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Maria T. Beltran

Publications and source records attributed to Maria T. Beltran.

At least 19 recordsLinked to original sources

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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The SOFIA Massive (SOMA) Star Formation Survey. V. Clustered Protostars

We present $\sim8-40\,μ$m SOFIA-FORCAST images of seven regions of ``clustered" star formation as part of the SOFIA Massive (SOMA) Star Formation Survey. We identify a total of 34 protostar candidates and build their spectral energy distributions (SEDs). We fit these SEDs with a grid of radiative transfer models based on the Turbulent Core Accretion (TCA) theory to derive key protostellar properties, including initial core mass, $M_c$, clump environment mass surface density, $Σ_{\rm cl}$, and current protostellar mass, $m_*$. We also carry out empirical graybody (GB) estimation of $Σ_{\rm cl}$, which allows a case of restricted SED fitting within the TCA model grid. We also release version 2.0 of the open-source Python package \emph{sedcreator}, designed to automate the aperture photometry and SED building and fitting process for sources in clustered environments, where flux contamination from close neighbors typically complicates the process. Using these updated methods, SED fitting yields values of $M_c\sim30-200\:M_{\odot}$, $Σ_{\text{cl,SED}}\sim0.1-3\:{\rm{g\:cm}}^{-2}$, and $m_*\sim4-50\:M_{\odot}$. The graybody fitting yields smaller values of $Σ_{\text{cl,GB}}\lesssim1\:{\rm{g\:cm}}^{-2}$. From these results, we do not find evidence for a critical $Σ_{\rm{cl}}$ needed to form massive ($\gtrsim 8\:M_\odot$) stars. However, we do find tentative evidence for a dearth of the most massive ($m_*\gtrsim30\:M_\odot$) protostars in the clustered regions suggesting a potential impact of environment on the stellar initial mass function.

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Magnetic Fields in Massive Star-forming Regions (MagMaR). V. The Magnetic Field at the Onset of High-mass Star Formation

A complete understanding of the initial conditions of high-mass star formation and what processes determine multiplicity require the study of the magnetic field (B-field) in young, massive cores. Using ALMA 250 GHz polarization (0.3" = 1000 au) and ALMA 220 GHz high-angular resolution observations (0.05" = 160 au), we have performed a full energy analysis including the B-field at core scales and have assessed what influences the multiplicity inside a massive core previously believed to be in the prestellar phase. With 31 Msun, the G11.92 MM2 core has a young CS outflow with a dynamical time scale of a few thousand years. At high-resolution, the MM2 core fragments into a binary system with a projected separation of 505 au and a binary mass ratio of 1.14. Using the DCF method with an ADF analysis, we estimate in this core a B-field strength of 6.2 mG and a mass-to-flux ratio of 18. The MM2 core is strongly subvirialized with a virial parameter of 0.064, including the B-field. The high mass-to-flux ratio and low virial parameter indicate that this massive core is very likely undergoing runaway collapse, which is in direct contradiction with the core-accretion model. The MM2 core is embedded in a filament that has a velocity gradient consistent with infall. In line with clump-fed scenarios, the core can grow in mass at a rate of 1.9--5.6 x 10^-4 Msun/yr. In spite of the B-field having only a minor contribution to the total energy budget at core scales, it likely plays a more important role at smaller scales by setting the binary properties. Considering energy ratios and a fragmentation criterion at the core scale, the binary could have been formed by core fragmentation. The binary properties (separation and mass ratio), however, are also consistent with radiation-magnetohydrodynamic simulations with super-Alfvenic, supersonic (or sonic) turbulence that form binaries by disk fragmentation.

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Magnetic Fields in Massive Star-forming Regions (MagMaR): Unveiling an Hourglass Magnetic Field in G333.46-0.16 using ALMA

