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Tie Liu

Publications and source records attributed to Tie Liu.

At least 145 records · Page 8Linked to original sources

The ALMA Survey of 70 $μ\rm m$ Dark High-mass Clumps in Early Stages (ASHES). VII: Chemistry of Embedded Dense Cores

We present a study of chemistry toward 294 dense cores in 12 molecular clumps using the data obtained from the ALMA Survey of 70 $μ\rm m$ dark High-mass clumps in Early Stages (ASHES). We identified 97 protostellar cores and 197 prestellar core candidates based on the detection of outflows and molecular transitions of high upper energy levels ($E_{u}/k > 45$ K). The detection rate of the N$_{2}$D$^{+}$ emission toward the protostellar cores is 38%, which is higher than 9% for the prestellar cores, indicating that N$_{2}$D$^{+}$ does not exclusively trace prestellar cores. The detection rates of the DCO$^{+}$ emission are 35% for the prestellar cores and 49% for the protostellar cores, which are higher than those of N$_{2}$D$^{+}$, implying that DCO$^{+}$ appears more frequently than N$_{2}$D$^{+}$ in both prestellar and protostellar cores. Both N$_{2}$D$^{+}$ and DCO$^{+}$ abundances appear to decrease from the prestellar to protostellar stage. The DCN, C$_{2}$D and $^{13}$CS emission lines are rarely seen in the dense cores of early evolutionary phases. The detection rate of the H$_{2}$CO emission toward dense cores is 52%, three times higher than that of CH$_{3}$OH (17%). In addition, the H$_{2}$CO detection rate, abundance, line intensities, and line widths increase with the core evolutionary status, suggesting that the H$_{2}$CO line emission is sensitive to protostellar activity.

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A Q-band line survey towards Orion KL using the Tianma radio telescope

We have conducted a line survey towards Orion KL using the Q-band receiver of Tianma 65 m radio telescope (TMRT), covering 34.8--50 GHz with a velocity resolution between 0.79 km s$^{-1}$ and 0.55 km s$^{-1}$ respectively. The observations reach a sensitivity on the level of 1-8 mK, proving that the TMRT is sensitive for conducting deep line surveys. In total, 597 Gaussian features are extracted. Among them, 177 radio recombination lines (RRLs) are identified, including 126, 40 and 11 RRLs of hydrogen, helium and carbon, with a maximum $Δn$ of 16, 7, and 3, respectively. The carbon RRLs are confirmed to originate from photodissociation regions with a $V_{\rm LSR}\sim$9 km s$^{-1}$. In addition, 371 molecular transitions of 53 molecular species are identified. Twenty-one molecular species of this survey were not firmly detected in the Q band by Rizzo et al. (2017), including species such as H$_2$CS, HCOOH, C$_2$H$_5$OH, H$_2^{13}$CO, H$_2$CCO, CH$_3$CHO, CH$_2$OCH$_2$, HCN $v_2=1$, and CH$_3$OCHO $v_t=1$. In particular, the vibrationally excited states of ethyl cyanide (C$_2$H$_5$CN $v$13/$v$21) are for the first time firmly detected in the Q band. NH$_3$ (15,15) and (16,16) are identified, and they are so far the highest transitions of the NH$_3$ inversion lines detected towards Orion KL. All the identified lines can be reproduced by a radiative transfer model.

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ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- XII: Fragmentation and multi-scale gas kinematics in protoclusters G12.42+0.50 and G19.88-0.53

We present new continuum and molecular line data from the ALMA Three-millimeter Observations of Massive Star-forming regions (ATOMS) survey for the two protoclusters, G12.42+0.50 and G19.88-0.53. The 3 mm continuum maps reveal seven cores in each of the two globally contracting protoclusters. These cores satisfy the radius-mass relation and the surface mass density criteria for high-mass star formation. Similar to their natal clumps, the virial analysis of the cores suggests that they are undergoing gravitational collapse ($\rm α_{vir} << 2$). The clump to core scale fragmentation is investigated and the derived core masses and separations are found to be consistent with thermal Jeans fragmentation. We detect large-scale filamentary structures with velocity gradients and multiple outflows in both regions. Dendrogram analysis of the H$^{13}$CO$^{+}$ map identifies several branch and leaf structures with sizes $\sim$ 0.1 and 0.03 pc, respectively. The supersonic gas motion displayed by the branch structures is in agreement with the Larson power-law indicating that the gas kinematics at this spatial scale is driven by turbulence. The transition to transonic/subsonic gas motion is seen to occur at spatial scales of $\sim$0.1 pc indicating the dissipation of turbulence. In agreement with this, the leaf structures reveal gas motions that deviate from the slope of Larson's law. From the large-scale converging filaments to the collapsing cores, the gas dynamics in G12.42+0.50 and G19.88-0.53 show scale-dependent dominance of turbulence and gravity and the combination of these two driving mechanisms needs to be invoked to explain massive star formation in the protoclusters.

