arXiv subjects

Akimasa Kataoka

Publications and source records attributed to Akimasa Kataoka.

At least 19 recordsLinked to original sources

arXiv2026

Dust characterization of the HD 163296 disk with high-resolution multi-wavelength ALMA observations

Context. Planets form through the growth and accumulation of dust grains in protoplanetary disks. Characterizing dust properties such as size, surface density, and temperature is key to understanding planet formation. Aims. We characterize the dust properties of the protoplanetary disk around HD 163296 by performing spectral energy distribution (SED) fitting of multi-wavelength high-resolution observations. Methods. We present new high-resolution ALMA Band 9 (0.45 mm) observations, which are sensitive to the temperature. We performed SED fitting at a common resolution of 0.066 arcsec using these new Band 9 observations along with archival ALMA Band 3, 4, 6, and 7 observations. We compared the fitted results with VLA observations and explored multiple dust models with different optical constants and porosities. Results. The Band 9 image shows the central disk, two rings at 0.67 and 1.00 arcsec, and outer extended emission previously seen at other wavelengths. At higher frequencies, the rings appear wider, the gaps appear shallower, and the extended emission appears brighter, which can be explained by optical-depth effects and/or size segregation. We characterized the dust properties, including temperature, surface density, and dust size, for each dust model. However, the inferred dust properties are dependent on the dust model, and the ALMA data alone do not allow us to determine which dust model is preferred. We identified the DSHARP Zubko (porous) model as the preferred model based on VLA profiles and physical and observational constraints. The outer ring temperature is lower than predicted by a passively irradiated disk model, suggesting shadowing by the inner ring. Although the surface density and dust size depend on the dust model, the preferred model indicates that the central disk, both rings, and the extended disk each contain more than a few Earth masses of dust.

astro-ph.EP↗

arXiv2026

An archival summary: 15 years of ALMA observations on disks and planet formation

The Atacama Large (sub-)millimeter Array (ALMA) has been in scientific operations for almost 15 years. We celebrate this achievement by providing a summary of the ``Disks and planet formation'' scientific category, with an emphasis on the disks located in the nearby star-forming regions. As of the beginning of February 2026, ALMA had observed 3933 independent coordinates, which we analyzed by their location in the sky, frequency coverage, exposure time, spectral line coverage, and angular resolution. We encourage the community to explore new scientific questions that are made possible through the archival datasets.

astro-ph.EP↗

arXiv2026

A fast tree algorithm for multi-component coagulation equation

Dust properties, such as mass and porosity, impact planet formation directly. Understanding the time evolution of dust distribution across multiple properties requires numerical computation. However, available ways to calculate the multi-component coagulation-fragmentation are highly time-consuming. This study aims to develop a fast and accurate algorithm for multi-component coagulation. We assumed that two pairs of colliding aggregates reproduce a similar outcome if the dust properties are similar, and that the ratio of dust properties in logarithmic space gives the similarity as a "distance". These assumptions enable us to apply the tree algorithm, which groups distant bins and calculates interactions together, to coagulation. The algorithm reduces the computational complexity from $O (N^{2d})$ to $O (d N^d \log N)$, considering $N$ bins per $d$ components. We tested the algorithm by comparing it with the conventional direct method for cases where analytic solutions are known. We measured the dependencies of the wall-clock time, $L_2$ error in the distribution, and relative error of the total mass, on the $d, N$, opening angle $θ_c$, and maximum dust distribution width after coagulation $k_c$. The algorithms are found to calculate coagulation consistently. For $d=1$, the tree method is faster than the direct method for a specific range of parameters. For $d=2$, however, the tree method is faster for all parameter regions surveyed, speeding it up by tens of times. Increasing $N$ and decreasing $θ_c$ or $k_c$ made it slower and more accurate. Additionally, using a small $k_c$ performs worse than when using a large $k_c$, suggesting that limiting $k_c$ is unnecessary. We present a fast tree algorithm for the multi-component coagulation equation. It will enable us to evolve the multi-component dust distribution, such as in mass-porosity space, in protoplanetary disks.

astro-ph.EP↗

arXiv2026

Millimeter dust continuum and polarization in protoplanetary disks with scattering: A slab model