The contribution of the magnetic field to the formation of high-mass stars is poorly understood. We report the high-angular resolution ($\sim0.3^{\prime\prime}$, 870 au) map of the magnetic field projected on the plane of the sky (B$_\mathrm{POS}$) towards the high-mass star forming region G333.46$-$0.16 (G333), obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) at 1.2 mm as part of the Magnetic Fields in Massive Star-forming Regions (MagMaR) survey. The B$_\mathrm{POS}$ morphology found in this region is consistent with a canonical ``hourglass'' which suggest a dynamically important field. This region is fragmented into two protostars separated by $\sim1740$ au. Interestingly, by analysing H$^{13}$CO$^{+}$ ($J=3-2$) line emission, we find no velocity gradient over the extend of the continuum which is consistent with a strong field. We model the B$_\mathrm{POS}$, obtaining a marginally supercritical mass-to-flux ratio of 1.43, suggesting an initially strongly magnetized environment. Based on the Davis-Chandrasekhar-Fermi method, the magnetic field strength towards G333 is estimated to be 5.7 mG. The absence of strong rotation and outflows towards the central region of G333 suggests strong magnetic braking, consistent with a highly magnetized environment. Our study shows that despite being a strong regulator, the magnetic energy fails to prevent the process of fragmentation, as revealed by the formation of the two protostars in the central region.

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Astrochemical Diagnostics of the Isolated Massive Protostar G28.20-0.05

We study the astrochemical diagnostics of the isolated massive protostar G28.20-0.05. We analyze data from ALMA 1.3~mm observations with resolution of 0.2 arcsec ($\sim$1,000 au). We detect emission from a wealth of species, including oxygen-bearing (e.g., $\rm{H_2CO}$, $\rm{CH_3OH}$, $\rm{CH_3OCH_3}$), sulfur-bearing (SO$_2$, H$_2$S) and nitrogen-bearing (e.g., HNCO, NH$_2$CHO, C$_2$H$_3$CN, C$_2$H$_5$CN) molecules. We discuss their spatial distributions, physical conditions, correlation between different species and possible chemical origins. In the central region near the protostar, we identify three hot molecular cores (HMCs). HMC1 is part of a mm continuum ring-like structure, is closest in projection to the protostar, has the highest temperature of $\sim300\:$K, and shows the most line-rich spectra. HMC2 is on the other side of the ring, has a temperature of $\sim250\:$K, and is of intermediate chemical complexity. HMC3 is further away, $\sim3,000\:$au in projection, cooler ($\sim70\:$K) and is the least line-rich. The three HMCs have similar mass surface densities ($\sim10\:{\rm{g\:cm}}^{-2}$), number densities ($n_{\rm H}\sim10^9\:{\rm{cm}}^{-3}$) and masses of a few $M_\odot$. The total gas mass in the cores and in the region out to $3,000\:$au is $\sim 25\:M_\odot$, which is comparable to that of the central protostar. Based on spatial distributions of peak line intensities as a function of excitation energy, we infer that the HMCs are externally heated by the protostar. We estimate column densities and abundances of the detected species and discuss the implications for hot core astrochemistry.

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The SOFIA Massive (SOMA) Star Formation Survey. IV. Isolated Protostars

We present $\sim10-40\,μ$m SOFIA-FORCAST images of 11 isolated protostars as part of the SOFIA Massive (SOMA) Star Formation Survey, with this morphological classification based on 37 $μ$m imaging. We develop an automated method to define source aperture size using the gradient of its background-subtracted enclosed flux and apply this to build spectral energy distributions (SEDs). We fit the SEDs with radiative transfer models, developed within the framework of turbulent core accretion (TCA) theory, to estimate key protostellar properties. Here, we release the sedcreator python package that carries out these methods. The SEDs are generally well fitted by the TCA models, from which we infer initial core masses $M_c$ ranging from $20-430\:M_\odot$, clump mass surface densities $Σ_{\rm cl}\sim0.3-1.7\:{\rm{g\:cm}}^{-2}$ and current protostellar masses $m_*\sim3-50\:M_\odot$. From a uniform analysis of the 40 sources in the full SOMA survey to date, we find that massive protostars form across a wide range of clump mass surface density environments, placing constraints on theories that predict a minimum threshold $Σ_{\rm cl}$ for massive star formation. However, the upper end of the $m_*-Σ_{\rm cl}$ distribution follows trends predicted by models of internal protostellar feedback that find greater star formation efficiency in higher $Σ_{\rm cl}$ conditions. We also investigate protostellar far-IR variability by comparison with IRAS data, finding no significant variation over an $\sim$40 year baseline.

