arXiv subjects

Xing Lu

Publications and source records attributed to Xing Lu.

At least 37 records · Page 2Linked to original sources

arXiv2026

ALMA Central molecular zone Exploration Survey (ACES) III: Molecular line data reduction and HNCO and HCO$^{+}$ data

The ALMA Central molecular zone Exploration Survey (ACES) large program has observed the inner ~ 200 pc of the Milky Way at 3 mm (Band 3) using ALMA's 12m, 7m, and Total Power arrays. With an angular resolution of ~ 2", ACES provides a contiguous, multi-scale view of the Central Molecular Zone (CMZ) via the dust continuum and a suite of molecular lines. We present an overview of the molecular line data processing for ACES and describe the first data release. We showcase the HNCO (4-3) and HCO$^{+}$ (1-0) data, which were targeted at high spectral resolution (0.2 km s$^{-1}$) to trace the kinematics of the molecular gas in the CMZ. The HNCO and HCO$^{+}$ maps are compared with previous single-dish CMZ surveys and discrete ALMA observations of CMZ clouds to demonstrate the quality of the data. We highlight the ubiquity of parsec-scale, linear absorption features traced by HCO$^{+}$. Their origin is unknown, and ACES provides the first opportunity to study these enigmatic features throughout the CMZ. We release the HNCO and HCO$^{+}$ cubes for all 45 ACES fields, along with the full cube mosaics which combine all fields into a contiguous mosaic of the CMZ. We additionally provide advanced products of these full mosaics, including integrated and peak intensity, noise, and position-velocity maps. These products provide substantial legacy value for the community, offering an unparalleled view of the physical and kinematic structure of the dense gas in the CMZ.

astro-ph.GA↗

arXiv2026

ALMA Central Molecular Zone Exploration Survey (ACES) I: Overview

The mass flows and energy cycles within the inner regions of galaxies exert a powerful influence on the evolution of the galaxy population. The centre of the Milky Way is the only galactic nucleus for which it is possible to resolve the physical mechanisms that drive these cycles, namely star formation and feedback, while also tracing global (>100 pc) processes which determine where and when star formation and feedback occur. We present an overview of ACES, the 'Atacama Large Millimeter/submillimeter Array (ALMA) CMZ Exploration Survey', a ~1.5" angular resolution, 0.2-3 km/s spectral resolution ALMA Band 3 (85-102 GHz), survey of the 'Central Molecular Zone' (CMZ) -- the inner-100 pc of the Galaxy (l = 359.4 deg to 0.8 deg). ACES spectral setup is tuned to observe optimal tracers of the physical, chemical, and kinematic conditions in over 70 spectral features (e.g. HCO+, HNCO, SiO, H40alpha, complex molecules) of the gas in the CMZ, to derive the properties of all potentially star-forming Galactic Centre gas, from global scales (100 pc) to dense ~0.05 pc structures that are expected to host individual star-forming cores, down to sub-sonic (<0.4 km/s) velocity resolution. In this overview paper, we provide the scientific justification for the ACES survey, explain the choice of observational setup, and describe the data legacy products. Finally, we show some of the initial ACES data which highlight the power of ACES' combination of high angular resolution, unprecedented spatial dynamic range, sensitivity, spectral resolution and spectral bandwidth as an illustration of how ACES aims to understand how global processes set the location, intensity, and timescales for star formation and feedback in the CMZ.

astro-ph.GA↗

arXiv2026

Digging into the Interior of Hot Cores with ALMA (DIHCA). VI. The Formation of Low-mass Multiple Systems in High-mass Cluster-forming Regions

Most stars form in multiple systems, with profound implications in numerous astronomical phenomena intrinsically linked to multiplicity. However, our knowledge about the process on how multiple stellar systems form is incomplete and biased toward nearby molecular clouds forming only low-mass stars, which are unrepresentative of the stellar population in the Galaxy. Most stars form within dense cores in clusters alongside high-mass stars (>8 M$_{\odot}$), as likely the Sun did. Here we report deep ALMA 1.33 mm dust continuum observations at ~160 au spatial resolution, revealing 72 low-mass multiple systems embedded in 23 high-mass cluster-forming regions, as part of the Digging into the Interior of Hot Cores with ALMA (DIHCA) survey. We find that the companion separation distribution presents a distinct peak at ~1200 au, in contrast to the one at ~4000 au observed in nearby low-mass regions. The shorter fragmentation scale can be explained by considering the higher pressure exerted by the surrounding medium, which is higher than the one in low-mass regions, due to the larger turbulence and densities involved. Because the peak of the companion separation distribution occurs at much larger scales than the expected disk sizes, we argue that the observed fragmentation is produced by turbulent core fragmentation. Contrary as predicted, the multiplicity fraction remains constant as the stellar density increases. We propose that in the extremely dense environments where high-mass stars form, dynamical interactions play an important role in disrupting weakly bound systems.