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ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- XI. From inflow to infall in hub-filament systems

We investigate the presence of hub-filament systems in a large sample of 146 active proto-clusters, using H$^{13}$CO$^{+}$ J=1-0 molecular line data obtained from the ATOMS survey. We find that filaments are ubiquitous in proto-clusters, and hub-filament systems are very common from dense core scales ($\sim$0.1 pc) to clump/cloud scales ($\sim$1-10 pc). The proportion of proto-clusters containing hub-filament systems decreases with increasing dust temperature ($T_d$) and luminosity-to-mass ratios ($L/M$) of clumps, indicating that stellar feedback from H{\sc ii} regions gradually destroys the hub-filament systems as proto-clusters evolve. Clear velocity gradients are seen along the longest filaments with a mean velocity gradient of 8.71 km s$^{-1}$pc$^{-1}$ and a median velocity gradient of 5.54 km s$^{-1}$pc$^{-1}$. We find that velocity gradients are small for filament lengths larger than $\sim$1~pc, probably hinting at the existence of inertial inflows, although we cannot determine whether the latter are driven by large-scale turbulence or large-scale gravitational contraction. In contrast, velocity gradients below $\sim$1~pc dramatically increase as filament lengths decrease, indicating that the gravity of the hubs or cores starts to dominate gas infall at small scales. We suggest that self-similar hub-filament systems and filamentary accretion at all scales may play a key role in high-mass star formation.

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ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP): How do dense core properties affect the multiplicity of protostars?

During the transition phase from a prestellar to a protostellar cloud core, one or several protostars can form within a single gas core. The detailed physical processes of this transition, however, still remain unclear. We present 1.3 mm dust continuum and molecular line observations with the Atacama Large Millimeter/submillimeter Array (ALMA) toward 43 protostellar cores in the Orion Molecular Cloud Complex ($λ$ Orionis, Orion B, and Orion A) with an angular resolution of $\sim$ 0.35" ($\sim$ 140 au). In total, we detect 13 binary/multiple systems. We derive an overall multiplicity frequency (MF) of 28$\%$ $\pm$ 4$\%$ and a companion star fraction (CSF) of 51$\%$ $\pm$ 6$\%$, over a separation range of 300-8900 au. The median separation of companions is about 2100 au. The occurrence of stellar multiplicity may depend on the physical characteristics of the dense cores. Notably, those containing binary/multiple systems tend to show higher gas density and Mach number than cores forming single stars. The integral-shaped filament (ISF) of Orion A giant molecular cloud (GMC), which has the highest gas density and hosts high-mass star formation in its central region (the Orion Nebula cluster), shows the highest MF and CSF among the Orion GMCs. In contrast, the $λ$ Orionis Giant Molecular Cloud (GMC) has a lower MF and CSF than the Orion B and Orion A GMCs, indicating that feedback from HII regions may suppress the formation of multiple systems. We also find that the protostars comprising a binary/multiple system are usually at different evolutionary stages.

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Improved Weakly Private Information Retrieval Codes

We study the problem of weakly private information retrieval (W-PIR), where a user wishes to retrieve a desired message from $N$ non-colluding servers in a way that the privacy leakage regarding the desired message's identity is less than or equal to a threshold. We propose a new code construction which significantly improves upon the best known result in the literature, based on the following critical observation. In previous constructions, for the extreme case of minimum download, the retrieval pattern is to download the message directly from $N-1$ servers; however this causes leakage to all these $N-1$ servers, and a better retrieval pattern for this extreme case is to download the message directly from a single server. The proposed code construction allows a natural transition to such a pattern, and for both the maximal leakage metric and the mutual information leakage metric, significant improvements can be obtained. We provide explicit solutions, in contrast to a previous work by Lin et al., where only numerical solutions were obtained.

