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Zhe-Yu Daniel Lin

Publications and source records attributed to Zhe-Yu Daniel Lin.

At least 19 recordsLinked to original sources

The ALMA View of the Edge-on Gomez's Hamburger System: A Highly-Dynamic, Asymmetric Protoplanetary Disk Reveals the Earliest Phases of Giant Planet Formation

Chemical tracers provide some of the strongest observational signatures of ongoing planet formation and localized dynamical perturbations in protoplanetary disks. In particular, sulfur-bearing molecules are predicted to be enhanced in regions of shock heating, ice sublimation, and gravitational instability. Here, we present high-angular-resolution ($\approx$0.$^{\prime\prime}$2) Atacama Large Millimeter/submillimeter Array observations of $^{12}$CO J=3-2, $^{13}$CO J=3-2, CS J=7-6, and SO J$_{\rm N}$=8$_8$-7$_7$ toward the large, edge-on Gomez's Hamburger ('GoHam'; IRAS 18059-3211) disk. We detect a narrow, one-sided arc of SO emission that peaks near a previously-identified gas over-density, suggesting localized heating around an early-stage giant protoplanet or disk fragment. The edge-on geometry of GoHam enables us to place this chemical signature in the broader context of the disk gas and dust structure. To do so, we map the vertical distribution of molecular gas relative to millimeter- and (sub)-micron-sized dust, identify a pronounced north-south continuum asymmetry, and detect non-Keplerian $^{12}$CO and $^{13}$CO emission indicative of a disk wind. We also derive a dynamical stellar mass of 2.2 $\pm$ 0.5 M$_{\odot}$ and a revised dust-extinction-map-based distance of 139 $\pm$ 24 pc, which places GoHam in the outskirts of the Scorpius-Centaurus association. Together, these observations reveal a highly dynamic disk in which localized sulfur chemistry may trace one of the earliest observable stages of wide-separation giant planet formation.

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A Multiband Study of the HR 4796A Disk in the Optical Using MagAO-X

We present total intensity images of the debris disk around HR 4796A from observations spanning 2023 to 2025 with the Magellan extreme adaptive optics instrument (MagAO-X). We detected the disk at high signal-to-noise ratios at $g' (527$ nm), $r' (615$ nm), $i' (762$ nm), and $z' (909 $ nm). Additionally, we present images collected using the "star-hopping" technique that show the entirety of the disk, including the dramatic forward-scattering at the minor axis. We subjected our images to a battery of modeling techniques to constrain the geometry and photometry of the disk. Leveraging our clear detections of the disk's minor axis, we modeled the scattering phase function (SPF) using a basis of the Legendre polynomials. To mitigate self-subtraction artifacts in our angular differential imaging, we implemented a forward-modeling pipeline that generates a pixel-based freeform disk forward model leading to a deconvolved image of the disk. Our best-fit disk models reveal: (1) highly forward-scattering SPFs with a minimum at the $\sim65^{\circ}$ scattering angle, (2) a faint halo of dust just exterior to the spine of the disk that is not well-described by a broken power law density profile, (3) a red spectral slope for the dust, and finally (4) a compact, clump-like feature in the freeform disk models. Our empirically-measured SPFs suggest that the scattering is dominated by large, highly-absorptive grains. However, we emphasize the need for testing advanced irregular grain models using our SPFs to learn more about the physical and chemical properties of this complex system.

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Azimuthal Dust Polarization from Aerodynamically Aligned Grains as Evidence for the Streaming Instability in Protoplanetary Disks

(Sub)millimeter dust polarization in protoplanetary disks has revealed the presence of large (~ 100 um) dust grains that are aligned along their long axis following the azimuthal direction of the disk. The novel badminton birdie-like aerodynamic alignment predicts large grains to align with their long axes following the direction of gas flow experienced by the dust, denoted as the A-field. With 3D streaming instability (SI) simulations, we find that the A-field is predominantly in the radial direction in regions of low dust-to-gas ratio, but in the azimuthal direction in regions of high dust-to-gas ratio. Through polarized radiation transfer, we find that the resulting polarization angle indeed follows the disk azimuthal direction in the high dust density regions. Therefore, ongoing SI is an attractive candidate for producing the azimuthal dust polarization pattern as observed in an increasing number of disks.