Millimeter continuum emission and self-scattering polarization from protoplanetary disks are widely used to constrain dust properties. Interpreting these observations requires practical prescriptions for the disk emission. However, only approximate formulae are available for the continuum emission, and no widely applicable formula has yet been established for the polarized emission. We aim (i) to assess the validity of commonly used analytic approximations for the (sub)millimeter continuum emission from protoplanetary disks, and (ii) to derive realistic prescriptions for the disk emission for both the continuum and the polarization. We numerically solve the radiative transfer equation in an isothermal, constant-density plane-parallel slab, including dust absorption, emission, and self-scattering with full Stokes parameters. We find that commonly used analytic approximations for the continuum emission are systematically about 10 to 15% lower than our numerical solutions. Consequently, SED analyses of (sub)millimeter observations that adopt these formulae are likely to overestimate the optical depth (and thus the disk mass) and the dust temperature, and underestimate the albedo (and thus altering the inferred constraints on grain size). We also provide empirical fitting formulae that reproduce our numerical results for the continuum emission and polarization fraction. These formulae will enable observational data analyses to be carried out more accurately and efficiently than with the conventional approaches. For the analysis of (sub)millimeter observations, we recommend using our new empirical formulae or interpolation of our numerical results, rather than commonly used approximations.

astro-ph.EP↗

arXiv2026

Multi-wavelength ALMA Imaging of HD 34282: Dust-trapping Signatures of a Vortex Candidate

Azimuthal arcs in millimeter continuum emission from protoplanetary disks are often attributed to dust-trapping vortices, but definitive observational confirmation of vortices remains lacking. We present sub-0.1" resolution ALMA continuum observations of the HD 34282 disk at 0.9, 1.3, 2.1, and 3.1 mm. These observations resolve a bright azimuthal arc superposed on a compact double-gap, triple-ring morphology, most clearly at shorter wavelengths, and enable us to probe the physical origin of the arc. It exhibits a lower spectral index than the surrounding rings, consistent with enhanced grain growth and/or higher dust surface density of a dust-trapping vortex. Its azimuthal width decreases with increasing wavelength, consistent with tighter confinement of larger grains, or lower optical depths at longer wavelengths. These observations probe dust with Stokes numbers St < 0.03. Vortex models predict negligible peak shifts in this regime, consistent with the 1.3 to 3.1 mm data. At 0.9 mm, however, the arc peak is offset by 15 +/- 4 degree in the direction of disk rotation relative to longer wavelengths, and the near-side ring emission is locally dimmer compared to the far-side, likely reflecting optical-depth or temperature effects. These observations are consistent with azimuthal dust trapping, potentially associated with a vortex-induced pressure maximum.

astro-ph.EP↗

arXiv2026

ALMA 873 $μ$m Polarization Observations of the PDS~70 Disk

At a 112.4 pc distance, the PDS70 protoplanetary disk is a rare case that has been confirmed to host two accreting planets. This makes it the most important laboratory for studying dust growth in the context of planet formation. Here we present the first deep, full polarization observations at 873 $μ$m wavelength. We detected $\sim$1%-2.5% linear polarization over the bulk of the $\sim$55-100 AU (sub)millimeter ring. The polarization position angles align preferentially with the projected minor axis of the disk. The standard interpretation is that the observed polarization is caused by dust self-scattering, with a maximum dust grain size of $\sim$100 $μ$m. On $\gtrsim$10 AU scales, which can be resolved by the presented 873-3075 $μ$m observations, the ring is marginally optical thick at 873 $μ$m wavelength. Using Monte Carlo radiative transfer simulations, we found that an azimuthally asymmetric, marginally optically thick ring with a maximum dust grain size of $\sim$87 $μ$m can reproduce the observed 873 $μ$m polarization position angles and percentages. This study indicates that the coagulation of ice-coated dust in the protoplanetary disk may be limited by fragmentation or bouncing.

astro-ph.EP↗

arXiv2025

Grain growth in protoplanetary disks in the Upper Scorpius revealed by millimeter-wave spectral indices

