Protoplanetary Disk Polarization at Multiple Wavelengths: Are Dust Populations Diverse?

Polarized emission from dust on protoplanetary disks has been observed at millimeter and sub-millimeter wavelengths in an increasing number of sources. Multiple mechanisms could theoretically produce this polarized emission, including the alignment of non-spherical dust grains to the magnetic field (e.g., Lazarian, 2007) or radiation anisotropy (Tazaki et al., 2017), aerodynamic alignment due to gas-dust interactions (Gold, 1952; Yang et al., 2019), or self-scattering of thermal dust emission (e.g., Kataoka et al., 2015; Yang et al., 2016, 2017). Multi-wavelength polarization observations are necessary to distinguish between these mechanisms and to extract information about dust properties from the polarized emission.

Because magnetic fields are thought to be critical to the accretion process, one of the initial goals of polarization studies of protoplanetary disks was to use polarized emission from grains aligned to the magnetic field to trace the field’s morphology (e.g., Stephens et al., 2014; Rao et al., 2014; Segura-Cox et al., 2015). However, with a small number of possible exceptions (e.g., Alves et al., 2018; Sadavoy et al., 2018; Ohashi et al., 2018), the polarized emission seen in most disks does not match the pattern that would be produced by dust grains aligning to magnetic field morphologies predicted by theory. Instead, the polarization seen in many disks is better explained by other mechanisms.

In an inclined axisymmetric disk, the collective scattering of thermal photons from dust grains by other dust grains produces polarization that is parallel to the disk minor axis (Kataoka et al., 2015; Yang et al., 2016). This pattern indicative of scattering has been observed in several sources (e.g., Stephens et al., 2017; Bacciotti et al., 2018; Dent et al., 2019). Scattering polarization fractions of up to a few percent if most of the grains are in the Rayleigh scattering regime (i.e., much smaller than the observing wavelength). For a given observing wavelength, the polarization fraction from scattering is highly dependent on the maximum dust grain size. The polarization fraction peaks when the maximum grain size is of order $\lambda$/2$\pi$, where $\lambda$ is the observing wavelength (Kataoka et al., 2015). Therefore, observing the scattering polarization spectrum of a source can constrain the maximum grain size. In addition to dust grain size, disk inclination, optical depth, and dust scale height can all affect the level of polarization from scattering (e.g., Yang et al., 2017; Ohashi & Kataoka, 2019a; Brunngräber & Wolf, 2020).

Polarization patterns not consistent with pure scattering have also been observed in some protoplanetary disks at millimeter wavelengths. At 3 mm, HL Tau, DG Tau, and Haro 6-13 all exhibit an azimuthal polarization pattern that likely arises from primarily thermal emission by aligned, elongated dust grains (Stephens et al., 2017; Harrison et al., 2019). Several mechanisms have been proposed for grain alignment, including alignment to the magnetic field or radiation anisotropy through radiative alignment torques (RAT’s) (Tazaki et al., 2017) and mechanical alignment (Gold, 1952; Yang et al., 2019; Kataoka et al., 2019). HL Tau’s polarization spectrum is particularly interesting: the disk’s polarization morphology transitions from a pattern consistent with scattering at $\sim$870 $\mu$m to an elliptical pattern at $\sim$3 mm, with an intermediate pattern at $\sim$1.3 mm (Stephens et al., 2017). Recently, Lin et al. (2022) and Lin et al. (2024) demonstrated that HL Tau’s polarization spectrum could be explained by polarization from thermal emission and scattering of aligned grains, and Stephens et al. (2014) demonstrated that the polarization seen at high resolution in HL Tau at 870 $\mu$m could be explained by the same mechanisms. At longer wavelengths, thermal polarization dominates because the low optical depth makes scattering inefficient. At shorter wavelengths, scattering polarization dominates because the high optical depth makes scattering events frequent and dichroic extinction decreases the contribution from thermal polarization. (Lin et al., 2022).