astro-ph.GA↗

arXiv2026

CH3CCH as a thermometer in warm molecular gas

Kinetic temperature is a fundamental parameter in molecular clouds. Symmetric top molecules, such as NH$_3$ and CH$_3$CCH, are often used as thermometers. However, at high temperatures, NH$_3$(2,2) can be collisionally excited to NH$_3$(2,1) and rapidly decay to NH$_3$(1,1), which can lead to an underestimation of the kinetic temperature when using rotation temperatures derived from NH$_3$(1,1) and NH$_3$(2,2). In contrast, CH$_3$CCH is a symmetric top molecule with lower critical densities of its rotational levels than those of NH$_3$, which can be thermalized close to the kinetic temperature at relatively low densities of about 10$^{4}$ cm$^{-3}$. To compare the rotation temperatures derived from NH$_3$(1,1)$\&$(2,2) and CH$_3$CCH rotational levels in warm molecular gas, we used observational data toward 55 massive star-forming regions obtained with Yebes 40m and TMRT 65m. Our results show that rotation temperatures derived from NH$_3$(1,1)$\&$(2,2) are systematically lower than those from CH$_3$CCH 5-4. This suggests that CH$_3$CCH rotational lines with the same $J$+1$\rightarrow$$J$ quantum number may be a more reliable thermometer than NH$_3$(1,1)$\&$(2,2) in warm molecular gas located in the surroundings of massive young stellar objects or, more generally, in massive star-forming regions.

astro-ph.GA↗

arXiv2026

Digging into the Interior of Hot Cores with ALMA (DIHCA). VII. Disk candidates around high-mass stars and evidence of anisotropic infall

We study the kinematics of condensations in 30 fields forming high-mass stars with ALMA at a high-resolution of ~0.08'' on average (~230 au). The presence of disks is important for feeding high-mass stars without feedback halting growth as their masses increase. In the search for velocity gradients resembling rotation that can reveal the presence of disks, we analyze the emission of gas tracers in 49 objects using CH$_3$OH, CH$_3$CN, and tentative detections of HNCO and cis-HCOOH. Most of the velocity distributions show velocity gradients indicative of rotation. We reveal a total of 32 disk candidates, the largest sample to date that has been uniformly analyzed at a few hundred au scales in the high-mass regime. Their position-velocity maps are generally asymmetric with one side brighter than the opposite. We successfully fit a power law to the position-velocity maps of the disk candidates and find indices between -0.5 (Keplerian rotation) and -1 (rotation under specific angular momentum conservation) with a median of -0.7. Under Keplerian rotation assumption, we estimate central masses, uncorrected for inclination, ranging between 7 to 45 M$_\odot$. Excluding outliers, the disk candidates are relatively more compact (<200 au) and less massive (<5 M$_\odot$) than previous results at coarser angular resolution. We calculate an average Toomre-$Q$ parameter and find that most are gravitationally unstable (median of 0.5). We conclude that these observations offer the first opportunity to separate the disk and envelope components of hot cores on a statistically significant sample, and confirm that anisotropic collapse plays an role in feeding high-mass (proto)stars.

astro-ph.SR↗

arXiv2026

Unveiling the 3D structure of the central molecular zone from stellar kinematics and photometry: The 50 and 20 km/s clouds

