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Hauyu Baobab Liu

Publications and source records attributed to Hauyu Baobab Liu.

At least 73 records · Page 4Linked to original sources

SMA 200-400 GHz Survey for Dust Properties in the Icy Class II Disks in the Taurus Molecular Cloud

We present a new SMA survey of 47 Class II sources in the Taurus-Auriga region. Our observations made 12 independent samples of flux densities over the 200-400 GHz frequency range. We tightly constrained the spectral indices of most sources to a narrow range of $2.0\pm0.2$; only a handful of spatially resolved (e.g., diameter $>$250 au) disks present larger spectral indices. The simplest interpretation for this result is that the (sub)millimeter luminosities of all of the observed target sources are dominated by very optically thick (e.g., $τ\gtrsim$5) dust thermal emission. Some previous works that were based on the optically thin assumption thus might have underestimated optical depths by at least one order of magnitude. Assuming DSHARP dust opacities, this corresponds to underestimates of dust masses by a similar factor. Moreover, some population synthesis models show that to explain the observed, narrowly distributed spectral indices, the disks in our selected sample need to have very similar dust temperatures ($T_{\small{dust}}$). Given a specific assumption of median $T_{\small{dust}}$, the maximum grain sizes ($a_{\small{max}}$) can also be constrained, which is a few times smaller than 0.1 mm for $T_{\small{dust}}\sim$100 K and a few mm for $T_{\small{dust}}\sim$24 K. The results may indicate that dust grain growth outside the water snowline is limited by the bouncing/fragmentation barriers. In the Class II disks, the dust mass budget outside of the water snowline may be largely retained instead of being mostly consumed by planet formation. While Class II disks still possess sufficient dust masses to feed planet formation at a later time, it is unknown whether or not dust coagulation and planet formation can be efficient or natural outside of the water snowline.

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INvestigations of massive Filaments ANd sTar formation (INFANT). I. Core Identification and Core Mass Function

Filamentary structures are ubiquitously found in high-mass star-forming clouds. To investigate the relationship between filaments and star formation, we carry out the INFANT (INvestigations of massive Filaments ANd sTar formation) survey, a multi-scale, multi-wavelength survey of massive filamentary clouds with ALMA band 3/band 6 and VLA K band. In this first paper, we present the ALMA band 6 continuum observations toward a sample of 8 high-mass star forming filaments. We covered each target with approximately rectangular mosaic field of view with two 12-m array configurations, achieving an angular resolution of $\sim$0.6" (2700 AU at 4.5 kpc) and a continuum rms of $\sim$0.1 mJy/beam ($\sim$0.06 Msun in gas mass assuming 15 K). We identify cores using the getsf and astrodendro and find the former is more robust in terms of both identification and measuring flux densities. We identify in total 183 dense cores (15--36 cores in each cloud) and classify their star formation states via outflow and warm gas tracers. The protostellar cores are statistically more massive than the prestellar cores, possibly indicating further accretion onto cores after formation of protostars. For the high-mass end ($M_\text{core}$ $>$ 1.5 Msun) of the core mass function (CMF) we derive a power-law index of $-$1.15 $\pm$ 0.12 for the whole sample, and $-$1.70 $\pm$ 0.25 for the prestellar population. We also find a steepening trend in CMF with cloud evolution ($-$0.89 $\pm$ 0.15 for the young group v.s. $-$1.44 $\pm$ 0.25 for the evolved group) and discuss its implication for cluster formation.

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Dark Dragon Breaks Magnetic Chain: Dynamical Substructures of IRDC G28.34 Form in Supported Environments

