arXiv subjects

Robert A. Gutermuth

Publications and source records attributed to Robert A. Gutermuth.

At least 19 recordsLinked to original sources

arXiv2024

JWST-IPA: Chemical Inventory and Spatial Mapping of Ices in the Protostar HOPS370 -- Evidence for an Opacity Hole and Thermal Processing of Ices

The composition of protoplanetary disks, and hence the initial conditions of planet formation, may be strongly influenced by the infall and thermal processing of material during the protostellar phase. Composition of dust and ice in protostellar envelopes, shaped by energetic processes driven by the protostar, serves as the fundamental building material for planets and complex organic molecules. As part of the JWST GO program, "Investigating Protostellar Accretion" (IPA), we observed an intermediate-mass protostar HOPS 370 (OMC2-FIR3) using NIRSpec/IFU and MIRI/MRS. This study presents the gas and ice phase chemical inventory revealed with the JWST in the spectral range of $\sim$2.9 to 28 $μ$m and explores the spatial variation of volatile ice species in the protostellar envelope. We find evidence for thermal processing of ice species throughout the inner envelope. We present the first high-spatial resolution ($\sim 80$ au) maps of key volatile ice species H$_{2}$O, CO$_{2}$, $^{13}$CO$_2$, CO, and OCN$^-$, which reveal a highly structured and inhomogeneous density distribution of the protostellar envelope, with a deficiency of ice column density that coincides with the jet/outflow shocked knots. Further, we observe high relative crystallinity of H$_{2}$O ice around the shocked knot seen in the H$_2$ and OH wind/outflow, which can be explained by a lack of outer colder material in the envelope along the line of sight due to the irregular structure of the envelope. These observations show clear evidence of thermal processing of the ices in the inner envelope, close to the outflow cavity walls, heated by the luminous protostar.

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arXiv2024

Feedback in Emerging extragAlactic Star clusTers, FEAST: JWST spots PAH destruction in NGC 628 during the emerging phase of star formation

We investigate the emergence phase of young star clusters in the nearby spiral galaxy NGC 628. We use JWST NIRCam and MIRI observations to create spatially resolved maps of the Pa$α$-1.87 $μ$m and Br$α$-4.05 $μ$m hydrogen recombination lines, as well as the 3.3 $μ$m and 7.7 $μ$m emission from polycyclic aromatic hydrocarbons (PAHs). We extract 953 compact HII regions and analyze the PAH emission and morphology at $\sim$10 pc scales in the associated photo-dissociation regions (PDRs). While HII regions remain compact, radial profiles help us to define three PAH morphological classes: compact ($\sim$ 42%), extended ($\sim$ 34%) and open ($\sim$ 24%). The majority of compact and extended PAH morphologies are associated with very young star clusters ($<$5 Myr), while open PAH morphologies are mainly associated with star clusters older than 3 Myr. We observe a general decrease in the 3.3 $μ$m and 7.7 $μ$m PAH band emission as a function of cluster age, while their ratio remains constant with age out to 10 Myr and morphological class. The recovered PAH$_{3.3 μ{\rm m}}$/PAH$_{7.7 μ{\rm m}}$ ratio is lower than values reported in the literature for reference models that consider neutral and ionized PAH populations and analyses conducted at galactic scales. The 3.3 $μ$m and 7.7 $μ$m bands are typically associated to neutral and ionised PAHs, respectively. While we expected neutral PAHs to be suppressed in proximity of the ionizing source, the constant PAH$_{3.3 μ{\rm m}}$/PAH$_{7.7 μ{\rm m}}$ ratio would indicate that both families of molecules disrupt at similar rates in proximity of the HII regions.

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arXiv2024

Feedback in Emerging Extragalactic Star Clusters (JWST--FEAST): Calibration of Star Formation Rates in the Mid-Infrared with NGC 628

