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Xing Lu

Publications and source records attributed to Xing Lu.

At least 19 recordsLinked to original sources

ACES VIII: A Survey of Compact, High-Velocity Features Observed in CS(2-1)

The extreme kinematics of the Milky Way's Central Molecular Zone (CMZ) are influenced by processes such as dynamical shearing, cloud collisions, and stellar feedback. These events are visible in molecular data as vertically spiked features in position-velocity (PV) diagrams referred to as high velocity dispersion compact clouds (HVCCs). Using ALMA CMZ Exploration Survey (ACES) CS (2-1) molecular data, we identify a total of 235 HVCC candidates, 163 of which are visually identified, and an additional 72 identified via automated dendrogram methods. For each HVCC we catalog and report the physical and kinematic properties, explore line ratios of the cold dense gas tracer \HNCO with C-shock tracers, classify the morphology of their PV diagrams, and view their position-position-velocity distribution. The sample includes structures which are compact (d<5 pc) and have large velocity extents (20 km/s $<\Delta \mathrm{V} <$ 140 km/s), with most structures showing thin, `spiked' PV morphologies. We highlight areas of high ratios between HNCO and C-shock tracers along the edge of known orbital streams, implying a buildup of bar lane gas accreting onto the CMZ. We also find a collection of HVCCs overlapping with the 50 km/s cloud and known circumnuclear disk features. This catalog will be used for future investigation of nuclear inflow and determining dominant mechanisms disrupting average CMZ gas flows.

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ACES VII. Compact Continuum Source Catalog of the Central Molecular Zone

The Central Molecular Zone (CMZ) resides in the inner few hundred parsecs of our Galaxy, and despite being the largest reservoir of dense molecular gas in the Milky Way, it has a relatively low present-day star formation rate (SFR) of $\sim0.08~M_{\odot}~\text{yr}^{-1}$. Continuum and spectral line observations from the Atacama Large Millimeter/submillimeter Array (ALMA) CMZ Exploration Survey (ACES) provide the first full-coverage, high-resolution map of the inner 200 parsecs of the CMZ at 3 mm. In this paper we present the ACES catalog of compact continuum sources, the most complete catalog of potential sites of star formation in the CMZ to date. Using an automated dendrogram-based source extraction procedure in combination with a by-eye morphological classification scheme, we produce a `full' catalog of 1735 detections in total. Additionally, we use spectral index measurements to generate a `filtered' catalog of 567 sources with minimal contamination from non-thermal filaments and extended free-free emission. We find that 359 ($\sim63\%$) of the filtered catalog sources are located at column densities $< 10^{23}$ cm$^{-2}$, outside of the densest molecular cloud regions, 195 of which have not been identified in previous surveys. After cross-referencing with various catalogs generated from data at different wavelengths, we consider it likely that many of these newly discovered detections are produced by pre/protostellar sources or compact HII regions.

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Dense Cores in the Vicinity of an HII Region

Massive stars strongly influence their surroundings through radiative and mechanical feedback, but its effects on dense gas structures at sub-pc scales remain poorly constrained. We investigate how feedback from a newly formed massive star affects dense cores in the filamentary molecular cloud IRAS 18530+0215. We analyze ALMA Band 6 observations of 1.3 mm dust continuum and DCN, N$_2$D$^+$, and $^{13}$CS line emission, together with VLA K-band continuum and NH$_3$ observations. Dense cores are identified with astrodendro, and their temperatures, masses, velocity dispersions, and virial parameters are derived. The dynamical state of the ultra-compact H II region is examined through energy and pressure estimates. The H II region has a radius of $\sim$0.1 pc and an expansion velocity of $\sim$2.5 km s$^{-1}$, corresponding to a shell dynamical age of $\sim$0.06 Myr. DCN and $^{13}$CS cores are concentrated near the H II region, whereas N$_2$D$^+$ cores preferentially lie farther away. Core temperatures and velocity dispersions decrease with projected distance from the H II region. Virial parameters increase within the inner $\sim$0.3 pc but decline sharply beyond this scale, while core masses show no significant trend with distance. Strong star formation signatures are found at $\sim$0.2 pc, whereas more distant regions still host quiescent, cold dense cores. The compact H II region appears trapped or choked within $\sim$0.1 pc, while its feedback extends to at least $\sim$0.3 pc. Within this region, feedback enhances core velocity dispersions, gas temperatures, and virial parameters, with no evidence that it promotes the formation of more massive dense cores.

