arXiv subjects

M. T. Beltran

Publications and source records attributed to M. T. Beltran.

At least 19 recordsLinked to original sources

arXiv2025

Filamentary accretion flows in high-mass star-forming clouds

We quantify the gas flows from a scale of up to several parsecs down to the sub-parsec scale along filamentary structures in the three high-mass star-forming regions G75.78, IRAS21078+5211 and NGC7538 with data obtained from the IRAM 30 m telescope. The analysis is carried out using the surface density derived from 1.2 mm continuum emission and velocity differences estimated from HCO$^+$ and H$^{13}$CO$^+$ molecular line data.

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arXiv2025

ALMAGAL I. The ALMA evolutionary study of high-mass protocluster formation in the Galaxy. Presentation of the survey and early results

Fundamental questions about the physics responsible for fragmenting molecular parsec-scale clumps into cores of ~1000 au are still open, that only a statistically significant investigation with ALMA is able to address: what are the dominant agents that determine the core demographics, mass, and spatial distribution as a function of the physical properties of the hosting clumps, their evolutionary stage and the different Galactic environments in which they reside? To what extent extent is fragmentation driven by clumps dynamics or mass transport in filaments? With ALMAGAL we observed the 1.38 mm continuum and lines toward more than 1000 dense clumps in our Galaxy, with M>500M_sun, surface density > 0.1 g/cm2 and d<7.5 kpc. The ACA and two 12-m array setups were used to deliver a minimum resolution of ~1000 au over the entire sample distance range. The sample covers all evolutionary stages from infrared dark clouds (IRDCs) to HII regions from the tip of the Galactic bar to the outskirts of the Galaxy. The spectral setup includes several molecular lines to trace the multiscale physics and dynamics of gas, notably CH3CN, H2CO, SiO, CH3OH, DCN, HC3N, SO etc. We present an initial overview of the observations and the early science product and results, with a first characterization of the morphological properties of the continuum emission. We use "perimeter-versus-area" and convex hull-versus-area metrics to classify the different morphologies. More extended and morphologically complex shapes are found toward clumps that are relatively more evolved and have higher surface densities.

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arXiv2023

Density distributions, magnetic field structures and fragmentation in high-mass star formation

Methods: Observing the large pc-scale Stokes I mm dust continuum emission with the IRAM 30m telescope and the intermediate-scale (<0.1pc) polarized submm dust emission with the Submillimeter Array toward a sample of 20 high-mass star-forming regions allows us to quantify the dependence of the fragmentation behaviour of these regions depending on the density and magnetic field structures. Results: We infer density distributions n~r^{-p} of the regions with typical power-law slopes p around ~1.5. There is no obvious correlation between the power-law slopes of the density structures on larger clump scales (~1pc) and the number of fragments on smaller core scales (<0.1pc). Comparing the large-scale single-dish density profiles to those derived earlier from interferometric observations at smaller spatial scales, we find that the smaller-scale power-law slopes are steeper, typically around ~2.0. The flattening toward larger scales is consistent with the star-forming regions being embedded in larger cloud structures that do not decrease in density away from a particular core. Regarding the magnetic field, for several regions it appears aligned with filamentary structures leading toward the densest central cores. Furthermore, we find different polarization structures with some regions exhibiting central polarization holes whereas other regions show polarized emission also toward the central peak positions. Nevertheless, the polarized intensities are inversely related to the Stokes I intensities. We estimate magnetic field strengths between ~0.2 and ~4.5mG, and we find no clear correlation between magnetic field strength and the fragmentation level of the regions. Comparison of the turbulent to magnetic energies shows that they are of roughly equal importance in this sample. The mass-to-flux ratios range between ~2 and ~7, consistent with collapsing star-forming regions.

