arXiv subjects

Zhi-Yun Li

Publications and source records attributed to Zhi-Yun Li.

At least 181 records · Page 10Linked to original sources

arXiv2018

The role of magnetic fields in the formation of protostellar discs

Truncated abstract: The formation of a protostellar disc is a natural outcome during the star formation process. As gas in a molecular cloud core collapses under self-gravity, the angular momentum of the gas will slow its collapse on small scales and promote the formation of a protostellar disc. Although the angular momenta of dense star-forming cores remain to be fully characterized observationally, existing data indicates that typical cores have enough angular momenta to form relatively large, rotationally supported discs. However, molecular clouds are observed to be permeated by magnetic fields, which can strongly affect the evolution of angular momentum through magnetic braking. Indeed, in the ideal MHD limit, magnetic braking has been shown to be so efficient as to remove essentially all of the angular momentum of the material close to the forming star such that disc formation is suppressed. This is known as the magnetic braking catastrophe. The catastrophe must be averted in order for the all-important rotationally supported discs to appear, but when and how this happens remains debated. We review the resolutions proposed to date, with emphasis on misalignment, turbulence and especially non-ideal effects. The dissipative non-ideal effects weaken the magnetic field, and the dispersive term redirects it to promote or hinder disc formation. When self-consistently applying non-ideal processes, rotationally supported discs of at least tens of au form, thus preventing the magnetic braking catastrophe. The non-ideal processes are sensitive to the magnetic field strength, cosmic ray ionization rate, and gas and dust grain properties, thus a complete understanding of the host molecular cloud is required. Therefore, the properties of the host molecular cloud -- and especially its magnetic field -- cannot be ignored when numerically modelling the formation and evolution of protostellar discs.

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arXiv2018

The formation of rings and gaps in wind-launching non-ideal MHD disks: three-dimensional simulations

Previous axisymmetric investigations in two dimensions (2D) have shown that rings and gaps develop naturally in non-ideal magnetohydrodynamic (MHD) disk-wind systems, especially in the presence of ambipolar diffusion (AD). Here we extend these 2D simulations to three dimensions (3D) and find that rings and gaps are still formed in the presence of a moderately strong ambipolar diffusion. The rings and gaps form from the same basic mechanism that was identified in the 2D simulations, namely, the redistribution of the poloidal magnetic flux relative to the disk material as a result of the reconnection of a sharply pinched poloidal magnetic field lines. Thus, the less dense gaps are more strongly magnetized with a large poloidal magnetic field compared to the less magnetized (dense) rings. The rings and gaps start out rather smoothly in 3D simulations that have axisymmetric initial conditions. Non-axisymmetric variations arise spontaneously at later times, but they do not grow to such an extent as to disrupt the rings and gaps. These disk substructures persist to the end of the simulations, lasting up to 3000 orbital periods at the inner edge of the simulated disk. The longevity of the perturbed yet still coherent rings make them attractive sites for trapping large grains that would otherwise be lost to rapid radial migration due to gas drag. As the ambipolar diffusivity decreases, both the disk and the wind become increasingly turbulent, driven by the magnetorotational instability, with tightly-wound spiral arms becoming more prominent in the disk.

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arXiv2018

Does HL Tau Disk Polarization in ALMA Band 3 Come from Radiatively Aligned Grains?

Disk polarization in (sub)millimeter dust continuum is a rapidly growing field in the ALMA era. It opens up the exciting possibility of detecting and characterizing magnetic fields and grain growth in disks around young stellar objects. However, to use polarization for probing the disk properties, its production mechanism must be ascertained first. To date, the conventional mechanism involving magnetically aligned grains fails to explain the polarization patterns detected in most disks. This is especially true for the inclined disk of HL Tau in ALMA Band 3 (wavelength $\sim 3$ mm), which has an elliptical polarization pattern. The elliptical pattern was taken as evidence for polarized emission by dust grains aligned with their long axes perpendicular the direction of the radiative flux. We show that the radiatively aligned grains produce a circular, rather than elliptical, polarization pattern even in inclined disks such as HL Tau. An elliptical polarization pattern can be produced if the grains are aligned aerodynamically by the difference in rotation speed between the dust and gas through the Gold mechanism. However, a strong azimuthal variation in polarized intensity is expected for both the radiative and aerodynamic alignment, but not observed in the HL Tau disk in ALMA Band 3. We conclude that neither of these two mechanisms alone can explain the data and the origin of the 3 mm polarization remains a mystery. We speculate that this mystery may be resolved by a combination of both direct emission and scattering by aerodynamically aligned grains.

