Resolving the Polarized Dust Emission of the Disk around the Massive Star Powering the HH 80–81 Radio Jet

The 1.14 mm continuum dust emission of GGD27 MM1 appears clearly resolved in an elliptical shape of ∼04 × 02 elongated along the northwest–southeast direction, perpendicular to the radio jet (Figure 1). The source radius, ∼300 au, suggests that the emission is tracing the expected putative disk around the massive protostar that powers the HH 80–81 jet. The peak intensity is 65.9 mJy beam⁻¹, which implies a signal-to-noise ratio of ∼3500. The brightness temperature at the peak for the achieved angular resolution is 676 K.

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We found that in the maps obtained using only baselines larger than ≳4000 kλ, the emission appears to arise from an unresolved, unpolarized source. This means that the source size is much smaller than the synthesized beam and that it has a very high brightness temperature, ≫750 K. The origin of this emission, probably ionized gas associated with the base of the jet, will be analyzed in a forthcoming publication (N. Añez-López et al. 2018, in preparation). Therefore, the compact source was removed from the visibilities and the maps were recreated with the same parameters (hereafter, we use maps without the compact source). Figure 1 shows the disk before and after the removal. The overall shape of the disk remains the same, but the peak brightness temperature decreases from 676 to 467 K.

Since the disk is very well resolved, a Gaussian cannot reproduce the intensity 2D profile. Alternatively, we assumed that the disk intensity can be modeled with two different power laws (${I}_{\nu }\propto {r}^{-q}$),¹⁶ one for the inner region (with a power law index ${q}_{\mathrm{inn}}$) and the other for the outer region (${q}_{\mathrm{out}}$). We define three radii: ${R}_{\mathrm{inn}}$ is the minimum radius where the dust emission is detected, R_turn is the radius where the power-law changes, and R_disk is the disk radius. As free parameters we also included the disk position angle (PA) and the angle between the disk normal and the line-of-sight, i. The disk model was convolved with a Gaussian with the same FWHM as the synthesized beam. The best fit was obtained for a disk with a radius of 171 ± 6 mas (291 ± 10 au), PA = 1129 ± 10, i = 488 ±05 and a total 1.14 mm flux density of 350 ± 1 mJy (see Figure 2). The inner and transition radius are R_inn = 7 ± 1 mas (12 ± 2 au) and R_turn = 92 ± 1 mas (156 au), respectively. In addition, the power-law index changes dramatically in the disk, from a steep index in the outer part (q_out = 4.5 ± 0.1) to a relatively flat index in the inner disk (q_inn = 0.7 ± 0.1). Previous 7 mm observations marginally resolved the dust emission associated with this disk, but the derived radius, ∼200 au, had a large uncertainty due to the lack of sensitivity and to the contamination from the radio jet emission (Carrasco-González et al. 2012). The 1.14 and 7 mm flux densities indicate a spectral index of 2.2, which implies that the disk dust emission is nearly optically thick.

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The dust linear polarization is detected almost all along the GGD27 MM1 disk (Figure 3). The polarized peak intensity, 0.28 mJy beam⁻¹ (≃0.67% of the Stokes I peak intensity), is offset 45 mas southwest of the Stokes I intensity peak. Remarkably, the polarization properties show two clear distinct regions in the disk with a sharp transition between them, which coincides with a location of zero-level polarization. This occurs at the Stokes I iso-intensity contour level of 11.8 mJy beam⁻¹, or, equivalently, at a dust brightness temperature of 120 K. Interestingly, this transition is located at a disk radius of R ≃ 010, which is precisely the transition radius, R_turn, where the power law of the Stokes I intensity profile changes (see previous section).

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The region inside the transition radius, R_turn, (hereafter the inner disk) has a very low polarization level region. Thus, within this radius the polarization degree has a mean value of 0.56% and a standard deviation of 0.33%. In the left panel of Figure 4, the histogram of the polarization position angles shows two main directions. Most of the angles are partially aligned with the minor axis (226), with an average direction of ∼36°. The other region arises from the northeast quadrant of the inner disk, and shows an average position angle of −38°.

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The outer disk (i.e., the region outside R_turn) has significantly higher polarization levels than the inner disk, with an average value of 4.0% and a standard deviation of 2.3%.¹⁷ The polarization position angles have a nearly azimuthal pattern (i.e., they follow a direction tangent to the iso-intensity contours of the Stokes I emission). At the position of each polarization position angle segment shown in Figure 3, we have computed the expected tangent angle for an ellipse centered in the disk center that crosses this point. The right panel of Figure 4 shows the histogram of the difference between this tangent angle and the observed polarization angle. The average angle difference, 11°, is relatively small. This confirms the azimuthal pattern in the outer disk.

