-size structures is important to understand how the magnetic field morphology is connected from a pseudo disk (${\approx}10^{3}$–$10^{4}$ AU) to a circumstellar disk ($\lesssim$ a few $\times$100 AU).

In addition, the origin of the linearly polarized dust continuum emission in the vicinity of protostars is not completely understood yet. It has been suggested recently that the linearly polarized (sub)millimeter dust emission may not be always associated with the magnetic field (e.g., Cox et al. 2018; Harris et al. 2018; Girart et al. 2018; Sadavoy et al. 2018). In §4.1, we summarize other possible mechanisms to align dust grains and/or to produce polarized emission, and, in §4.2, we compare the observed ALMA data with the various models. Finally, in §4.3, we further discuss the magnetic field morphology as inferred from the polarized emission and compare it with MHD simulations.

4.1 Potential Origins of the Polarized Dust Emission

Figure 6 shows three possible mechanisms to produce polarized emission in the millimeter and submillimeter wavelengths. The first mechanism to produce the polarized dust emission is from magnetically aligned dust grains as proposed originally by Spitzer & Tukey (1949) – see also Davis & Greenstein (1951), Hildebrand (1988), and Lazarian (2007). Spinning dust grains interact with the magnetic fields and align their major axes perpendicular to the magnetic field. Therefore, thermal radiation from these grains produce polarized emission with the $E$-vector aligned perpendicular to the magnetic field as presented in Figure 6(A) (e.g., Lazarian 2007). This is what has been mainly detected on the size scales of clouds, cores, and envelopes (e.g., Rao et al. 1998, 2009; Lai et al. 2003; Hull et al. 2014, 2017; Girart et al. 2006, 2009, 2013; Zhang et al. 2014; Tang et al. 2013; Koch et al. 2018; Kwon et al. 2018; Lee et al. 2018).

The second mechanism to produce millimeter wavelength polarized dust emission is self-scattering of the dust grains as proposed by Kataoka et al. (2015) and Yang et al. (2016). Even without any alignment of the grains in the disk, polarized emission is expected when the dust grains scatter an anisotropic radiation field. If the radiation energy flux is dominated in the azimuthal direction rather than in the radial direction, the self-scattering is expected to produce net polarization in the radial direction as shown in Figure 6(B) by the polarization from a dust ring. Kataoka et al. (2015) predicted that the scattering at millimeter wavelengths is efficient if the dust grains are as large as 100 $\mu$m. In this model, a polarization degree of a few percent is expected for assuming spherical dust grains. This mechanism explains well some of the recent ALMA polarization results obtained toward protoplanetary disks or circumstellar disks including: HL Tau (Kataoka et al., 2017; Stephens et al., 2017); HD 14527 (Kataoka et al., 2016); IM Lup (Hull et al., 2018); DG Tau (Bacciotti et al., 2018); HD 163296 (Dent et al., 2019); VLA 1623 (Sadavoy et al., 2018; Harris et al., 2018); and GGD 27 MMS 1 (Girart et al., 2018), as well as Class 0/I sources in the Perseus Molecular Cloud (Cox et al., 2018).

The third mechanism comes from dust grain alignment due to the anisotropic radiation as proposed by Tazaki et al. (2017). Near the star, the dust alignment solely due to the anisotropic radiation is expected in the direction determined by the radiation flux. The dust grains are expected to be aligned with their minor axis parallel to the radiation direction as illustrated in Figure 6(C). The polarization degree depends mainly on the maximum grain size, the shape of the grains, and the intrinsic alignment efficiency of the grains.

4.2 Comparison of Each Model

The ALMA polarization images presented in Figures 2 and 4 highlights the complex substructures within the protostellar core, MMS 6. Therefore, it is possible that the polarized emission may be different by regions. In this section, we discuss possible origins of the dust polarization by regions using the proposed three theoretical models.

4.2.1 Origin of the Polarized Dust Emission Scales of

a few $\times$1000 AU

As described in §3.1, the organized $E$-vectors with P.A.${\approx}135^{\circ}$ is detected at low angular resolution image presented in Figure 2. The $E$-vector orientations are consistent with those previously measured in the filament, the core (a few $\times$0.1 pc), and the envelope size scales (a few $\times$1000 AU) as reported by Matthews & Wilson (2000); Matthews et al. (2001, 2005); Poidevin et al. (2010); Hull et al. (2014). The mechanism to align the dust grains in those extended structures has been widely accepted to be the magnetic field. Hence, the origin of the extended polarized emission measured by the ALMA low angular resolution image appears consistent with a magnetic alignment of dust grains.