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ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP): Deriving Inclination Angle and Velocity of the Protostellar Jets from their SiO Knots

We have selected six sources (G209.55-19.68S2, G205.46-14.56S1$_{-}$A, G203.21-11.20W2, G191.90-11.21S, G205.46-14.56S3, and G206.93-16.61W2) from the Atacama Large Millimeter/submillimeter Array Survey of Orion Planck Galactic Cold Clumps (ALMASOP), in which these sources have been mapped in the CO (J=2-1), SiO (J=5-4), and C$^{18}$O (J=2-1) lines. These sources have high-velocity SiO jets surrounded by low-velocity CO outflows. The SiO jets consist of a chain of knots. These knots have been thought to be produced by semi-periodical variations in jet velocity. Therefore, we adopt a shock-forming model, which uses such variations to estimate the inclination angle and velocity of the jets. We also derive the inclination angle of the CO outflows using the wide-angle wind-driven shell model, and find it to be broadly consistent with that of the associated SiO jets. In addition, we apply this shock-forming model to another three protostellar sources with SiO jets in the literature -- HH 211, HH 212, and L1448C(N) -- and find that their inclination angle and jet velocity are consistent with those previously estimated from proper motion and radial velocity studies.

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ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP): Evidence for a Molecular Jet Launched at an Unprecedented Early Phase of Protostellar evolution

Protostellar outflows and jets play a vital role in star formation as they carry away excess angular momentum from the inner disk surface, allowing the material to be transferred toward the central protostar. Theoretically, low velocity and poorly collimated outflows appear from the beginning of the collapse, at the first hydrostatic core (FHSC) stage. With growing protostellar core mass, high-density jets are launched which entrain an outflow from the infalling envelope. Until now, molecular jets have been observed at high velocity ($\gtrsim$ 100 km/s) in early Class\,0 protostars. We, for the first time, detect a dense molecular jet in SiO emission with small-velocity ($\sim$ 4.2 km\,s$^{-1}$, deprojected $\sim$ 24 km\,s$^{-1}$) from source G208.89-20.04Walma (hereafter, G208Walma) using ALMA Band\,6 observations. This object has some characteristics of FHSCs, such as a small outflow/jet velocity, extended 1.3\,mm continuum emission, and N$_2$D$^+$ line emission. Additional characteristics, however, are typical of early protostars: collimated outflow and SiO jet. The full extent of the outflow corresponds to a dynamical time scale of $\sim$ 930$^{+200}_{-100}$ years. The spectral energy distribution also suggests a very young source having an upper limit of T$_{bol}$ $\sim$ 31 K and L$_{bol}$ $\sim$ 0.8 L$_\sun$. We conclude that G208Walma is likely in the transition phase from FHSC to protostar, and the molecular jet has been launched within a few hundred years of initial collapse. Therefore, G208Walma may be the earliest object discovered in the protostellar phase with a molecular jet.

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ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP): A Hot Corino Survey toward Protostellar Cores in the Orion Cloud

The presence of complex organic molecules (COMs) in the interstellar medium (ISM) is of great interest since it may link to the origin and prevalence of life in the universe. Aiming to investigate the occurrence of COMs and their possible origins, we conducted a chemical census toward a sample of protostellar cores as part of the ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP) project. We report the detection of 11 hot corino sources, which exhibit compact emissions from warm and abundant COMs, among 56 Class 0/I protostellar cores. All the hot corino sources discovered are likely Class 0 and their sizes of the warm region ($>$ 100 K) are comparable to 100 au. The luminosity of the hot corino sources exhibits positive correlations with the total number of methanol and the extent of its emissions. Such correlations are consistent with the thermal desorption picture for the presence of hot corino and suggest that the lower luminosity (Class 0) sources likely have a smaller region with COMs emissions. With the same sample selection method and detection criteria being applied, the detection rates of the warm methanol in the Orion cloud (15/37) and the Perseus cloud (28/50) are statistically similar when the cloud distances and the limited sample size are considered. Observing the same set of COM transitions will bring a more informative comparison between the cloud properties.