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arXiv2018

Inclination-Induced Polarization of Scattered Millimeter Radiation from Protoplanetary Disks: The Case of HL Tau

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 ($i \sim 45^\circ$): 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 ($\sim 1\%$), 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 $β\lesssim 1$ 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.

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arXiv2018

The VLA/ALMA Nascent Disk and Multiplicity (VANDAM) Survey of Perseus Protostars. VI. Characterizing the Formation Mechanism for Close Multiple Systems

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of multiple protostar systems in the Perseus molecular cloud previously detected by the Karl G. Jansky Very Large Array (VLA). We observed 17 close ($<$600~AU separation) multiple systems at 1.3~mm in continuum and five molecular lines (i.e., \twco, \cateo, \thco, H$_2$CO, SO) to characterize the circum-multiple environments in which these systems are forming. We detect at least one component in the continuum for the 17 multiple systems. In three systems, one companion is not detected, and for two systems the companions are unresolved at our observed resolution. We also detect circum-multiple dust emission toward 8 out of 9 Class 0 multiples. Circum-multiple dust emission is not detected toward any of the 8 Class I multiples. Twelve systems are detected in the dense gas tracers toward their disks/inner envelopes. For these 12 systems, we use the dense gas observations to characterize their formation mechanism. The velocity gradients in the circum-multiple gas are clearly orthogonal to the outflow directions in 8 out of the 12 systems, consistent with disk fragmentation. Moreover, only two systems with separations $<$200~AU are \textit{inconsistent} with disk fragmentation, in addition to the two widest systems ($>$500~AU). Our results suggest that disk fragmentation via gravitational instability is an important formation mechanism for close multiple systems, but further statistics are needed to better determine the relative fraction formed via this method.

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arXiv2018

Submillimeter Polarization Spectrum of the Carina Nebula

Linear polarization maps of the Carina Nebula were obtained at 250, 350, and 500 $μ$m during the 2012 flight of the BLASTPol balloon-borne telescope. These measurements are combined with Planck 850 $μ$m data in order to produce a submillimeter spectrum of the polarization fraction of the dust emission, averaged over the cloud. This spectrum is flat to within $\pm$15% (relative to the 350 $μ$m polarization fraction). In particular, there is no evidence for a pronounced minimum of the spectrum near 350 $μ$m, as suggested by previous ground-based measurements of other molecular clouds. This result of a flat polarization spectrum in Carina is consistent with recently-published BLASTPol measurements of the Vela C molecular cloud, and also agrees with a published model for an externally-illuminated, dense molecular cloud by Bethell and collaborators. The shape of the spectrum in Carina does not show any dependence on the radiative environment of the dust, as quantified by the Planck-derived dust temperature or dust optical depth at 353 GHz.

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arXiv2018

The VLA Nascent Disk and Multiplicity Survey of Perseus Protostars (VANDAM). V. 18 Candidate Disks around Class 0 and I Protostars in the Perseus Molecular Cloud

We present the full disk-fit results VANDAM survey of all Class 0 and I protostars in the Perseus molecular cloud. We have 18 new protostellar disk candidates around Class 0 and I sources, which are well described by a simple, parametrized disk model fit to the 8 mm VLA dust-continuum observations. 33% of Class 0 protostars and just 11% of Class I protostars have candidate disks, while 78% of Class 0 and I protostars do not have signs of disks within our 12 AU disk diameter resolution limit, indicating that at 8 mm most disks in the Class 0 and I phases are <10 AU in radius. These small radii may be a result of surface brightness sensitivity limits. Modeled 8 mm radii are similar to the radii of known Class 0 disks with detected Keplerian rotation. Since our 8 mm data trace a population of larger dust grains which radially drift towards the protostar and are lower limits on true disk sizes, large disks at early times do not seem to be particularly rare. We find statistical evidence that Class 0 and I disks are likely drawn from the same distribution, meaning disk properties may be defined early in the Class 0 phase and do not undergo large changes through the Class I phase. By combining our candidate disk properties with previous polarization observations, we find a qualitative indication that misalignment between inferred envelope-scale magnetic fields and outflows may indicate disks on smaller scales in Class 0 sources.

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arXiv2018

ALMA observations of the very young Class 0 protostellar system HH 211-mms: a 30-au dusty disk with a disk-wind traced by SO?