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MIAO-ALMA: Shocks and Protostellar Outflows in 70 $\mu$m-dark clumps with $L/M$ $<$ 1 $L_{\odot}$/$M_{\odot}$

To investigate the initial conditions of high-mass star-forming regions, we use SiO (2-1) emission to trace early shock-related kinematics toward sixteen 70 $\mu$m-dark and massive clumps with luminosity-to-mass ratios ($L/M$) $< 1\,L_{\odot}/M_{\odot}$, as part of the Multiwavelength Line-Imaging Survey of the 70 $\mu$m-dark and bright clouds (MIAO) project. Using ALMA observations at a spatial resolution of $\sim$0.06 pc and a velocity resolution of 0.21 km s$^{-1}$, we identify a total of thirty-seven outflows with a variety of morphologies. Outflow parameters were derived by integrating the HCO$^+$ (1-0) line wings, excluding the quiescent dense core component traced by H$^{13}$CO$^+$ (1-0). We find that outflow masses and velocities show moderate positive correlations with the masses of their driving cores. Owing to the high sensitivity of our observations, which yield longer projected outflow lengths compared to previous studies, the derived outflow dynamical ages span $\sim10^{3}$-$10^{5}$ yr. We detect six narrow-linewidth (0.6-1.4 km s$^{-1}$) and three broad ($>$ 2 km s$^{-1}$) SiO (2-1) features not associated with outflows driven by clearly identified protostars. Lacking coincident 3 mm dust continuum cores, their origins may be young outflows from undetected low-mass protostars, dissipating shocks, cloud-cloud collisions, or projection effects when the outflows lie close to the plane of the sky. The detection of these shocks and outflows in such extremely young environments demonstrates that protostellar activity has already begun.

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Electron temperature and emission measure of HII regions in the central molecular zone (CMZ) from H40 \alpha recombination line and continuum emissions by ALMA CMZ Exploration Survey - ACES -

Star formation activity in the Central Molecular Zone (CMZ) directly manifests itself as radio continuum free-free emission (Bremsstrahlung) and radio recombination line emission from HII regions surrounding newly formed massive stars. We derive the overall distribution of the HII regions and their fundamental properties: electron temperature ($\Te$) and emission measure ($EM$), and hence electron density in the form of two dimensional distribution maps over the CMZ by analyzing the ACES (ALMA CMZ Exploration Survey) \h40 (99.02 GHz) recombination line and 99.6 GHz continuum emission data with synthesized beam widths of $2''.45$ (0.097 pc at 8.2 kpc) and $2''.14$, respectively. We apply the 'TeEM' method ($\Te$--$EM$ mapping), which creates $\Te$ and $EM$ maps from input 2D maps of the continuum and integrated line intensity. The analysis covers the entire ACES field from $l\sim -0^\circ.6$ to $+0^\circ.8$ and from $b\sim -0^\circ.2$ to $+0^\circ.1$. The area analyzed is complete and includes previously known HII regions such as Sgr B2, Sgr B1, the Sickle, the Pistol, thermal filaments (Bridges), Sgr A HII regions, the Minispiral, and many other known HII regions. Sgr C is not included in the analysis due to the insufficient signal-to-noise ratio in the recombination line map. The mean electron temperature over the CMZ is determined to be $\Tcmz= 5872 \pm 78 ~{\rm (SE)} ~\pm 3682~{\rm (SD)}$ K (SE:standard error of the mean, SD: pixel-to-pixel standard deviation). Some HII regions, such as Sgr B2 Main and the Minispiral, exhibit large scatter and an internal $\Te$ gradient of several thousand K per parsec. The $EM$ distribution is more diverse, varying by orders of magnitude from $\sim 10^5$ to $\sim 3\times 10^8$ \emunit within the CMZ, as well as within individual HII regions.