We have comprehensively studied the multi-scale physical properties of the infrared dark cloud (IRDC) G28.34 (the Dragon cloud) with dust polarization and molecular line data from Planck, FCRAO-14m, JCMT, and ALMA. We find that the averaged magnetic fields of clumps tend to be either parallel with or perpendicular to the cloud-scale magnetic fields, while the cores in clump MM4 tend to have magnetic fields aligned with the clump fields. Implementing the relative orientation analysis (for magnetic fields, column density gradients, and local gravity), Velocity Gradient Technique (VGT), and modified Davis-Chandrasekhar-Fermi (DCF) analysis, we find that: G28.34 is located in a trans-to-sub-Alfvénic environment ($\mathcal{M}_{A}=0.74$ within $r=15$ pc); the magnetic field is effectively resisting gravitational collapse in large-scale diffuse gas, but is distorted by gravity within the cloud and affected by star formation activities in high-density regions; and the normalized mass-to-flux ratio tends to increase with increasing density and decreasing radius. Considering the thermal, turbulent, and magnetic supports, we find that the environmental gas of G28.34 is in a super-virial (supported) state, the infrared dark clumps may be in a near-equilibrium state, and core MM4-core4 is in a sub-virial (gravity-dominant) state. In summary, we suggest that magnetic fields dominate gravity and turbulence in the cloud environment at large scales, resulting in relatively slow cloud formation and evolution processes. Within the cloud, gravity could overwhelm magnetic fields and turbulence, allowing local dynamical star formation to happen.

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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.

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The role of turbulence in high-mass star formation: Subsonic and transonic turbulence are ubiquitously found at early stages

Context. Traditionally, supersonic turbulence is considered to be one of the most likely mechanisms to slow down the gravitational collapse in dense clumps, thereby enabling the formation of massive stars. However, several recent studies have raised differing points of view based on observations carried out with sufficiently high spatial and spectral resolution. These studies call for a re-evaluation of the role turbulence plays in massive star-forming regions. Aims. Our aim is to study the gas properties, especially the turbulence, in a sample of massive star-forming regions with sufficient spatial and spectral resolution, which can both resolve the core fragmentation and the thermal line width. Methods. We observed NH3 metastable lines with the Very Large Array (VLA) to assess the intrinsic turbulence. Results. Analysis of the turbulence distribution histogram for 32 identified NH3 cores reveals the presence of three distinct components. Furthermore, our results suggest that (1) sub- and transonic turbulence is a prevalent (21 of 32) feature of massive star-forming regions and those cold regions are at early evolutionary stage. This investigation indicates that turbulence alone is insufficient to provide the necessary internal pressure required for massive star formation, necessitating further exploration of alternative candidates; and (2) studies of seven multi-core systems indicate that the cores within each system mainly share similar gas properties and masses. However, two of the systems are characterized by the presence of exceptionally cold and dense cores that are situated at the spatial center of each system. Our findings support the hub-filament model as an explanation for this observed distribution

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Massive clumps in W43-main: Structure formation in an extensively shocked molecular cloud

W43-main is a massive molecular complex located at the interaction of the Scutum arm and the Galactic bar undergoing starburst activities. We aim to investigate the gas dynamics, in particular, the prevailing shock signatures from the cloud to clump scale and assess the impact of shocks on the formation of dense gas and early-stage cores. We have carried out NOEMA and IRAM-30m observations at 3 mm with an angular resolution of $\sim$0.1 pc towards five massive clumps in W43 main. We use CH$_{3}$CCH and H$_{2}$CS lines to trace the extended gas temperature and CH$_{3}$OH lines to probe the volume density of the dense gas ($\gtrsim$10$^{5}$ cm$^{-3}$). The emission of SiO (2-1) is extensive across the region ($\sim$4 pc) and is mostly contained within a low-velocity regime, hinting at a large-scale origin of the shocks. The position-velocity maps of multiple tracers show systematic spatio-kinematic offsets supporting the cloud-cloud collision/merging scenario. We identify an additional extended velocity component in CCH emission, which coincides with one of the velocity components of the larger scale $^{13}$CO (2-1) emission, likely representing an outer, less dense gas layer in the cloud merging process. We find that the V-shaped, asymmetric SiO wings are tightly correlated with localised gas density enhancements, which is direct evidence of dense gas formation and accumulation in shocks. We resolve two categories of NH$_{2}$D cores: ones exhibiting only subsonic to transonic velocity dispersion, and the others with an additional supersonic velocity dispersion. The centroid velocities of the latter cores are correlated with the shock front seen by SiO. The kinematics of the $\sim$0.1 pc NH$_{2}$D cores are heavily imprinted by shock activities, and may represent a population of early-stage cores forming around the shock interface.