HH 211-mms is one of the youngest Class 0 protostellar systems in Perseus at ~ 235 pc away. We have mapped its central region at up to ~ 7 AU (0.03") resolution. A dusty disk is seen deeply embedded in a flattened envelope, with an intensity jump in dust continuum at ~ 350 GHz. It is nearly edge-on and is almost exactly perpendicular to the jet axis. It has a size of ~ 30 au along the major axis. It is geometrically thick, indicating that the (sub)millimeter light emitting grains have yet to settle to the midplane. Its inner part is expected to have transformed into a Keplerian rotating disk with a radius of ~ 10 au. A rotating disk atmosphere and a compact rotating bipolar outflow are detected in SO. The outflow fans out from the inner disk surfaces and is rotating in the same direction as the flattened envelope, and hence could trace a disk wind carrying away angular momentum from the inner disk. From the rotation of the disk atmosphere, the protostellar mass is estimated to be <~ 50 M_Jup. Together with results from the literature, our result favors a model where the disk radius grows linearly with the protostellar mass, as predicted by models of pre-stellar dense core evolution that asymptotes to an $r^{-1}$ radial profile for both the column density and angular velocity.

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arXiv2018

The VLA Nascent Disk And Multiplicity Survey of Perseus Protostars (VANDAM). IV. Free-Free Emission from Protostars: Links to Infrared Properties, Outflow Tracers, and Protostellar Disk Masses

Emission from protostars at centimeter radio wavelengths has been shown to trace the free-free emission arising from ionizing shocks as a result of jets and outflows driven by protostars. Therefore, measuring properties of protostars at radio frequencies can provide valuable insights into the nature of their outflows and jets. We present a C-band (4.1 cm and 6.4 cm) survey of all known protostars (Class 0 and Class I) in Perseus as part of the VLA Nascent Disk and Multiplicity (VANDAM) Survey. We examine the known correlations between radio flux density and protostellar parameters such as bolometric luminosity and outflow force, for our sample. We also investigate the relationship between radio flux density and far-infrared line luminosities from Herschel. We show that free-free emission originates most likely from J-type shocks; however, the large scatter indicates that those two types of emission probe different time and spatial scales. Using C-band fluxes, we removed an estimation of free-free contamination from the corresponding Ka-band (9 mm) flux densities that primarily probe dust emission from embedded disks. We find that the compact ($<$~1") dust emission is lower for Class I sources (median dust mass 96 M$_{\oplus}$) relative to Class 0 (248 M$_{\oplus}$), but several times higher than in Class II (5-15 M$_{\oplus}$). If this compact dust emission is tracing primarily the embedded disk, as is likely for many sources, this result provides evidence for decreasing disk masses with protostellar evolution, with sufficient mass for forming giant planet cores primarily at early times.

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arXiv2018

ALMA Observations of Polarized 872 $μ$m Dust Emission from the Protostellar Systems VLA 1623 and L1527

We present high-sensitivity ($σ_I\sim0.2-0.5$ mJy, $σ_{QU}\sim0.05$ mJy), high-resolution (0.12-0.2 arcsec) observations of polarized 872 $μ$m dust emission from the young multiple system VLA 1623 in $ρ$ Ophiuchus and the protostar L1527 in Taurus. We detect the circumstellar material of VLA 1623A, the extended Keplerian disk surrounding VLA 1623A which we call VLA 1623CBdisk, VLA 1623B, VLA 1623W, and L1527 strongly in the polarized emission, at the $\sim1-3\%$ level. We spatially resolve VLA 1623A into two sources, VLA 1623Aa and VLA 1623Ab, separated by $\sim30$ au and located within a cavity of radius $\sim50$ au within the circumbinary Keplerian disk, as well as the edge-on disk of VLA 1623W. The polarization angle of the emission is uniform across each protostellar source and nearly coincides with each disk's minor axis. The offsets between the minor axis and the polarization angle are not uniformly distributed at the $P\lesssim2\times10^{-4}$ level. The circumbinary disk surrounding VLA 1623Aab is azimuthally symmetrically polarized. Each compact source's emission is partially optically thick ($τ\gtrsim1$) at 872 $μ$m, complicating interpretations of polarization involving aligned grains. We find evidence against alignment by radiative flux in each source, particularly in the edge-on VLA 1623W and L1527. We detect astrometric offsets between the polarized emission and the total intensity in VLA 1623Aa, VLA 1623Ab, and VLA 1623B, as predicted if self-scattering in the optically thick limit operates. We conclude that self-scattering is likely responsible for disk-scale polarization at 872 $μ$m in these systems.