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Nobeyama Survey of Inward Motions toward Cores in Orion Identified by SCUBA-2

In this study, 36 cores (30 starless and 6 protostellar) identified in Orion were surveyed to search for inward motions. We used the Nobeyama 45 m radio telescope, and mapped the cores in the $J = 1\rightarrow0$ transitions of HCO$^+$, H$^{13}$CO$^+$, N$_2$H$^+$, HNC, and HN$^{13}$C. The asymmetry parameter $δV$, which was the ratio of the difference between the HCO$^+$ and H$^{13}$CO$^+$ peak velocities to the H$^{13}$CO$^+$ line width, was biased toward negative values, suggesting that inward motions were more dominant than outward motions. Three starless cores (10% of all starless cores surveyed) were identified as cores with blue-skewed line profiles (asymmetric profiles with more intense blue-shifted emission), and another two starless cores (7%) were identified as candidate blue-skewed line profiles. The peak velocity difference between HCO$^+$ and H$^{13}$CO$^+$ of them was up to 0.9 km s$^{-1}$, suggesting that some inward motions exceeded the speed of sound for the quiescent gas ($\sim10-17$ K). The mean of $δV$ of the five aforementioned starless cores was derived to be $-$0.5$\pm$0.3. One core, G211.16$-$19.33North3, observed using the ALMA ACA in DCO$^+$ $J = 3\rightarrow2$ exhibited blue-skewed features. Velocity offset in the blue-skewed line profile with a dip in the DCO$^+$ $J = 3\rightarrow2$ line was larger ($\sim 0.5$ km s$^{-1}$) than that in HCO$^+$ $J = 1\rightarrow0$ ($\sim 0.2$ km s$^{-1}$), which may represent gravitational acceleration of inward motions. It seems that this core is at the last stage in the starless phase, judging from the chemical evolution factor version 2.0 (CEF2.0).

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Magnetic fields in star formation: from clouds to cores

In this chapter we review recent advances in understanding the roles that magnetic fields play throughout the star formation process, gained through observations and simulations of molecular clouds, the dense, star-forming phase of the magnetised, turbulent interstellar medium (ISM). Recent results broadly support a picture in which the magnetic fields of molecular clouds transition from being gravitationally sub-critical and near equipartition with turbulence in low-density cloud envelopes, to being energetically sub-dominant in dense, gravitationally unstable star-forming cores. Magnetic fields appear to play an important role in the formation of cloud substructure by setting preferred directions for large-scale gas flows in molecular clouds, and can direct the accretion of material onto star-forming filaments and hubs. Low-mass star formation may proceed in environments close to magnetic criticality; high-mass star formation remains less well-understood, but may proceed in more supercritical environments. The interaction between magnetic fields and (proto)stellar feedback may be particularly important in setting star formation efficiency. We also review a range of widely-used techniques for quantifying the dynamic importance of magnetic fields, concluding that better-calibrated diagnostics are required in order to use the spectacular range of forthcoming observations and simulations to quantify our emerging understanding of how magnetic fields influence the outcome of the star formation process.

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ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions-IX. A pilot study towards IRDC G034.43+00.24 on multi-scale structures and gas kinematics

We present a comprehensive study of the gas kinematics associated with density structures at different spatial scales in the filamentary infrared dark cloud, G034.43+00.24 (G34). This study makes use of the H13CO+ (1-0) molecular line data from the ALMA Three-millimeter Observations of Massive Star-forming regions (ATOMS) survey, which has spatial and velocity resolution of 0.04 pc and 0.2 km/s, respectively. Several tens of dendrogram structures have been extracted in the position-position-velocity space of H13CO+, which include 21 small-scale leaves and 20 larger-scale branches. Overall, their gas motions are supersonic but they exhibit the interesting behavior where leaves tend to be less dynamically supersonic than the branches. For the larger-scale, branch structures, the observed velocity-size relation (i.e., velocity variation/dispersion versus size) are seen to follow the Larson scaling exponent while the smaller-scale, leaf structures show a systematic deviation and display a steeper slope. We argue that the origin of the observed kinematics of the branch structures is likely to be a combination of turbulence and gravity-driven ordered gas flows. In comparison, gravity-driven chaotic gas motion is likely at the level of small-scale leaf structures. The results presented in our previous paper and this current follow-up study suggest that the main driving mechanism for mass accretion/inflow observed in G34 varies at different spatial scales. We therefore conclude that a scale-dependent combined effect of turbulence and gravity is essential to explain the star-formation processes in G34.