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Shadowing in the protoplanetary disk of ZZ Tau IRS with HST

An inner component misaligned from an outer component in a protoplanetary disk can result in the former casting shadows on the latter. We present a new instance of shadowing on the outer disk around a very low mass star, ZZ~Tau~IRS. Through the analysis of near-infrared (NIR) archival data at $λ=1.6$~$μ$m acquired with the Wide Field Camera 3 on the Hubble Space Telescope, we identified brightness asymmetries in the top and bottom halves of the highly inclined outer disk, separated by a dark lane. The brighter sides in the top and bottom halves are on the opposite sides, which we attributed to shadows cast by a misaligned inner disk. Radiative transfer modeling of the system with a misaligned angle of 15~deg between the inner and outer disks well reproduced the observations. Additionally, we found an elevated brightness temperature of $^{12}$CO~(3-2) at $r\sim30$~au on the brighter side in NIR wavelengths in the top half disk, which can be explained by the shadowing effect too. While the origin of the misaligned inner disk remains unclear, future monitoring observations to search for temporal variations in brightness asymmetries will likely provide useful clues.

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Radio survey of the stellar population in the infrared dark cloud G14.225-0.506

The IRDC G14.225-0.506 is associated with a network of filaments, which result in two different dense hubs, as well as with several signposts of star formation activity. The aim of this work is to study the cm continuum emission to characterize the stellar population in G14.2. We performed deep (~1.5-3 microJy) radio continuum observations at 6 and 3.6 cm using the VLA in the A configuration (~0.3''). We have also made use of observations taken during different days to study the presence of variability at short timescales. We detected a total of 66 sources, 32 in the northern region G14.2-N and 34 in the southern region G14.2-S. Ten of the sources are found to be variable. Based on their spectral index, the emission in G14.2-N is mainly dominated by non-thermal sources while G14.2-S contains more thermal emitters. Approximately 75% of the sources present a counterpart at other wavelengths. In the inner 0.4~pc region around the center of each hub, the number of IR sources in G14.2-N is larger than in G14.2-S by a factor of 4. We also studied the relation between the radio luminosity and the bolometric luminosity, finding that the thermal emission of the studied sources is compatible with thermal radio jets. For our sources with X-ray counterparts, the non-thermal emitters follow a Güdel-Benz relation with k = 0.03. We found similar levels of fragmentation between G14.2-N and G14.2-S, suggesting that both regions are most likely twin hubs. The non-thermal emission found in the less evolved objects suggests that G14.2-N may be composed of more massive YSOs as well as being in a more advanced evolutionary stage, consistent with the filament-halo gradient in age and mass from previous works. Our results confirm a wider evolutionary sequence starting in G14.2-S as the youngest part, followed by G14.2-N, and ending with the most evolved region M17.

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Exploring the dust grain size and polarization mechanism in the hot and massive Class 0 disk IRAS 16293-2422 B

Multiwavelength dust continuum and polarization observations arising from self-scattering have been used to investigate grain sizes in young disks. However, the polarization by self-scattering is low in face-on optically thick disks and puts some of the size constraints from polarization on hold, particularly for the younger and more massive disks. The 1.3 mm emission detected toward the hot ($\gtrsim$400 K) Class 0 disk IRAS 16293-2422 B has been attributed to self-scattering, predicting grain sizes between 200-2000 $μ$m. We investigate the effects of grain size in the resultant flux and polarization fractions from self-scattering using a hot and massive Class 0 disk model and compare with observations. We compared new and archival high-resolution observations between 1.3 and 18 mm to a set of synthetic models. We have developed a new public tool to automate this process called Synthesizer. This is an easy-to-use program to generate synthetic observations from numerical simulations. Optical depths are in the range of 130 to 2 from 1.3 to 18 mm, respectively. Predictions from significant grain growth populations, including millimetric grains are comparable to the observations at all wavelengths. The polarization fraction produced by self-scattering reaches a maximum of $\sim$0.1% at 1.3 mm for a maximum grain size of 100 $μ$m, being an order of magnitude lower than that observed with ALMA. From the comparison of Stokes I fluxes, we conclude that significant grain growth could be present in the young Class 0 disk IRAS 16293 B, particularly in the inner hot region ($<10$ au, $T>$ 300 K) where refractory organics evaporate. The polarization produced by self-scattering in our model is not high enough to explain the observations at 1.3 and 7 mm, and effects like dichroic extinction or polarization reversal of elongated aligned grains remain other possible but untested scenarios.