The changes in polarization with wavelength seen in HL Tau invite the question of whether other disks exhibit similar polarization patterns at these wavelengths. Harrison et al. (2019) demonstrated that otherwise similar protoplanetary disks can exhibit different polarization morphologies at the same observing wavelength. The polarized emission in the Class II protoplanetary disks observed at 3 mm with ALMA in Harrison et al. (2019) can be qualitatively split into two categories: those with polarization consistent with scattering (RY Tau, MWC 480, and potentially DL Tau), and those with azimuthally-oriented polarization vectors (DG Tau, Haro 6-13, and V892 Tau). Given how strongly scattering is affected by the grain size with respect to the observing wavelength and how thermal polarization from aligned grains depends on the optical depth, differences in the polarization spectra could indicate differences in the grain sizes and conditions of grain alignment. These dust grains are the building blocks of potential planets in such systems. We present the results of total intensity and continuum linear polarization observations of five Class II disks at 870 $\mu$m and 3 mm: Haro 6-13, MWC 480, RY Tau, DL Tau, and V892 Tau. With these observations, we have significantly expanded the number of protoplanetary disks observed in polarization at multiple wavelengths.

We observed DL Tau, Haro 6-13, RY Tau, MWC 480, and V892 Tau at 870 $\mu$m (ALMA Band 7). These sources are all Class II disks located in the Taurus Molecular Cloud. The disks surround low-mass protostars with a range of ages, luminosities, and masses. The disks of DL Tau, Haro 6-13, RY Tau, and MWC 480 all surround single stars, while V892 Tau is a circumbinary disk around a close binary with a third stellar object orbiting outside the disk (Long et al., 2021). Protostar masses, luminosities, ages, disk inclinations, and distances are listed in Table 1. Table 2 lists the radii of known rings and gaps in the disks.

The observations were taken with ALMA between 18 September and 19 September 2018 in configuration C43-4. The observations were at a frequency range of 337.48-349.51 GHz (ALMA Band 7). J0438+3004 was the phase calibrator, J0522–3627 was the polarization calibrator, and J0510+1800 was the bandpass and flux calibrator.

The datasets were calibrated by data analysts at the North American ALMA Science Center. After this initial calibration, we performed three rounds of phase-only self-calibration on all Stokes parameters ($I$, $Q$, $U$, and $V$). The gain calibration solution interval was equal to the scan length for the first round of self-calibration, 30 seconds for the second round, and 15 seconds for the third round. We used the CASA task tclean with stokes=’IQUV’, Briggs weighting, and a robust parameter of 0.5. Polarization angle and intensity maps were produced from the Stokes $Q$ and $U$ data. The polarized intensity maps were debiased using the average noise value determined from the $Q$ and $U$ maps, an estimator used by e.g. Wardle & Kronberg (1974) and Vidal et al. (2016):

While V892 Tau and DL Tau were reported as unpolarized at 3 mm in Harrison et al. (2019), upon closer examination we found that small regions of these disks were polarized at the $>3\sigma$ level. V892 Tau exhibits azimuthal polarization at 3 mm.

DL Tau has a polarized region near the center of the disk that is less than half the size of the beam, and the peak polarized intensity is $3.5\sigma_{P}$. This region’s peak polarization fraction is 0.9%, and the direction of polarization is along the disk’s minor axis. DL Tau also has several smaller polarized regions outside the disk center with polarization fractions up to 30%, whose direction of polarization angle is along the disk’s minor axis. The polarized regions in DL Tau are so small that few independent measurements of the polarization angle can be made. Higher sensitivity observations will be needed to determine whether this tentative polarization detection is real. We also note that while the majority of the polarized emission at Band 3 in MWC 480 is consistent with scattering, with the angle of polarization along the disk minor axis, there are two sub-beam-sized regions of polarized emission $>3\sigma$ in the outer part of the disk whose polarization angles are not along the minor axis. It is possible that these non-scattering polarized regions arise from aligned grains; however, they do not form a complete ring as the azimuthally-oriented polarized emission in DG Tau, Haro 6-13, and HL Tau does at 3 mm.