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Early Planet Formation in Embedded Disks (eDisk). XVIII. Indication of a possible spiral structure in the dust-continuum emission of the protostellar disk around IRAS 16544-1604 in CB 68

We performed numerical simulations along with radiative transfer calculations to reproduce an intriguing asymmetric shoulder feature in the dust-continuum emission of the protostellar disk around one of the eDisk targets, the Class 0 protostar IRAS 16544-1604 in CB 68. This is our first attempt to bridge the theoretical works of protostellar disk evolution and the eDisk observations. We found that while our hydrodynamic simulations form spiral structures caused by gravitational instability, they become less discernible after the disk is inclined and convolved with the telescope beam. The widths of the spiral structure as obtained by our numerical simulations are ~0.1-0.8 times the eDisk beam size of 4.5 au. Our modeling effor implies that the apparent absence of spiral features in the eDisk observations does not necessarily indicate the real absence of internal substructures and gravitational instability. We also found that the asymmetric shoulder structure of the continuum profile along the major axis appears when the disk is massive enough with a Toomre parameter Q~1. This mechanism offers a potential explanation for the observed, asymmetric shoulder features in the disks surrounding IRAS 16544-1604 and the other eDisk sources.

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Multi-band ALMA Polarization Observations of BHB07-11 Reveal Aligned Dust Grains in Complex Spiral Arm Structures

Polarization-mode observations from the Atacama Large Millimeter/submillimeter Array (ALMA) are powerful tools for studying the dust grain populations in circumstellar disks. Many sources exhibit polarization signatures consistent with aligned dust grains, yet the physical origin of this alignment remains uncertain. One such source is BHB07-11, a Class I protobinary object in the Pipe Nebula with complex spiral arm structures in its circumbinary disk. While magnetic fields are often invoked to explain grain alignment in the interstellar medium, the contrasting conditions in circumstellar disk environments demand further investigation into grain alignment mechanisms. To determine BHB07-11's dominant polarization mechanism, we leverage ALMA polarization-mode dust continuum observations in Bands 3 ($\lambda$=3.1 mm), 6 ($\lambda$=1.3 mm), and 7 ($\lambda$=0.87 mm), in combination with high-resolution dust continuum and spectral line observations in Band 6. Observed polarization vectors in each band are consistent with emission from aligned grains and follow the structure of the spiral arms as shown in the high-resolution observations. Given the relationship between the observed polarization vector orientation and the spiral arms, we find that the polarization morphology is most consistent with grains aligned through a relative velocity flow between gas and dust in the spiral arms, as envisioned in the recently developed badminton birdie-like alignment mechanism, rather than alignment with a magnetic field or other known alignment mechanisms.

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glitterin: Towards Replacing the Role of Lorenz-Mie Theory in Astronomy Using Neural Networks Trained on Light Scattering of Irregularly Shaped Grains

Light scattering by dust particles is often modeled assuming the dust is spherical for numerical simplicity and speed. However, real dust particles have highly irregular morphologies that significantly affect their scattering properties. We have developed glitterin, a neural network trained to predict light scattering from irregularly shaped dust grains, offering a computationally efficient alternative to Lorenz-Mie theory. We computed scattering properties using the Discrete Dipole Approximation code ADDA for irregularly shaped particles across size parameters x from 0.1 to 65, covering a range in complex refractive index m that includes astrosilicates, pyroxene, enstatite, water-ice, etc. The neural network operates at millisecond timescales while maintaining superior accuracy compared to linear interpolation. Irregular grains exhibit x-dependent deviations from spherical predictions. At small x, cross-sections approach volume-equivalent spheres for low m. At large x, irregular grains show enhanced cross-sections due to greater geometric extension. Increasing m also enhances the absorption cross-section relative to the volume-equivalent spheres. This differential x and m dependence creates mid-IR solid-state features distinct from predictions from spherical grains. Validation against laboratory measurements of forsterite and hematite demonstrates that our neural network captures both qualitative and quantitative behaviors more accurately than spherical models. Millimeter-wavelength applications reveal that spherical grains produce opposite polarization signatures compared to irregular grains, potentially relaxing stringent ~100um grain size constraints in protoplanetary disks. glitterin is publicly available and alleviates the computational barriers to incorporating emission and scattering of realistic grain morphologies.