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RZ Piscium Hosts a Compact and Highly Perturbed Debris Disk

RZ Piscium (RZ Psc) is well-known in the variable star field because of its numerous, irregular optical dips in the past five decades, but the nature of the system is heavily debated in the literature. We present multiyear infrared monitoring data from Spitzer and WISE to track the activities of the inner debris production, revealing stochastic infrared variability as short as weekly timescales that is consistent with destroying a 90-km-size asteroid every year. ALMA 1.3 mm data combined with spectral energy distribution modeling show that the disk is compact ($\sim$0.1--13 au radially) and lacks cold gas. The disk is found to be highly inclined and has a significant vertical scale height. These observations confirm that RZ Psc hosts a close to edge-on, highly perturbed debris disk possibly due to migration of recently formed giant planets which might be triggered by the low-mass companion RZ Psc B if the planets formed well beyond the snowlines.

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Initial conditions of star formation at $\lesssim$2000 au: physical structure and NH$_{3}$ depletion of three early-stage cores

Pre-stellar cores represent a critical evolutionary phase in low-mass star formation. We aim to unveil the detailed thermal structure and density distribution of three early-stage cores, starless core L1517B, and prestellar core L694-2 and L429, with the high angular resolution observations of the NH$_{3}$ (1,1) and (2,2) inversion transitions obtained with VLA and GBT. In addition, we explore where/if NH$_{3}$ depletes in the central regions. Applying the mid-infrared extinction method to the $\textit{Spitzer}$ 8$~μ$m map we obtain a high angular resolution hydrogen column density map, and derive the gas density profile to assess the variation of NH$_{3}$ abundance as a function of gas volume density. The measured temperature profiles of L429 and L1517B show a minor decrease towards the core center, dropping from $\sim$9K to below 8K, and $\sim$11 K to 10 K, while L694-2 has a rather uniform temperature distribution around $\sim$9 K. Among the three cores, L429 has the highest central gas density, close to sonic velocity line-width, and largest localised velocity gradient, all indicative of an advanced evolutionary stage. We resolve that the abundance of NH$_{3}$ becomes two times lower in the central region of L429, occurring around a gas density of 4.4$\times$10$^{4}$$~cm^{-3}$. Compared to Ophiuchus/H-MM1 which shows an even stronger drop of the NH$_{3}$ abundance at 2$\times$10$^{5}$$~cm^{-3}$, the abundance variations of the three cores plus Ophiuchus/H-MM1 suggest a progressive NH$_{3}$ depletion with increasing central density of the core.

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Centimeter-sized Grains in the Compact Dust Ring around Very Low Mass Star CIDA 1

We examined the grain size in the dust ring encircling the 0.19~$M_\sun$ T Tauri star CIDA 1 using the Karl G. Jansky Very Large Array (JVLA) at multiple centimeter wavelengths, with a spatial resolution of 0$\farcs$2--0$\farcs$9. We detected distinct partial-ring structures at these wavelengths around CIDA~1. Based on spatial distributions and spectral indexes, we determined that these centimeter emissions originated from dust, rather than free-free or synchrotron emissions. To estimate the maximum grain size ($a_{\rm max}$) within the ring, we compared the observed spectral energy distribution (SED) with SEDs calculated for different $a_{\rm max}$ values using radiative transfer calculations. Our findings indicate an $a_{\rm max}$ value of approximately 2.5~cm in the ring, assuming the dust opacity can be approximated by the DSHARP models. These results suggest that grain growth took place within the CIDA~1 ring, potentially facilitating more efficient planet formation through pebble accretion scenarios involving centimeter-sized pebbles.