The $E$-vectors detected in the “arm-like structure” (Figure 2), are aligned perpendicular to the elongated structure. Assuming that the mechanism producing the polarized emission is the magnetic alignment of dust grains (Figure 6A), the magnetic fields then run along the “arm-like structure” as denoted in Figure 5(a). However, without investigating the gas dynamics, it is difficult to conclude what the origin of the “arm-like structure” is. This structure could be explained by a physical arm or just asymmetrical substructures within the pseudo disk. Similarly, extended substructures likely associated with the envelope are also detected toward Class 0/I sources, for example Per-emb-11, Per-emb-29, Per-emb-2, and Per-emb-5, in the Perseus Molecular Cloud by Cox et al. (2018). They are also bright in the polarized emission and $E$-vectors are aligned to the minor axis of those extended substructures. Cox et al. (2018) interpreted this as a part of the hourglass morphology expected if the polarization traces magnetic field dragged by the accreting material. Their morphology, size scale, and $E$-vector orientations are similar to those observed in the “arm-like structure” in MMS 6. In any case, the magnetic field does not deter gas infalling motions toward the central protostar through this structure. In §4.3, we will make further comparisons of the magnetic field models using a MHD simulation result.

4.2.2 Origin of the Polarized Dust Emission within the Central 200 AU

Our ALMA high angular resolution polarization image and the polarization $E$-vectors within the central 200 AU show the two major components of “centrally concentrated component” and “ring-like structure” (Figure 4). We also identify the following characteristics: (i) there are very different spatial distributions between the Stokes $I$ and the $PI$, (ii) there is a clear positional offset between the peak positions of the Stokes $I$ and the $PI$, (iii) a clear ring-like gap that shows no detection of the polarized emission, (iv) and a significant change in the P.A. of the polarization $E$-vector occurs across the gap, and finally (v) we measure a high polarization degree $\gtrsim$10%) within the central 200 AU. Each of these characteristics may be crucial in identifying the polarization mechanisms at play, and, hereafter we examine which of the five characteristics can be explained by the proposed polarization models. Table 4 summarizes how each of the characteristics could fit in each proposed polarization mechanism.

First, we consider the dust grain alignment due to the anisotropic radiation (Figure 6C). The azimuthally aligned polarized emission is expected for this case. The “ring-like structure”, shown in MMS 6, shows a similar azimuthal pattern but it does not trace back precisely to the center. In particular, the NW component is pointed to the NE of the Stokes $I$ peak position. In addition, the $E$-vectors associated with the “centrally concentrated component” are aligned with the minor axis of the disk-like structure, but not pointing toward the protostar, which is different from the predictions of the anisotropic radiation model. Our observational results, therefore, cannot unambiguously support this scenario.

Second, we consider the polarization $E$-vectors originated from the self-scattering of the dust (Figure 6B). The observed polarization $E$-vector is aligned with the minor axis of the “centrally concentrated component”. This is not inconsistent with the prediction of the $E$-vector orientation for a tilted disk (Kataoka et al., 2015; Yang et al., 2016, 2017). The observed positional offset between the Stokes $I$ emission and the polarized emission can be explained by the optical depth effect, which is presented by Yang et al. (2017). Their model considers a finite optical depth and a finite thickness of the emitting and scattering dust grains within the disk, and then calculate the optical depth effect analytically. Their calculation showed that the absorption optical depth remains well below unity. However, the scattering optical depth becomes larger than unity. This produces an asymmetry of the polarized emission. Assuming that the disk-like structure is perpendicular to the blue and red shifted outflow gas presented in Figure 3, the near-side and far-side of the disk are then on the SE and NW sides, respectively. Our results show that the peak position of the polarized emission is shifted to the near-side of the disk (i.e., south-east) with respect to the peak position of the Stokes $I$ emission. This is consistent with what Yang et al. (2017) predicted.

