Magnetically aligned dust and SiO maser polarization in the envelope of the red supergiant VY CMa

TL;DR

This study uses ALMA observations to analyze polarization in dust and SiO masers around VY CMa, revealing magnetic field structures and strengths in the circumstellar environment.

Contribution

First detection of millimeter dust polarization in VY CMa, providing insights into magnetic field strength and configuration in the star's envelope.

Findings

Detected ~3% dust polarization with uniform electric vector angle

Observed linear polarization up to 30% in SiO maser lines

Estimated magnetic field strength of 13 mG in dust and 1-3 G in gas

Abstract

We use Atacama Large Millimeter/submillimeter Array Band 5 science verification observations of the red supergiant VY CMa to study the polarization of SiO thermal/masers lines and dust continuum at ~1.7 mm wavelength. We analyse both linear and circular polarization and derive the magnetic field strength and structure, assuming the polarization of the lines originates from the Zeeman effect, and that of the dust originates from aligned dust grains. We also discuss other effects that could give rise to the observed polarization. We detect, for the first time, significant polarization (~3%) of the circumstellar dust emission at millimeter wavelengths. The polarization is uniform with an electric vector position angle of $\sim8^\circ$. Varying levels of linear polarization are detected for the J=4-3 28SiO v=0, 1, 2, and 29SiO v=0, 1 lines, with the strongest polarization fraction of ~30% found for the 29SiO v=1 maser. The linear polarization vectors rotate with velocity, consistent with earlier observations. We also find significant (up to ~1%) circular polarization in several lines, consistent with previous measurements. We conclude that the detection is robust against calibration and regular instrumental errors, although we cannot yet fully rule out non-standard instrumental effects. Emission from magnetically aligned grains is the most likely origin of the observed continuum polarization. This implies that the dust is embedded in a magnetic field >13 mG. The maser line polarization traces the magnetic field structure. The magnetic field in the gas and dust is consistent with an approximately toroidal field configuration, but only higher angular resolution observations will be able to reveal more detailed field structure. If the circular polarization is due to Zeeman splitting, it indicates a magnetic field strength of ~1-3 Gauss, consistent with previous maser observations.

Tables

Table 1. Table 1: Spectral window setup

Spw	Center frequency	Channel Width		Number of Channels	Total Bandwidth	Line(s)
	[GHz]	[MHz]	[km s-1]		[GHz]
0	183.310	0.244	0.40	960	0.2344	para-H2O $3_{13}-2_{20}$
1	183.884	1.953	3.18	960	1.8750	-
2	170.999	1.953	3.42	960	1.8750	28SiO $\left(J=4-3,v=2\right)$
						29SiO $\left(J=4-3,v=0\right)$
						29SiO $\left(J=4-3,v=1\right)$
3	172.481	0.244	0.42	480	0.1172	28SiO $\left(J=4-3,v=1\right)$
4	173.668	0.244	0.42	480	0.1172	28SiO $\left(J=4-3,v=0\right)$

Table 2. Table 2: Observed SiO lines

Rest Frequency	Transition	Eu/k	$A$	Peak Flux	$P_{l,\max }$	$\left|P_{c,\max }\right|$
$\left[\mathrm{GHz}\right]$		[K]	[s-1]	[Jy]	[$\%$]	[$\%$]
28SiO
173.688a𝑎aa𝑎a$a$Observed at $0.42$ km s-1 spectral resolution.	$J=4-3,v=0$	21	$2.602\times {10}^{-4}$	2.4	4.0	1.4
172.481a𝑎aa𝑎a$a$Observed at $0.42$ km s-1 spectral resolution.	$J=4-3,v=1$	1790	$2.569\times {10}^{-4}$	104.2	20.1	0.8
171.275b𝑏bb𝑏b$b$Observed at $3.4$ km s-1 spectral resolution.	$J=4-3,v=2$	3542	$2.547\times {10}^{-4}$	69.4	18.5	-1.1
29SiO
171.512b𝑏bb𝑏b$b$Observed at $3.4$ km s-1 spectral resolution.	$J=4-3,v=0$	21	$2.505\times {10}^{-4}$	3.2	2.0	¡0.3
170.328b𝑏bb𝑏b$b$Observed at $3.4$ km s-1 spectral resolution.	$J=4-3,v=1$	1779	$2.484\times {10}^{-4}$	7.4	28.6	0.9

Equations

$$R\sim \frac{Ak{T}_b\Delta \Omega }{4\pi h\nu }.$$

$$V=zB\cos \theta \frac{dI}{d\nu }.$$

$$|B|>4.1\times 10^{-11}\frac{a}{s^2}{n}_g{T}_d\sqrt{T_g}\text{leavevmode}[\mathrm{G}].$$

Full text

*Methods. *We use Atacama Large Millimeter/submillimeter Array Band 5 science verification observations of the red supergiant VY CMa to study the polarization of SiO thermal/masers lines and dust continuum at $\sim 1.7$ mm wavelength. We analyse both linear and circular polarization and derive the magnetic field strength and structure, assuming the polarization of the lines originates from the Zeeman effect, and that of the dust originates from aligned dust grains. We also discuss other effects that could give rise to the observed polarization.