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Early Planet Formation in Embedded Disks (eDisk) XXII: Keplerian disk, disk structures and jets/outflows in the Class 0 protostar IRAS 04166+2706

We present ALMA observations of the Class 0 protostar IRAS 04166+2706, obtained as part of the ALMA large program Early Planet Formation in Embedded Disks (eDisk). These observations were made in the 1.3 mm dust continuum and molecular lines at angular resolutions of $\sim 0.05''$ ($\sim 8$ au) and $\sim 0.16''$ ($\sim25$ au), respectively. The continuum emission shows a disk-like structure with a radius of $\sim22$ au. Kinematical analysis of $^{13}$CO(2-1), C$^{18}$O(2-1), H$_2$CO (3$_{0,3}$-2$_{0,2}$), CH$_3$OH (4$_2$-3$_1$) emission demonstrates that these molecular lines trace the infalling-rotating envelope and possibly a Keplerian disk, enabling us to estimate the protostar mass to be $0.15 \rm{M_\odot} < \rm{M_\star} < 0.39 M_\odot$. The dusty disk is found to exhibit a brightness asymmetry along its minor axis in the continuum emission, probably caused by a flared distribution of the dust and the high optical depth of the dust emission. In addition, the CO(2-1) and SiO(5-4) emissions show knotty and wiggling motions in the jets. Our high angular resolution observations revealed the most recent mass ejection events, which have occurred within the last $\sim 25$ years.

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Detailed radial scale height profile of dust grains as probed by dust self-scattering in HL Tau

The vertical settling of dust grains in a circumstellar disk, characterized by their scale height, is a pivotal process in the formation of planets. This study offers in-depth analysis and modeling of the radial scale height profile of dust grains in the HL Tau system, leveraging high-resolution polarization observations. We resolve the inner disk's polarization, revealing a significant near-far side asymmetry, with the near side being markedly brighter than the far side in polarized intensity. This asymmetry is attributed to a geometrically thick inner dust disk, suggesting a large aspect ratio of $H/R \ge 0.15$. The first ring at 20 au exhibits an azimuthal contrast, with polarization enhanced along the minor axis, indicating a moderately thick dust ring with $H/R \approx 0.1$. The absence of the near-far side asymmetry at larger scales implies a thin dust layer, with $H/R < 0.05$. Taken together, these findings depict a disk with a turbulent inner region and a settled outer disk, requiring a variable turbulence model with $\alpha$ increasing from $10^{-5}$ at 100 au to $10^{-2.5}$ at 20 au. This research sheds light on dust settling and turbulence levels within protoplanetary disks, providing valuable insights into the mechanisms of planet formation.

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Early Planet Formation in Embedded Disks (eDisk) XVII: A Compact but Structured Keplerian Disk and Large-scale Streamers Revealed in the Class I Protostellar System IRAS 04169+2702

We present high-resolution ($\sim$0.05"; 8 au) dust continuum and molecular line observations toward the Class I protostellar system IRAS 04169+2702 in the Taurus B213 region, as part of the ALMA Large Program Early Planet Formation in Embedded Disks (eDisk). The 1.3-mm dust continuum emission traces a circumstellar disk with a central depression toward the protostar. Our VLA observations of the same target reveal a single central peak dominated by the free-free emission, which coincides with the depression of the thermal dust emission. The mean spectral index of the thermal dust emission from 1.3 mm to 1.4 cm is approximately 2.8, suggestive of the presence of grains grown to millimeter or centimeter sizes in the disk. Velocity gradients along the disk major axis are seen in emission from $^{12}$CO (2-1), $^{13}$CO (2-1), and C$^{18}$O (2-1) molecular lines. The position-velocity diagrams of these lines unveil a Keplerian-rotating disk with a radius of $\sim$21 au around a 1.3 $M_{\odot}$ protostar, as well as an infalling and rotating envelope with the angular momentum conserved. In addition to the compact disk, large-scale infalling spiral structures extending up to approximately 1400 au, streamers, are discovered in C$^{18}$O (2-1), SO (6$_5$-5$_4$), and H$_2$CO (3$_{0, 3}$-2$_{0, 2}$) as well as in the 1.3-mm continuum emission. Notably, in the region closer to the protostar, the spatial coincidence of C$^{18}$O and SO may indicate the presence of a shock related to accretion through the spiral arms.