The images had angular resolutions between 0.2 and 0.3 arcseconds. The uncertainty on absolute flux calibrations with ALMA is estimated at $\sim$10%. ALMA’s instrumental limit for a 3$\sigma$ detection of polarized emission is 0.1% polarization for compact sources within one-third of the primary beam. The typical sensitivities of the Stokes $Q$ and $U$ images are about 50-60 $\mu$Jy/beam. For the rest of this paper only statistical uncertainties are considered.

Here, we describe the results of the 870 $\mu$m observations and compare them to the polarized emission observed in the same sources at 3 mm in Harrison et al. (2019). At 870 $\mu$m, all five disks exhibit polarization morphologies consistent with scattering, regardless of stellar mass, age, luminosity, multiplicity, or polarization at 3 mm. Figure 1 shows the total intensity, polarized intensity, polarization angle, and polarization fraction for the five disks at 870 $\mu$m. Other observations of protoplanetary disks at 870 $\mu$m (e.g., Stephens et al., 2017; Bacciotti et al., 2018; Dent et al., 2019) and 1.3 mm (Sadavoy et al., 2019) have found that scattering polarization is fairly common at these wavelengths. This indicates that dust in these sources has grown large enough to produce scattering polarization at wavelengths of $\sim$1 mm (likely a few hundred $\mu$m, assuming the grains are compact and spherical). These disks must also be optically thick enough ($\tau\gtrsim 1$) at the observed wavelengths to produce an observable polarization fraction.

Table LABEL:obs_870 lists the measured values for total intensity (as determined from a Gaussian fit to the source) and peak polarized intensity, as well as the beam size. Figure 1 shows composite images of the Stokes $I$ and polarized emission observed in Haro 6-13, MWC 480, RY Tau, DL Tau, and V892 Tau at 870 $\mu$m. The contours indicate total intensity of the dust emission in multiples of $\sigma$, and the blue shading indicates the polarized intensity. The red lines indicate the polarization angle, and are scaled to correspond to the polarization fraction. We refer to these lines as “vectors”, though there is a 180^∘ ambiguity in their direction.

Figure 2 shows the polarization fractions and angles for each disk detected in polarization at both 3 mm and 870 $\mu$m. The vectors are superimposed on the Stokes $I$ contours at 870 $\mu$m from Figure 1. The data in Figure 2 have been smoothed to the same resolution. For Haro 6-13, MWC 480, and RY Tau, the 870 $\mu$m data have been smoothed to the resolution of the 3 mm data. The negative bowl seen around MWC 480 is also present in the non-smoothed data, and may be due to large-scale structure being resolved out. The V892 Tau data from both bands has been smoothed to a resolution of $0\farcs 25$; this resolution is slightly larger than the major and minor axes of the beams at 3 mm and 870 $\mu$m. The angular resolutions of the data in Figure 2 are listed in Table LABEL:tab:3mm_res.

Polarized emission was not detected in the center of V892 Tau’s disk at 3 mm. We examined the possibility that non-thermal emission could affect the observed polarization fraction. Since only thermal emission contributes to polarized emission by scattering, contamination from non-thermal emission could reduce the observed polarization fraction. Long et al. (2021) observed a spectral index of $\sim$0 in V892 Tau between 8 mm and 9.8 mm near the center of the disk, which they report may be due to free-free emission from ionized gas. Hamidouche (2010) estimated the contamination from free-free emission in V892 Tau to be 10% at 2.7 mm. If the level of contamination is similar at 3 mm, then the free-free emission would only lower the observed polarization fraction by $\sim$0.1%, which is at the threshold of ALMA’s polarization detection limits. If the azimuthally-oriented polarization pattern continues in the center of V892 Tau, beam smearing effects are a more likely explanation for the lack of polarized emission in the disk’s center.

We calculated the average values of the spectral index ($\alpha$) in a region at the centers of the disks with an area equivalent to the beam FWHM in Table LABEL:tab:3mm_res. The average values of $\alpha$ at the centers of the disks were 2.0 for Haro 6-13, 2.5 for MWC 480, 2.3 for RY Tau, and 2.3 for V892 Tau. There was no obvious correlation between the spectral indices at the centers of the disks and their polarization spectra. These values of $\alpha$ are consistent with the disk either being optically thick in the center or having small $\beta$. Figure 3 shows the radial profiles of the spectral index along the disks’ major and deprojected minor axes. Full optical depth modeling of these disks would require high-resolution observations that resolved disk substructure, namely rings and gaps, since disk substructure can significantly affect both the spectral index and polarization fraction and morphology.