The brightness temperature of the disk dust emission reaches high values, up to ∼400 K, but it drops well below 10 K in the outskirts of the disk. This suggests that the inner part of the disk is optically thick and that the dust optical depth decreases with radius, becoming optically thin. A multi-line analysis of SO₂, at scales of a few hundred au, indicates that the average kinetic temperature of the traced molecular gas is ∼120 K (Fernández-López et al. 2011b). Thus, we can roughly use this temperature as a proxy to define where the dust emission becomes optically thick, i.e., where the dust brightness temperature reaches a value similar to the gas temperature (assuming that gas and dust are well coupled). The dust brightness temperature reaches this value at the R_turn radius, i.e., at the radius where the Stokes intensity profile changes significantly in its slope, so it becomes much flatter in the inner disk with respect to the outer disk. In addition, this is the radius where there is a sharp transition between the polarization properties. Together, all of this evidence strongly suggests that the R_turn radius (01 or 170 au) indicates the change between the optically thick and the optically thin regimes in the disk. This implies that observations at 1.14 mm or at shorter wavelength cannot be used to properly study the disk density and temperature as well as the kinematics in the inner disk. Observations at longer wavelengths may alleviate this problem to a certain extent.

Because of the clearly different polarization properties of the inner and outer regions of the disk, here we discuss separately the properties of the two regions.

Initial observation suggests that the overall polarization pattern of the inner disk matches well the prediction of self-scattering from an optically thick disk where dust settling (into the mid-plane) has not yet occurred (Yang et al. 2017). First, the clearest sign of the optically thick case is that the strongest polarization signal is offset along the minor axis with respect to the total intensity peak. In addition, the strongest polarized emission is extended along the major axis with a curved shape, similar to what is expected (see Figure 4(h) from Yang et al. 2017). Furthermore, the outflow geometry (e.g., Heathcote et al. 1998) indicates that this region appears in the nearest side of the disk (with respect to the observer), which is also a strong prediction by the aforementioned model. Another strong indication of self-scattering in an optically thick disk is the bifurcation in the polarization orientation, with respect to the minor axis direction, along the major axis. Thus, in an optically thin disk the orientation is basically uniform and parallel to the minor axis. In the optically thick case, where only the surface layer of a (dust) disk of an appreciable geometric thickness is directly observable, the polarization orientation is predicted to deviate significantly from that of the minor axis in a well-defined manner. The observed position angles in the inner disk show a reasonable agreement with this predicted pattern, except on its northeast side (see Section 3.2). This can be better observed by making slices along the major axis and along a parallel line to the major axis in the near and far sides of the disk (see Figure 5). For the case of an optically thick disk, polarization angles in cuts parallel to the major axis are expected to be symmetrical with respect to the origin (defined as the peak position relative to the minor axis), as is shown in the bottom panel of Figure 5. This behavior is partially observed in the data. In spite of being slightly offset, the slice in the near side of the disk is the one that matches better the expected shape. The other two slices show that the position angles in the eastern side deviate significantly, by 30°–50°, with respect to the expected values. One possibility for this significant departure from the predicted scattering pattern is that the (dust) disk surface is highly perturbed, potentially by a disk-wind or some other means. Another possibility is that they are modified by polarized emission from, e.g., magnetically aligned grains in the envelope surrounding the disk.

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The average polarization fraction detected in the inner region, 0.56%, is well within the expected values for self-scattering, but it is lower than the predicted average maximum values (Kataoka et al. 2016; Yang et al. 2017). A rough estimate of the maximum grain size in the GGD27 MM1 disk can be obtained from the studies carried out by Kataoka et al. (2016, and references therein). From Figure 3 of Kataoka et al. (2016) and from taking into account the average polarization fraction in GGD27 MM1, we estimate that the maximum grain size should be in the 50 and 500 μm range.

In the outer part of the disk, the azimuthal pattern is remarkable (Figures 3 and 4(b)). This is expected for the outer layers of the disk, where the radially anisotropic radiation is basically dominated by the radiation from the inner part of the disk. In models of optically thin disks around low-mass stars, this layer is typically very thin, ∼2%–3%, with a polarization degree higher than in the center (Kataoka et al. 2016; Yang et al. 2017). The GGD27 MM1 disk presents three clear differences with respect to these published predictions. First, the azimuthal layer is significantly broader and appears to extend outward starting from the transition radius between optically thick and thin regions. Second, the polarization fraction in many zones reaches values of 5%–7%, which appears to be higher than the predicted values. Third, the polarization fraction in the outer part of the disk is apparently larger along the minor axis than along the major axis. It is possible that these discrepancies with the existing scattering models (that are not tailored for our particular source) can be resolved with an outer disk where the temperature drops more quickly with radius than is assumed in the existing models. We have carried out some preliminary models that confirm this hypothesis (a more detailed study is out of the scope of this paper and will be part of a future work). It is also plausible that the polarization in the outer disk is due to non-spherical grains aligned by anisotropic radiation (Tazaki et al. 2017).

Finally, this work has shown the unique case of a fully linearly polarized disk around a massive protostar. Observations at multiple wavelengths but with similar angular resolution are needed to better constrain the polarization origin in the outer disk, the maximum grain size in the inner and outer disk, and to determine the origin of the southeast–northwest asymmetry in the inner disk.