Recent ALMA results of two embedded protostellar sources, GGD27 MMS 1 (an early B-type protostar; Girart et al. 2018) and VLA 1623 in $\rho$ Ophiuchus (a proto-binary Class 0 source; Sadavoy et al. 2018; Harris et al. 2018), show similar features that the one we observe in MMS 6. Both GGD27 MMS 1 and VLA 1623 show $\approx$200 AU scale circumstellar disks, both of which are likely optically thick. Their $E$-vector orientations show the azimuthal ring-like pattern at the outer part of the disk, while the $E$-vectors at the inner disk are aligned to the minor axis of the disk (i.e., aligned to the minor axis of the elongated continuum structure). A positional offset between the Stokes $I$ and $PI$ was reported for these two sources, and this can also be explained by the optical depth effect (Yang et al., 2017). These features are very similar to what we see in MMS 6.

On the other hand, there are some significant differences between MMS 6 and other objects. First, the “centrally concentrated structure” (i.e., elongated continuum structure at the center) detected in MMS 6 is not extending in the perpendicular direction to the axis of the outflow, hence it is not clear whether the structure is actually a disk. This is different from structures seen in GGD27 MMS 1 and VLA 1623, both of which show that the disks are clearly extending in the perpendicular direction to the axis of the outflow. Second, the polarized emission should be correlated more or less with the Stokes $I$ emission if the origin of the polarized emission is dominated by the self-scattering because the amount of polarized emission correlates with the total flux. This is not the case for MMS 6. Third, and most importantly, the measured polarization degree in MMS 6 is very high compared to any other sources within the central 200 AU scale. For example, in both GGD27 MMS 1 and VLA 1623, the polarization degree is measured to be less than 3% at the inner disk, while in the case of MMS 6 shows the polarization degree as high as 11% at the central peak and over 20% at the NE part of the “ring-like structure”.

Furthermore, another recent ALMA study by Cox et al. (2018) of 10 young Class 0/I protostars shows that the polarization degree is relatively high (${\gtrsim}5\%$) in the envelope, while low in the inner disk (${\lesssim}1\%$). They suggested that self-scattering is dominant in the inner disk, while the magnetically aligned dust is likely dominant in the envelopes. In contrast, MMS 6 shows consistently high polarization degrees in the central 200 AU, both for the “centrally concentrated structure” and the “ring-like structure”. Note that our MMS 6 image has a 10 AU resolution, while the study by Cox et al. (2018) has a resolution of only $\approx$80 AU. Alternative possible explanations of the very different polarization degree observed within the central 200 AU may be caused by the beam dilution effect as pointed out in §3.3.

In summary, the self-scattering model can explain the polarization pattern and positional offset between the Stokes $I$ and the $PI$, detected at the “centrally concentrated component”. This is consistent with other protostellar sources such as; GGD27 MMS 1 and VLA 1623. However, the self-scattering model cannot reproduce the high polarization degree observed in MMS 6. In order to further explore the possibility of the self-scattering effect for MMS 6, multi-wavelength dust polarization experiments are crucial. If self-scattering is a dominant mechanism, we expect changes in the polarization degree as a function of the wavelength (Kataoka et al., 2015).

Finally, as a third model, we consider the magnetically aligned dust grain model (Figure 6A). In this model, the direction of the (uniform) interstellar magnetic field is given by the direction of the $B$-vector. Thus, the magnetic field projected onto the celestial plane is obtained as the perpendicular direction to the observed $E$-vectors as presented in Figure 5(c). In the “centrally concentrated component”, the interstellar magnetic field seems to run parallel to the major axis. The P.A. is measured to be 45*∘*, which is consistent with the orientation of the large-scale magnetic field (Matthews & Wilson, 2000; Matthews et al., 2001, 2005; Poidevin et al., 2010; Hull et al., 2014).

On the other hand, the magnetic field vectors located on the “ring-like structure”, especially at the SE and NW components, show the $E$-vectors (P.A.=115–130*∘) almost perpendicular to those associated with the “centrally concentrated components” . One possible way to explain the observed field configuration is a toroidal wrapping of the magnetic field lines. Tomisaka (2011) modeled magnetically driven molecular outflows through MHD and radiative transfer simulations. The results suggest that the toroidal magnetic field is dominant on $\lesssim$400 AU (i.e., size scale of pseudo disks) and the projected magnetic field vectors change significantly depending on their viewing angle. According to Figure 5 of Tomisaka (2011), ALMA results share some characteristic structures expected from the simulation results when choosing the inclined models (i.e., the viewing angle of 45∘-60∘* in this model). First, the magnetic field structures at the 200 AU scale do not seem to follow the orientation of the large scale outflow, but rather are associated with the toroidal component of the pseudo disk. Second, the brightness of the polarized emission within the toroidal component is not uniform depending on the azimuthal angle. The “ring-like structure” observed in MMS 6 somewhat looks similar to those presented in Tomisaka (2011). Moreover, the relation between the magnetic field orientation and the core rotational axis (outflow axis) also adds another important factor in determining the magnetic field orientations (Kataoka et al., 2012). This will be discussed further in §4.3.