*Results. *We detect, for the first time, significant polarization ($\sim 3\%$) of the circumstellar dust emission at millimeter wavelengths. The polarization is uniform with an electric vector position angle of $\sim 8^{\circ}$. Varying levels of linear polarization are detected for the $J=4-3$ 28SiO $v=0,\leavevmode\nobreak\ 1,\leavevmode\nobreak\ 2,$ and 29SiO $v=0,\leavevmode\nobreak\ 1$ lines, with the strongest polarization fraction of $\sim 30\%$ found for the 29SiO $v=1$ maser. The linear polarization vectors rotate with velocity, consistent with earlier observations. We also find significant (up to $\sim 1\%$) circular polarization in several lines, consistent with previous measurements. We conclude that the detection is robust against calibration and regular instrumental errors, although we cannot yet fully rule out non-standard instrumental effects.

*Conclusions. *Emission from magnetically aligned grains is the most likely origin of the observed continuum polarization. This implies that the dust is embedded in a magnetic field $>13$ mG. The maser line polarization traces the magnetic field structure. The magnetic field in the gas and dust is consistent with an approximately toroidal field configuration, but only higher angular resolution observations will be able to reveal more detailed field structure. If the circular polarization is due to Zeeman splitting, it indicates a magnetic field strength of $\sim 1-3$ Gauss, consistent with previous maser observations.

1 Introduction

The study of the stellar winds of evolved massive stars is important not only because the amount of expelled mass is a key factor in determining the subsequent evolution of the star, and its eventual fate, but also because they have a profound impact on the interstellar medium and evolution of the Galaxy via their material and energy output. However, the mechanisms that drive mass loss from these massive stars are not well understood. It is generally assumed that the acceleration of the stellar wind in low- to intermediate mass asymptotic giant branch (AGB) stars is mainly due to radiation pressure on dust grains (e.g. Habing, 1996; Höfner, 2008, and references therein). However, the formation of dust grains that are non-transparent to stellar radiation is inhibited in the vicinities of evolved massive stars due to their extreme luminosity (Speck et al., 2000; Woitke, 2006; Norris et al., 2012). It is thus puzzling how the material is transported from the surface of the star to the radius where non-transparent dust species form. Furthermore, it has been observed that the distribution of material in the circumstellar envelope (CSE) of red supergiant stars is far from spherical (e.g. Humphreys et al., 2007; O’Gorman et al., 2015). This suggests the action of an aspherical mechanism in the acceleration of the gas. While several models have been proposed to explain the (anisotropic) mass loss in evolve massive stars (including convection, pulsation, scattering off large grains, acoustic and magnetic waves; e.g. Hartmann & MacGregor, 1980; Josselin & Plez, 2007; Höfner, 2008), it remains unclear which of these mechanisms plays the dominant role.

Spectroscopic imaging of the outflows in evolved stars give important clues about their geometry and velocity fields, thus the physics that governs them. In addition, polarimetric observations of the molecular and continuum emission provide valuable information on the magnetic field and characteristics of the dust grains. Specifically, polarimetric continuum observations can reveal the common orientation of elongated dust grains around evolved stars due to the effect of a global magnetic field in a similar way as has been observed in star forming regions (e.g. Cortes et al., 2016), and planetary nebulae (e.g. Sabin et al., 2014). Observations of polarized maser emission, from molecules such as SiO, H2O and OH, have also been important in the determination of the strength and geometry of the magnetic field in the expanding envelopes of evolved stars (e.g. Kemball & Diamond, 1997; Vlemmings et al., 2005; Etoka & Diamond, 2010). This type of observations can be used to probe the magnetic field in the circumstellar envelope (CSE) of evolved massive stars and determine its relation to the mass loss phenomenon.

VY CMa is an excellent example of a massive evolved star with a high mass loss rate (\sim$$10^{-4}M_{\odot} yr*-1*) and high dust content in its CSE (Danchi et al., 1994; Decin et al., 2006; Humphreys et al., 2007), which makes it an attractive target to explore the processes of mass loss and dust formation in massive stars (Richards et al., 2014; De Beck et al., 2015; O’Gorman et al., 2015). It is one of the largest red supergiant stars, located at a distance of 1.2 kpc (Zhang et al., 2012). Recent high angular resolution ALMA Band 7 (around $\sim 321$ GHz) and 9 (around $658$ GHz) observations, tracing scales down to $60$ mas, revealed the presence of two enigmatic features detected only in continuum emission at submillimetre wavelengths. The brightest of them, dubbed “clump C”, is located 334 mas south-east of VY CMa, while the other structure, VY, is located toward the north, elongated in the direction perpendicular to the line that connects the star and clump C (O’Gorman et al., 2015, hereafter OG+15). It is unlikely that these structures formed from convection cells since it would require a constant mass loss in a single direction for a few decades, but it has been suggested that they could have been formed as a result of localised long-lived MHD disturbances in the photosphere (OG+15). From polarization observations of the maser emission it has been found that the strength of the magnetic field in the CSE ranges from few mG to few G (Vlemmings et al., 2002; Herpin et al., 2006; Richter et al., 2016). Such observations however, do not clearly reveal the global structure of the magnetic field within the CSE. In this paper we present the analysis of ALMA full polarization Band 5 science verification observations toward the star VY CMa and report the detection of polarized line and continuum emission around the star that is used to probe the magnetic field and determine its association with features seen in its CSE.

2 Observations and data reduction

These observations are part of the ALMA Band 5 ($163-211$ GHz) Science Verification (SV) campaign. The VY CMa observations took place on 16 October 2016, starting at 05:45 UT and lasting for about 6.4 hours. A total of 13 antennas were used in the calibration and imaging. The observations were performed using five spectral windows (spws). The spw setup is presented in Table. 1.