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Effects of low resolution on the column density PDF of molecular clouds

Observational resolution significantly impacts the interpretation of column density probability distribution functions (N-PDFs) in molecular clouds, which are essential for understanding turbulent structures and star formation processes. This study quantifies how low spatial resolution truncates the high-density power-law tails of N-PDFs by simulating distant observations (2-10 kpc) of 17 local massive molecular clouds/regions using Herschel-based column density maps. We propose a parameter-free model, assuming proportional embedding of dense regions within lower-density gas, to predict the truncation column density where the survival function equals the beam-to-threshold area ratio. Comparisons with simulations show good agreement, with deviations up to 0.3 dex attributed to cloud multiplicity in large complexes and flatter power-law tails in coherent structures. Characteristic cloud scales, derived from Delta-variance spectra, indicate that global smearing dominates when beam sizes exceed these scales. We further develop a reverse method to recover the intrinsic high-density tail from low-resolution data. Our findings link N-PDF shapes to morphologies, suggesting that feedback-compressed extended structures resist smearing, while multiplicity accelerates truncation. These insights caution against biases in N-PDF decompositions and provide a framework for correcting resolution effects in distant cloud studies, enhancing constraints on star formation theories.

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Magnetic Fields in Massive Star-forming Regions (MagMaR). VII. On the dynamical importance of B-fields in massive protocluster W33 A

Magnetic fields (B-fields) are likely important in massive protocluster formation, but their role remains poorly constrained. We present 1.2 mm ALMA full-polarization observations of W33 A, a massive star-forming region at 2.4 kpc, with an angular resolution of 0.3 arcsec (730 au). The region is resolved into 20 dense cores and 9 filaments. The plane-of-sky B-field, inferred from linearly polarized dust emission, shows diverse structures: two nearly perpendicular large-scale components oriented northwest-southeast (NW-SE) and northeast-southwest (NE-SW), and two localized features toward the millimeter peaks MM1 and MM2. The NW-SE component could be shaped by a molecular outflow. The NE-SW component is coherent along the main filaments F1, F-Main, and Tail, all of which show trans-Alfvenic turbulence. In F-Main, the line mass exceeds the turbulent critical value, implying that magnetic support is required to prevent radial collapse and suppress fragmentation. In F1 and Tail, turbulence alone can support the gas against gravity, although B-fields may provide additional support. Toward MM1, the B-field follows a spiral-like infalling streamer traced by CH3CN. The trans-Alfvenic state of the accreting gas suggests efficient magnetic damping of turbulence and a magnetically regulated, laminar accretion flow feeding the core. Toward MM2, the B-field shows an hourglass morphology fitted by parabolic curves. Two independent methods give a consistent field strength of about 8.1(1.9) mG, and virial analysis indicates that the B-field is dynamically important in delaying collapse of MM2. Within a single protocluster, B-fields can stabilize filaments, regulate accretion, and delay core collapse, highlighting their diverse dynamic role in high-mass star formation.

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Mass Segregation in the CMZoom Survey

We employ a Minimum Spanning Tree (MST) approach to characterize the spatial distribution and mass segregation of compact millimeter continuum sources within the Central Molecular Zone (CMZ) of the Milky Way. We use a modified form of the complete version of the 1.3 mm dust continuum catalog from the CMZoom survey, which identifies 685 compact sources with typical effective radii of $\sim0.1$ pc. For 22 of 35 CMZ clouds, we calculate the thermal and turbulent Jeans lengths and masses, and determine that compact source separations, as well as compact source masses, are more consistent with thermal fragmentation at $\sim0.1$ pc size scales. We construct the mass segregation ratios for compact sources in 17 CMZ clouds and determine that 5 of the analyzed clouds display some form of mass segregation ($\Lambda_{MSR} > 1.5$), while the remaining clouds show either inverse mass segregation ($\Lambda_{MSR} < 0.75$), or no evidence of true mass segregation ($0.75 < \Lambda_{MSR} < 1.5$). Finally, we find that although some actively star-forming clouds do exhibit mass segregation, other similarly active clouds do not, indicating an unclear correlation with evolutionary stage for star forming clouds in the CMZ, given the current available data.