New JWST near-infrared imaging of the nearby galaxy NGC 628 from the Cycle 1 program JWST-FEAST is combined with archival JWST mid-infrared imaging to calibrate the 21 $μ$m emission as a star formation rate indicator (SFR) at $\sim$120 pc scales. The Pa$α$ ($λ$1.8756 $μ$m) hydrogen recombination emission line targeted by FEAST provides a reference SFR indicator that is relatively insensitive to dust attenuation, as demonstrated by combining this tracer with the HST H$α$ imaging. Our analysis is restricted to regions that appear compact in nebular line emission and are sufficiently bright to mitigate effects of both age and stochastic sampling of the stellar initial mass function. We find that the 21 $μ$m emission closely correlates with the nebular line emission, with a power-law with exponent=1.07$\pm$0.01, in agreement with past results. We calibrate a hybrid SFR indicator using a combination of H$α$ and 24 $μ$m (extrapolated from 21 $μ$m) tracers and derive the proportionality constant between the two tracers $b=0.095\pm0.007$, which is $\sim$ 3-5 times larger than previous derivations using large regions/entire galaxies. We model these discrepancies as an increasing contribution to the dust heating by progressively older stellar populations for increasing spatial scales, in agreement with earlier findings that star formation is hierarchically distributed in galaxies. Thus, use of hybrid SFR indicators requires prior knowledge of the mean age of the stellar populations dominating the dust heating, which makes their application uncertain. Conversely, non-linear calibrations of SFRs from L(24) alone are more robust, with a factor $\lesssim$2.5 variation across the entire range of L(24) luminosities from HII regions to galaxies.

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arXiv2024

Feedback in emerging extragalactic star clusters, FEAST: The relation between 3.3 $μ$m PAH emission and Star Formation Rate traced by ionized gas in NGC 628

We present maps of ionized gas (traced by Pa$α$ and Br$α$) and 3.3 $μ$m Polycyclic Aromatic Hydrocarbon (PAH) emission in the nearby spiral galaxy NGC 628, derived from new JWST/NIRCam data from the FEAST survey. With this data, we investigate and calibrate the relation between 3.3 $μ$m PAH emission and star formation rate (SFR) in and around emerging young star clusters (eYSCs) on a scale of ${\sim}40$ pc. We find a tight (correlation coefficient $ρ$${\sim}$0.9) sub-linear (power-law exponent $α$${\sim}$0.75) relation between the 3.3 $μ$m PAH luminosity surface density and SFR traced by Br$α$ for compact, cospatial (within 0.16$''$ or ${\sim}$7 pc) peaks in Pa$α$, Br$α$, and 3.3 $μ$m (eYSC-I). The scatter in the relationship does not correlate well with variations in local interstellar medium (ISM) metallicity due to a radial metallicity gradient, but rather is likely due to stochastic sampling of the stellar initial mass function (IMF) and variations in the PAH heating and age of our sources. The deviation from a linear relation may be explained by PAH destruction in more intense ionizing environments, variations in age, and IMF stochasticity at intermediate to low luminosities. We test our results with various continuum subtraction techniques using combinations of NIRCam bands and find that they remain robust with only minor differences in the derived slope and intercept. An unexpected discrepancy is identified between the relations of hydrogen recombination lines (Pa$α$ versus Br$α$; H$α$ versus Br$α$).

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arXiv2024

JWST/MIRI detection of suprathermal OH rotational emissions: probing the dissociation of the water by Lyman alpha photons near the protostar HOPS 370

Using the MIRI/MRS spectrometer on JWST, we have detected pure rotational, suprathermal OH emissions from the vicinity of the intermediate-mass protostar HOPS 370 (OMC2/FIR3). These emissions are observed from shocked knots in a jet/outflow, and originate in states of rotational quantum number as high as 46 that possess excitation energies as large as $E_U/k = 4.65 \times 10^4$ K. The relative strengths of the observed OH lines provide a powerful diagnostic of the ultraviolet radiation field in a heavily-extinguished region ($A_V \sim 10 - 20$) where direct UV observations are impossible. To high precision, the OH line strengths are consistent with a picture in which the suprathermal OH states are populated following the photodissociation of water in its $\tilde B - X$ band by ultraviolet radiation produced by fast ($\sim 80\,\rm km\,s^{-1}$) shocks along the jet. The observed dominance of emission from symmetric ($A^\prime$) OH states over that from antisymmetric ($A^{\prime\prime}$) states provides a distinctive signature of this particular population mechanism. Moreover, the variation of intensity with rotational quantum number suggests specifically that Ly$α$ radiation is responsible for the photodissociation of water, an alternative model with photodissociation by a 10$^4$ K blackbody being disfavored at a high level of significance. Using measurements of the Br$α$ flux to estimate the Ly$α$ production rate, we find that $\sim 4\%$ of the Ly$α$ photons are absorbed by water. Combined with direct measurements of water emissions in the $ν_2 = 1 -0$ band, the OH observations promise to provide key constraints on future models for the diffusion of Ly$α$ photons in the vicinity of a shock front.