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Gravitational instability, spiral substructure, and modest grain growth in a typical protostellar disk: Modeling multi-wavelength dust continuum observation of TMC1A

Embedded, Class 0/I protostellar disks represent the initial condition for planet formation. This calls for better understandings of their bulk properties and the dust grains within them. We model multi-wavelength dust continuum observations of the disk surrounding the Class I protostar TMC1A to provide insight on these properties. The observations can be well fit by a gravitationally self-regulated (i.e., marginally gravitationally unstable and internally heated) disk model, with surface density $Σ\sim 1720 (R/10au)^{-1.96} g/cm^2$ and midplane temperature $T_{mid} \sim 185 (R/10au)^{-1.27} K$. The observed disk contains a $m=1$ spiral substructure; we use our model to predict the spiral's pitch angle and the prediction is consistent with the observations. This agreement serves as both a test of our model and strong evidence of the gravitational nature of the spiral. Our model estimates a maximum grain size $a_{max}\sim 196(R/10au)^{-2.45} μm$, which is consistent with grain growth being capped by a fragmentation barrier with threshold velocity $\sim 1 m/s$. We further demonstrate that observational properties of TMC1A are typical among the observed population of Class 0/I disks, which hints that traditional methods of disk data analyses based on Gaussian fitting and the assumption of the optically thin dust emission could have systematically underestimated disk size and mass and overestimated grain size.

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Anisotropic Ionizing Illumination from an M-type Pre-main Sequence Star, DM Tau

The powerful, high-energy magnetic activities of young stars play important roles in the magnetohydrodynamics in the innermost parts of the protoplanetary disks. In addition, the associated UV and X-ray emission dictates the photochemistry; moreover, the corona activities can affect the atmosphere of a newborn extra-solar planet. How the UV and X-ray photons are generated, and how they illuminate the disks, are not well understood. Here we report the analyses of the optical and infrared (OIR) photometric monitoring observations and the high angular-resolution centimeter band images of the low-mass (M1 type) pre-main sequence star, DM Tau. We found that the OIR photometric light curves present periodic variations, which is consistent with that the host young star is rotating in the same direction as the natal disk and is hosting at least one giant cold spot. In addition, we resolved that the ionized gas in the DM Tau disk is localized, and its spatial distribution is varying with time. All the present observations can be coherently interpreted, if the giant cold spot is the dominant anisotropic UV and/or X-ray source that illuminates the ambient cone-like region. These results indicate that a detailed theoretical model of the high-energy protostellar emission is essential in the understanding of the space weather around the extra-solar planets and the origin of life.

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Deviation from a Continuous and Universal Turbulence Cascade in NGC 6334 due to Massive Star Formation Activity

We use molecular line data from ALMA, SMA, JCMT, and NANTEN2 to study the multi-scale ($\sim$15-0.005 pc) velocity statistics in the massive star formation region NGC 6334. We find that the non-thermal motions revealed by the velocity dispersion function (VDF) stay supersonic over scales of several orders of magnitudes. The multi-scale non-thermal motions revealed by different instruments do not follow the same continuous power-law, which is because the massive star formation activities near central young stellar objects have increased the non-thermal motions in small-scale and high-density regions. The magnitudes of VDFs vary in different gas materials at the same scale, where the infrared dark clump N6334S in an early evolutionary stage shows a lower level of non-thermal motions than other more evolved clumps due to its more quiescent star formation activity. We find possible signs of small-scale-driven (e.g., by gravitational accretion or outflows) supersonic turbulence in clump N6334IV with a three-point VDF analysis. Our results clearly show that the scaling relation of velocity fields in NGC 6334 deviates from a continuous and universal turbulence cascade due to massive star formation activities.

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Multiple Rings and Asymmetric Structures in the Disk of SR 21

Crescent-like asymmetric dust structures discovered in protoplanetary disks indicate dust aggregations. Thus, the research on them helps us understand the planet formation process. Here we analyze the ALMA data of the protoplanetary disk around the T-Tauri star SR 21, which has asymmetric structures detected in previous sub-millimeter observations. Imaged at ALMA Band 6 (1.3 mm) with a spatial resolution of about 0.$\arcsec$04, the disk is found to consist of two rings and three asymmetric structures, with two of the asymmetric structures being in the same ring. Compared to the Band 6 image, the Band 3 (2.7 mm) image also shows the three asymmetric structures but with some clumps. The elongated asymmetric structures in the outer ring could be due to the interactions of a growing planet. By fitting the Band 3 and Band 6 dust continuum data, two branches of solutions of maximum dust size in the disk are suggested: one is larger than 1 mm, and the other is smaller than 300 $μm$. High-resolution continuum observations at longer wavelengths as well as polarization observations can help break the degeneracy. We also suggest that the prominent spiral previously identified in VLT/SPHERE observations to the south of the star at 0.$\arcsec$25 may be the scattered light counterpart of the Inner Arc, and the structure is a dust-trapping vortex in nature. The discovered features in SR 21 make it a good target for studying the evolution of asymmetric structures and planet formation.