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The Keplerian disk, envelope, and streamers surrounding an early O-type protostar in the Sagittarius C cloud of the Central Molecular Zone

Disk-mediated accretion is central to theories of massive star formation, setting the initial conditions for their evolution. Yet observations of Keplerian disks around early O-type protostars remain scarce, as they are often blended into complex surrounding structures. We report ALMA Band 6 observations (300 au resolution) of an accretion disk surrounding a high-mass protostar in the Sagittarius C (Sgr C) cloud in the Central Molecular Zone (CMZ) around the Galactic Center. We identify spectral lines and analyze the spatial distribution of the emission of the complex organic molecules. We use a dynamical model with an inner Keplerian disk and an outer free-fall envelope to fit the three-dimensional position-position-velocity data of the stacked CH$_3$OCHO molecular lines and constrain the mass of the central protostar to be $\sim40^{+2}_{-3} M_{\odot}$. The fitting results additionally show that the disk has a centrifugal radius at about 1300 au. Considering the infall velocity, radius, and mass of the envelope, we estimate the accretion rate from the envelope onto the disk to be $\sim7\times 10^{-3}\ M_{\odot}\,\mathrm{yr^{-1}}$. We also identify spiral-like structures in the disk that can be described by free-falling streamers. Our results highlight the critical role of accretion disks and streamers in the mass accumulation of early O-type stars in the CMZ.

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What Heats the Dense Gas in the Galactic Center?

Previous studies using p-H$_2$CO $J=3$--$2$ transitions at 218 GHz suggested widespread high-temperature gas exceeding 60 K and even 100 K in the CMZ, with heating mechanisms possibly related to cosmic rays or turbulent dissipation. However, at temperatures above 100 K, p-H$_2$CO $J=3$--$2$ line emission may lead to significant overestimates of kinetic temperature. This study combines o-H$_2$CO $J=5$--$4$ data from JCMT with p-H$_2$CO $J=3$--$2$ data from APEX to analyze three molecular clouds (The Brick, Sgr A1, and Sgr A2) with high temperatures. We used the non-LTE radiative transfer code RADEX to model spectral lines and constrain physical parameters with multiple line ratios, obtaining more reliable kinetic temperatures. Our results show that the previously reported extreme temperatures ($>100$ K) based on p-H$_2$CO $J=3$--$2$ line ratios are revised downward, with the average kinetic temperatures now constrained to 84--95 K using o-H$_2$CO $J=5$--$4$ line ratios, indicating systematic overestimation in the earlier studies. Further analysis reveals that the relationship between temperature and gas line width aligns more closely with predictions from models incorporating both high cosmic ray ionization rate and turbulent heating, suggesting that these molecular clouds are likely heated by a combination of cosmic-ray and turbulent dissipation mechanisms.

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The dominance of turbulence over magnetism in the formation of massive star cluster seeds

High-mass stars form in protoclusters, where gravo-magnetic processes shape collapsing clouds and clumps to be elongated preferentially perpendicular to magnetic (B) fields. Yet it remains unclear whether gravo-magnetic processes still govern the formation of smaller-scale condensations in massive-star-forming protoclusters, which are crucial for understanding the stellar initial mass function and multiplicity. Here we report the first statistical evidence that the condensation elongations are preferentially aligned with local B fields, based on high-resolution data from the largest dust polarization survey toward 30 massive star-forming regions with the Atacama Large Millimeter/submillimeter Array (ALMA). Our clustered massive star formation simulations reveal that this more parallel alignment is exclusively observed in models where initial turbulence dominates B fields. In contrast, models with initial B fields dominating turbulence distinctly exhibit a more perpendicular alignment. The comparison between observations and simulations suggests that turbulence could play a more important role than B fields in the formation of condensations in the context of clustered massive star formation, contradicting the prediction of classical magnetically regulated models. Moreover, we find a possibly turbulence-induced preferential misalignment between the B field and rotation axis of condensations, which may potentially reduce the magnetic braking efficiency and facilitate the formation of large protostellar disks. Our findings indicate that turbulence could be critical in determining the initial stellar properties.

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ALMA Central molecular zone Exploration Survey (ACES) V: CS(2-1), SO(2_3-1_2), CH3CHO(5_1,4-4_1,3), HC3N(11-10), and H40a lines data

We present data from the ALMA Central Molecular Zone Exploration Survey (ACES) Large Program, which provides broad spectral-line and 3 mm continuum coverage of the Central Molecular Zone (CMZ) at a spatial resolution of 0.1 pc. The survey delivers homogeneous, wide-field mosaics that enable direct comparisons of the physical and chemical conditions across diverse environments in the Galactic center. In this data release paper, we present the CS(2-1), SO(2_3-1_2), CH3CHO(5_1,4-4_1,3), HC3N(11-10), and H40a lines observed simultaneously within two broad spectral windows. These lines reveal pronounced spatial and chemical variations across the CMZ, tracing distinct components of molecular gas, shock-affected regions, and ionized structures. The high angular resolution and multi-line capability of the ACES dataset make it a powerful resource for future studies of gas dynamics, star formation activity, and the physical connection between the CMZ and Sgr A*.