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arXiv2022

CHEMOUT: CHEMical complexity in star-forming regions of the OUTer Galaxy. II. Methanol formation at low metallicity

The outer Galaxy is an environment with metallicity lower than the Solar one and, because of this, the formation and survival of molecules in star-forming regions located in the inner and outer Galaxy is expected to be different. To gain understanding on how chemistry changes throughout the Milky Way, it is crucial to observe outer Galaxy star-forming regions to constrain models adapted for lower metallicity environments. The project "chemical complexity in star-forming regions of the outer Galaxy" (CHEMOUT) aims to address this problem observing a sample of 35 high-mass star-forming cores at Galactocentric distances up to ~23 kpc with the IRAM 30m telescope in various 3mm and 2mm bands. In this work we analyse observations of methanol (CH3OH), one of the simplest complex organic molecules crucial for organic chemistry in star-forming regions, and of two chemically related species, HCO and formaldehyde (H2CO), towards 15 out of the 35 targets of the CHEMOUT sample. In fact, only targets previously detected in both HCO and H2CO, both precursors of methanol, were considered. We detected CH3OH in all 15 targets. Using a Local Thermodynamic Equilibrium approach, we derive CH3OH excitation temperatures in the range 7 - 16 K and line widths smaller than 4 km/s, consistent with emission from a cold and quiescent envelope. The CH3OH fractional abundances w.r.t. H2 range between ~0.6 x 10^{-9} and ~7.4 x 10^{-9}. These values are comparable to those found in star-forming regions in the inner and local Galaxy. Our results have important implications in the organic, and possibly pre-biotic, chemistry occurring in the outermost star-forming regions of the Galaxy, and can help setting the frontiers of the Galactic habitable zone.

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arXiv2021

Molecular cloud catalogue from $^{13}$CO(1-0) data of the Forgotten Quadrant Survey

New-generation spectroscopic surveys of the Milky Way plane have been revealing the structure of the interstellar medium, allowing the simultaneous study of dense structures from single star-forming objects or systems to entire spiral arms. We present the catalogue of molecular clouds extracted from the $^{13}$CO(1-0) data cubes of the Forgotten Quadrant Survey, which mapped the Galactic plane in the range 220°<l<240°, and -2.5°<b<0°in $^{12}$CO(1-0) and $^{13}$CO(1-0).The catalogue contains 87 molecular clouds for which the main physical parameters such as area, mass, distance, velocity dispersion, and virial parameter were derived. These structures are overall less extended and less massive than the molecular clouds identified in the $^{12}$CO(1-0) data-set because they trace the brightest and densest part of the $^{12}$CO(1-0) clouds. Conversely, the distribution of aspect ratio, equivalent spherical radius, velocity dispersion, and virial parameter in the two catalogues are similar. The mean value of the mass surface density of molecular clouds is 87$\pm$55 M$_{\odot}$ pc$^{-2}$ and is almost constant across the galactocentric radius, indicating that this parameter, which is a proxy of star formation, is mostly affected by local conditions.In data of the Forgotten Quadrant Survey, we find a good agreement between the total mass and velocity dispersion of the clouds derived from $^{12}$CO(1-0) and $^{13}$CO(1-0). This is likely because in the surveyed portion of the Galactic plane, the H$_2$ column density is not particularly high, leading to a CO emission with a not very high optical depth. This mitigates the effects of the different line opacities between the two tracers on the derived physical parameters. This is a common feature in the outer Galaxy, but our result cannot be readily generalised to the entire Milky Way.

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arXiv2021

Fragmentation and kinematics in high-mass star formation: CORE-extension targeting two very young high-mass star-forming regions

Context: The formation of high-mass star-forming regions from their parental gas cloud and the subsequent fragmentation processes lie at the heart of star formation research. Aims: We aim to study the dynamical and fragmentation properties at very early evolutionary stages of high-mass star formation. Methods: Employing the NOrthern Extended Millimeter Array (NOEMA) and the IRAM 30m telescope, we observed two young high-mass star-forming regions, ISOSS22478 and ISOSS23053, in the 1.3mm continuum and spectral line emission at a high angular resolution (~0.8''). Results: We resolved 29 cores that are mostly located along filament-like structures. Depending on the temperature assumption, these cores follow a mass-size relation of approximately M~r^2.0, corresponding to constant mean column densities. However, with different temperature assumptions, a steeper mass-size relation up to M~r^3.0, which would be more likely to correspond to constant mean volume densities, cannot be ruled out. The correlation of the core masses with their nearest neighbor separations is consistent with thermal Jeans fragmentation. We found hardly any core separations at the spatial resolution limit, indicating that the data resolve the large-scale fragmentation well. Although the kinematics of the two regions appear very different at first sight - multiple velocity components along filaments in ISOSS22478 versus a steep velocity gradient of more than 50km/s/pc in ISOSS23053 - the findings can be explained within the framework of a dynamical cloud collapse scenario. Conclusions: While our data are consistent with a dynamical cloud collapse scenario and subsequent thermal Jeans fragmentation, the importance of additional environmental properties, such as the magnetization of the gas or external shocks triggering converging gas flows, is nonetheless not as well constrained and would require future investigation.