Among the three proposed scenarios, the magnetic field model seems to explain the overall distribution of both the Stokes $I$ and polarized emission, not only the displacement of the peaks of Stokes $I$ and polarized emission, but also the “ring-like structures” and depolarization gaps. The Stokes $I$ emissions correspond to the spatial distribution of the column density combined with the dust temperature, while the polarized emissions correspond to the locations where the $E$-vectors, and therefore the magnetic fields, are most organized, and not necessary to correlate with the Stokes $I$ emission. The observed high polarization degree, that cannot be reproduced by the self-scattering mechanism, can also be explained by the magnetically aligned dust model.

In addition to the listed individual mechanisms, the importance of a hybrid model combining them, and the change of the dust alignment mechanisms across the wavelengths, has been pointed out from the ALMA observations of HL Tau (Kataoka et al., 2017; Stephens et al., 2017). Their results suggest that the self-scattering mechanism dominates at 870 $\mu$m, a hybrid model of the self-scattering and the dust alignment due to the anisotropic radiation explains the results obtained at 1.3 mm, and the anisotropic radiation mechanism dominates at 3.1 mm. Multi-wavelength polarization experiments will therefore be essential in order to distinguish the origins of the polarized emission and to disentangle the multiple mechanisms at play.

Moreover, we would like to note that a strong wind or jet might mechanically align the dust grains. Gold (1952) discussed dynamical interaction between gas and elongated dust particles. In this model, the major axis of dust grains prefers to align parallel to the supersonic gaseous flow, hence the $E$-vectors should be observed along the outflow axis. Figure 7 presents a zoomed image of the SiO collimated outflow 444SiO data will be presented in a separated paper (Takahashi et al. 2019, in prep.) overlaid with the polarized emission. The observed $E$-vectors are aligned perpendicular to the cavity of the outflow, particularly in the southern lobe 555Majority of the $E$-vectors on the northern lobe seems to trace the large-scale magnetic fields (P.A.$\approx$45*∘* in Figure 7b), which likely originated from the foreground fields associated with the cloud or envelope.. The observational result does not support the scenario expected by Gold (1952), while the result is more consistent with a scenario proposed by Lazarian & Hoang (2007), involving an alternative mechanical alignment of helical dust grains. In this scenario, the helical dust grains align with the minor axis being parallel to the gaseous flow (both supersonic and subsonic cases). This results in $E$-vector that are perpendicular to the gas outflow. However, the magnetic alignment also predicts $E$-vectors perpendicular to the gas outflow if the magnetic field is parallel to the gas velocity. Thus, the mechanical alignment proposed by Lazarian & Hoang (2007) and the magnetic alignment predict the same polarization pattern for the outflow region. Recent ALMA dust polarization observations reported similar $E$-vector configurations, likely tracing the outflow cavity in two other Class 0 sources, namely: B335 (Maury et al., 2018) and L1157 (Kwon et al., 2018).

Finally, it is interesting to note that the polarized emission peaks seem to avoid to overlap with the SiO collimated outflow. The outflow may have impacted the “ring-like structure”, pushing aside the gas. Alternatively, the outflow and the ring-like structure are not in the same plane, but are projected along the line of sight.

4.3 Comparisons with the MHD simulations

High sensitivity and high angular resolution at millimeter and submillimeter wavelengths of the polarized dust emission became available with ALMA, enabling us to make direct comparisons between high angular resolution images and detailed theoretical models. In this section, we present comparison using our ALMA data MMS 6 with MHD simulations, and we discuss how the observational results could be further interpreted with a magnetic field model (i.e., the third model discussed in §4.2.2).