The full calibration and imaging was performed in CASA 4.7.0, and is described in the Band 5 polarization calibration memo (Martí-Vidal et al., 2016) that was released with the data. The gain calibration (bandpass, amplitude, absolute flux-density scale and phase) was performed following the standard ALMA procedures. The amplitude and phase gains for spw 0 (i.e., the window centered at 183.299 GHz), which has the narrowest bandwidth (234.4 MHz), were derived by transferring the gain solutions from spw 1 (total bandwidth of 1.875 GHz).

The polarization calibration was also performed following standard ALMA procedures, although with some improvements that we summarize here. The X-Y cross-polarization phases at the reference antenna were fitted by pre-averaging spw 0 and spw 1 in chunks of 200 and 20 channels, respectively. This was done to increase the SNR of the gain solutions close to the atmospheric water-vapour line. Also, the calibration tables were created on a per-spw basis. This was needed to properly derive the ambiguities of the X-Y phases (see Martí-Vidal et al. (2016), Sect. 4.2, for more details).

Finally, we performed four iterations of self-calibration on a strong channel of the SiO maser in spw 3. These solutions were applied to all the other spw. We then reimaged all the spws at full spectral resolution and both the continuum and lines at full polarization, producing data cubes in Stokes I, Q, U, and V. The imaging of the spectral lines was performed using Briggs weighting with a robustness parameter of $0.5$, which resulted in a synthesized beam of $\sim 0.8\times 0.3\arcsec$. The typical rms noise in line free channels around the SiO lines was $\sim 3.8$ mJy beam*-1* for spw 3, and 4, and $\sim 1.4$ mJy beam*-1* for the coarser spectral resolution of spw 2. The continuum was imaged using a robust gridding weighting parameter of $-0.5$ resulting in a beam of $\sim 0.5\times 0.2\arcsec$. We achieved an rms noise of $0.1$ mJy beam*-1*.

According to the calibration procedure described in Martí-Vidal et al. (2016) and used here, the estimates of the instrumental polarization in the spws close to the atmospheric water line (i.e., spw 0 and spw 1) may be biased due to the higher noise in the water-vapour frequency window and/or to the mapping function (i.e., dependence with antenna elevation) of the atmospheric absorption. The polarization calibration in these spws should thus be taken with care. With respect to spw 2$-$4, the polarization calibration is not affected by such a bias. Therefore, we use only the linear-polarization results from spw 2$-$4 (covering the SiO masers and the continuum) in our analysis. Regarding the images in circular polarization (i.e., Stokes V), a Stokes V signal can be affected by defects or biases in the calibration of the instrumental polarization; from a biased estimate of the phase between the polarizers at the reference antenna to biased (and correlated) estimates of the polarization leakage at all the antennas. A justification of the fidelity of these Stokes V images, together with a robustness test of the instrumental polarization calibration of these data, is described in Appendix A). Based on this analysis, we rule out calibration errors or standard instrumental effects as the origin of the observed circular polarization. However, as these are the first reported ALMA circular polarization results, there is still the chance that they are affected by unkown instrumental issues.

3 Results

3.1 Dust continuum

In order to map the continuum, we only used line-free channels sufficiently far from the atmospheric H2O line. The resulting aggregate bandwidth was 2.25 GHz. The VY CMa continuum, centered around 178 GHz, is extended. Although the beam is elongated exactly along the direction between component VY and the continuum clump C seen in (OG+15), the distribution appears identical when the ALMA Band 7 and Band 9 observations (OG+15) are convolved with the Band 5 beam. In Fig. 1(left) we show the Band 5 continuum overplotted on the ALMA Band 9 observations around 658 GHz. Deconvolving the two components, we measure a total flux of $36\pm 3$ mJy for the star and $94\pm 9$ mJy for clump C. These values are completely consistent with the average spectral index of the two component determined from the Band 7 ($321$ GHz) and Band 9 ($658$ GHz) observations (OG+15). This implies that clump C is still optically thick at 178 GHz and increases, following the analysis from OG+15, the dust mass to $>1.2\times 10^{-3}$ M⊙ and decreases the dust temperature to $\sim 100$ K. As in OG+15, we did not detect the SW clump seen in Hubble observations of scattered light and a number of molecular lines (e.g. Humphreys et al., 2007; De Beck et al., 2015).

We also detect clear linear polarization. The maximum fractional polarization is $\sim 3\%$. The polarized intensity is indicated in greyscale in Fig. 1 and clearly peaks at the location of Clump C. Despite the large beam, there is no polarization found associated with VY or the North-East dust extension, even though the sensitivity would have been sufficient to detect both down to $1-2\%$. In Fig. 1(right) we show the polarization vectors rotated by $90^{\circ}$ to reflect the magnetic field direction if the polarization is due to the emission from magnetically aligned grains. The average (non-rotated) electric vector position angle (EVPA) is $8\pm 4^{\circ}$ (East of North), where the error includes both the scatter around the average and the error due to the noise in the polarization images. The vectors are thus neither tangential nor parallel to the direction of the star to clump C, which has a position angle of $\sim 130^{\circ}$.