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Magnetic Fields in the Pillars of Creation

Due to dust grain alignment with magnetic fields, dust polarization observations of far-infrared emission from cold molecular clouds are often used to trace magnetic fields, allowing a probe of the effects of magnetic fields on the star formation process. We present inferred magnetic field maps of the Pillars of Creation region within the larger M16 emission nebula, derived from dust polarization data in the 89 and 154 micron continuum using SOFIA/HAWC+. We derive magnetic field strength estimates using the Davis-Chandrasekhar-Fermi method. We compare the polarization and magnetic field strengths to column densities and dust continuum intensities across the region to build a coherent picture of the relationship between star forming activity and magnetic fields in the region. The projected magnetic field strengths derived are in the range of 50-130 microGauss, which is typical for clouds of similar n(H2), i.e., molecular hydrogen volume density on the order of 10^4-10^5 cm^(-3). We conclude that star formation occurs in the finger tips when the magnetic fields are too weak to prevent radial collapse due to gravity but strong enough to oppose OB stellar radiation pressure, while in the base of the fingers the magnetic fields hinder mass accretion and consequently star formation. We also support an initial weak field model (<50 microGauss) with subsequent strengthening through realignment and compression, resulting in a dynamically important magnetic field.

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L1448 IRS3B: Dust Polarization Aligned with Spiral Features, Tracing Gas Flows

Circumstellar disk dust polarization in the (sub)millimeter is, for the most part, not from dust grain alignment with magnetic fields but rather indicative of a combination of dust self-scattering with a yet unknown alignment mechanism that is consistent with mechanical alignment. While the observational evidence for scattering has been well established, that for mechanical alignment is less so. Circum-multiple dust structures in protostellar systems provide a unique environment to probe different polarization alignment mechanisms. We present ALMA Band 4 and Band 7 polarization observations toward the multiple young system L1448 IRS3B. The polarization in the two Bands is consistent with each other, presenting multiple polarization morphologies. On the size scale of the inner envelope surrounding the circum-multiple disk, the polarization is consistent with magnetic field dust grain alignment. On the very small scale of compact circumstellar regions, we see polarization that is consistent with scattering around source a and c, which are likely the most optically thick components. Finally, we see polarization that is consistent with mechanical alignment of dust grains along the spiral dust structures, which would suggest that the dust is tracing the relative gas flow along the spiral arms. If the gas-flow dust grain alignment mechanism is dominant in these cases, disk dust polarization may provide a direct probe of the small-scale kinematics of the gas flow relative to the dust grains.

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Early Grain Growth in the Young Protostellar Disk HH 212 Supported by Dust Self-Scattering Modeling

Grain growth in disks around young stars plays a crucial role in the formation of planets. Early grain growth has been suggested in the HH 212 protostellar disk by previous polarization observations. To confirm it and to determine the grain size, we analyze high-resolution multi-band observations of the disk obtained with Atacama Large Millimeter/submillimeter Array (ALMA) in Bands 9 (0.4 mm), 7 (0.9 mm), 6 (1.3 mm), 3 (3 mm) as well as with Very Large Array (VLA) in Band Ka (9 mm) and present new VLA data in Bands Q (7 mm), K (1.3 cm), and X (3 cm). We adopt a parameterized flared disk model to fit the continuum maps of the disk in these bands and derive the opacities, albedos, and opacity spectral index $\mathrm{\beta}$ of the dust in the disk, taking into account the dust scattering ignored in the previous work modeling the multi-band data of this source. For the VLA bands, we only include the Band Q data in our modeling to avoid free-free emission contamination. The obtained opacities, albedos, and opacity spectral index $\beta$ (with a value of $\sim$ 1.2) suggest that the upper limit of maximum grain size in the disk be $\sim$ 130 $\mu$m, consistent with that implied in the previous polarization observations in Band 7, supporting the grain growth in this disk. The values of the absorption opacities further highlight the need for a new dust composition model for Class 0/I disks.