Figures 4 and 5 show the polarization fractions of each disk vs. distance from the Stokes $I$ center along the disks’ major and deprojected minor axes, respectively. In Haro 6-13, MWC 480, RY Tau, and DL Tau, the Stokes $I$ center is defined as the location of the Stokes $I$ peak. In V892 Tau, the Stokes $I$ center is defined as the midpoint between the two Stokes $I$ peaks. Each point in the plots represents the average value of a line of pixels the length of one-half of the beam width projected along the major and minor axes. To determine the value of the points, we calculated the average values of $I$, $Q$, and $U$ in each half-beam-width line of pixels along each axis, then calculated the percent polarization $p$ as

To determine the uncertainties on $I$, $Q$, and $U$, we calculated the average value of sixteen rectangular regions half the size of the beam in regions of the image outside of any emission. We take the variance of those means as the uncertainty on the average values of $I$, $Q$, and $U$. We calculate the uncertainty on the percent polarization, $\sigma_{p}$ as

The debiased percent polarization, $p^{\prime}$, which is plotted in Figures 4 and 5 is calculated as

In disks known to have rings and gaps, ring locations are indicated by solid vertical lines, and gap locations are indicated by dashed vertical lines. The black scale bar indicates the beam size in the smoothed images.

It is immediately clear from Figure 2 that the disks in this survey exhibit two different morphological groups across two wavelengths. Of the four disks in which we have observed polarized emission at the 3-$\sigma$ level at 3 mm and 870 $\mu$m, Haro 6-13 and V892 Tau show a transition of polarization patterns similar to HL Tau at the same wavelengths, while MWC 480 and RY Tau show polarization patterns indicative of scattering at both wavelengths (i.e., polarization vectors well-aligned to the disk minor axis, as described in Yang et al. (2016)). Additionally, we observed polarization consistent with scattering at 870 $\mu$m in DL Tau.

One notable feature of RY Tau and MWC 480’s polarization spectra is the relative polarization fractions at the two wavelengths. Both wavelengths have polarization fractions $>$0.4%, with a higher polarization fraction at 3 mm in the center of the disk. This is in contrast to previous scattering models such as those presented in Kataoka et al. (2017), which predict a steep correlation between polarization fraction and observing wavelength. In the scattering polarization models for RY Tau and MWC 480 discussed in Section 4, we have aimed to reproduce an observable degree of scattering polarization at both observing wavelengths, and a higher polarization fraction at 3 mm in the center of the disk.

The morphological differences in the polarization spectra of our sources are of interest because they may point toward differences in the disks’ dust environments and/or correlations between polarization and protostar properties. Dust grain sizes and optical depths affect the degree of scattering polarization observed, as well whether polarization from scattering or from aligned grains dominates. In Section 4.1, we compare the data from RY Tau and MWC 480 to models of the scattering polarization for various dust grain populations. In Section 4.2, we explore possible causes of the differences in polarization morphology transitions between the two wavelengths.

Because scattering efficiency at a given wavelength is heavily dependent on dust grain size (Kataoka et al., 2015), the polarization fraction from scattering is expected to vary significantly with observing wavelength for a disk whose dust grain sizes are defined by a simple power-law distribution (Kataoka et al., 2017). However, MWC 480 and RY Tau show a fairly similar degree of scattering polarization at two widely-separated observing wavelengths. Several scenarios that could give rise to the significant degree of polarization in these sources at 870 $\mu$m and 3 mm, including:

1. 1.

   Optical depth effects: The dust is well-described by a single population with a defined maximum grain size. Polarization fraction depends on the optical depth, which differs at different wavelengths. In the optically thin limit, the polarization fraction increases with increasing optical depth. The polarization peaks when the optical depth is of order unity after which decreases to a constant value in the optically thick limit (Yang et al. 2017). If the disk is optically thick at 870 $\mu$m, optical depth effects would attenuate scattering polarization at that wavelength.