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Discovery of a Photoionized Bipolar Outflow towards the Massive Protostar G45.47+0.05

Massive protostars generate strong radiation feedback, which may help set the mass they achieve by the end of the accretion process. Studying such feedback is therefore crucial for understanding the formation of massive stars. We report the discovery of a photoionized bipolar outflow towards the massive protostar G45.47+0.05 using high-resolution observations at 1.3 mm with the Atacama Large Millimeter/Submillimeter Array (ALMA) and at 7 mm with the Karl G. Jansky Very Large Array (VLA). By modeling the free-free continuum, the ionized outflow is found to be a photoevaporation flow with an electron temperature of 10,000 K and an electron number density of ~1.5x10^7 cm^-3 at the center, launched from a disk of radius of 110 au. H30alpha hydrogen recombination line emission shows strong maser amplification, with G45 being one of very few sources to show such millimeter recombination line masers. The mass of the driving source is estimated to be 30-50 Msun based on the derived ionizing photon rate, or 30-40 Msun based on the H30alpha kinematics. The kinematics of the photoevaporated material is dominated by rotation close to the disk plane, while accelerated to outflowing motion above the disk plane. The mass loss rate of the photoevaporation outflow is estimated to be ~(2-3.5)x10^-5 Msun/yr. We also found hints of a possible jet embedded inside the wide-angle ionized outflow with non-thermal emissions. The possible co-existence of a jet and a massive photoevaporation outflow suggests that, in spite of the strong photoionization feedback, accretion is still on-going.

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Dynamics of a Massive Binary at Birth

Almost all massive stars have bound stellar companions, existing in binaries or higher-order multiples. While binarity is theorized to be an essential feature of how massive stars form, essentially all information about such properties is derived from observations of already formed stars, whose orbital properties may have evolved since birth. Little is known about binarity during formation stages. Here we report high angular resolution observations of 1.3 mm continuum and H30alpha recombination line emission, which reveal a massive protobinary with apparent separation of 180 au at the center of the massive star-forming region IRAS07299-1651. From the line-of-sight velocity difference of 9.5 km/s of the two protostars, the binary is estimated to have a minimum total mass of 18 solar masses, consistent with several other metrics, and maximum period of 570 years, assuming a circular orbit. The H30alpha line from the primary protostar shows kinematics consistent with rotation along a ring of radius of 12 au. The observations indicate that disk fragmentation at several hundred au may have formed the binary, and much smaller disks are feeding the individual protostars.

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An Ordered Envelope-disk Transition in the Massive Protostellar Source G339.88-1.26

We report molecular line observations of the massive protostellar source G339.88-1.26 with the Atacama Large Millimeter/Submillimeter Array. The observations reveal a highly collimated SiO jet extending from the 1.3 mm continuum source, which connects to a slightly wider but still highly collimated CO outflow. Rotational features perpendicular to the outflow axis are detected in various molecular emissions, including SiO, SO2, H2S, CH3OH, and H2CO emissions. Based on their spatial distributions and kinematics, we find that they trace different parts of the envelope-disk system. The SiO emission traces the disk and inner envelope in addition to the jet. The CH3OH and H2CO emissions mostly trace the infalling-rotating envelope, and are enhanced around the transition region between envelope and disk, i.e., the centrifugal barrier. The SO2 and H2S emissions are enhanced around the centrifugal barrier, and also trace the outer part of the disk. Envelope kinematics are consistent with rotating-infalling motion, while those of the disk are consistent with Keplerian rotation. The radius and velocity of the centrifugal barrier are estimated to be about 530 au and 6 km/s, leading to a central mass of about 11 solar masses, consistent with estimates based on spectral energy distribution fitting. These results indicate that an ordered transition from an infalling-rotating envelope to a Keplerian disk through a centrifugal barrier, accompanied by changes of types of molecular line emissions, is a valid description of this massive protostellar source. This implies that at least some massive stars form in a similar way as low-mass stars via Core Accretion.