In order to take account of the viewing angle of the system, the relation between the magnetic field orientation and the core rotational axis (outflow axis), and finally compare the model results with our ALMA data, we executed a three dimensional non-ideal MHD simulation according to the following steps. As the initial state of the prestellar core, we assumed a Bonnor-Ebert sphere with a central density of 2 $\times$ 105 cm*-3* and an isothermal temperature of 10 K. A uniform magnetic field ($B_{0}$=26 $\mu$G) and rigid rotation ($\Omega_{0}$ = 1.0 $\times$ 10*-13* s*-1*) are imposed, in which the magnetic field direction is inclined from the rotation axis by 45*∘*. We use the Cartesian coordinate, in which we choose the direction of the $z$-axis to coincide with the direction of the initial magnetic field, i.e., $\vec{B}_{0}=(0,0,B_{0})$. The rotation axis is in the $x-z$ plane as $\vec{\Omega_{0}}=\Omega_{0}(1/\sqrt{2},0,1/\sqrt{2})$. Here, the offset between the magnetic field axis and rotation axis is determined from the measured magnetic field direction (Hull et al., 2014) and the outflow axis (Takahashi & Ho, 2012). The mass and radius of the prestellar core are $M_{\rm{core}}$=8.7 $M_{\odot}$, and $R_{\rm{core}}$ = 2.5 $\times$ 104 AU, respectively. Using the nested grid method (for details, see Machida et al. 2005), we calculated the core evolution from the protostellar run-away collapse phase to the protostellar phase, during which the outflow is launched, and the outflow reaches $\sim$ 5000 AU. The cell size of the finest grid is 0.2 AU. The details of the MHD simulation are described in Machida & Hosokawa (2013). Note that, in this simulation, we used a sink cell technique, in which the central region was masked by the sink cell. Thus, we cannot resolve the central region or protostar itself.

The column density (reflects Stokes $I$), the polarized emission, and the magnetic field vectors are calculated, and integrated along the line of sight in order to make a projected polarization map (Tomisaka, 2011). Optically thin condition was assumed when making this projection. A viewing angle of $i$=60*∘* was used 666The inclination angle $i$ is the angle between the direction of the initial magnetic field and the line of sight. $i$=0*∘* is defined as the $z$-direction. This viewing angle was chosen so that the blue and red shifted outflow lobes do not overlap in agreement with previous outflow observations (Takahashi & Ho, 2012). Also the inclination angle of 60*∘* appears to be a better fit to explain our observed results as presented in Figure 5(c).

Figure 8 presents the MHD simulation result obtained for MMS 6 with $i=60^{\circ}$. Figure 9(a) and 9(b) show the expected polarization maps plotted for two different size scales. We found that our ALMA images presented in Figure 5(a) and 5(c) share some characteristic structures predicted from the MHD simulation. First, the simulation results show that arms on the size scale of $\gtrsim$500 AU are connected to the central component (Figure 9a). The magnetic field structures ($B$-vectors) within the arms are aligned along the major axis. The spiral arms are seen within the pseudo disk, which is produced owing to the magnetic field and the core rotation. The material in the arms accretes towards the central region through the spiral arms. Our ALMA data presented in Figure 5(a), show that the “arm-like structure” extend to the 2000 AU scale. The $B$-vector orientations are also aligned along the major axis of the structure, and the “arm-like structure” is connected to the central component from the western side.

Second, within the central 100 AU, the MHD simulation result shows a ring-like structure that produces a relatively high $PI$(Figure 9b). We see local peaks within the ring-like structure due to the effect of integrating polarized emission along the line of sight. The magnetic field vectors in the ring-like structure are aligned more or less along the minor axis of the structure with some fluctuation. In this simulation, while the $PI$ shows a ring-like emission distribution, the column density (reflects Stokes $I$) increases toward the center. Moreover, within the ring-like structure, we can see $PI$ variation (local peaks). $B$-vector orientations in the “ring-like structure” are also aligned along the minor axis of the structure as seen in Figure 4(c). In addition, the ALMA observations show a depolarization within this structure. These qualitative features seen in the MHD simulation are all similar to what we see in the observational results (Figures 4b and 5c). The difference is a bright compact component, which is only seen in the ALMA data and is not reproduced in the MHD simulation. Because we calculated the MHD simulation using a sink technique, the current simulations neither reproduce the protostar itself nor include the radiation field from the central protostar. This underestimate emission from the circumstellar disk at the most internal region. At this moment, it is not obvious how these effects are reflected in the polarized emission, magnetic field, and polarization degree for the innermost region, where we see the “centrally concentrated component” from the ALMA data.