The measurement of dust size from millimeter-wavelength spectra provides direct constraints on grain growth in protoplanetary disks. The spectral indices between 0.88 mm and 2.9 mm have been measured in multiple young star-forming regions, such as Taurus, Ophiuchus, and Lupus, which have ages of 1-3 Myr. These spectral indices are as low as 2-3, suggesting that grains in disks are much larger than those in the interstellar medium. In this study, we analyze the ALMA archival data of 23 disks in the Upper Scorpius region. The observed wavelength is 2.9 mm in Band 3, the angular resolution is 3.3 arcsec x 2.1 arcsec, which is not high enough to resolve the targets, and the rms noise is below 0.075 mJy beam$^{-1}$ for almost all sources. Together with the literature values of the Band 7 fluxes of the same targets, we find that the average spectral index of the disks in the Upper Scorpius region is $α_\mathrm{mm}=2.09 \pm 0.10$, which is equal to or slightly smaller than those at the other younger regions. To explain the relationship between the fluxes and spectral indices of the disks in the Taurus, Ophiuchus, Lupus, and Upper Scorpius regions, we construct simple disk evolution models. The observations are best reproduced by models in which the inner radius of the disk increases. This suggests that a substantial amount of dust mass must persist in the outer disk regions where the dust temperature is lower than 20 K even at late evolutionary stages. These findings offer key insights into the grain growth and the temporal evolution of protoplanetary disks.

astro-ph.EP↗

arXiv2025

Modeling the Contact Surfaces Formed by Pebble Collisions: Application to Formation of Comet 67P/Churyumov--Gerasimenko

Modeling the contact surfaces formed by pebble collisions is crucial to understanding the formation process of comets, which are thought to be composed of pebbles. In this paper, we develop a new model to estimate the contact surface radius and the number of contact points as functions of collision velocity, and examine the formation process of comet 67P/Churyumov--Gerasimenko. Our model is based on the compressive strength of dust aggregates obtained from numerical simulations and assumes that all the impact energy of the pebbles is used for their mutual compression. We compare our model with numerical simulations of pebble collisions, in which we prepare the initial pebbles in the form of compressed dust aggregate spheres and measure the contact surface and pebble radii using two- and three-dimensional characteristic radii, respectively. We also apply our model to the formation scenario of comet 67P, whose tensile strength and bulk density have already been estimated in the literature. We find that its low tensile strength points to formation via pebble collisions at velocities below $\sim10\mathrm{\ cm\ s^{-1}}$ when a microscopic filling factor of pebbles is lower than 0.6, suggesting that inelastic bouncing collisions played a role in damping the collision velocities. By assuming that the pebble collision velocity is determined by the transition velocity between bouncing and sticking, we estimate the pebble radius inside comet 67P to be 130 $\mathrm{μm}$ or smaller.

astro-ph.EP↗

arXiv2025

Multi-Wavelength Dust Characterization of the HL Tau Disk and Implications for Planet Formation

We present a comprehensive analysis of the HL Tau dust disk by modeling its intensity profiles across six wavelengths (0.45 to 7.9 mm) with a resolution of 0.05 arcsec ($\sim7$ au). Using a Markov Chain Monte Carlo (MCMC) approach, we constrain key dust properties including temperature, surface density, maximum grain size, composition, filling factor, and size distribution. The full fitting, with all parameters free, shows a preference for organics-rich dust with a low filling factor in the outer region ($r \gtrsim 40$ au), where the spectral index is $\sim3.7$, but amorphous-carbon-rich dust also reasonably reproduces the observed intensity profiles. Considering the scattering polarization observed at 0.87 mm, compact, amorphous-carbon-rich dust is unlikely, and moderately porous dust is favored. Beyond 40 au, the maximum dust size is likely $\sim100~{\rm μm}$ if dust is compact or amorphous-carbon rich. However, if the dust is moderately porous and organics-rich, both the predicted dust surface density and dust size can be sufficiently large for the pebble accretion rate to reach $\sim10M_{\oplus}~{\rm Myr^{-1}}$ in most regions, suggesting that pebble accretion could be a key mechanism for forming planets in the disk. In contrast, if the dust is amorphous-carbon-rich, forming a giant planet core via pebble accretion is unlikely due to the combined effects of low dust surface density and small dust size required to match the observed emission, suggesting other mechanisms, such as disk fragmentation due to gravitational instability, may be responsible for planet formation in the HL Tau disk.

astro-ph.EP↗

arXiv2025

Observationally derived magnetic field strength and 3D components in the HD 142527 disk