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arXiv2023

Extension of HOPS Out to 500 ParSecs (eHOPS). I. Identification and Modeling of Protostars in the Aquila Molecular Clouds

We present a Spitzer/Herschel focused survey of the Aquila molecular clouds ($d \sim 436$~pc) as part of the eHOPS (extension of HOPS Out to 500 ParSecs) census of nearby protostars. For every source detected in the Herschel/PACS bands, the eHOPS-Aquila catalog contains 1-850~$μ$m SEDs assembled from 2MASS, Spitzer, Herschel, WISE, and JCMT/SCUBA-2 data. Using a newly developed set of criteria, we classify objects by their SEDs as protostars, pre-ms sequence stars with disks, and galaxies. A total of 172 protostars are found in Aquila, tightly concentrated in the molecular filaments that thread the clouds. Of these, 71 (42\%) are Class 0 protostars, 54 (31\%) are Class I protostars, 43 (25\%) are flat-spectrum protostars, and 4 (2\%) are Class II sources. Ten of the Class 0 protostars are young PACS Bright Red Sources similar to those discovered in Orion. We compare the SEDs to a grid of radiative transfer models to constrain the luminosities, envelope densities, and envelope masses of the protostars. A comparison of the eHOPS-Aquila to the HOPS protostars in Orion finds that the protostellar luminosity functions in the two star-forming regions are statistically indistinguishable, the bolometric temperatures/envelope masses of eHOPS-Aquila protostars are shifted to cooler temperatures/higher masses, and the eHOPS-Aquila protostars do not show the decline in luminosity with evolution found in Orion. We briefly discuss whether these differences are due to biases between the samples, diverging star formation histories, or the influence of environment on protostellar evolution.

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arXiv2022

Deep Near-Infrared Survey Toward the W40 and Serpens South Region in Aquila Rift: A Comprehensive Catalog of Young Stellar Objects

Active star forming regions are excellent laboratories for studying the origins and evolution of young stellar object (YSO) clustering. The W40 - Serpens South region is such a region, and we compile a super near-and-mid-infrared catalog of point sources in it, based on deep NIR observations of CFHT in combination with 2MASS, UKIDSS, and Spitzer catalogs. From this catalog, we identify 832 YSOs, and classify 15, 135, 647, and 35 of them to be the deeply embedded sources, Class I, Class II YSOs, and transition disk sources, respectively. In general, these YSOs are well correlated with the filamentary structures of molecular clouds, especially the deeply embedded sources and the Class I YSOs. The W40 central region is dominated by Class II YSOs, but in the Serpens South region, a half of the YSOs are Class I. We further generate a minimum spanning tree (MST) for all the YSOs. Around the W40 cluster, there are eight prominent MST branches that may trace vestigial molecular gas filaments that once fed gas to the central natal gas clump. Of the eight, only two now include detectable filamentary gas in Herschel data and corresponding Class I YSOs, while the other six are exclusively populated with Class II. Four MST branches overlap with the Serpens South main filament, and where they intersect, molecular gas "hubs" and more Class I YSOs are found. Our results imply a mixture of YSO distributions composed of both primordial and somewhat evolved YSOs in this star forming region.

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arXiv2022

Hierarchical Structure of YSO Clusters in the W40 and Serpens South Region: Group Extraction and Comparison with Fractal Clusters

Young stellar clusters are believed to inherit the spatial distribution like hierarchical structures of their natal molecular cloud during their formation. However, the change of the structures between the cloud and the young clusters is not well constrained observationally. We select the W40 - Serpens South region (~ 7 $\times$ 9 pc$^{2}$) of the Aquila Rift as a testbed and investigate hierarchical properties of spatial distribution of young stellar objects (YSOs) in this region. We develop a minimum spanning tree (MST)-based method to group stars into several levels by successively cutting down edges longer than an algorithmically determined critical value. A total of 832 YSOs are divided into 5 levels with 23 groups. For describing the hierarchical properties in a controlled way, we construct a set of synthetic source distributions at various fractal dimensions, and apply the same method to explore their group characters. By comparing the $Q$ parameter and the surface density profiles of the observed and the synthetic data, we find that the YSO observation matches spatial patterns from multi-fractal dimensions. In the periphery region where the molecular clouds are more diffuse, the YSO structure is close to a fractal dimension of 2.0, while in the core regions the fractal dimensions are close to 1.6 and 1.4 for the W40 and the Serpens South regions, respectively. Therefore, the YSOs may inherit the fractal pattern of the dense part of the molecular clouds, but such pattern dissipates slowly in several Myr.