In summary, by adjusting the viewing angle around the outflow driving region, the present MHD simulation can qualitatively explain the characteristic features of the ALMA observations such as the $B$-vector orientations both in the large (1000 AU scale) and small (within a few 100 AU) scales. The magnetic field model also explains differences in the spatial distribution between the Stokes $I$ and the $PI$.

5 Summary and Future Prospects

Using ALMA, we performed full polarization high angular resolution observations of the dust continuum emission at 1.1 mm toward a very young intermediate mass protostellar source, MMS 6/ OMC-3. We have achieved the spatial angular resolution of $0^{\prime\prime}.03{\times}0^{\prime\prime}.02$ corresponding to a linear size scale of $\approx$10 AU at the distance to the source. The main findings of the study are as follows.

Our high angular resolution image shows the complexity of the total and $PI$ within 200 AU of the center. While Stokes $I$ emission shows a single peak toward the center, the dust polarization map shows two different components which are characterized as the “centrally concentrated component” and the “ring-like structure” with a clear depolarization gap between the two components. Stokes $I$ emission and $PI$ also show a clear positional offset. 2. 2.

The detected $E$-vectors are spatially resolved in the central 200 AU and clearly show organized structures. Significant changes in the $E$-vector position angles of 90*∘–105∘* are observed from the partial “ring-like structure” particularly at the NE and SW components to the “centrally concentrated component”. A high polarization percentage of ${\gtrsim}10\%$ is derived in the central 200 AU both in the “ring-like structure” and the “centrally concentrated component”. 3. 3.

We have analyzed origin of the polarized emission and three main mechanisms to align dust grains and/or to produce polarization: (i) magnetic field, (ii) self-scattering, and (iii) anisotropic radiation. Based on a comparison with the available data, the magnetic field scenario appears to explain best the observed characteristics. The $E$-vector orientations in the “centrally concentrated component” are also consistent with the self-scattering model with an optically thick disk-like structure. However, the polarization degree appears to be significantly higher than the expected value for the self-scattering mechanism. 4. 4.

The “arm-like structure” is also observed on large scales ($\approx$2000 AU). The detected polarization $E$-vectors are aligned along the minor axis of the “arm-like structure”, which is consistent with magnetically aligned dust in the field parallel to the major axis of the arm. 5. 5.

We also performed a MHD simulation to further explore the magnetic field structures at the vicinity of the protostar. After taking into account the viewing angle effect and the misalignment between the initial magnetic field orientation and core rotational axis (i.e., outflow axis adjusted for the case of MMS 6), the calculated projected polarization image reproduces most of the characteristic structures observed in the ALMA images including the “ring-like structure” and the “arm-like structure”. This agreement further supports that the origin of the dust alignment for this source can be explained by a toroidal wrapping of the magnetic fields. However, the observed “centrally concentrated component” is not reproduced due to the limitations of the current MHD simulations.

This is the first time that study of the polarization could be done in such details in a protostellar core and that new question and issues have come up that need to be further scrutinized. From the observational side, multi-wavelength polarization experiments with similarly high angular resolution will be crucial in order to assess the hybrid models by investigating contributions from the self-scattering and dust alignment by anisotropic radiation. From the theoretical side, taking into account the optical depth effect and the contribution from the central protostar will help to further study the polarization properties in the central 200 AU. These improvements will be done in our next papers.

Acknowledgements. We thank the anonymous referee for providing very helpful comments and suggestions. S. Takahashi thanks Zhi-Yun Li, A. Kataoka, P. Cox, S. Koga, Y.-N., Su, G.H.-M. Bertrang, K. Saigo, and S. Iguchi for fruitful comments and discussion. We also thank T. Michiyama and B. Dent for providing us information regarding polarization calibration accuracy and observing condition, respectively. This paper makes use of the following ALMA data: ADS/JAO.ALMA #2015.1.00341.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. This work was supported by JSPS KAKENHI Grant Numbers 17K05387 and 15K05032. This research used computational resources from the high-performance computing infrastructure (HPCI) system provided by the Cyberscience Center, Tohoku University, and the Cybermedia Center, Osaka University through the HPCI System Research Project (Project ID: hp170047, hp180001). P.T.P. Ho acknowledges support from MOST 105-2112-M001-025-MY3. Facilities: ALMA.