3.2 SiO emission

The observational setup included several lines of SiO and its 29SiO isotope. They display maser emission in the vibrationally excited states and predominantly thermal emission in the $v=0$ state. These SiO maser and thermal emissions are associated with the VY component towards the star, and not with clump C. The line strength and polarization of the SiO lines covered are listed in Table 2 along with their transition energy and Einstein $A$ coefficients (Müller et al., 2001). In the rest of the paper we omit $J=4-3$ when we describe the transitions. All the maser lines show a complicated line structure, but are not, or only marginally, spatially resolved in our $0.8\times 0.3\arcsec$ beam. Their spectra, in Stokes I, linear polarization fraction, EVPA, and Stokes V, are shown in Figs. 2, 3, and 4. The strongest linear polarization, with a fraction up to $\sim 30\%$, is detected for the 29SiO $v=1$ transition with polarization up to $\sim 20\%$ detected for 28SiO $v=2$. With the exception of a single, possibly saturated maser feature (as discussed in section 4.1), the polarization of the 28SiO $v=1$ line is around $5\%$. The linear polarization fraction is consistent with estimates based on recent APEX observations of the same transitions (Humphreys et al., 2017). In Fig. 5, we present a number of channel maps of the linear polarization for this transition. For all maser lines we also detect cicular polarization at a level up to $\sim 1\%$. The spectral resolution for all but the 28SiO $v=1$ line is not sufficient for a more detailed analysis. Hence, unless otherwise noted, the rest of our analysis is based on the 28SiO $v=1$ transition.

The thermal SiO $v=0$ line is significantly spatially extended, both in Stokes I as well as in linear polarization. The polarization spectrum in Fig. 6, extracted in an apperture encompassing the extended polarized emission, shows two distinct spectral features. For illustration, two channel maps representing the two components, blue-shifted at $V_{\rm LSR}=21$ km s*-1* and red-shifted at $V_{\rm LSR}=48$ km s*-1*, are shown in Fig. 7. The neighbouring channels show a similar structure. The polarization pattern at $V_{\rm LSR}=21$ km s*-1* shows that the fractional polarization peaks away from VY and that the polarization vectors point radially towards the star. However, at $V_{\rm LSR}=48$ km s*-1*, the polarization peaks at the stellar position and does not show the radial pattern. The two linearly polarized components are also seen in the circular polarization spectrum, which shows no sign of a typical S-shaped Zeeman pattern.

4 Discussion

4.1 SiO maser polarization

In the framework of basic maser theory, it is important to investigate the rate of stimulated emission of the maser $R$, the maser decay rate $\Gamma$ and the Zeeman frequency $g\Omega$, in order to determine if the SiO maser polarization is the result of Zeeman or non-Zeeman properties (Pérez-Sánchez & Vlemmings, 2013, and references therein). If $g\Omega>R$, and the maser is not strongly saturated ($R\lesssim 10\Gamma$), the magnetic field determines the linear and circular polarization of the maser. Under those conditions, the maximum fractional linear polarization for the SiO transitions we observed will be of the order of $15\%$, depending on the angle $\theta$ between the maser propagation direction and the magnetic field. However, SiO masers often display higher levels of fractional polarization. This is likely due to anisotropic pumping of the energy levels involved in the maser (e.g. Nedoluha & Watson, 1990). However, even in that case, the relationships between $R$, $\Gamma$, and $g\Omega$ still determine whether the magnetic field can be traced by the maser polarization (Watson, 2002).

Using the parameters from Pérez-Sánchez & Vlemmings (2013), $g\Omega\sim 150$ s*-1* for the magnetic field strength of $\sim 0.1$ G in the H2O maser region (Vlemmings et al., 2002). The radiative decay rate $\Gamma$ can be approximated by $\Gamma=5$ s*-1*, which corresponds to the rate for the radiative decay from the first vibrationally excited state to the ground-vibrational state (Nedoluha & Watson, 1990). The stimulated emission rate $R$ depends on the maser brightness temperature $T_{b}$, beaming angle $\Delta\Omega$, Einstein $A$ coefficient and transition frequency $\nu$ through:

[TABLE]

We adopt a value of $\Delta\Omega=10^{-2}$ sr. The brightness temperature itself depends on the size of the maser emission region. Based on VLBI observations (e.g. Richter et al., 2016), we adopt a typical maser spot size of $\sim 1$ mas. As VLBI observations generally do not recover all maser flux observed with larger angular resolution, this size corresponds to the core of the maser emission and likely results in an overestimate of $T_{b}$. From this, we find that $T_{b}<2\times 10^{9}$ K for the 28SiO and $T_{b}<1\times 10^{8}$ K for the 29SiO masers. For the stimulated emission rate, we thus find $R<50$ s*-1* for 28SiO, and $R<8$ s*-1* for 29SiO. Thus, while the strongest of the 28SiO masers could be approaching saturation, $g\Omega>R$ and $g\Omega>\Gamma$. We thus expect the magnetic field to determine the polarization characteristics of the majority of the maser features. This agrees well with the observed fractional linear polarization, which is mostly $<15\%$. Only one of the strongest maser features of the 28SiO $v=1$ transition reaches a polarization fraction of $\sim 20\%$, which could imply that this feature is strongly saturated. This feature, around $V_{\rm lsr}=15$ km s*-1* also displays a change in polarization vector that could be the result of saturation.