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arXiv2018

ALMA observations of polarization from dust scattering in the IM Lup protoplanetary disk

We present 870 $μ$m ALMA observations of polarized dust emission toward the Class II protoplanetary disk IM Lup. We find that the orientation of the polarized emission is along the minor axis of the disk, and that the value of the polarization fraction increases steadily toward the center of the disk, reaching a peak value of ~1.1%. All of these characteristics are consistent with models of self-scattering of submillimeter-wave emission from an optically thin inclined disk. The distribution of the polarization position angles across the disk reveals that while the average orientation is along the minor axis, the polarization orientations show a significant spread in angles; this can also be explained by models of pure scattering. We compare the polarization with that of the Class I/II source HL Tau. A comparison of cuts of the polarization fraction across the major and minor axes of both sources reveals that IM Lup has a substantially higher polarization fraction than HL Tau toward the center of the disk. This enhanced polarization fraction could be due a number of factors, including higher optical depth in HL Tau, or scattering by larger dust grains in the more evolved IM Lup disk. However, models yield similar maximum grain sizes for both HL Tau (72 $μ$m) and IM Lup (61 $μ$m, this work). This reveals continued tension between grain-size estimates from scattering models and from models of the dust emission spectrum, which find that the bulk of the (unpolarized) emission in disks is most likely due to millimeter (or even centimeter) sized grains.

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arXiv2018

Constraint on ion-neutral drift velocity in the Class 0 protostar B335 from ALMA observations

Ambipolar diffusion can cause a velocity drift between ions and neutrals. This is one of the non-ideal MHD effects proposed to enable the formation of Keplerian disks with sizes of tens of au. To observationally study ambipolar diffusion in collapsing protostellar envelopes, we compare gas kinematics traced by the H13CO+ (3-2) and C18O (2-1) lines in the Class 0 protostar B335 obtained with our ALMA observations. A central compact (~1"-2") component that is elongated perpendicular to the outflow direction and exhibits a clear velocity gradient along the outflow direction is observed in both lines and most likely traces the infalling flattened envelope. We constructed kinematical models to fit the observed velocity structures and to measure the infalling velocities of the ionized and neutral gas on a 100 au scale in B335. The infalling velocities in the H13CO+ and C18O emission are both measured to be 0.85+/-0.2 km/s at a radius of 100 au, suggesting that the velocity drift between the ionized and neutral gas is at most 0.3 km/s at a radius of 100 au. The Hall parameter for H13CO+ is estimated to be >>1 on a 100 au scale in B335, so that H13CO+ is expected to be attached to the magnetic field. Our non-detection or upper limit of the velocity drift between ions and neutrals could suggest that the magnetic field remains rather well coupled to the bulk neutral material on a 100 au scale in this source, and that any significant field-matter decoupling, if present, likely occurs only on a smaller scale, leading to an accumulation of magnetic flux and thus efficient magnetic braking in the inner envelope. However, because of our limited angular resolution, we cannot rule out a significant ambipolar drift only in the midplane of the infalling envelope. Future observations with higher angular resolutions (~0.1") are needed to examine this possibility and ambipolar diffusion on a smaller scale.

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arXiv2018

The formation of rings and gaps in magnetically coupled disk-wind systems: ambipolar diffusion and reconnection

Radial substructures in circumstellar disks are now routinely observed by ALMA. There is also growing evidence that disk winds drive accretion in such disks. We show through 2D (axisymmetric) simulations that rings and gaps develop naturally in magnetically coupled disk-wind systems on the scale of tens of au, where ambipolar diffusion (AD) is the dominant non-ideal MHD effect. In simulations where the magnetic field and matter are moderately coupled, the disk remains relatively laminar with the radial electric current steepened by AD into a thin layer near the midplane. The toroidal magnetic field sharply reverses polarity in this layer, generating a large magnetic torque that drives fast accretion, which drags the poloidal field into a highly pinched radial configuration. The reconnection of this pinched field creates magnetic loops where the net poloidal magnetic flux (and thus the accretion rate) is reduced, yielding dense rings. Neighbouring regions with stronger poloidal magnetic fields accrete faster, forming gaps. In better magnetically coupled simulations, the so-called `avalanche accretion streams' develop continuously near the disk surface, rendering the disk-wind system more chaotic. Nevertheless, prominent rings and gaps are still produced, at least in part, by reconnection, which again enables the segregation of the poloidal field and the disk material similar to the more diffusive disks. However, the reconnection is now driven by the non-linear growth of MRI channel flows. The formation of rings and gaps in rapidly accreting yet laminar disks has interesting implications for dust settling and trapping, grain growth, and planet formation.