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arXiv2021

The physical and chemical structure of high-mass star-forming regions. Unraveling chemical complexity with the NOEMA large program "CORE"

We use sub-arcsecond resolution ($\sim$0.4$''$) observations with NOEMA at 1.37 mm to study the dust emission and molecular gas of 18 high-mass star-forming regions. We combine the derived physical and chemical properties of individual cores in these regions to estimate their ages. The temperature structure of these regions are determined by fitting H2CO and CH3CN line emission. The density profiles are inferred from the 1.37 mm continuum visibilities. The column densities of 11 different species are determined by fitting the emission lines with XCLASS. Within the 18 observed regions, we identify 22 individual cores with associated 1.37 mm continuum emission and with a radially decreasing temperature profile. We find an average temperature power-law index of q = 0.4$\pm$0.1 and an average density power-law index of p = 2.0$\pm$0.2 on scales on the order of several 1 000 au. Comparing these results with values of p derived in the literature suggest that the density profiles remain unchanged from clump to core scales. The column densities relative to N(C18O) between pairs of dense gas tracers show tight correlations. We apply the physical-chemical model MUSCLE to the derived column densities of each core and find a mean chemical age of $\sim$60 000 yrs and an age spread of 20 000-100 000 yrs. With this paper we release all data products of the CORE project available at https://www.mpia.de/core. The CORE sample reveals well constrained density and temperature power-law distributions. Furthermore, we characterize a large variety in molecular richness that can be explained by an age spread confirmed by our physical-chemical modeling. The hot molecular cores show the most emission lines, but we also find evolved cores at an evolutionary stage, in which most molecules are destroyed and thus the spectra appear line-poor again.

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arXiv2020

The SEDIGISM survey: Molecular clouds in the inner Galaxy

We use the 13CO(2-1) emission from the SEDIGISM high-resolution spectral-line survey of the inner Galaxy, to extract the molecular cloud population with a large dynamic range in spatial scales, using the SCIMES algorithm. This work compiles a cloud catalogue with a total of 10663 molecular clouds, 10300 of which we were able to assign distances and compute physical properties. We study some of the global properties of clouds using a science sample, consisting of 6664 well resolved sources and for which the distance estimates are reliable. In particular, we compare the scaling relations retrieved from SEDIGISM to those of other surveys, and we explore the properties of clouds with and without high-mass star formation. Our results suggest that there is no single global property of a cloud that determines its ability to form massive stars, although we find combined trends of increasing mass, size, surface density and velocity dispersion for the sub-sample of clouds with ongoing high-mass star formation. We then isolate the most extreme clouds in the SEDIGISM sample (i.e. clouds in the tails of the distributions) to look at their overall Galactic distribution, in search for hints of environmental effects. We find that, for most properties, the Galactic distribution of the most extreme clouds is only marginally different to that of the global cloud population. The Galactic distribution of the largest clouds, the turbulent clouds and the high-mass star-forming clouds are those that deviate most significantly from the global cloud population. We also find that the least dynamically active clouds (with low velocity dispersion or low virial parameter) are situated further afield, mostly in the least populated areas. However, we suspect that part of these trends may be affected by some observational biases, and thus require further follow up work in order to be confirmed.

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arXiv2020

A search for radio jets from massive young stellar objects. Association of radio jets with H2O and CH3OH masers