2. 2.

   Multiple dust grain populations: The disks contain multiple dust grain populations with different maximum sizes. The vertical component of the stellar gravity pulls the grains towards the disk midplane, causing them to settle, and this effect is stronger for larger grains (Barrière-Fouchet et al., 2005). The larger grains dominate the optical depth at longer wavelengths, whereas the smaller grains are effectively invisible and do not contribute to polarization. At shorter wavelengths, increase in the optical depth of the smaller grains that are elevated can screen out emission of the large grains near the midplane (Ueda et al., 2021), meaning that scattering polarization from smaller grains above the midplane would dominate.

3. 3.

   Dust grain porosity: The dust grains in the disk are highly porous. Scattering from porous dust grains leads to a flatter polarization spectrum than scattering from non-porous grains (see, e.g., Figure 10 of Tazaki et al. 2019).

4. 4.

   Disk substructure: Ring/gap structures in the disk create radial variations in optical depth. These variations in optical depth then affect the observed polarization fraction from scattering, as described in Lin et al. (2020).

Investigating the effects of disk substructure on these sources’ polarization spectra will require higher resolution observations. At the native resolution of the 870 $\mu$m images, only the ring and gap in MWC 480 are resolved. Higher sensitivity observations will also be necessary to explore the effects of disk substructure; the polarized region of MWC 480 only extends to the disk’s gap, and higher sensitivity observations would reveal fainter polarized emission at larger radii. Since dust porosity is poorly constrained and disk substructure is not well resolved in our sources, we will explore only scenarios 1 and 2 further by comparing the 3 mm and 870 $\mu$m data to models of the polarized emission produced by scattering for several different dust grain populations in Section 4.1.

In this multi-wavelength survey of dust polarization in protoplanetary disks, we have shown that Class II disks in the same molecular cloud can exhibit different transitions between polarization morphologies at observing wavelengths of 3 mm and 870 $\mu$m. The transition between azimuthal and scattering polarization in Haro 6-13 and V892 Tau can be explained by how optical depth affects whether a source’s observed polarization comes primarily from thermal emission of aligned grains or self-scattering. Polarization observations at wavelengths longer than 3 mm, possibly with the Next Generation Very Large Array, will be needed to locate where the transition between the two polarization morphologies occurs in RY Tau and MWC 480.

In contrast to Haro 6-13 and V892 Tau, the polarized emission in RY Tau and MWC 480 is consistent with scattering at both wavelengths. Using models of scattering polarization, we aimed to determine what dust grain population(s) could produce a significant polarization fraction at both wavelengths and a polarization fraction that was higher at 3 mm than at 870 $\mu$m in the center of the disk. We found that in RY Tau, dust grains with a maximum radius ($a_{max}$) of 200 $\mu$m and an optical depth at 50 au ($\tau_{0}$) of 10 could reproduce these features. In MWW 480, the model with $a_{max}$ = 200 $\mu$m and $\tau_{0}$ = 10 could reproduce the key features. The model with large grains ($a_{max}$ = 490 $\mu$m, $\tau_{0}$ = 1) near the midplane and small grains ($a_{max}$ = 140 $\mu$m and $\tau_{0}$ = 9) above and below the midplane can also reproduce the key features in MWC 480. With two observing wavelengths, the effects of dust grain size and optical depth (i.e., dust grain number density) on the observed polarization are still somewhat degenerate. The region of degeneracy shrinks as the source is observed at more wavelengths, providing stricter constraints on dust grain properties.

This paper makes use of the following ALMA data: ALMA #2017.1.00470.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. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We thank the anonymous reviewer, whose comments helped to strengthen this manuscript. REH and LWL acknowledge support from NSF AST-1910364. LWL acknowledges support from NSF AST-1910364 and NSF AST-2307844. REH also acknowledges support from the ALMA Student Observing Support (SOS). ZYDL acknowledges support from the Jefferson Foundation, NASA 80NSSC18K1095, and also support from the ALMA Student Observing Support (SOS). ZYL is supported in part by NASA 80NSSC20K0533 and NSF AST-1910106.