In protoplanetary disks around young stars, magnetic fields play an important role for disk evolution and planet formation. Polarized thermal emission from magnetically aligned grains is one of the reliable methods to trace magnetic fields. However, it has been difficult to observe magnetic fields from dust polarization in protoplanetary disks because other polarization mechanisms involving grown dust grains become efficient. Here, we report multi-wavelength (0.87 mm, 1.3 mm, 2.1 mm, and 2.7 mm) observations of polarized thermal emission in the protoplanetary disk around HD 142527, showing the lopsided dust distribution. We revealed that the smaller dust still exhibits magnetic alignment in the southern part of the disk. Furthermore, angular offsets between the observed magnetic field and the disk azimuthal direction were discovered, which can be used as a method to measure the relative strengths of each component (radial ($B_r$), azimuthal ($B_ϕ$), and vertical ($B_z$)) of 3D magnetic field. Applying this method, we derived the magnetic field around a 200-au radius from the protostar as $|B_r |:|B_ϕ|:|B_z | \sim 0.26:1:0.23$ and a strength of $\sim 0.3$ milli-Gauss. Our observations provide some key parameters of magnetic activities including the plasma beta, which have only been assumed in theoretical studies. In addition, the radial and vertical angular momentum transfer are found to be comparable, which poses a challenge to theoretical studies of protoplanetary disks.

astro-ph.EP↗

arXiv2024

A Tale of Three: Magnetic Fields along the Orion Integral-Shaped Filament as Revealed by JCMT BISTRO survey

As part of the BISTRO survey, we present JCMT 850 $μ$m polarimetric observations towards the Orion Integral-Shaped Filament (ISF) that covers three portions known as OMC-1, OMC-2, and OMC-3. The magnetic field threading the ISF seen in the JCMT POL-2 map appears as a tale of three: pinched for OMC-1, twisted for OMC-2, and nearly uniform for OMC-3. A multi-scale analysis shows that the magnetic field structure in OMC-3 is very consistent at all the scales, whereas the field structure in OMC-2 shows no correlation across different scales. In OMC-1, the field retains its mean orientation from large to small scales, but shows some deviations at small scales. Histograms of relative orientations between the magnetic field and filaments reveal a bimodal distribution for OMC-1, a relatively random distribution for OMC-2, and a distribution with a predominant peak at 90$^\circ$ for OMC-3. Furthermore, the magnetic fields in OMC-1 and OMC-3 both appear to be aligned perpendicular to the fibers, which are denser structures within the filament, but the field in OMC-2 is aligned along with the fibers. All these suggest that gravity, turbulence, and magnetic field are each playing a leading role in OMC-1, 2, and 3, respectively. While OMC-2 and 3 have almost the same gas mass, density, and non-thermal velocity dispersion, there are on average younger and fewer young stellar objects in OMC-3, providing evidence that a stronger magnetic field will induce slower and less efficient star formation in molecular clouds.

astro-ph.GA↗

arXiv2024

Dust Scattering Albedo at Millimeter-Wavelengths in the TW Hya Disk

Planetary bodies are formed by coagulation of solid dust grains in protoplanetary disks. Therefore, it is crucial to constrain the physical and chemical properties of the dust grains. In this study, we measure the dust albedo at mm-wavelength, which depends on dust properties at the disk midplane. Since the albedo and dust temperature are generally degenerate in observed thermal dust emission, it is challenging to determine them simultaneously. We propose to break this degeneracy by using multiple optically-thin molecular lines as a dust-albedo independent thermometer. In practice, we employ pressure-broadened CO line wings that provide an exceptionally high signal-to-noise ratio as an optically thin line. We model the CO $J=2-1$ and $3-2$ spectra observed by the Atacama Large Millimeter/sub-millimeter Array (ALMA) at the inner region ($r<6\ {\rm au}$) of the TW Hya disk and successfully derived the midplane temperature. Combining multi-band continuum observations, we constrain the albedo spectrum at $0.9-3$ mm for the first time without assuming a dust opacity model. The albedo at these wavelengths is high, $\sim0.5-0.8$, and broadly consistent with the Ricci et al. (2010), DIANA, and DSHARP dust models. Even without assuming dust composition, we estimate the maximum grain size to be $\sim 340\ μm$, the power law index of the grain size distribution to be $>-4.1$, and porosity to be $<0.96$. The derived dust size may suggest efficient fragmentation with the threshold velocity of $\sim 0.08\ {\rm m\ s^{-1}}$. We also note that the absolute flux uncertainty of $\sim10\%$ ($1σ$) is measured and used in the analysis, which is approximately twice the usually assumed value.

astro-ph.EP↗

arXiv2024

Asymmetric dust accumulation of the PDS 70 disk revealed by ALMA Band 3 observations