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Polarization Substructure in the Spiral-Dominated HH 111 Disk: Evidence for Grain Growth

The HH 111 protostellar disk has recently been found to host a pair of spiral arms. Here we report the dust polarization results in the disk as well as the inner envelope around it, obtained with the Atacama Large Millimeter/submillimeter Array in continuum at lambda ~ 870 micron and ~ 0. 05" resolution. In the inner envelope, polarization is detected with a polarization degree of ~ 6% and an orientation almost everywhere parallel to the minor axis of the disk, and thus likely to be due to the dust grains magnetically aligned mainly by toroidal fields. In the disk, the polarization orientation is roughly azimuthal on the far side and becomes parallel to the minor axis on the near side, with a polarization gap in between on the far side near the central protostar. The disk polarization degree is ~ 2%. The polarized intensity is higher on the near side than the far side, showing a near-far side asymmetry. More importantly, the polarized intensity and thus polarization degree are lower in the spiral arms, but higher in between the arms, showing an anticorrelation of the polarized intensity with the spiral arms. Our modeling results indicate that this anticorrelation is useful for constraining the polarization mechanism and is consistent with the dust self-scattering by the grains that have grown to a size of ~ 150 micron. The interarms are sandwiched and illuminated by two brighter spiral arms and thus have higher polarized intensity. Our dust self-scattering model can also reproduce the observed polarization orientation parallel to the minor axis on the near side and the observed azimuthal polarization orientation at the two disk edges in the major axis.

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Early Planet Formation in Embedded Disks (eDisk) XVI: An asymmetric dust disk driving a multi-component molecular outflow in the young Class 0 protostar GSS30 IRS3

We present the results of the ALMA Large Program Early Planet Formation in Embedded disks observations of the Class 0 protostar GSS30 IRS3. Our observations included 1.3 mm continuum with a resolution of 0.''05 (7.8 au) and several molecular species including $^{12}$CO, $^{13}$CO, C$^{18}$O, H$_{2}$CO and c-C$_{3}$H$_{2}$. The dust continuum analysis unveiled a disk-shaped structure with a major axis size of $\sim$200 au. We observed an asymmetry in the minor axis of the continuum emission suggesting that the emission is optically thick and the disk is flared. On the other hand, we identified two prominent bumps along the major axis located at distances of 26 and 50 au from the central protostar. The origin of the bumps remains uncertain and might be due to an embedded substructure within the disk or the result of the temperature distribution instead of surface density due to optically thick continuum emission. The $^{12}$CO emission reveals a molecular outflow consisting of three distinct components: a collimated one, an intermediate velocity component exhibiting an hourglass shape, and a wider angle low-velocity component. We associate these components with the coexistence of a jet and a disk-wind. The C$^{18}$O emission traces both a Keplerian rotating circumstellar disk and the infall of the rotating envelope. We measured a stellar dynamical mass of 0.35$\pm$0.09 M$_{\odot}$.

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Early Planet Formation in Embedded Disks (eDisk). XI. A high-resolution view toward the BHR 71 Class 0 protostellar wide binary

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of the binary Class 0 protostellar system BHR 71 IRS1 and IRS2 as part of the Early Planet Formation in Embedded Disks (eDisk) ALMA Large Program. We describe the $^{12}$CO ($J$=2--1), $^{13}$CO ($J$=2--1), C$^{18}$O ($J$=2--1), H$_2$CO ($J=3_{2,1}$--$2_{2,0}$), and SiO ($J$=5--4) molecular lines along with the 1.3 mm continuum at high spatial resolution ($\sim$0.08" or $\sim$5 au). Dust continuum emission is detected toward BHR 71 IRS1 and IRS2, with a central compact component and extended continuum emission. The compact components are smooth and show no sign of substructures such as spirals, rings or gaps. However, there is a brightness asymmetry along the minor axis of the presumed disk in IRS1, possibly indicative of an inclined geometrically and optically thick disk-like component. Using a position-velocity diagram analysis of the C$^{18}$O line, clear Keplerian motions were not detected toward either source. If Keplerian rotationally-supported disks are present, they are likely deeply embedded in their envelope. However, we can set upper limits of the central protostellar mass of 0.46 M$_\odot$ and 0.26 M$_\odot$ for BHR 71 IRS1 and BHR 71 IRS2, respectively. Outflows traced by $^{12}$CO and SiO are detected in both sources. The outflows can be divided into two components, a wide-angle outflow and a jet. In IRS1, the jet exhibits a double helical structure, reflecting the removal of angular momentum from the system. In IRS2, the jet is very collimated and shows a chain of knots, suggesting episodic accretion events.