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ALMA Band 6 high-resolution observations of the transitional disk around SY Cha

In this study, we reported the results of high-resolution (0.14 arcsec) Atacama Large Millimeter/submillimeter Array (ALMA) observations of the 225 GHz dust continuum and CO molecular emission lines from the transitional disk around SY Cha. Our high-resolution observations clearly revealed the inner cavity and the central point source for the first time. The radial profile of the ring can be approximated by a bright narrow ring superimposed on a fainter wide ring. Furthermore, we found that there is a weak azimuthal asymmetry in dust continuum emission. For gas emissions, we detected $\rm{}^{12}CO$(2$-$1), $\rm{}^{13}CO$(2$-$1) and $\rm{}C^{18}O$(2$-$1), from which we estimated the total gas mass of the disk to be $2.2\times10^{-4}M_\odot$, assuming a CO/H$_2$ ratio of $10^{-4}$. The observations showed that the gas is present inside the dust cavity. The analysis of the velocity structure of the $\rm{}^{12}CO$(2$-$1) emission line revealed that the velocity is distorted at the location of the dust inner disk, which may be owing to warping of the disk or radial gas flow within the cavity of the dust disk. High-resolution observations of SY Cha showed that this system is composed of a ring and a distorted inner disk, which may be common, as indicated by the survey of transitional disk systems at a resolution of $\sim$0.1~arcsec.

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Multi-scale physical properties of NGC 6334 as revealed by local relative orientations between magnetic fields, density gradients, velocity gradients, and gravity

We present ALMA dust polarization and molecular line observations toward 4 clumps (I(N), I, IV, and V) in the massive star-forming region NGC 6334. In conjunction with large-scale dust polarization and molecular line data from JCMT, Planck, and NANTEN2, we make a synergistic analysis of relative orientations between magnetic fields ($θ_{\mathrm{B}}$), column density gradients ($θ_{\mathrm{NG}}$), local gravity ($θ_{\mathrm{LG}}$), and velocity gradients ($θ_{\mathrm{VG}}$) to investigate the multi-scale (from $\sim$30 pc to 0.003 pc) physical properties in NGC 6334. We find that the relative orientation between $θ_{\mathrm{B}}$ and $θ_{\mathrm{NG}}$ changes from statistically more perpendicular to parallel as column density ($N_{\mathrm{H_2}}$) increases, which is a signature of trans-to-sub-Alfvénic turbulence at complex/cloud scales as revealed by previous numerical studies. Because $θ_{\mathrm{NG}}$ and $θ_{\mathrm{LG}}$ are preferentially aligned within the NGC 6334 cloud, we suggest that the more parallel alignment between $θ_{\mathrm{B}}$ and $θ_{\mathrm{NG}}$ at higher $N_{\mathrm{H_2}}$ is because the magnetic field line is dragged by gravity. At even higher $N_{\mathrm{H_2}}$, the angle between $θ_{\mathrm{B}}$ and $θ_{\mathrm{NG}}$ or $θ_{\mathrm{LG}}$ transits back to having no preferred orientation or statistically slightly more perpendicular, suggesting that the magnetic field structure is impacted by star formation activities. A statistically more perpendicular alignment is found between $θ_{\mathrm{B}}$ and $θ_{\mathrm{VG}}$ throughout our studied $N_{\mathrm{H_2}}$ range, which indicates a trans-to-sub-Alfvénic state at small scales as well. The normalised mass-to-flux ratio derived from the polarization-intensity gradient (KTH) method increases with $N_{\mathrm{H_2}}$.

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