As shown in Fig. 2(right), the observations of the 28SiO $v=1$ also reveal significant circular polarization. Possible spurious circular polarization is discussed in Appendix A. Assuming a general Zeeman splitting origin, the circular polarization spectrum $V$ is expected to be proportional to the derivative of the total intensity $I$, with a proportionality coefficient that depends on the magnetic field strength. This assumes a constant magnetic field strength with uniform direction throughout the maser. As indicated by the linear polarization, such a uniform structure is unlikely. Still, we show that $V\propto dI/d\nu$ is a reasonable approximation of the observed spectrum if one assumes a magnetic field reversal at $V_{\rm lsr}\sim 15$ and $30$ km s*-1*, which is close to symmetric around the stellar velocity ($V_{\rm lsr}\sim 22$ km s*-1*). This strongly supports the basic Zeeman interpretation of the circular polarization. Although the spectral resolution was significantly worse, circular polarization was also detected for the 28SiO $v=2$ and the 29SiO $v=1$ maser. Also in this case $V\propto dI/d\nu$ is a good approximation. In order to obtain an estimate of the magnetic field strength required to produce the observed circular polarization, we use the fractional circular polarization (following Herpin et al., 2006; Kemball & Diamond, 1997; Elitzur, 1996). For the $J=4-3$ masers, we find $B\approx 1.3P_{c}\cos{\theta}$ assuming a typical maser linewidth of $\sim 1$ km s*-1*. We thus find $B/\cos{\theta}\approx 0.85$ G. This is similar to the field strengths of $1-2$ G found using the same method from previous $J=1-0$ and $J=2-1$ SiO maser observations (Herpin et al., 2006; Richter et al., 2016), supporting the Zeeman interpretation of the observed circular polarization. The above approximation assumes saturated masers (Elitzur, 1996) and slightly different results are obtained when applying the basic Zeeman fitting that might be more applicable to the non-saturated masers we observe. We thus also determine the field strength using

[TABLE]

Here, the proportionality term $z=g\Omega\approx 1500$ s*-1* [Gauss]-1. Our fit shown in Fig. 2(right) then yields a magnetic field strength of $B\cos{\theta}\sim 2.4$ G. Thus, in either method, the magnetic field is indeed strong enough for $g\Omega>R$. Both field strength estimates are easily sufficient to magnetically align the dust grains in clump C in sufficiently short time scale (as described in § 4.3).

Alternatively, Houde (2014) suggests the SiO maser circular polarization could arise from resonant scattering of magnetised foreground SiO gas. This causes linear polarization to be converted to circular polarization. The effect has been able to explain the circular polarization of 43 GHz SiO masers. The conversion phenomenon depends on the excitation of the molecular transition in the foreground, and the much lower column density of 29SiO would lead to a conversion efficiency lower than that of 28SiO. As we observe a similar circular polarization fraction, it appears that the resonant scattering does not contribute significantly to the maser transitions presented here.

4.2 Thermal SiO polarization

Linearly polarized line emission from non-maser molecular lines can arise due to differences in excitation of the magnetic sublevels within a transition. This can occur already in a weak magnetic field when the magnetic sublevels of a rotational state experience anisotropic emission. This effect is generally called the Goldreich-Kylafis effect (hereafter GK-effect) and is described in Goldreich & Kylafis (1981, 1982). Alternatively, linear polarization in a circumstellar envelope can occur from molecules with a preferred rotation axis because of strong, radial, infrared emission from a central star (Morris et al., 1985). Significantly polarized (thermal) molecular line emission around evolved stars has so far been observed for SiO $v=0$ and CO in the envelope of the M-type AGB star IK Tau (Vlemmings et al., 2012) and for CS, SiS and CO around the C-type AGB star IRC+10216 (Glenn et al., 1997; Girart et al., 2012). In the case of radiative molecular alignment in the absence of a magnetic field, the linear polarization should mainly be perpendicular to the radial direction. Already for few $\mu$G magnetic field strength however, the molecular alignment in much of the circumstellar envelope is determined by magnetic field (Morris et al., 1985). In case of the GK-effect, the linear polarization is along the magnetic field as long as the Zeeman splitting dominates the collisional and spontaneous emission rates (Kylafis, 1983).

The behaviour of thermal line polarization will thus change depending on optical depth, distance from the star, and magnetic field strength and geometry. Our observations seem to indicate such a change, as shown in Fig. 6(right) and Fig. 7. The polarization is confined to a velocity range between $V_{\rm lsr}=11-25$ km s*-1* close to and slightly blue-shifted from the stellar velocity, and a clearly redshifted component between $V_{\rm lsr}=42-52$ km s*-1*. While the (slightly) blue-shifted component displays a radial polarization pattern that could indicate that the radiation field dominates the molecular alignment, the red-shifted component is neither radial nor tangential. The red-shifted polarization component also peaks towards the star, contrary to prediction of radiative alignment. It thus appears that the red-shifted component traces the magnetic field according to the GK-effect. This implies a magnetic field position angle of $\sim 40^{\circ}$ in the most red-shifted part of the circumstellar envelope which is consistent with the extreme velocity SiO masers.

We also detect significant circular polarization in the 28SiO v=0 thermal line. As seen in Fig. 6(left), the circular polarization spectrum is significantly different from that observed for the maser lines. It displays similarities to the linear polarization (Stokes Q, and U) spectra, although it does not show the negatives seen in those. It peaks at approximately $1.6\%$ but does not show a typical Zeeman spectrum. In Appendix A, we rule out calibration errors, although unknown instrumental effects in the ALMA system can only be ruled out once the observations are repeated. Non-Zeeman circular polarization has previously been reported for CO and has been suggested to be due to the resonant scattering of foreground molecules via the same mechanism suggested for SiO masers (Houde, 2014). The excitations conditions of the thermal SiO foreground gas can explain why the effect is seen in the $v=0$ transition and not the maser transitions. The lower abundance of 29SiO is then the reason why no circular polarization was detected for the 29SiO $v=0$ line despite the total intensity being of equal strength to the 28SiO $v=0$ line.