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SMA Observations of the Hot Molecular Core IRAS 18566+0408

We present Submillimeter Array (SMA) observations toward the high-mass star-forming region IRAS 18566+0408. Observations at 1.3 mm continuum and in several molecular line transitions were performed in the compact (2."4 angular resolution) and very-extended (~0."4 angular resolution) configurations. The continuum emission from the compact configuration shows a dust core of 150 Msun, while the very-extended configuration reveals a dense (2.6 x 10^7 cm^-3) and compact (~4,000 AU) condensation of 8 Msun. We detect 31 molecular transitions from 14 species including CO isotopologues, SO, CH3OH, OCS, and CH3CN. Using the different k-ladders of the CH3CN line, we derive a rotational temperature at the location of the continuum peak of 240 K. The 12CO(2-1), 13CO(2-1), and SO(6_5-5_4) lines reveal a molecular outflow at PA ~135^o centered at the continuum peak. The extended 12CO(2-1) emission has been recovered with the IRAM 30 m telescope observations. Using the combined data set, we derive an outflow mass of 16.8 Msun. The chemically rich spectrum and the high rotational temperature confirm that IRAS 18566+0408 is harboring a hot molecular core. We find no clear velocity gradient that could suggest the presence of a rotational disk-like structure, even at the high resolution observations obtained with the very-extended configuration.

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The SOFIA Massive (SOMA) Star Formation Survey. I. Overview and First Results

We present an overview and first results of the Stratospheric Observatory For Infrared Astronomy Massive (SOMA) Star Formation Survey, which is using the FORCAST instrument to image massive protostars from $\sim10$--$40\:\rmμ\rm{m}$. These wavelengths trace thermal emission from warm dust, which in Core Accretion models mainly emerges from the inner regions of protostellar outflow cavities. Dust in dense core envelopes also imprints characteristic extinction patterns at these wavelengths, causing intensity peaks to shift along the outflow axis and profiles to become more symmetric at longer wavelengths. We present observational results for the first eight protostars in the survey, i.e., multiwavelength images, including some ancillary ground-based MIR observations and archival {\it{Spitzer}} and {\it{Herschel}} data. These images generally show extended MIR/FIR emission along directions consistent with those of known outflows and with shorter wavelength peak flux positions displaced from the protostar along the blueshifted, near-facing sides, thus confirming qualitative predictions of Core Accretion models. We then compile spectral energy distributions and use these to derive protostellar properties by fitting theoretical radiative transfer models. Zhang and Tan models, based on the Turbulent Core Model of McKee and Tan, imply the sources have protostellar masses $m_*\sim10$--50$\:M_\odot$ accreting at $\sim10^{-4}$--$10^{-3}\:M_\odot\:{\rm{yr}}^{-1}$ inside cores of initial masses $M_c\sim30$--500$\:M_\odot$ embedded in clumps with mass surface densities $Σ_{\rm{cl}}\sim0.1$--3$\:{\rm{g\:cm}^{-2}}$. Fitting Robitaille et al. models typically leads to slightly higher protostellar masses, but with disk accretion rates $\sim100\times$ smaller. We discuss reasons for these differences and overall implications of these first survey results for massive star formation theories.

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Massive Star Formation

The enormous radiative and mechanical luminosities of massive stars impact a vast range of scales and processes, from the reionization of the universe, to the evolution of galaxies, to the regulation of the interstellar medium, to the formation of star clusters, and even to the formation of planets around stars in such clusters. Two main classes of massive star formation theory are under active study, Core Accretion and Competitive Accretion. In Core Accretion, the initial conditions are self-gravitating, centrally concentrated cores that condense with a range of masses from the surrounding, fragmenting clump environment. They then undergo relatively ordered collapse via a central disk to form a single star or a small-N multiple. In this case, the pre-stellar core mass function has a similar form to the stellar initial mass function. In Competitive Accretion, the material that forms a massive star is drawn more chaotically from a wider region of the clump without passing through a phase of being in a massive, coherent core. In this case, massive star formation must proceed hand in hand with star cluster formation. If stellar densities become very high near the cluster center, then collisions between stars may also help to form the most massive stars. We review recent theoretical and observational progress towards understanding massive star formation, considering physical and chemical processes, comparisons with low and intermediate-mass stars, and connections to star cluster formation.