Recent theoretical and observational studies debate the similarities between the formation process of high-mass (>8 Msun) and low-mass stars. The formation of low-mass star formation is directly associated with the presence of disks and jets. According to this scenario, radio jets are expected to be common in high-mass star-forming regions. We aim to increase the number of known radio jets in high-mass star forming regions by searching for radio jet candidates at radio continuum wavelengths. We have used the Karl G. Jansky Very Large Array (VLA) to observe 18 high-mass star-forming regions in the C band (6 cm, ~1.0 arcsec resolution) and K band (1.3 cm, ~0.3 arcsec resolution). We have searched for radio jet candidates by studying the association of radio continuum sources with shock activity signposts. We have identified 7 as the most probable radio jets. The radio luminosity of the radio jet candidates is correlated with the bolometric luminosity and the outflow momentum rate. About 7-36% of the radio jet candidates are associated with non-thermal emission. The radio jet candidates associated with 6.7 GHz CH3OH maser emission are preferentially thermal winds and jets, while a considerable fraction of radio jet candidates associated with H2O masers show non-thermal emission, likely due to strong shocks. Our sample of 18 regions is divided in 8 less evolved, infrared-dark regions and 10 more evolved, infrared-bright regions. We have found that ~71% of the identified radio jet candidates are located in the more evolved regions. Similarly, 25% of the less evolved regions harbor one of the most probable radio jets, while up to 50% of the more evolved regions contain one of these radio jet candidates. This suggests that the detection of radio jets in high-mass star forming regions is larger in slightly more evolved regions.

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arXiv2020

The Forgotten Quadrant Survey. $^{12}$CO and $^{13}$CO (1-0) survey of the Galactic Plane in the range 220°$<l<$240° -2.5°$<b<$0°

We present the Forgotten Quadrant Survey (FQS), an ESO large project that used the 12m antenna of the Arizona Radio Observatory to map the Galactic Plane in the range 220°$<l<$240°and -2.5°$<b<$0°, both in $^{12}$CO(1-0) and $^{13}$CO(1-0), at a spectral resolution of 0.65 km s$^{-1}$ and 0.26 km s$^{-1}$. Our dataset allows us to easily identify how the molecular dense gas is organised at different spatial scales: from the giant clouds with their denser filamentary networks, down to the clumps and cores that host the newborn stars and to obtain reliable estimates of their key physical parameters. We present the first release of the FQS data and discuss their quality. Spectra with 0.65 km s$^{-1}$ velocity channels have a noise ranging from 0.8 K to 1.3 K for $^{12}$CO(1-0) and from 0.3 K to 0.6 K for $^{13}$CO(1-0). In this paper, we used the $^{12}$CO(1-0) spectral cubes to produce a catalogue of 263 molecular clouds. This is the first selfconsistent, statistical catalogue of molecular clouds of the outer Galaxy, obtained with a subarcminute spatial resolution and therefore able to detect not only the classical giant molecular clouds, but also the small clouds and to resolve the cloud structure at the subparsec scale up to a distance of a few kpc. We found two classes of objects: structures with size above a few parsecs that are typical molecular clouds and may be self-gravitating, and subparsec structures that cannot be in gravitational equilibrium and are likely transient or confined by external pressure. We used the ratio between the Herschel H$_2$ column density and the integrated intensity of the CO lines to calculate the CO conversion factor and we found mean values of (3.3$\pm$1.4)$\times 10^{20}$ cm$^{-2}$(K km s$^{-1})^{-1}$ and (1.2$\pm$0.4)$\times 10^{21}$ cm$^{-2}$(K km s$^{-1})^{-1}$, for $^{12}$CO(1-0) and $^{13}$CO(1-0), respectively.

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arXiv2019

Substructures in the Keplerian disc around the O-type (proto)star G17.64+0.16

We present the highest angular resolution (20x15mas - 44x33au) Atacama Large Millimeter/sub-millimeter Array (ALMA) observations currently possible of the proto-O-star G17.64+0.16 in Band 6. The Cycle 5 observations with baselines out to 16km probes scales <50au and reveal the rotating disc around G17.64+0.16, a massive forming O-type star. The disc has a ring-like enhancement in the dust emission, especially visible as arc structures to the north and south. The Keplerian kinematics are most prominently seen in the vibrationally excited water line, H2O (Eu=3461.9K). The mass of the central source found by modelling the Keplerian rotation is consistent with 45+/-10Mo. The H30alpha (231.9GHz) radio-recombination line and the SiO (5-4) molecular line were detected at up to the 10 sigma$ level. The estimated disc mass is 0.6-2.6Mo under the optically thin assumption. Analysis of the Toomre Q parameter, in the optically thin regime, indicates that the disc stability is highly dependent on temperature. The disc currently appears stable for temperatures >150K, this does not preclude that the substructures formed earlier through disc fragmentation.