The PDS 70 system, hosting two planets within its disk, is an ideal target for examining the effect of planets on dust accumulation, growth, and ongoing planet formation. Here, we present high-resolution ($0.''07 = 8 \ \mathrm{au}$) dust continuum observations of the PDS 70 disk in ALMA Band 3 (3.0 mm). While previous Band 7 observations showed a dust ring with slight asymmetry, our Band 3 observations reveal a more prominent asymmetric peak in the northwest direction, where the intensity is 2.5 times higher than in other directions and the spectral index is at the local minimum with $α_{\mathrm{SED}} \sim 2.2$. This indicates that a substantial amount of dust is accumulated both radially and azimuthally in the peak. We also detect point-source emission around the stellar position in the Band 3 image, which is likely to be free-free emission. We constrain the eccentricity of the outer ring to be $e<0.04$ from the position of the central star and the outer ring. From the comparison with numerical simulations, we constrain the mass of PDS 70c to be less than 4.9 Jupiter masses if the gas turbulence strength $α_{\mathrm{turb}} = 10^{-3}$. Then, we discuss the formation mechanism of the disk structures and further planet formation scenarios in the disk.

astro-ph.EP↗

arXiv2024

The Bulk Densities of Small Solar System Bodies as a Probe of Planetesimal Formation

Constraining the formation processes of small solar system bodies is crucial for gaining insights into planetesimal formation. Their bulk densities, determined by their compressive strengths, offer valuable information about their formation history. In this paper, we utilize a formulation of the compressive strength of dust aggregates obtained from dust $N$-body simulations to establish the relation between bulk density and diameter. We find that this relation can be effectively approximated by a polytrope with an index of 0.5, coupled with a formulation of the compressive strength of dust aggregates. The lowest-density trans-Neptunian objects (TNOs) and main-belt asteroids (MBAs) are well reproduced by dust aggregates composed of 0.1-$\mathrmμ$m-sized grains. However, most TNOs, MBAs, comets, and near-Earth asteroids (NEAs) exhibit higher densities, suggesting the influence of compaction mechanisms such as collision, dust grain disruption, sintering, or melting, leading to further growth. We speculate that there are two potential formation paths for small solar system bodies: one involves the direct coagulation of primordial dust grains, resulting in the formation of first-generation planetesimals, including the lowest-density TNOs, MBAs, and parent bodies of comets and NEAs. In this case, comets and NEAs are fragments or rubble piles of first-generation planetesimals, and objects themselves or rubbles are composed of 0.1-$\mathrmμ$m-sized grains. The other path involves further potential fragmentation of first-generation planetesimals into compact dust aggregates observed in protoplanetary disks, resulting in the formation of second-generation planetesimals composed of compact dust aggregates, which may contribute to explaining another formation process of comets and NEAs.

astro-ph.EP↗

arXiv2024

Forming localized dust concentrations in a dust ring: DM Tau case study

The previous, high angular resolution 225 GHz ($\sim$1.3 mm) continuum observations on the transitional disk DM Tau have resolved an outer ring at 20-120 au radii that is weakly azimuthally asymmetric. We aimed to examine dust growth and filtration in the outer ring. We performed the $\sim$0$''$.06 ($\sim$8.7 au) resolution Karl G. Jansky Very Large Array (JVLA) 40-48 GHz ($\sim$7 mm; Q band) continuum observations and the complementary observations at lower frequencies. In addition, we analyzed the archival JVLA observations that were taken since 2010. Intriguingly, the Q band image resolved the azimuthally highly asymmetric, knotty dust emission sources close to the inner edge of the outer ring. Fitting the 8-700 GHz spectral energy distribution (SED) with two dust components indicates that the maximum grain size in these knotty dust emission sources is likely $\gtrsim$300 $μ$m while it is $\lesssim$50 $μ$m in the rest of the ring. These results may be explained by trapping of inward migrating grown dust close to the ring inner edge. The exact mechanism for developing the azimuthal asymmetry has not yet been identified, which may be due to planet-disk interaction that might also be responsible for the creation of the dust cavity and pressure bump, or the fluid instabilities and vortex formation due to shear motions. Finally, we remark that the asymmetries in DM Tau are hard to diagnose from the $\gtrsim$225 GHz observations owing to a high optical depth at the ring. In other words, the apparent symmetric or asymmetric morphology of the transitional disks may be related to the optical depths of those disks at the observing frequency.