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A Massive Protostar Forming by Ordered Collapse of a Dense, Massive Core

We present 30 and 40 micron imaging of the massive protostar G35.20-0.74 with SOFIA-FORCAST. The high surface density of the natal core around the protostar leads to high extinction, even at these relatively long wavelengths, causing the observed flux to be dominated by that emerging from the near-facing outflow cavity. However, emission from the far-facing cavity is still clearly detected. We combine these results with fluxes from the near-infrared to mm to construct a spectral energy distribution (SED). For isotropic emission the bolometric luminosity would be 3.3x10^4 Lsun. We perform radiative transfer modeling of a protostar forming by ordered, symmetric collapse from a massive core bounded by a clump with high mass surface density, Sigma_cl. To fit the SED requires protostellar masses ~20-34 Msun depending on the outflow cavity opening angle (35 - 50 degrees), and Sigma_cl ~ 0.4-1 g cm-2. After accounting for the foreground extinction and the flashlight effect, the true bolometric luminosity is ~ (0.7-2.2)x10^5 Lsun. One of these models also has excellent agreement with the observed intensity profiles along the outflow axis at 10, 18, 31 and 37 microns. Overall our results support a model of massive star formation involving the relatively ordered, symmetric collapse of a massive, dense core and the launching bipolar outflows that clear low density cavities. Thus a unified model may apply for the formation of both low and high mass stars.

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Young starless cores embedded in the magnetically dominated Pipe Nebula

The Pipe Nebula is a massive, nearby dark molecular cloud with a low star-formation efficiency which makes it a good laboratory to study the very early stages of the star formation process. The Pipe Nebula is largely filamentary, and appears to be threaded by a uniform magnetic field at scales of few parsecs, perpendicular to its main axis. The field is only locally perturbed in a few regions, such as the only active cluster forming core B59. The aim of this study is to investigate primordial conditions in low-mass pre-stellar cores and how they relate to the local magnetic field in the cloud. We used the IRAM 30-m telescope to carry out a continuum and molecular survey at 3 and 1 mm of early- and late-time molecules toward four selected starless cores inside the Pipe Nebula. We found that the dust continuum emission maps trace better the densest regions than previous 2MASS extinction maps, while 2MASS extinction maps trace better the diffuse gas. The properties of the cores derived from dust emission show average radii of ~0.09 pc, densities of ~1.3x10^5 cm^-3, and core masses of ~2.5 M_sun. Our results confirm that the Pipe Nebula starless cores studied are in a very early evolutionary stage, and present a very young chemistry with different properties that allow us to propose an evolutionary sequence. All of the cores present early-time molecular emission, with CS detections toward all the sample. Two of them, Cores 40 and 109, present strong late-time molecular emission. There seems to be a correlation between the chemical evolutionary stage of the cores and the local magnetic properties that suggests that the evolution of the cores is ruled by a local competition between the magnetic energy and other mechanisms, such as turbulence.

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Infall of gas as the formation mechanism of stars up to 20 times more massive than the Sun

Theory predicts and observations confirm that low-mass stars (like the Sun) in their early life grow by accreting gas from the surrounding material. But for stars ~ 10 times more massive than the Sun (~10 M_sun), the powerful stellar radiation is expected to inhibit accretion and thus limit the growth of their mass. Clearly, stars with masses >10 M_sun exist, so there must be a way for them to form. The problem may be solved by non-spherical accretion, which allows some of the stellar photons to escape along the symmetry axis where the density is lower. The recent detection of rotating disks and toroids around very young massive stars has lent support to the idea that high-mass (> 8 M_sun) stars could form in this way. Here we report observations of an ammonia line towards a high-mass star forming region. We conclude from the data that the gas is falling inwards towards a very young star of ~20 M_sun, in line with theoretical predictions of non-spherical accretion.

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Who Is Eating the Outflow?: High-Angular Resolution Study of an Intermediate-Mass Protostar in L1206

Up to now only a few intermediate-mass molecular outflows have been studied with enough high-angular resolution. The aim of this work is to study in detail the intermediate-mass YSO IRAS 22272+6358A, which is embedded in L1206, and its molecular outflow, in order to investigate the interaction of the outflow with the dense protostellar material, and to compare their properties with those of lower mas counterparts. We carried out OVRO observations of the 2.7 mm continuum emission, CO(1-0), C18O(1-0), and HC3N(12-11) in order to map with high-angular resolution the core of L1206, and to derive the properties of the dust emission, the molecular outflow and the dense protostellar envelope. The 2.7 mm continuum emission has been resolved into four sources, labeled OVRO~1, 2, 3, and 4. The intermediate-mass Class~0/I object OVRO 2, with a mass traced by the dust emission of 14.2 Msun, is the source associated with IRAS 22272+6358A. The CO(1-0) observations have revealed a very collimated outflow driven by OVRO 2, at a PA ~140 degr, that has a very weak southeastern red lobe and a much stronger northwestern blue lobe. Photodissociation toward the red lobe produced by the ionization front coming from the bright-rimmed diffuse HII region could be responsible of the morphology of the outflow. The spatial correlation between the outflow and the elongated dense protostellar material traced by HC3N(12-11) suggests an interaction between the molecular outflow and the protostellar envelope. Shocks produced by the molecular outflow, and possibly by the shock front preceding the ionization front could account for the southern enhancement of HC3N. The properties of the intermediate-mass protostar OVRO 2 and the molecular outflow are consistent with those of lower mass counterparts.