The central molecular zone (CMZ), surrounding the Galactic centre, is the largest reservoir of dense molecular gas in the Galaxy. Despite its relative proximity, the 3D structure of the CMZ remains poorly constrained, primarily due to projection effects. We aim to constrain the line-of-sight location of two molecular clouds in the CMZ -- the 50 and 20 km/s clouds -- and to investigate their possible physical connection using stellar kinematics and photometry. This study serves as a pilot for future applications across the full CMZ. We estimated the line-of-sight position of the clouds by analysing stellar kinematics, stellar densities, and stellar populations towards the cloud regions and a control field. We find an absence of westward moving stars in the cloud regions, which indicates that they lie on the near side of the CMZ. This interpretation is supported by the stellar density distributions. The similar behaviour observed in the two clouds, as well as in the region between them (the ridge), suggests that they are located at comparable distances and are physically linked. We also identified an intermediate-age stellar population (2-7 Gyr) in both regions, consistent with that observed on the near side of the CMZ. We estimated the line-of-sight distances at which the clouds and the ridge become kinematically detectable (i.e. where the proper motion component parallel to the Galactic plane differs from that of the control field at the 3 sigma level) by converting their measured proper motions parallel to the Galactic plane using a theoretical model of the stellar distribution. We find that the 50 and 20 km/s clouds are located at $43\pm8$ pc and $56\pm11$ pc from Sgr A*, respectively, and that the ridge lies at $56\pm11$ pc; this supports the idea that the clouds are physically connected through the ridge.

astro-ph.GA↗

arXiv2025

ACES: The Magnetic Field in Large Filaments in the Galactic Center

The Galactic Center (GC) is an extreme region of the Milky Way that is host to a complex set of thermal and non-thermal structures. In particular, the GC contains high-density gas and dust that is collectively referred to as the Central Molecular Zone (CMZ). In this work, we study a subset of HNCO filaments identified in band 3 ALMA observations of the GC obtained by the ALMA CMZ Exploration Survey (ACES) that are comparable to high density filaments identified in the Galactic Disk. We compare the orientation of the magnetic field derived from 214 um SOFIA and 850 um JCMT observations with the filament orientation to determine which mechanisms dominate the formation of these filaments. We observe a large range of magnetic orientations in our observed filaments indicating the complex environments the filaments are located in. We also compare the observational results to synthetic data sets created using an MHD model of the GC. Our analysis reveals that the dominant mechanisms local to the HNCO filaments vary throughout the GC with some filaments being dominated by supersonic turbulence and others by subsonic turbulence. The comparison to synthetic observations indicates that the observed filaments are in magnetically dominated environments that could be supporting these filaments against collapse. Our results on the CMZ filaments are also compared to results obtained on similar filaments located in the Galactic Disk, and we find that the filaments studied here are possible CMZ analogs to the dense filamentary "bones" observed previously in the Galactic Disk.

astro-ph.GA↗

arXiv2025

Tails of Gravity: Persistence of Star Formation in the CMZ Environment

We characterize star-forming gas in six molecular clouds (Sgr B1-off, Sgr B2, Sgr C, the 20 km s$^{-1}$ and 50 km s$^{-1}$ molecular clouds, and the Brick) in the Galactic central molecular zone (CMZ), and compare their star-forming activities with those in molecular clouds outside the CMZ. Using multi-band continuum observations taken from ${\it Planck}$, ${\it Herschel}$, JCMT/SCUBA-2, and CSO/SHARC2, we derived 8.5" resolution column density maps for the CMZ clouds and evaluated the column density probability distribution functions (N-PDFs). With the archival Atacama Large Millimeter/submillimeter Array (ALMA) 1.3 mm dust continuum data, we further evaluated the mass of the most massive cores ($M_{\rm core}^{\rm ma x}$). We find that the N-PDFs of four of the selected CMZ clouds are well described by a piecewise log-normal + power-law function, while the N-PDFs of the remaining two can be approximated by log-normal functions. In the first four targets, the masses in the power-law component ($M_{\rm gas}^{\rm bound}$), $M_{\rm core}^{\rm max}$, and star formation rate (SFR) are correlated. These correlations are very similar to those derived from low-mass clouds in the Solar neighborhood and massive star-forming regions on the Galactic disk. These findings lead to our key hypotheses: (1) In the extreme environment of the CMZ, the power-law component in the N-PDF also represents self-gravitationally bound gas structures, and (2) evolution and star-forming activities of self-gravitationally bound gas structures may be self-regulated, insensitive to the exterior environment on $\gtrsim$5-10 pc scales.

astro-ph.GA↗

arXiv2025

The ALMA Survey of 70 μm Dark High-mass Clumps in Early Stages (ASHES). XIII. Core Mass Function, Lifetime, and Growth of Prestellar Cores

