Spatially resolved polarized millimeter/submillimeter emission has been observed in the disk of HL Tau and two other young stellar objects. It is usually interpreted as coming from magnetically aligned grains, but can also be produced by dust scattering, as demonstrated explicitly by Kataoka et al. for face-on disks. We extend their work by including the polarization induced by disk inclination with respect to the line of sight. Using a physically motivated, semi-analytic model, we show that the polarization fraction of the scattered light increases with the inclination angle i, reaching 1/3 for edge-on disks. The inclination-induced polarization can easily dominate that intrinsic to the disk in the face-on view. It provides a natural explanation for the two main features of the polarization pattern observed in the tilted disk of HL Tau (i ∼ 45• ): the polarized intensity concentrating in a region elongated more or less along the major axis, and polarization in this region roughly parallel to the minor axis. This broad agreement provides support to dust scattering as a viable mechanism for producing, at least in part, polarized millimeter radiation. In order to produce polarization at the observed level (∼ 1%), the scattering grains must have grown to a maximum size of tens of microns. However, such grains may be too small to produce the opacity spectral index of β 1 observed in HL Tau and other sources; another population of larger, millimeter/centimeter-sized, grains may be needed to explain the bulk of the unpolarized continuum emission.
The mechanism for producing polarized emission from protostellar disks at (sub)millimeter wavelengths is currently uncertain. Classically, polarization is expected from non-spherical grains aligned with the magnetic field. Recently, two alternatives have been suggested. One polarization mechanism is caused by self-scattering from dust grains of sizes comparable with the wavelength, while the other mechanism is due to grains aligned with their short axes along the direction of radiation anisotropy. The latter has recently been shown as a likely mechanism for causing the dust polarization detected in HL Tau at 3.1 mm. In this paper, we present ALMA polarization observations of HL Tau for two more wavelengths: 870 μm and 1.3 mm. The morphology at 870 μm matches the expectation for self-scattering, while that at 1.3 mm shows a mix between self-scattering and grains aligned with the radiation anisotropy. The observations cast doubt on the ability of (sub)millimeter continuum polarization to probe disk magnetic fields for at least HL Tau. By showing two distinct polarization morphologies at 870 μm and 3.1 mm and a transition between the two at 1.3 mm, this paper provides definitive evidence that the dominant (sub)millimeter polarization mechanism transitions with wavelength. In addition, if the polarization at 870 μm is due to scattering, the lack of polarization asymmetry along the minor axis of the inclined disk implies that the large grains responsible for the scattering have already settled into a geometrically thin layer, and the presence of asymmetry along the major axis indicates that the HL Tau disk is not completely axisymmetric.
Disk polarization at (sub)millimeter wavelengths is being revolutionized by ALMA observationally, but its origin remains uncertain. Dust scattering was recently recognized as a potential contributor to polarization, although its basic properties have yet to be thoroughly explored. Here, we quantify the effects of optical depth on the scattering-induced polarization in inclined disks through a combination of analytical illustration, approximate semi-analytical modeling using formal solution to the radiative transfer equation, and Monte Carlo simulations. We find that the near-side of the disk is significantly brighter in polarized intensity than the far-side, provided that the disk is optically thick and that the scattering grains have yet to settle to the midplane. This asymmetry is the consequence of a simple geometric effect: the near-side of the disk surface is viewed more edge-on than the far-side. It is a robust signature that may be used to distinguish the scattering-induced polarization from that by other mechanisms, such as aligned grains. The asymmetry is weaker for a geometrically thinner dust disk. As such, it opens an exciting new window on dust settling. We find anecdotal evidence from dust continuum imaging of edge-on disks that large grains are not yet settled in the youngest (Class 0) disks, but become more so in older disks. This trend is corroborated by the polarization data in inclined disks showing that younger disks have more pronounced near-far side asymmetry and thus less grain settling. If confirmed, the trend would have far-reaching implications for grain evolution and, ultimately, the formation of planetesimals and planets.
We present 870 µm ALMA dust polarization observations of 10 young Class 0/I protostars in the Perseus Molecular Cloud. At ∼ 0.35 (80 au) resolution, all of our sources show some degree of polarization, with most (9/10) showing significantly extended emission in the polarized continuum. Each source has incredibly intricate polarization signatures. In particular, all three disk-candidates have polarization vectors roughly along the minor axis, which is indicative of polarization produced by dust scattering. On ∼ 100 au scales, the polarization is at a relatively low level ( 1%) and is quite ordered. In sources with significant envelope emission, the envelope is typically polarized at a much higher ( 5%) level and has a far more disordered morphology. We compute the cumulative probability distributions for both the small (disk-scale) and large (envelope-scale) polarization percentage. We find that the two are intrinsically different, even after accounting for the different detection thresholds in the high/low surface brightness regions. We perform Kolmogorov-Smirnov and Anderson-Darling tests on the distributions of angle offsets of the polarization from the outflow axis. We find disk-candidate sources are different from the non-disk-candidate sources. We conclude that the polarization on the 100 au scale is consistent with the signature of dust scattering for diskcandidates and that the polarization on the envelope-scale in all sources may come from another mechanism, most likely magnetically aligned grains.
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