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Search for massive protostar candidates in the southern hemisphere: II. Dust continuum emission

In an ongoing effort to identify and study high-mass protostellar candidates we have observed in various tracers a sample of 235 sources selected from the IRAS Point Source Catalog, mostly with dec < -30 deg, with the SEST antenna at millimeter wavelengths. The sample contains 142 Low sources and 93 High, which are believed to be in different evolutionary stages. Both sub-samples have been studied in detail by comparing their physical properties and morphologies. Massive dust clumps have been detected in all but 8 regions, with usually more than one clump per region. The dust emission shows a variety of complex morphologies, sometimes with multiple clumps forming filaments or clusters. The mean clump has a linear size of ~0.5 pc, a mass of ~320 Msolar for a dust temperature Td=30 K, an H_2 density of 9.5E5 cm-3, and a surface density of 0.4 g cm-2. The median values are 0.4 pc, 102 Msolar, 4E4 cm-3, and 0.14 g cm-2, respectively. The mean value of the luminosity-to-mass ratio, L/M ~99 Lsolar/Msolar, suggests that the sources are in a young, pre-ultracompact HII phase. We have compared the millimeter continuum maps with images of the mid-IR MSX emission, and have discovered 95 massive millimeter clumps non-MSX emitters, either diffuse or point-like, that are potential prestellar or precluster cores. The physical properties of these clumps are similar to those of the others, apart from the mass that is ~3 times lower than for clumps with MSX counterpart. Such a difference could be due to the potential prestellar clumps having a lower dust temperature. The mass spectrum of the clumps with masses above M ~100 Msolar is best fitted with a power-law dN/dM proportional to M-alpha with alpha=2.1, consistent with the Salpeter (1955) stellar IMF, with alpha=2.35.

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A detailed study of the rotating toroids in G31.41+0.31 and G24.78+0.08

We present the results of high angular resolution millimeter observations of gas and dust toward G31.41+0.31 and G24.78+0.08, two high-mass star forming regions where four rotating massive toroids have been previously detected by Beltran et al. (2004). The CH3CN (12-11) emission of the toroids in G31.41+0.31 and core A1 in G24.78+0.08 has been modeled assuming that it arises from a disk-like structure seen edge-on, with a radial velocity field. For G31.41+0.31 the model properly fits the data for a velocity v_rot~1.7 km/s at the outer radius R_out~13400 AU and an inner radius R_inn~1340 AU, while for core A1 in G24.78+0.08 the best fit is obtained for v_rot~2.0 km/s at R_out~7700 AU and R_inn~2300 AU. Unlike the rotating disks detected around less luminous stars, these toroids are not undergoing Keplerian rotation. From the modeling itself, however, it is not possible to distinguish between constant rotation or constant angular velocity, since both velocity fields suitably fit the data. The best fit models have been computed adopting a temperature gradient of the type T proportional R^{-3/4}, with a temperature at the outer radius T_out~100 K for both cores. The M_dyn needed for equilibrium derived from the models is much smaller than the mass of the cores, suggesting that such toroids are unstable and undergoing gravitational collapse. The collapse is also supported by the CH3^{13}CN or CH3CN line width measured in the cores, which increases toward the center of the toroids. The estimates of v_inf and \dot M_acc are ~2 km/s and 3x10^{-2} M_sun/yr for G31.41+0.31, and ~1.2 km/s and ~9x10^{-3} M_sun/yr for G24.78+0.08 A1. Such large accretion rates could weaken the effect of stellar winds and radiation pressure and allow further accretion on the star.

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