Alternatively the velocity ranges displaying polarized emission could be those including maser components. In this case, the circular polarization of 28SiO $v=0$ may instead arise from weaklu saturated maser features. This can only be confirmed with future, higher angular resolution observations.

4.3 Dust polarization of clump C

We consider two possible scenarios to explain the observed polarized radiation in the continuum emission towards clump C, scattering off large dust particles or emission from non-spherical grains with a preferred orientation direction. In our analysis, we also include that observations of polarized visible light obtained with Hubble (Jones et al., 2007) and SPHERE/VLT (Scicluna et al., 2015) show that the polarization vectors seen towards clump C in visible wavelengths are roughly perpendicular to those observed at mm wavelength presented here.

For the polarization signal at mm wavelengths to be produced by scattering off dust particles, the presence of grains with $a_{\rm grain}\sim\lambda/2\pi$ is required (for our observations this means $a_{\rm grain}\gtrsim 250\leavevmode\nobreak\ \mu$m). This is because the scattering cross-sections are too small unless the grains are made large. However, if the grains are too large, $a_{\rm grain}\gtrsim 500\mu$m for observations at 1 mm, the polarization efficiency becomes too small and polarized light is not efficiently produced (see, e.g. Kataoka et al., 2015). Scattering of radiation from a point source due to randomly aligned dust particles in an optically thin medium produces polarization vectors tangential to the radiation field. Hence, in this scenario, our observations of non-tangential polarization vectors would imply that the source of millimeter radiation is more complex, that the grains have a preferable alignment direction, or that the photons suffer multiple scattering episodes. We disfavour multiple scattering as a possible explanation because the effect of high scattering optical depths is to decrease the polarization degree, as shown by Kataoka et al. (2015). Their models show that a maximum polarization degree of $2.5\%$ is obtained in the optically-thin regime and decreases for larger optical depths. Regarding the asymmetry of the incident radiation field, the source of millimeter flux is clearly not point-like, with detectable emission arising from the star itself and from an extended N-NE feature, apart from clump C. The direction of the polarization vectors cannot be explained by the N-NE feature contributing to the source of unpolarized photons, because that would cause the vectors to be rotated in the opposite direction we observe. If we consider photons emitted by clump C itself to be the primary source of unpolarized radiation, the resolution of the observations would cause any polarization created to be erased, unless Clump C has a very special morphology. We consider this explanation unlikely, as higher angular-resolution observations indicate that Clump C is elongated but still approximately spherically symmetric (OG+15). Moreover, none of these possible solutions is able to explain the direction of the polarization vectors in visible wavelengths naturally.

The polarization at millimeter wavelengths can also be explained by emission of dust particles aligned with the local magnetic field. Several alignment mechanisms have been proposed (For recent reviews, see e.g. Voshchinnikov, 2012; Andersson et al., 2015). The currently favoured theory for this alignment is the Radiative Alignment Torque (RAT) theory (e.g. Lazarian & Hoang, 2007). In this case, the grains are expected to spin about their minor axis, with their major axis aligned perpendicularly to the magnetic field lines. Hence, the direction of polarization of photons emitted by the dust would be perpendicular to that of the magnetic field lines. This scenario can also explain the direction of the polarization seen in visible wavelengths, because absorption and scattering rather than emission are expected to dominate at visible wavelengths. Therefore, background scattered visible light would be more efficiently absorbed or scattered out of the line-of-sight in the direction of grain alignment. The resulting polarization would then have a direction parallel to that of the magnetic field lines and perpendicular to the polarization observed in emission. This is exactly what we find in our observations.

The RAT theory was mainly developed for interstellar dust grains. To investigate if the mechanism would work in the much denser circumstellar environment we need to compare the alignment timescale, given by the Larmor precession timescale, with the timescale set by gas-dust interaction (e.g. Hoang & Lazarian, 2009; Reissl et al., 2016). This comparison yields a lower limit for the magnetic field strength that, following Hoang & Lazarian (2009), can be written as:

[TABLE]

We assume typical grains with a grain size of $a=10^{-5}$ cm $[=0.1\leavevmode\nobreak\ \mu$m$]$ and aspect ratio $s=0.5$. We now assume the gas and dust temperature to be equal to the maximum allowed by the observations of clump C, $T_{d}=T_{g}=100$ K. The gas particle density $n_{g}$ is more uncertain, as no molecular gas has yet been detected in clump C (e.g. OG+15, De Beck et al., 2015). Taking the dust mass derived from our measured fluxes, the size of clump C from OG+15, and assuming a gas-to-dust ratio of $100$, we find $n_{g}\approx 9\times 10^{9}$ cm*-3*. For the dust alignment to be efficient, we find $B>13$ mG (or less if clump C is indeed severely depleted in gas). This increases to $\sim 65$ mG for grain sizes of $0.5\leavevmode\nobreak\ \mu$m that are suggested to exist in part of the VY CMa outflow (Scicluna et al., 2015). Even taking into account uncertainties on grain size and aspect ratios, and gas temperature and density, these values are still less than the field strength ($>100$ mG) derived from H2O masers at a similar distance to the star as clump C (Vlemmings et al., 2002). Even in the strong radiation field of VY CMa, the radiative alignment timescale, following Hoang & Lazarian (2009), becomes of the order of a few years. This is still significantly more than the Larmor precession timescale for a $13$ mG field of only $\sim 0.5$ day. This means that the grains will have had the time to align with the magnetic fields. Emission from aligned grains under the RAT alignment theory can thus explain our observations.