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Badminton Birdie-Like Aerodynamic Alignment of Drifting Dust Grains by Subsonic Gaseous Flows in Protoplanetary Disks

Recent (sub)millimeter polarization observations of protoplanetary disks reveal toroidally aligned, effectively prolate dust grains large enough (at least ~100 $\mu$m) to efficiently scatter millimeter light. The alignment mechanism for these grains remains unclear. We explore the possibility that gas drag aligns grains through gas-dust relative motion when the grain's center of mass is offset from its geometric center, analogous to a badminton birdie's alignment in flight. A simple grain model of two non-identical spheres illustrates how a grain undergoes damped oscillations from flow-induced restoring torques which align its geometric center in the flow direction relative to its center of mass. Assuming specular reflection and subsonic flow, we derive an analytical equation of motion for spheroids where the center of mass can be shifted away from the spheroid's geometric center. We show that a prolate or an oblate grain can be aligned with the long axis parallel to the gas flow when the center of mass is shifted along that axis. Both scenarios can explain the required effectively prolate grains inferred from observations. Application to a simple disk model shows that the alignment timescales are shorter than or comparable to the orbital time. The grain alignment direction in a disk depends on the disk (sub-)structure and grain Stokes number (St) with azimuthal alignment for large St grains in sub-Keplerian smooth gas disks and for small St grains near the gas pressure extrema, such as rings and gaps.

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

Millimeter and sub-millimeter observations of continuum linear dust polarization provide insight into dust grain growth in protoplanetary disks, which are the progenitors of planetary systems. We present the results of the first survey of dust polarization in protoplanetary disks at 870 $μ$m and 3 mm. We find that protoplanetary disks in the same molecular cloud at similar evolutionary stages can exhibit different correlations between observing wavelength and polarization morphology and fraction. We explore possible origins for these differences in polarization, including differences in dust populations and protostar properties. For RY Tau and MWC 480, which are consistent with scattering at both wavelengths, we present models of the scattering polarization from several dust grain size distributions. These models aim to reproduce two features of the observational results for these disks: (1) both disks have an observable degree of polarization at both wavelengths and (2) the polarization fraction is higher at 3 mm than at 870 $μ$m in the centers of the disks. For both disks, these features can be reproduced by a power-law distribution of spherical dust grains with a maximum radius of 200 $μ$m and high optical depth. In MWC 480, we can also reproduce features (1) and (2) with a model containing large grains ($a_{max}$ = 490 $μ$m ) near the disk midplane and small grains ($a_{max}$ = 140 $μ$m) above and below the midplane.

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Early Planet Formation in Embedded Disks (eDisk) XIII: Aligned Disks with Non-Settled Dust Around the Newly Resolved Class 0 Protobinary R CrA IRAS 32

Young protostellar binary systems, with expected ages less than $\sim$10$^5$ years, are little modified since birth, providing key clues to binary formation and evolution. We present a first look at the young, Class 0 binary protostellar system R CrA IRAS 32 from the Early Planet Formation in Embedded Disks (eDisk) ALMA large program, which observed the system in the 1.3 mm continuum emission, $^{12}$CO (2-1), $^{13}$CO (2-1), C$^{18}$O (2-1), SO (6$_5$-5$_4$), and nine other molecular lines that trace disk, envelope, shocks, and outflows. With a continuum resolution of $\sim$0.03$^{\prime\prime}$ ($\sim$5 au, at a distance of 150 pc), we characterize the newly discovered binary system with a separation of 207 au, their circumstellar disks, and a circumbinary disk-like structure. The circumstellar disk radii are 26.9$\pm$0.3 and 22.8$\pm$0.3 au for sources A and B, respectively, and their circumstellar disk dust masses are estimated as 22.5$\pm$1.1 and 12.4$\pm$0.6 M$_{\Earth}$. The circumstellar disks and the circumbinary structure have well aligned position angles and inclinations, indicating formation in a smooth, ordered process such as disk fragmentation. In addition, the circumstellar disks have a near/far-side asymmetry in the continuum emission suggesting that the dust has yet to settle into a thin layer near the midplane. Spectral analysis of CO isotopologues reveals outflows that originate from both of the sources and possibly from the circumbinary disk-like structure. Furthermore, we detect Keplerian rotation in the $^{13}$CO isotopologues toward both circumstellar disks and likely Keplerian rotation in the circumbinary structure; the latter suggests that it is probably a circumbinary disk.

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