astro-ph.EP↗

arXiv2024

Filamentary Network and Magnetic Field Structures Revealed with BISTRO in the High-Mass Star-Forming Region NGC2264 : Global Properties and Local Magnetogravitational Configurations

We report 850 $μ$m continuum polarization observations toward the filamentary high-mass star-forming region NGC 2264, taken as part of the B-fields In STar forming Regions Observations (BISTRO) large program on the James Clerk Maxwell Telescope (JCMT). These data reveal a well-structured non-uniform magnetic field in the NGC 2264C and 2264D regions with a prevailing orientation around 30 deg from north to east. Field strengths estimates and a virial analysis for the major clumps indicate that NGC 2264C is globally dominated by gravity while in 2264D magnetic, gravitational, and kinetic energies are roughly balanced. We present an analysis scheme that utilizes the locally resolved magnetic field structures, together with the locally measured gravitational vector field and the extracted filamentary network. From this, we infer statistical trends showing that this network consists of two main groups of filaments oriented approximately perpendicular to one another. Additionally, gravity shows one dominating converging direction that is roughly perpendicular to one of the filament orientations, which is suggestive of mass accretion along this direction. Beyond these statistical trends, we identify two types of filaments. The type-I filament is perpendicular to the magnetic field with local gravity transitioning from parallel to perpendicular to the magnetic field from the outside to the filament ridge. The type-II filament is parallel to the magnetic field and local gravity. We interpret these two types of filaments as originating from the competition between radial collapsing, driven by filament self-gravity, and the longitudinal collapsing, driven by the region's global gravity.

astro-ph.SR↗

arXiv2023

Aligned Grains and Scattered Light Found in Gaps of Planet-Forming Disk

Polarized (sub)millimeter emission from dust grains in circumstellar disks was initially thought to be due to grains aligned with the magnetic field. However, higher resolution multi-wavelength observations along with improved models found that this polarization is dominated by self-scattering at shorter wavelengths (e.g., 870 $μ$m) and by grains aligned with something other than magnetic fields at longer wavelengths (e.g., 3 mm). Nevertheless, the polarization signal is expected to depend on the underlying substructure, and observations hitherto have been unable to resolve polarization in multiple rings and gaps. HL Tau, a protoplanetary disk located 147.3 $\pm$ 0.5 pc away, is the brightest Class I or Class II disk at millimeter/submillimeter wavelengths. Here we show deep, high-resolution 870 $μ$m polarization observations of HL Tau, resolving polarization in both the rings and gaps. We find that the gaps have polarization angles with a significant azimuthal component and a higher polarization fraction than the rings. Our models show that the disk polarization is due to both scattering and emission from aligned effectively prolate grains. The intrinsic polarization of aligned dust grains is likely over 10%, which is much higher than what was expected in low resolution observations (~1%). Asymmetries and dust features are revealed in the polarization observations that are not seen in non-polarimetric observations.

astro-ph.GA↗

arXiv2023

Panchromatic (Sub)millimeter Polarization Observations of HL Tau Unveil Aligned Scattering Grains

Polarization is a unique tool to study the properties of dust grains of protoplanetary disks and detail the initial conditions of planet formation. Polarization around HL Tau was previously imaged using the Atacama Large Millimeter/submillimeter Array (ALMA) at Bands 3 (3.1 mm), 6 (1.3 mm), and 7 (0.87 mm), showing that the polarization orientation changes across wavelength $λ$. The polarization morphology at Band 7 is predominantly parallel to the disk minor axis but appears azimuthally oriented at Band 3, with the morphology at Band 6 in between the two. We present new ~0.2" (29 au) polarization observations at Q-Band (7.0 mm) using the Karl G. Jansky Very Large Array (VLA) and at Bands 4 (2.1 mm), 5 (1.5 mm), and 7 using ALMA, consolidating HL Tau's position as the protoplanetary disk with the most complete wavelength coverage in dust polarization. The polarization patterns at Bands 4 and 5 continue to follow the morphological transition with wavelength previously identified in Bands 3, 6, and 7. Based on the azimuthal variation, we decompose the polarization into contributions from scattering ($s$) and thermal emission ($t$). We find that $s$ decreases slowly with increasing $λ$, and $t$ increases more rapidly with $λ$ which are expected from optical depth effects of toroidally aligned, scattering prolate grains. The relatively weak $λ$ dependence of $s$ is consistent with large, porous grains. The sparse polarization detections from the Q-band image are also consistent with toroidally aligned prolate grains.

astro-ph.EP↗