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arXiv2018

Effect of Grain Size on Differential Desorption of Volatile Species and on Non-ideal MHD Diffusivity

We developed a chemical network for modeling the chemistry and non-ideal MHD effects from the collapsing dense molecular clouds to protostellar disks. First, we re-formulated the cosmic-ray desorption rate by considering the variations of desorption rate over the grain size distribution. We find that the differential desorption of volatile species is amplified by the grains larger than 0.1 $μ$m, because larger grains are heated to a lower temperature by cosmic-rays and hence more sensitive to the variations in binding energies. As a result, atomic nitrogen N is $\sim$2 orders of magnitude more abundant than CO; N$_2$H$^+$ also becomes a few times more abundant than HCO$^+$ due to the increased gas-phase N$_2$. However, the changes in ionization fraction due to freeze-out and desorption only have minor effects on the non-ideal MHD diffusivities. Our chemical network confirms that the very small grains (VSGs: below a few 100 $Å$) weakens the efficiency of both ambipolar diffusion and Hall effect. In collapsing dense cores, a maximum ambipolar diffusion is achieved when truncating the MRN size distribution at 0.1 $μ$m, and for a maximum Hall effect, the truncation occurs at 0.04 $μ$m. We conclude that the grain size distribution is crucial to the differential depletion between CO and N$_2$ related molecules, as well as to the non-ideal MHD diffusivities in dense cores.

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arXiv2018

A 100 au-Wide Bipolar Rotating Shell Emanating From The HH 212Protostellar Disk: A Disk Wind?

HH 212 is a Class 0 protostellar system found to host a "hamburger"-shaped dusty disk with a rotating disk atmosphere and a collimated SiO jet at a distance of ~ 400 pc. Recently, a compact rotating outflow has been detected in SO and SO2 toward the center along the jet axis at ~ 52 au (0.13") resolution. Here we resolve the compact outflow into a small-scale wide-opening rotating outflow shell and a collimated jet, with the observations in the same S-bearing molecules at ~ 16 au (0.04") resolution. The collimated jet is aligned with the SiO jet, tracing the shock interactions in the jet. The wide-opening outflow shell is seen extending out from the inner disk around the SiO jet and has a width of ~ 100 au. It is not only expanding away from the center, but also rotating around the jet axis. The specific angular momentum of the outflow shell is ~ 40 au km/s. Simple modeling of the observed kinematics suggests that the rotating outflow shell can trace either a disk wind or disk material pushed away by an unseen wind from the inner disk or protostar. We also resolve the disk atmosphere in the same S-bearing molecules, confirming the Keplerian rotation there.

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arXiv2018

ALMA's Polarized View of 10 Protostars in the Perseus Molecular Cloud

We present 870 $μ$m ALMA dust polarization observations of 10 young Class 0/I protostars in the Perseus Molecular Cloud. At $\sim$ 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 $\sim$ 100 au scales, the polarization is at a relatively low level ($\lesssim 1\%$) and is quite ordered. In sources with significant envelope emission, the envelope is typically polarized at a much higher ($\gtrsim 5\%$) 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 disk-candidates 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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arXiv2018

ALMA Dust Polarization Observations of Two Young Edge-on Protostellar Disks

Polarized emission is detected in two young nearly edge-on protostellar disks in 343 GHz continuum at ~ 50 au (~ 0.12") resolution with Atacama Large Millimeter/submillimeter Array. One disk is in HH 212 (Class 0) and the other in HH 111 (early Class I) protostellar system. Polarization fraction is ~ 1%. The disk in HH 212 has a radius of ~ 60 au. The emission is mainly detected from the nearside of the disk. The polarization orientations are almost perpendicular to the disk major axis, consistent with either self-scattering or emission by grains aligned with a poloidal field around the outer edge of the disk because of optical depth effect and temperature gradient; the presence of a poloidal field would facilitate the launching of a disk wind, for which there is already tentative evidence in the same source. The disk of HH 111 VLA 1 has a larger radius of ~ 220 au and is thus more resolved. The polarization orientations are almost perpendicular to the disk major axis in the nearside, but more along the major axis in the farside, forming roughly half of an elliptical pattern there. It appears that toroidal and poloidal magnetic field may explain the polarization on the near and far side of the disk, respectively. However, it is also possible that the polarization is due to self-scattering. In addition, alignment of dust grains by radiation flux may play a role in the farside. Our observations reveal a diversity of disk polarization patterns that should be taken into account in future modeling efforts.

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arXiv2017

ALMA Reveals Transition of Polarization Pattern with Wavelength in HL Tau's Disk

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 to 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 $μ$m and 1.3 mm. The morphology at 870 $μ$m 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 $μ$m 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 $μ$m 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.

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