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arXiv2022

Completing the Protostellar Luminosity Function in Cygnus-X with SOFIA/FORCAST Imaging

We present a new SOFIA/FORCAST mid-IR survey of luminous protostars and crowded star-forming environments in Cygnus X, the nearest million-solar mass molecular cloud complex. We derive bolometric luminosities for over 1000 sources in the region with these new data in combination with extant Spitzer and UKIDSS photometry, with 63 new luminous protostar candidates identified by way of the high quality SOFIA/FORCAST data. By including FORCAST data, we construct protostellar luminosity functions (PLFs) with improved completeness at the high luminosity end. The PLFs are well described by a power law function with an index of ~-0.5. Based on the Herschel temperature and column density measurements, we find no obvious dependence of the PLFs on the local gas temperature, but PLFs in regions of high stellar density or gas column density exhibit some excess at higher luminosities. Through the comparison between our observed PLFs and existing accretion models, both the turbulent core (TC) and the competitive accretion (CA) models are consistent with our results, while the isothermal sphere (IS) model is disfavored. The implications of these results on the star formation process are discussed.

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arXiv2021

High-precision star formation efficiency measurements in nearby clouds

On average molecular clouds convert only a small fraction epsilon_ff of their mass into stars per free-fall time, but differing star formation theories make contrasting claims for how this low mean efficiency is achieved. To test these theories, we need precise measurements of both the mean value and the scatter of epsilon_ff, but high-precision measurements have been difficult because they require determining cloud volume densities, from which we can calculate free-fall times. Until recently, most density estimates assume clouds as uniform spheres, while their real structures are often filamentary and highly non-uniform, yielding systematic errors in epsilon_ff estimates and smearing real cloud-to-cloud variations. We recently developed a theoretical model to reduce this error by using column density distributions in clouds to produce more accurate volume density estimates. In this letter, we apply this model to recent observations of 12 nearby molecular clouds. Compared to earlier analyses, our method reduces the typical dispersion of epsilon_ff within individual clouds from 0.35 dex to 0.31 dex, and decreases the median value of epsilon_ff over all clouds from ~ 0.02 to ~ 0.01. However, we find no significant change in the ~ 0.2 dex cloud-to-cloud dispersion of epsilon_ff, suggesting the measured dispersions reflect real structural differences between clouds.

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arXiv2021

AzTEC Survey of the Central Molecular Zone: Data Reduction, Analysis, and Preliminary Results

We present a large-scale survey of the central molecular zone (CMZ) of our Galaxy, as well as a monitoring program of Sgr A*, with the AzTEC/Large Millimeter Telescope (LMT) in the 1.1 mm continuum. Our 1.1 mm map covers the main body of the CMZ over a field of $1.6 \times 1.1$ deg$^2$ with an angular resolution of $10.5''$ and a depth of 15 mJy/beam. To account for the intensity loss due to the background removal process, we combine this map with lower resolution CSO/Bolocam and \textit{Planck}/HFI data to produce an effective full intensity 1.1 mm continuum map. With this map and existing \textit{Herschel} surveys, we have carried out a comprehensive analysis of the spectral energy distribution (SED) of dust in the CMZ. A key component of this analysis is the implementation of a model-based deconvolution approach, incorporating the Point Spread Functions (PSFs) of the different instruments, and hence recovering a significant amount of spatial information on angular scales larger than $10.5''$. The monitoring of Sgr A* was carried out as part of a worldwide, multi-wavelength campaign when the so-called G2 object was undergoing the pericenter passage around the massive black hole (MBH). Our preliminary results include 1) high-resolution maps of column density, temperature and dust spectral index across the CMZ; 2) a 1.1~mm light curve of Sgr A* showing an outburst of $140\%$ maximum amplitude on 9th May, 2014 but otherwise only stochastic variations of $10\%$ and no systematic long-term change, consistent with other observations.