The core mass function (CMF) of prestellar cores is essential for understanding the initial conditions of star and cluster formation. However, the universality of the CMF and its relationship to the initial mass function (IMF) remain unclear. We study the CMF in the earliest stage of high-mass star formation using 461 prestellar core candidates and 254 protostellar cores as a part of the ALMA Survey of 70 μm Dark High-mass Clumps in Early Stages (ASHES). We find that prestellar core candidates tend to have lower masses than protostellar cores. We also find that the lifetime of prestellar cores is several times longer than the freefall time, although it approaches the freefall time as the core mass increases. The CMF, including both protostellar and prestellar cores, has a power-law slope of $-2.05\pm0.04$, shallower than Salpeter's IMF slope of -2.35. Conversely, the CMF of gravitationally bound, prestellar cores has a steeper slope ($-2.32\pm0.30$), indistinguishable from Salpeter's slope. This finding is consistent with observations in both low-mass star-forming regions and high-mass protoclusters, implying a universal core formation mechanism. The protostellar CMF with a larger maximum core mass can be reproduced by the prestellar CMF when an external gas infall is considered. The inferred mass infall rate is higher than the Bondi-Hoyle-Lyttleton accretion rate and follows a shallower mass dependence (smaller power-law index), more consistent with the tidal-lobe accretion. This may contribute to the evolution of CMFs seen in later stages.

astro-ph.GA↗

arXiv2025

The JWST Galactic Center Survey -- A White Paper

The inner hundred parsecs of the Milky Way hosts the nearest supermassive black hole, largest reservoir of dense gas, greatest stellar density, hundreds of massive main and post main sequence stars, and the highest volume density of supernovae in the Galaxy. As the nearest environment in which it is possible to simultaneously observe many of the extreme processes shaping the Universe, it is one of the most well-studied regions in astrophysics. Due to its proximity, we can study the center of our Galaxy on scales down to a few hundred AU, a hundred times better than in similar Local Group galaxies and thousands of times better than in the nearest active galaxies. The Galactic Center (GC) is therefore of outstanding astrophysical interest. However, in spite of intense observational work over the past decades, there are still fundamental things unknown about the GC. JWST has the unique capability to provide us with the necessary, game-changing data. In this White Paper, we advocate for a JWST NIRCam survey that aims at solving central questions, that we have identified as a community: i) the 3D structure and kinematics of gas and stars; ii) ancient star formation and its relation with the overall history of the Milky Way, as well as recent star formation and its implications for the overall energetics of our galaxy's nucleus; and iii) the (non-)universality of star formation and the stellar initial mass function. We advocate for a large-area, multi-epoch, multi-wavelength NIRCam survey of the inner 100\,pc of the Galaxy in the form of a Treasury GO JWST Large Program that is open to the community. We describe how this survey will derive the physical and kinematic properties of ~10,000,000 stars, how this will solve the key unknowns and provide a valuable resource for the community with long-lasting legacy value.

astro-ph.GA↗

arXiv2025

Widespread Hot Molecular Gas Heated by Shear-induced Turbulence in the Galactic Center

We observed NH3 metastable inversion lines from (3, 3) to (18, 18) toward G0.66-0.13 in the Galactic center with the Shanghai Tianma 65m radio telescope and Yebes 40 m telescope. Highly-excited lines of NH3 (17, 17), (18, 18) were detected in emission for the first time in the interstellar medium, with upper energy levels up to 3100 K. Mapping observations reveal widespread hot molecular gas traced by NH3 (13, 13) toward G0.66-0.13. The rotation temperatures of hot gas traced by NH3 exceed 400 K, which amounts to five percent of the total NH3 in the Galactic Center. Hot gas (>400 K) and warm gas (100-140 K) are found in distinct clumps, with the hot gas located at the interfacing regions between different warm clouds. The theory of intermittency in turbulence reproduces the complex temperature structure in the central molecular zone, especially the hot gas observed here. The results presented here demonstrate that turbulence heating dominates the heating of the molecular gas in the Central Molecular Zone, while the turbulence is induced by the shear-motion of molecular clouds under the gravitational potential of the nuclear star clusters and the supermassive black hole. Our results suggest that shear-induced turbulence heating could be a widespread factor influencing galactic evolution.

astro-ph.GA↗

arXiv2025

Automating Modelica Module Generation Using Large Language Models: A Case Study on Building Control Description Language