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Chemical exploration of Galactic cold cores

A solar-type system starts from an initial molecular core that acquires organic complexity as it evolves. The so-called prestellar cores that can be studied are rare, which has hampered our understanding of how organic chemistry sets in and grows. Aims. We selected the best prestellar core targets from the cold core catalogue that represent a diversity in terms of their environment to explore their chemical complexity: 1390 (in the compressed shell of Lambda Ori), 869 (in the MBM12 cloud), and 4149 (in the California nebula). We obtained a spectral survey with the IRAM 30 m telescope in order to explore the molecular complexity of the cores. We carried out a radiative transfer analysis of the detected transitions in order to place some constraints on the physical conditions of the cores and on the molecular column densities. We also used the molecular ions in the survey to estimate the cosmic-ray ionisation rate and the S/H initial elemental abundance using a gas-phase chemical model to reproduce their abundances. We found large differences in the molecular complexity (deuteration, complex organic molecules, sulphur, carbon chains, and ions) and compared their chemical properties with a cold core and two prestellar cores. The chemical diversity we found in the three cores seems to be correlated with their chemical evolution: two of them are prestellar (1390 and 4149), and one is in an earlier stage (869). The influence of the environment is likely limited because cold cores are strongly shielded from their surroundings. The high extinction prevents interstellar UV radiation from penetrating deeply into the cores. Higher spatial resolution observations of the cores are therefore needed to constrain the physical structure of the cores, as well as a larger-scale distribution of molecular ions to understand the influence of the environment on their molecular complexity.

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On Linear Separability under Linear Compression with Applications to Hard Support Vector Machine

This paper investigates the theoretical problem of maintaining linear separability of the data-generating distribution under linear compression. While it has been long known that linear separability may be maintained by linear transformations that approximately preserve the inner products between the domain points, the limit to which the inner products are preserved in order to maintain linear separability was unknown. In this paper, we show that linear separability is maintained as long as the distortion of the inner products is smaller than the squared margin of the original data-generating distribution. The proof is mainly based on the geometry of hard support vector machines (SVM) extended from the finite set of training examples to the (possibly) infinite domain of the data-generating distribution. As applications, we derive bounds on the (i) compression length of random sub-Gaussian matrices; and (ii) generalization error for compressive learning with hard-SVM.

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Stochastic Chaining and Strengthened Information-Theoretic Generalization Bounds

We propose a new approach to apply the chaining technique in conjunction with information-theoretic measures to bound the generalization error of machine learning algorithms. Different from the deterministic chaining approach based on hierarchical partitions of a metric space, previously proposed by Asadi et al., we propose a stochastic chaining approach, which replaces the hierarchical partitions with an abstracted Markovian model borrowed from successive refinement source coding. This approach has three benefits over deterministic chaining: 1) the metric space is not necessarily bounded, 2) facilitation of subsequent analysis to yield more explicit bound, and 3) further opportunity to optimize the bound by removing the geometric rigidity of the partitions. The proposed approach includes the traditional chaining as a special case, and can therefore also utilize any deterministic chaining construction. We illustrate these benefits using the problem of estimating Gaussian mean and that of phase retrieval. For the former, we derive a bound that provides an order-wise improvement over previous results, and for the latter we provide a stochastic chain that allows optimization over the chaining parameter.