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arXiv2021

The Single-Cloud Star Formation Relation

One of the most important and well-established empirical results in astronomy is the Kennicutt-Schmidt (KS) relation between the density of interstellar gas and the rate at which that gas forms stars. A tight correlation between these quantities has long been measured at galactic scales. More recently, using surveys of YSOs, a KS relationship has been found within molecular clouds relating the surface density of star formation to the surface density of gas; however, the scaling of these laws varies significantly from cloud to cloud. In this Letter, we use a recently developed, high-accuracy catalog of young stellar objects from $\textit{Spitzer}$ combined with high-dynamic-range gas column density maps of twelve nearby ($<$1.5 kpc) molecular clouds from $\textit{Herschel}$ to re-examine the KS relation within individual molecular clouds. We find a tight, linear correlation between clouds' star formation rate per unit area and their gas surface density normalized by the gas free-fall time. The measured intracloud KS relation, which relates star formation rate to the volume density, extends over more than two orders of magnitude within each cloud and is nearly identical in each of the twelve clouds, implying a constant star formation efficiency per free-fall time $ε_{\rm ff}\approx 0.026$. The finding of a universal correlation within individual molecular clouds, including clouds that contain no massive stars or massive stellar feedback, favors models in which star formation is regulated by local processes such as turbulence or stellar feedback such as protostellar outflows, and disfavors models in which star formation is regulated only by galaxy properties or supernova feedback on galactic scales.

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arXiv2021

Reconstructing three-dimensional densities from two-dimensional observations of molecular gas

Star formation has long been known to be an inefficient process, in the sense that only a small fraction $ε_{\rm ff}$ of the mass of any given gas cloud is converted to stars per cloud free-fall time. However, developing a successful theory of star formation will require measurements of both the mean value of $ε_{\rm ff}$ and its scatter from one molecular cloud to another. Because $ε_{\rm ff}$ is measured relative to the free-fall time, such measurements require accurate determinations of cloud volume densities. Efforts to measure the volume density from two-dimensional projected data, however, have thus far relied on treating molecular clouds as simple uniform spheres, while their real shapes are likely filamentary and their density distributions far from uniform. The resulting uncertainty in the true volume density is likely one of the major sources of error in observational estimates of $ε_{\rm ff}$. In this paper, we use a suite of simulations of turbulent, magnetized, radiative, self-gravitating star-forming clouds to examine whether it is possible to obtain more accurate volume density estimates and thereby reduce this error. We create mock observations from simulations, and show that current analysis methods relying on the spherical assumption likely yield ~ 0.26 dex underestimations and ~ 0.51 dex errors in volume density estimates, corresponding to a ~ 0.13 dex overestimation and a ~ 0.25 dex scatter in $ε_{\rm ff}$, comparable to the scatter in observed cloud samples. We build a predictive model that uses information accessible in two-dimensional measurements -- most significantly the Gini coefficient of the surface density distribution -- to estimate volume density with ~ 0.3 dex less scatter. We test our method on a recent observation of the Ophiuchus cloud, and show that it successfully reduces the $ε_{\rm ff}$ scatter.

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arXiv2020

Star-Gas Surface Density Correlations in Twelve Nearby Molecular Clouds I: Data Collection and Star-Sampled Analysis

We explore the relation between the stellar mass surface density and the mass surface density of molecular hydrogen gas in twelve nearby molecular clouds that are located at $<$1.5 kpc distance. The sample clouds span an order of magnitude range in mass, size, and star formation rates. We use thermal dust emission from $Herschel$ maps to probe the gas surface density and the young stellar objects from the most recent $Spitzer$ Extended Solar Neighborhood Archive (SESNA) catalog to probe the stellar surface density. Using a star-sampled nearest neighbor technique to probe the star-gas surface density correlations at the scale of a few parsecs, we find that the stellar mass surface density varies as a power-law of the gas mass surface density, with a power-law index of $\sim$2 in all the clouds. The consistent power-law index implies that star formation efficiency is directly correlated with gas column density, and no gas column density threshold for star formation is observed. We compare the observed correlations with the predictions from an analytical model of thermal fragmentation, and with the synthetic observations of a recent hydrodynamic simulation of a turbulent star-forming molecular cloud. We find that the observed correlations are consistent for some clouds with the thermal fragmentation model and can be reproduced using the hydrodynamic simulations.

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arXiv2019

CASI: A Convolutional Neural Network Approach for Shell Identification

We utilize techniques from deep learning to identify signatures of stellar feedback in simulated molecular clouds. Specifically, we implement a deep neural network with an architecture similar to U-Net and apply it to the problem of identifying wind-driven shells and bubbles using data from magneto-hydrodynamic simulations of turbulent molecular clouds with embedded stellar sources. The network is applied to two tasks, dense regression and segmentation, on two varieties of data, simulated density and synthetic 12 CO observations. Our Convolutional Approach for Shell Identification (CASI) is able to obtain a true positive rate greater than 90\%, while maintaining a false positive rate of 1\%, on two segmentation tasks and also performs well on related regression tasks. The source code for CASI is available on GitLab.