Dynamic energy systems and controls require advanced modeling frameworks to design and test supervisory and fault tolerant strategies. Modelica is a widely used equation based language, but developing control modules is labor intensive and requires specialized expertise. This paper examines the use of large language models (LLMs) to automate the generation of Control Description Language modules in the Building Modelica Library as a case study. We developed a structured workflow that combines standardized prompt scaffolds, library aware grounding, automated compilation with OpenModelica, and human in the loop evaluation. Experiments were carried out on four basic logic tasks (And, Or, Not, and Switch) and five control modules (chiller enable/disable, bypass valve control, cooling tower fan speed, plant requests, and relief damper control). The results showed that GPT 4o failed to produce executable Modelica code in zero shot mode, while Claude Sonnet 4 achieved up to full success for basic logic blocks with carefully engineered prompts. For control modules, success rates reached 83 percent, and failed outputs required medium level human repair (estimated one to eight hours). Retrieval augmented generation often produced mismatches in module selection (for example, And retrieved as Or), while a deterministic hard rule search strategy avoided these errors. Human evaluation also outperformed AI evaluation, since current LLMs cannot assess simulation results or validate behavioral correctness. Despite these limitations, the LLM assisted workflow reduced the average development time from 10 to 20 hours down to 4 to 6 hours per module, corresponding to 40 to 60 percent time savings. These results highlight both the potential and current limitations of LLM assisted Modelica generation, and point to future research in pre simulation validation, stronger grounding, and closed loop evaluation.

cs.SE↗

arXiv2025

Detection of a septuple stellar system in formation via disk fragmentation

Stellar multiple systems play a pivotal role in cluster dynamics and stellar evolution, leading to intense astronomical phenomena like X-ray binaries, gamma-ray bursts, Type Ia supernova, and stellar mergers, which are prime sources of gravitational waves. However, their origin remains poorly understood. Here we report the discovery of a septuple protostellar system embedded in a Keplerian disk within the high-mass star-forming region NGC\,6334IN, with close separations of 181-461 AU. The stability analysis reveals that the disk surrounding the septuple system is dynamically unstable, indicating that the septuple system formed via disk fragmentation. Previous studies have typically found only 2--3 members forming via disk fragmentation in both low- and high-mass star-forming regions. Our findings provide compelling observational evidence that the fragmentation of a gravitationally unstable disk is a viable mechanism for the formation of extreme high-order multiplicity, confirming what was previously only a theoretical concept. The results shed new light on the formation of extreme high-order multiplicity in cluster environments.

astro-ph.GA↗

arXiv2025

Massive extended streamers feed high-mass young stars

Stars are born in a variety of environments that determine how they gather gas to achieve their final masses. It is generally believed that disks are ubiquitous around protostars as a result of angular momentum conservation and are natural places to grow planets. As such, they are proposed to be the last link in the inflow chain from the molecular cloud to the star. However, disks are not the only form that inflows can take. Here we report on high-resolution observations performed with the Atacama Large Millimeter/submillimeter Array that reveal inflows in the form of streamers. These streamers persist well within the expected disk radius, indicating that they play a substitute role channeling material from the envelope directly to an unresolved small disk or even directly to the forming high-mass protostar. These flows are massive enough to feed the central unresolved region at a rate sufficient to quench the feedback effects of the young massive star.

astro-ph.GA↗

arXiv2025

Chemical templates of the Central Molecular Zone. Shock and protostellar object signatures under Galactic Center conditions

(Abridged) The Central Molecular Zone (CMZ) of the Milky Way exhibits extreme conditions, including high gas densities, elevated temperatures, enhanced cosmic-ray ionization rates, and large-scale dynamics. Large-scale molecular surveys reveal increasing chemical and physical complexity in the CMZ. A key step to interpreting the molecular richness found in the CMZ is to build chemical templates tailored to its diverse conditions. The combined impact of high ionization, elevated temperatures, and dense gas remains insufficiently explored for observable tracers. In this study, we utilized UCLCHEM, a gas-grain time-dependent chemical model, to link physical conditions with their corresponding molecular signatures and identify key tracers of temperature, density, ionization, and shock activity. We ran a grid of models of shocks and protostellar objects representative of typical CMZ conditions, focusing on twenty-four species, including complex organic molecules. Shocked and protostellar environments show distinct evolutionary timescales ($\lesssim 10^4$ vs. $\gtrsim 10^4$ years), with 300 K emerging as a key temperature threshold for chemical differentiation. We find that cosmic-ray ionization and temperature are the main drivers of chemical trends. HCO$^+$, H$_2$CO, and CH$_3$SH trace ionization, while HCO, HCO$^+$, CH$_3$SH, CH$_3$NCO, and HCOOCH$_3$ show consistent abundance contrasts between shocks and protostellar regions over similar temperature ranges. While our models underpredict some complex organics in shocks, they reproduce observed trends for most species, supporting scenarios involving recurring shocks in Galactic Center clouds and enhanced ionization towards Sgr B2(N2). Future work should assess the role of shock recurrence and metallicity in shaping chemistry.