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arXiv2019

IRAS23385+6053: An embedded massive cluster in the making

This study is part of the project ``CORE'', an IRAM/NOEMA large program consisting of observations of the millimeter continuum and molecular line emission towards 20 selected high-mass star forming regions. We focus on IRAS23385+6053, which is believed to be the least evolved source of the CORE sample. The observations were performed at ~1.4 mm and employed three configurations of NOEMA and additional single-dish maps, merged with the interferometric data to recover the extended emission. Our correlator setup covered a number of lines from well-known hot core tracers and a few outflow tracers. The angular (~0.45"$-$0.9") and spectral (0.5 km/s) resolutions were sufficient to resolve the clump in IRAS23385+6053 and investigate the existence of large-scale motions due to rotation, infall, or expansion. We find that the clump splits into six distinct cores when observed at sub-arcsecond resolution. These are identified through their 1.4 mm continuum and molecular line emission. We produce maps of the velocity, line width, and rotational temperature from the methanol and methyl cyanide lines, which allow us to investigate the cores and reveal a velocity and temperature gradient in the most massive core. We also find evidence of a bipolar outflow, possibly powered by a low-mass star. We present the tentative detection of a circumstellar self-gravitating disk lying in the most massive core and powering a large-scale outflow previously known in the literature. In our scenario, the star powering the flow is responsible for most of the luminosity of IRAS23385+6053 (~$3000~L_\odot$). The other cores, albeit with masses below the corresponding virial masses, appear to be accreting material from their molecular surroundings and are possibly collapsing or on the verge of collapse. We conclude that we are observing a sample of star-forming cores that is bound to turn into a cluster of massive stars.

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arXiv2015

Accretion disks in luminous young stellar objects

An observational review is provided of the properties of accretion disks around young stars. It concerns the primordial disks of intermediate- and high-mass young stellar objects in embedded and optically revealed phases. The properties were derived from spatially resolved observations and therefore predominantly obtained with interferometric means, either in the radio/(sub)millimeter or in the optical/infrared wavelength regions. We make summaries and comparisons of the physical properties, kinematics, and dynamics of these circumstellar structures and delineate trends where possible. Amongst others, we report on a quadratic trend of mass accretion rates with mass from T Tauri stars to the highest mass young stellar objects and on the systematic difference in mass infall and accretion rates.

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arXiv2015

Italian Science Case for ALMA Band 2+3

The Premiale Project "Science and Technology in Italy for the upgraded ALMA Observatory - iALMA" has the goal of strengthening the scientific, technological and industrial Italian contribution to the Atacama Large Millimeter/submillimeter Array (ALMA), the largest ground based international infrastructure for the study of the Universe in the microwave. One of the main objectives of the Science Working Group (SWG) inside iALMA, the Work Package 1, is to develop the Italian contribution to the Science Case for the ALMA Band 2 or Band 2+3 receiver. ALMA Band 2 receiver spans from ~67 GHz (bounded by an opaque line complex of ozone lines) up to 90 GHz which overlaps with the lower frequency end of ALMA Band 3. Receiver technology has advanced since the original definition of the ALMA frequency bands. It is now feasible to produce a single receiver which could cover the whole frequency range from 67 GHz to 116 GHz, encompassing Band 2 and Band 3 in a single receiver cartridge, a so called Band 2+3 system. In addition, upgrades of the ALMA system are now foreseen that should double the bandwidth to 16 GHz. The science drivers discussed below therefore also discuss the advantages of these two enhancements over the originally foreseen Band 2 system.

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arXiv2013

The B1 shock in the L1157 outflow as seen at high spatial resolution

We present high spatial resolution (750 AU at 250 pc) maps of the B1 shock in the blue lobe of the L1157 outflow in four lines: CS (3-2), CH3OH (3_K-2_K), HC3N (16-15) and p-H2CO (2_02-3_01). The combined analysis of the morphology and spectral profiles has shown that the highest velocity gas is confined in a few compact (~ 5 arcsec) bullets while the lowest velocity gas traces the wall of the gas cavity excavated by the shock expansion. A large velocity gradient model applied to the CS (3-2) and (2-1) lines provides an upper limit of 10^6 cm^-3 to the averaged gas density in B1 and a range of 5x10^3< n(H2)< 5x10^5 cm^-3 for the density of the high velocity bullets. The origin of the bullets is still uncertain: they could be the result of local instabilities produced by the interaction of the jet with the ambient medium or could be clump already present in the ambient medium that are excited and accelerated by the expanding outflow. The column densities of the observed species can be reproduced qualitatively by the presence in B1 of a C-type shock and only models where the gas reaches temperatures of at least 4000 K can reproduce the observed HC3N column density.