In addition to the RAT alignment theory, a number of other grain alignment theories exist. Several of these theories make specific predictions and so far only the RAT theory can explain all observational characteristics of aligned dust (e.g. Voshchinnikov, 2012; Andersson et al., 2015). However, different mechanism can operate or dominate in different astrophysical regions, and the special conditions in the dense circumstellar environment can provide further tests for the different alignment mechanisms. The earliest proposed mechanism is the imperfect Davis-Greenstein (IDG) mechanism (Davis & Greenstein, 1951) that has seen several adjustments over the last decades. In this mechanism the dissipation of magnetization energy (for grains including small amounts of iron) aligns the spin axis with the magnetic field. This theory specifically aligns the small grains and the alignment efficiency depends on the temperature difference between the dust and the gas. Under our earlier assumptions, of equal dust- and gas-temperatures, we would thus not expect any alignment. However, further detailed observations of clump C are needed to determine if conditions are such that the IDG mechanism can operate. Thus, while our observations are fully consistent with the RAT theory, and provide strong constraints on the alignment timescales, we cannot yet rule out other mechanisms that align the grains with the magnetic field.

4.4 Magnetic field morphology

Having determined that the linear polarization of the majority of the SiO masers traces the magnetic field, we notice, with the exception of the potentially saturated maser feature at $V_{\rm lsr}=15$ km s*-1*, a clear structure in the $v=1$ 28SiO EVPAs. The vectors rotate from $\sim 130^{\circ}$ at blue-shifted velocities to $\sim-50^{\circ}$ around the stellar velocity and back to $\sim 140^{\circ}$ on the red-shifted side. Almost exacly the same rotating behaviour was seen in the 86 GHz 28SiO $J=2-1,v=1$ polarization vectors observed by Herpin et al. (2006). The EVPAs we observe are also consistent with the angles measured for the 28SiO ($J=5-4,v=1$) masers in Shinnaga et al. (2004).

The actual magnetic field direction is parallel or perpendicular to the measured polarization vectors, depending on whether the angle $\theta$ between the maser propagation and the line of sight is respectively smaller or larger than the Van Vleck angle $\theta_{cr}\approx 55^{\circ}$, where the fractional polarization is equal to zero. Considering the dust polarization vectors arising in clump C, which is thought to be close to the plane of the stellar velocity, are perpendicular to the magnetic field direction, the same appears to be true for the SiO masers. For most masers, we can thus conclude that $\theta>55^{\circ}$ and that the magnetic field is perpendicular to the SiO maser EVPA. That is also consistent with the $\sim 40^{\circ}$ magnetc field angle determined from the extreme red-shifted thermal SiO.

Such polarization behaviour may be consistent with a predominantly toroidal field morphology, with an inclination $>55^{\circ}$ and a position angle on the sky of $\sim 40^{\circ}$. The magnetic field strength dependence on radius of $B\propto r^{-1}$ for a toroidal field also fits the field strength derived from the SiO masers observed here and previously observations (Herpin et al., 2006; Richter et al., 2016), together with the OH, and H2O masers (Vlemmings et al., 2002).

The hypothesis of a predominantly toroidal magnetic field, however, can only be confirmed with high angular resolution observations, as it depends on the position of the individual maser components. Component fitting of the SiO masers presented here indicates that they occur within $\sim 20$ mas, or $\sim 2$ R∗, from the star. As the positional uncertainty for most masers is of similar order, it is not possible to produce a more detailed map of the magnetic field with the current data.

Assuming a toroidal field configuration would place clump C in the magnetic equator, possibly the result of a magnetically controlled ejecta. This scenario is supported by the observations of Richter et al. (2016). Although on much smaller scales, their VLBI observations indicate elongation of $v=1J=1-0$ SiO maser features from the star in the general direction of clump C. For these masers they derive a $2-5$ Gauss magnetic field strength. Richter et al. (2016) speculate that the elongated features, at least their ”F1” feature studied in detail, may be associated with a highly magnetized outflow above a stellar surface magnetic cool spot or convective cell.

5 Conclusions

The ALMA Band 5 178 GHz continuum observations of VY CMa reveal that the dust structure at this wavelength is similar to the structure found in previous 321, and 658 GHz ALMA observations. The derived spectral index map indicates the dust of clump C is mostly optically thick even at 178 GHz. Assuming standard dust properties, this means the estimated clump C dust mass is $>1.2\times 10^{-3}$ M⊙.