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ALMA Central Molecular Zone Exploration Survey (ACES)-IV. Data of the two intermediate-width spectral windows

We release the intermediate-width spectral window data from the ALMA Central Molecular Zone Exploration Survey (ACES) Large Program, which covers SiO(2-1), SO(2_2-1_1), H13CO+(1-0), H13CN(1-0), HN13C(1-0), and HC15N (1-0), among other molecular line transitions, with an angular resolution of ~2 arcsec and a velocity resolution of 1.7 km s-1 . The full cubes of the two spectral windows as well as the key data products will be available to the community. We also present the integrated brightness, peak brightness, centroid velocity, and Galactic longitude-velocity maps of the six lines. We briefly discuss morphological correlations between the continuum and the molecular line emission, and brightness ratios between pairs of isotopologue or isotopomer lines. We highlight features and trends in the data that will be followed up in upcoming ACES science papers.

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ALMA Central Molecular Zone Exploration Survey (ACES) II: 3mm continuum images

The ALMA Central Molecular Zone Exploration Survey, ACES, has mapped $\gtrsim1000$ square arcminutes at 3 mm toward the center of our Galaxy. ACES provides the first large-scale, high-resolution ($\sim2.5$") view of the central $\sim200$ parsecs of the Milky Way. In this work, we describe the continuum data processing and present the continuum data products. In the combined mosaic of 45 individual ALMA mosaics, the typical RMS noise achieved is $\sim0.1$ mJy per $\sim2.5$" beam, though there is a tail of substantially higher noise toward regions with bright continuum structure, especially around Sgr A* and Sgr B2. In-band spectral indices are measurable for a small fraction of the brightest and most compact sources, enabling distinction between dust-dominated and free-free- or synchrotron-dominated sources. To recover emission on large angular scales, we present the GBT MUSTANG-2 Three millimeter Extended Nucleus Survey (TENS), a new 10"resolution survey of the CMZ, which we combine with the ACES image by feathering. To demonstrate the quality and reliability of the ACES data, we compare to previously-published ALMA data obtained with higher resolution and sensitivity, finding overall good agreement with past results, but some disagreement toward the brightest sources.

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ALMA Central molecular zone Exploration Survey (ACES) VI: ALMA Large Program Reveals a Highly Filamentary Central Molecular Zone

The Central Molecular Zone (CMZ) of the Milky Way is the way station that primarily controls how much gas flows from the disk of the Galaxy towards the central nucleus. While this region is well documented to have extreme gas properties that clearly distinguish it from the rest of the Galaxy, the properties of the bulk molecular gas at high angular resolution are relatively unexplored. Band 3 data from the ALMA (Atacama Large Millimeter/Submillimeter Array) large program ACES (ALMA CMZ Exploration Survey) reveal the highly filamentary nature of CMZ molecular gas at high resolution (3" or 0.1pc) across the entire CMZ. Visual inspection of these data suggests that there are at least two general classes of elongated structures, which we identify as: i) large-scale (10 pc) filamentary structures (LFs) and ii) a ubiquitous population of small-scale (about 1 pc) filamentary structures (SFs). We present detailed morphological and kinematic properties towards three structures in each category, as well as their association with magnetic fields and the correlation of HNCO 4(0,4)-3(0,3) with other molecular species. Our investigation reveals that these structures are largely coherent in position-position-velocity space. The alignment with the magnetic field structure is mixed, with some parallel, some perpendicular, and some intermediate alignments. We find that LFs likely trace pieces of contiguous CMZ orbital structures and are a manifestation of global CMZ dynamics. The second class, SFs, are pervasive and may be the result of complicated turbulence and shearing dynamics in the CMZ gas flows, as seen in numerical simulations.

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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.

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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.

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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.

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