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arXiv2013

Physical properties of high-mass clumps in different stages of evolution

(Abridged) Aims. To investigate the first stages of the process of high-mass star formation, we selected a sample of massive clumps previously observed with the SEST at 1.2 mm and with the ATNF ATCA at 1.3 cm. We want to characterize the physical conditions in such sources, and test whether their properties depend on the evolutionary stage of the clump. Methods. With ATCA we observed the selected sources in the NH3(1,1) and (2,2) transitions and in the 22 GHz H2O maser line. Ammonia lines are a good temperature probe that allow us to accurately determine the mass and the column-, volume-, and surface densities of the clumps. We also collected all data available to construct the spectral energy distribution of the individual clumps and to determine if star formation is already occurring, through observations of its most common signposts, thus putting constraints on the evolutionary stage of the source. We fitted the spectral energy distribution between 1.2 mm and 70 microns with a modified black body to derive the dust temperature and independently determine the mass. Results. The clumps are cold (T~10-30 K), massive (M~10^2-10^3 Mo), and dense (n(H2)>~10^5 cm^-3) and they have high column densities (N(H2)~10^23 cm^-2). All clumps appear to be potentially able to form high-mass stars. The most massive clumps appear to be gravitationally unstable, if the only sources of support against collapse are turbulence and thermal pressure, which possibly indicates that the magnetic field is important in stabilizing them. Conclusions. After investigating how the average properties depend on the evolutionary phase of the source, we find that the temperature and central density progressively increase with time. Sources likely hosting a ZAMS star show a steeper radial dependence of the volume density and tend to be more compact than starless clumps.

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arXiv2013

Evolution and excitation conditions of outflows in high-mass star-forming regions

Theoretical models suggest that massive stars form via disk-mediated accretion, with bipolar outflows playing a fundamental role. A recent study toward massive molecular outflows has revealed a decrease of the SiO line intensity as the object evolves. The present study aims at characterizing the variation of the molecular outflow properties with time, and at studying the SiO excitation conditions in outflows associated with massive YSOs. We used the IRAM30m telescope to map 14 massive star-forming regions in the SiO(2-1), SiO(5-4) and HCO+(1-0) outflow lines, and in several dense gas and hot core tracers. Hi-GAL data was used to improve the spectral energy distributions and the L/M ratio, which is believed to be a good indicator of the evolutionary stage of the YSO. We detect SiO and HCO+ outflow emission in all the sources, and bipolar structures in six of them. The outflow parameters are similar to those found toward other massive YSOs. We find an increase of the HCO+ outflow energetics as the object evolve, and a decrease of the SiO abundance with time, from 10^(-8) to 10^(-9). The SiO(5-4) to (2-1) line ratio is found to be low at the ambient gas velocity, and increases as we move to high velocities, indicating that the excitation conditions of the SiO change with the velocity of the gas (with larger densities and/or temperatures for the high-velocity gas component). The properties of the SiO and HCO+ outflow emission suggest a scenario in which SiO is largely enhanced in the first evolutionary stages, probably due to strong shocks produced by the protostellar jet. As the object evolves, the power of the jet would decrease and so does the SiO abundance. During this process, however, the material surrounding the protostar would have been been swept up by the jet, and the outflow activity, traced by entrained molecular material (HCO+), would increase with time.

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arXiv2013

A candidate circumbinary Keplerian disk in G35.20-0.74 N: A study with ALMA

We report on ALMA observations of continuum and molecular line emission with 0.4" resolution towards the high-mass star forming region G35.20-0.74 N. Two dense cores are detected in typical hot-core tracers, such as CH3CN, which reveal velocity gradients. In one of these cores, the velocity field can be fitted with an almost edge-on Keplerian disk rotating about a central mass of 18 Msun. This finding is consistent with the results of a recent study of the CO first overtone bandhead emission at 2.3mum towards G35.20-0.74 N. The disk radius and mass are >2500 au and 3 Msun. To reconcile the observed bolometric luminosity (3x10^4 Lsun) with the estimated stellar mass of 18 Msun, we propose that the latter is the total mass of a binary system.

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