Significant linear polarization of up to $3\%$ is detected from clump C. This is the first detection of dust polarization at millimeter wavelengths in the inner circumstellar environment of an evolved star. The EVPA is $\sim 8^{\circ}$ and is neither radial nor tangential to the stellar radiation field. If the continuum polarization is the result of emission from magnetically aligned dust grains, then the observations indicate that, according to RAT grain alignment theory, the grains cannot be diamagnetic (e.g. purely carbonaceous). This is not unexpected for the oxygen rich environment of VY CMa where for example Si, Mg, and/or Fe are expected to be present in the dust. The magnetic field would have a preferred angle of $98^{\circ}$ and should be $>13$ mG in strength. As higher field strengths of $0.1$ to a few Gauss are measured in the maser region, the magnetic field thus has no problem aligning the dust grains in clump C. Higher angular resolution observations could subsequently be done to determine the magnetic field structure and its possible role in confining the dense clump C. Although we show it to be unlikely, we cannot yet completely rule out a self-scattering origin of the polarization. In this case, the grains in clump C would need to be extremely large $(>250\leavevmode\nobreak\ \mu$m$)$. The origin of the preferred polarization direction would then also imply a very specific dust geometry.

The linear polarization of the SiO masers is typically $\sim 5-10\%$, and goes up to $\sim 20-30\%$ for specific features. The average polarization is at the level that could be expected from regular maser polarization theory of non- to intermediately saturated masers, and does not require anisotropic pumping of the magnetic substates. The EVPAis also neither tangential nor radial and indicates a possible toroidal magnetic field morphology. For the thermal SiO, the linear polarization appears consistent with a direction set by the stellar radiation field at the blue-shifted side, but not at the red-shifted side, where it also seems to probe the magnetic field.

Circular polarization is also detected for the maser and thermal lines. The magnitude and spectral bevaviour of the circular polarization indicates it is unlikely to be caused by standard instrumental effects or calibration errors. The observed polarization is also consistent with previous measurements. Finally, since the calibrators and VY CMa continuum show no sign of circular polarization and the Stokes V charactistics are very different for the maser and thermal lines, we suggest that the circular polarization is likely intrinsic to the source. However, as this constitutes the first circular polarization imaged with ALMA, additional observations are needed to rule out possible unknown instrumental contributions to Stokes V and confirm our observations. A normal Zeeman interpretation of the maser lines would imply a field of $\sim 1-3$ G in the SiO maser region of VY CMa. This is consistent with previous lower frequency SiO and H2O maser observations and the toroidal field interpretation. The circular polarization of the thermal line could potentially originate from resonant scattering of magnetized SiO gas at larger distance from the star.

Acknowledgements.

This work was supported by ERC consolidator grant 614264. WV and TK also acknowledge support from the Swedish Research Council. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2011.0.00011.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC 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. We thank the ALMA Band 5 Science Verification team for their efforts in preparing and performing the observations and the ARC node network reduction team and the hosts of the Nordic ARC for their reduction work.

Appendix A Monte Carlo analysis of spurious circular polarization

The calibration of the instrumental polarization can be described by two different quantities: on the one hand, the relative phase between the polarizers at the reference antenna (we call this quantity X-Y phase) and, on the other hand, the leakage between the polarizers of all the antennas, which are modelled by complex-valued quantities called D-terms. In order to simulate the effects that a residual X-Y phase and/or polarization leakage would have on the final SiO images in Stokes V, we have performed a Monte Carlo analysis. We have assumed that both the X-Y phase and the D-terms are smooth functions of the frequency within the band, so that the channel noise in the calibration plots shown in (Martí-Vidal et al., 2016) reflects the uncertainties related to the process of antenna-gain estimation. All these uncertainties, combined, may bias the final images, introducing spurious signals in all four Stokes parameters.

Judging from the calibration plots in (Martí-Vidal et al., 2016) (their Fig. 8), we estimate an upper bound in the X-Y phase uncertainty of $\sim$10 degrees. Regarding the D-terms (Fig. 11), the typical scatter among neighbouring frequency channels (of the same antenna) is 1$-$2%.

Based on this assumptions, we have generated one thousand sets of random D-terms for all the ALMA antennas, together with random X-Y phases for the reference antenna. Then, we applied these quantities to the calibrated data and generated modified images of VY CMa for all four Stokes parameters. The random D-terms in our analysis follow a Gaussian distribution with a 1$\sigma$ amplitude of 1%. The X-Y phase follows a Gaussian distribution with a 1$\sigma$ deviation of 10 degrees.

After the imaging, we have computed the difference between the calibration-corrupted full-polarization images and those obtained from the original calibration (we call this difference the spurious source polarization). In Figs. 8, and 9, we show the spurious polarization (in all four Stokes parameters) resulting from 5 representative Monte Carlo iterations for spw 3, and 4. The spectra are taken at the peak intensity of Stokes I.

A seen in Fig. 8, we notice that the spurious fractional Stokes V has typical wide-band average values of the order of $\pm$0.1% across the entire SiO line. This is similar to the measured average Stokes V from the original polarization calibration: $-0.1$% and indicates our assumed uncertainties in the calibration are correct.

In any case, the spurious Stokes V in our Monte Carlo analysis is typically below 0.1% in absolute value, and has a smooth frequency dependence across the line. On the contrary, the Stokes V recovered from the original calibration shows a much stronger frequency dependence, with extreme changes between close by channels that are up to 4–5 time higher than those seen in the spurious Stokes V. This is a clear indication that the differential Stokes V (i.e., the frequency dependence of Stokes V) is a robust quantity, almost independent of calibration biases. A similar conclusion can be derived from the Monte Carlo analysis on spw 4 (Fig. 9). We can thus conclude that the observed Stokes V behaviour of the SiO lines is likely real and not an artifact of calibration. However, to rule out an unkown instrumental effect introduced in the ALMA system would require further observations.