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ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- VIII. A search for hot cores by using C$_2$H$_5$CN, CH$_3$OCHO and CH$_3$OH lines

Hot cores characterized by rich lines of complex organic molecules are considered as ideal sites for investigating the physical and chemical environments of massive star formation. We present a search for hot cores by using typical nitrogen- and oxygen-bearing complex organic molecules (C$_2$H$_5$CN, CH$_3$OCHO and CH$_3$OH), based on ALMA Three-millimeter Observations of Massive Star-forming regions (ATOMS). The angular resolutions and line sensitivities of the ALMA observations are better than 2 arcsec and 10 mJy/beam, respectively. A total of 60 hot cores are identified with 45 being newly detected, in which the complex organic molecules have high gas temperatures ($>$ 100 K) and small source sizes ($<$ 0.1 pc). So far this is the largest sample of hot cores observed with similar angular resolution and spectral coverage. The observations have also shown nitrogen and oxygen differentiation in both line emission and gas distribution in 29 hot cores. Column densities of CH$_3$OH and CH$_3$OCHO increase as rotation temperatures rise. The column density of CH$_3$OCHO correlates tightly with that of CH$_3$OH. The pathways for production of different species are discussed. Based on the spatial position difference between hot cores and UC~H{\sc ii} regions, we conclude that 24 hot cores are externally heated while the other hot cores are internally heated. The observations presented here will potentially help establish a hot core template for studying massive star formation and astrochemistry.

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ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- VII. A catalogue of SiO clumps from ACA observations

To understand the nature of SiO emission, we conducted ACA observations of the SiO (2-1) lines toward 146 massive star-forming regions, as part of the ALMA Three-millimeter Observations of Massive Star-forming regions (ATOMS) survey. We detected SiO emission in 128 (87.7$\%$) sources and identified 171 SiO clumps, 105 of which are spatially separated from 3 mm continuum emission. A large amount of the SiO line profiles (60$\%$) are non-Gaussian. The velocity dispersion of the SiO lines ranges from 0.3 to 5.43 km s$^{-1}$. In 63 sources the SiO clumps are associated with H$_\rm{II}$ regions characterized by H40$α$ emission. We find that 68$\%$ (116) of the SiO clumps are associated with strong outflows. The median velocity dispersion of the SiO line for outflow sources and non-outflow sources is 1.91 km s$^{-1}$ and 0.99 km s$^{-1}$, respectively. These results indicate that outflow activities could be connected to strongly shocked gas. The velocity dispersion and [SiO]/[H$^{13}$CO$^+$] intensity ratio do not show any correlation with the dust temperature and particle number density of clumps. We find a positive correlation between the SiO line luminosity and the bolometric luminosity, implying stronger shock activities are associated with more luminous proto-clusters. The SiO clumps in associations with H$_\rm{II}$ regions were found to show a steeper feature in $L_\rm{sio}$/$L_\rm{bol}$. The SiO line luminosity and the fraction of shocked gas have no apparent evidence of correlation with the evolutionary stages traced by luminosity to mass ratio ($L_\rm{bol}/M$).

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B-fields in Star-Forming Region Observations (BISTRO): Magnetic Fields in the Filamentary Structures of Serpens Main

We present 850 $μ$m polarimetric observations toward the Serpens Main molecular cloud obtained using the POL-2 polarimeter on the James Clerk Maxwell Telescope (JCMT) as part of the B-fields In STar-forming Region Observations (BISTRO) survey. These observations probe the magnetic field morphology of the Serpens Main molecular cloud on about 6000 au scales, which consists of cores and six filaments with different physical properties such as density and star formation activity. Using the histogram of relative orientation (HRO) technique, we find that magnetic fields are parallel to filaments in less dense filamentary structures where $N_{H_2} < 0.93\times 10^{22}$ cm$^{-2}$ (magnetic fields perpendicular to density gradients), while being perpendicular to filaments (magnetic fields parallel to density gradients) in dense filamentary structures with star formation activity. Moreover, applying the HRO technique to denser core regions, we find that magnetic field orientations change to become perpendicular to density gradients again at $N_{H_2} \approx 4.6 \times 10^{22}$ cm$^{-2}$. This can be interpreted as a signature of core formation. At $N_{H_2} \approx 16 \times 10^{22}$ cm$^{-2}$ magnetic fields change back to being parallel to density gradients once again, which can be understood to be due to magnetic fields being dragged in by infalling material. In addition, we estimate the magnetic field strengths of the filaments ($B_{POS} = 60-300~μ$G)) using the Davis-Chandrasekhar-Fermi method and discuss whether the filaments are gravitationally unstable based on magnetic field and turbulence energy densities.

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