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arXiv2019

Variability in the Assembly of Protostellar Systems

Understanding the collapse of clouds and the formation of protoplanetary disks is essential to understanding the formation of stars and planets. Infall and accretion, the mass-aggregation processes that occur at envelope and disk scales, drive the dynamical evolution of protostars. While the observations of protostars at different stages constrain their evolutionary tracks, the impact of variability due to accretion bursts on dynamical and chemical evolution of the source is largely unknown. The lasting effects on protostellar envelopes and disks are tracked through multi-wavelength and time domain observational campaigns, requiring deep X-ray, infrared, and radio imaging and spectroscopy, at a sufficient level of spatial detail to distinguish contributions from the various substructures (i.e., envelope from disk from star from outflow). Protostellar models derived from these campaigns will illuminate the initial chemical state of protoplanetary disks during the epoch of giant planet formation. Insight from individual star formation in the Milky Way is also necessary to understand star formation rates in extragalactic sources. This cannot be achieved with ground-based observatories and is not covered by currently approved instrumentation. Requirements: High (v < 10 km/s for survey; v < 1 km/s for followup) spectral resolution capabilities with relatively rapid response times in the IR (3-500 um), X-ray (0.1-10 keV), and radio (cm) are critical to follow the course of accretion and outflow during an outburst. Complementary, AU-scale radio observations are needed to probe the disk accretion zone, and 10 AU-scale to probe chemical and kinematic structures of the disk-forming regions, and track changes in the dust, ice, and gas within protostellar envelopes.

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arXiv2018

Catalogue of High Protostellar Surface Density Regions in Nearby Embedded Clusters

We analyze high-quality stellar catalogs for 24 young and nearby (within 1 kpc) embedded clusters and present a catalogue of 32 groups which have a high concentration of protostars. The median effective radius of these groups is 0.17 pc. The median protostellar and pre-main sequence star surface densities are 46 M_{\odot} pc^{-2} and 11 M_{\odot} pc^{-2}, respectively. We estimate the age of these groups using a model of constant birthrate and random accretion stopping and find a median value of 0.25 Myr. Some groups in Aquila and Serpens, Corona Australia and Ophichus L1688 show high protostellar surface density and high molecular gas surface density, which seem to be undergoing vigorous star formation. These groups provide an excellent opportunity to study initial conditions of clustered star formation. Comparison of protostellar and pre-main-sequence stellar surface densities reveal continuous low-mass star formation of these groups over several Myr in some clouds. For groups with typical protostellar separations of less than 0.4 pc, we find that these separations agree well with the thermal Jeans fragmentation scale. On the other hand, for groups with typical protostellar separations larger than 0.4 pc, these separations are always larger than the associated Jeans length.

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arXiv2017

Hierarchical fragmentation in the Perseus molecular cloud: From the cloud scale to protostellar objects

We present a study of hierarchical structure in the Perseus molecular cloud, from the scale of the entire cloud ($\gtrsim$10 pc) to smaller clumps ($\sim$1 pc), cores ($\sim$0.05-0.1 pc), envelopes ($\sim$300-3000 AU) and protostellar objects ($\sim$15 AU). We use new observations from the Submillimeter Array (SMA) large project "Mass Assembly of Stellar Systems and their Evolution with the SMA (MASSES)" to probe the envelopes, and recent single-dish and interferometric observations from the literature for the remaining scales. This is the first study to analyze hierarchical structure over five scales in the same cloud complex. We compare the number of fragments with the number of Jeans masses in each scale to calculate the Jeans efficiency, or the ratio of observed to expected number of fragments. The velocity dispersion is assumed to arise either from purely thermal motions, or from combined thermal and non-thermal motions inferred from observed spectral line widths. For each scale, thermal Jeans fragmentation predicts more fragments than observed, corresponding to inefficient thermal Jeans fragmentation. For the smallest scale, thermal plus non-thermal Jeans fragmentation also predicts too many protostellar objects. However at each of the larger scales thermal plus non-thermal Jeans fragmentation predicts fewer than one fragment, corresponding to no fragmentation into envelopes, cores, and clumps. Over all scales, the results are inconsistent with complete Jeans fragmentation based on either thermal or thermal plus non-thermal motions. They are more nearly consistent with inefficient thermal Jeans fragmentation, where the thermal Jeans efficiency increases from the largest to the smallest scale.

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