astro-ph.GA↗

arXiv2025

Network of velocity-coherent filaments formed by supersonic turbulence in a very-high-velocity HI cloud

The warm neutral medium (WNM) was thought to be subsonically/transonically turbulent, and it lacks a network of intertwined filaments that are commonly seen in both molecular clouds and cold neutral medium (CNM). Here, we report HI~21 cm line observations of a very-high-velocity (-330 km s$^{-1}$ $<V_{\rm LSR}<$ -250 km s$^{-1}$) cloud (VHVC), using the Five-hundred-meter Aperture Spherical radio Telescope (FAST) with unprecedented resolution and sensitivity. For the first time, such a VHVC is clearly revealed to be a supersonic WNM system consisting of a network of velocity-coherent HI~filaments. The filaments are in the forms of slim curves, hubs, and webs, distributed in different layers within the position-position-velocity ({\it ppv}) data cube. The entire cloud has skewed log-normal probability distribution of column density and the filaments themselves show asymmetrical radial density profiles, indicating shock compression by supersonic magnetohydrodynamic (MHD) turbulence, as is also confirmed by our MHD simulation (sonic Mach number $M_{\rm s}=3$ and Alfvén Mach number $M_{\rm A}=1$). This work suggests that hierarchical filaments can be established by shocks in a low-density WNM, where gravity is negligible, offering a viable pathway to structure formation in the earliest evolutionary phases of the interstellar medium (ISM).

astro-ph.GA↗

arXiv2025

Super-Jeans fragmentation in massive star-forming regions revealed by triangulation analysis

Understanding the fragmentation of the gas cloud and the formation of massive stars remains one of the most challenging questions of modern astrophysical research. Either the gas fragments in a Jeans-like fashion, after which the fragments grow through accretion, or the fragmentation length is larger than the Jeans length from the start. Despite significant observational efforts, a consensus has not been reached. The key is to infer the initial density distribution upon which gravitational fragmentation occurs. Since cores are the products of the fragmentation process, the distances between adjacent cores serve as a scale indicator. Based on this observation, we propose a Delaunay triangulation-based approach to infer the density structure before the fragmentation and establish the link between density distribution and gas fragmentation length. We find that at low density, the fragmentation is Jeans-like, and at high densities, the core separations are larger than the prediction of the Jeans fragmentation. This super-Jeans fragmentation is a key step toward the formation of massive stars.

astro-ph.GA↗

arXiv2025

Gravitationally Bound Gas Determines Star Formation in the Galaxy

Stars form from molecular gas under complex conditions influenced by multiple competing physical mechanisms, such as gravity, turbulence, and magnetic fields. However, accurately identifying the fraction of gas actively involved in star formation remains challenging. Using dust continuum observations from the Herschel Space Observatory, we derived column density maps and their associated probability distribution functions (N-PDFs). Assuming the power-law component in the N-PDFs corresponds to gravitationally bound (and thus star-forming) gas, we analyzed a diverse sample of molecular clouds spanning a wide range of mass and turbulence conditions. This sample included 21 molecular clouds from the solar neighborhood ($d<$500 pc) and 16 high-mass star-forming molecular clouds. For these two groups, we employed the counts of young stellar objects (YSOs) and mid-/far-infrared luminosities as proxies for star formation rates (SFR), respectively. Both groups revealed a tight linear correlation between the mass of gravitationally bound gas and the SFR, suggesting a universally constant star formation efficiency in the gravitationally bound gas phase. The star-forming gas mass derived from threshold column densities ($N_{\mbox {threshold}}$) varies from cloud to cloud and is widely distributed over the range of $\sim$1--17$\times$10$^{21}$ cm$^{-2}$ based on N-PDF analysis. But in solar neighborhood clouds, it is in rough consistency with the traditional approach using $A_{\rm V}$ $\ge$ 8 mag. In contrast, in high turbulent regions (e.g., the Central Molecular Zone) where the classical approach fails, the gravitationally bound gas mass and SFR still follow the same correlation as other high-mass star-forming regions in the Milky Way. Our findings also strongly support the interpretation that gas in the power-law component of the N-PDF is undergoing self-gravitational collapse to form stars.

astro-ph.GA↗