Clump Mass Function Research Articles

Nobeyama 45 m Cygnus-X CO Survey. II. Physical Properties of C18O Clumps

Abstract We report the statistical physical properties of the C18O(J = 1–0) clumps present in a prominent cluster-forming region, Cygnus X, using the data set obtained by the Nobeyama 45 m radio telescope. This survey covers 9 deg2 of the northern and southern regions of Cygnus X, and, in total, 174 C18O clumps are identified using the dendrogram method. Assuming a distance of 1.4 kpc, these clumps have radii of 0.2–1 pc, velocity dispersions of <2.2 km s−1, gas masses of 30–3000 M ⊙, and H2 densities of (0.2–5.5) × 104 cm−3. We confirm that the C18O clumps in the northern region have a higher H2 density than those in the southern region, supporting the existence of a difference in the evolutionary stages, consistent with the star-formation activity of these regions. The difference in the clump properties of the star-forming and starless clumps is also confirmed by the radius, velocity dispersion, gas mass, and H2 density. The average virial ratio of 0.3 supports that these clumps are gravitationally bound. The C18O clump mass function shows two spectral index components, α = −1.4 in 55–140 M ⊙ and α = −2.1 in >140 M ⊙, which are consistent with the low- and intermediate-mass parts of the Kroupa’s initial mass function. The spectral index of the star-forming clumps >140 M ⊙ is consistent with that of the starless clumps ranging from 55–140 M ⊙, suggesting that the latter will evolve into star-forming clumps while retaining the gas accretion. Assuming a typical star-formation efficiency of molecular clumps (10%), about 10 C18O clumps having a gas mass of >103 M ⊙ will evolve into open clusters containing one or more OB stars.

An ALMA archival study of the clump mass function in the Large Magellanic Cloud

We present 1.3 and 3.2 mm continuum maps of three star forming regions in the Large Magellanic Cloud (LMC) observed with the Atacama Large Millimeter/Submillimeter Array (ALMA). The data were taken as part of two projects retrieved from the ALMA public archive plus one project observed specifically for this work. We develop a technique to combine maps at these wavelengths to estimate dust-only emission corrected for free-free emission contamination. From these observations we identify 32 molecular clumps in the LMC and estimate their total mass from their dust emission to range from 205 to 5740 M$_{\odot}$. We derive a cumulative clump mass function ($N(\geq M) \propto M^{\alpha + 1}$) and fit it with a double power law to find $\alpha_{\mathrm{low}} = -1.76^{+0.04}_{-0.05}$, $\alpha_{\mathrm{high}} = -3.3 \pm 0.2$, and a break mass of 2500$^{+300}_{-200}$ M$_{\odot}$. A comparison to the 30 Doradus-10 mass function derived previously from CO (2-1) data reveals a consistent range of clump masses and good agreement between the fitted slopes. We also find that the low mass index of the LMC mass function agrees well with the high mass index for core and clump mass functions from several star forming regions in the Milky Way. This agreement may indicate an extension of the Milky Way power law to higher masses than previously observed.

First constraints on the stellar mass function of star-forming clumps at the peak of cosmic star formation

Abstract Star-forming clumps dominate the rest-frame ultraviolet morphology of galaxies at the peak of cosmic star formation. If turbulence driven fragmentation is the mechanism responsible for their formation, we expect their stellar mass function to follow a power law of slope close to −2. We test this hypothesis performing the first analysis of the stellar mass function of clumps hosted in galaxies at $z$ ∼ 1–3.5. The clump sample is gathered from the literature with similar detection thresholds and stellar masses determined in a homogeneous way. To overcome the small number statistics per galaxy (each galaxy hosts up to a few tens of clumps only), we combine all high-redshift clumps. The resulting clump mass function follows a power law of slope ∼−1.7 and flattens at masses below $2\times 10^7\, \mathrm{M}_{\odot }$. By means of randomly sampled clump populations, drawn out of a power-law mass function of slope −2, we test the effect of combining small clump populations, detection limits of the surveys, and blending on the mass function. Our numerical exercise reproduces all the features observed in the real clump mass function confirming that it is consistent with a power law of slope ≃ − 2. This result supports the high-redshift clump formation through fragmentation in a similar fashion as in local galaxies, but under different gas conditions.

Spatially associated clump populations in Rosette from CO and dust maps

Spatial association of clumps from different tracers turns out to be a valuable tool to determine the physical properties of molecular clouds. It provides a reliable estimate for the $X$-factors, serves to trace the density of clumps seen in column densities only and allows to measure the velocity dispersion of clumps identified in dust emission. We study the spatial association between clump populations, extracted by use of the GAUSSCLUMPS technique from $^{12}$CO (1-0), $^{13}$CO (1-0) line maps and Herschel dust-emission maps of the star-forming region Rosette, and analyse their physical properties. All CO clumps that overlap with another CO or dust counterpart are found to be gravitationally bound and located in the massive star-forming filaments of the molecular cloud. They obey a single mass-size relation $M_{\rm cl}\propto R_{\rm cl}^\gamma$ with $\gamma\simeq3$ (implying constant mean density) and display virtually no velocity-size relation. We interpret their population as low-density structures formed through compression by converging flows and still not evolved under the influence of self-gravity. The high-mass parts of their clump mass functions are fitted by a power law ${\rm d}N_{\rm cl}/{\rm d}\,\log M_{\rm cl}\propto M_{\rm cl}^{\Gamma}$ and display a nearly Salpeter slope $\Gamma\sim-1.3$. On the other hand, clumps extracted from the dust-emission map exhibit a shallower mass-size relation with $\gamma=2.5$ and mass functions with very steep slopes $\Gamma\sim-2.3$ even if associated with CO clumps. They trace density peaks of the associated CO clumps at scales of a few tenths of pc where no single density scaling law should be expected.

Source clustering in the Hi-GAL survey determined using a minimum spanning tree method

Aims. The aims are to investigate the clustering of the far-infrared sources from the Herschel infrared Galactic Plane Survey (Hi-GAL) in the Galactic longitude range of −71 to 67 deg. These clumps, and their spatial distribution, are an imprint of the original conditions within a molecular cloud. This will produce a catalogue of over-densities. Methods. The minimum spanning tree (MST) method was used to identify the over-densities in two dimensions. The catalogue was further refined by folding in heliocentric distances, resulting in more reliable over-densities, which are cluster candidates. Results. We found 1633 over-densities with more than ten members. Of these, 496 are defined as cluster candidates because of the reliability of the distances, with a further 1137 potential cluster candidates. The spatial distributions of the cluster candidates are different in the first and fourth quadrants, with all clusters following the spiral structure of the Milky Way. The cluster candidates are fractal. The clump mass functions of the clustered and isolated are statistically indistinguishable from each other and are consistent with Kroupa’s initial mass function.

THE AGORA HIGH-RESOLUTION GALAXY SIMULATIONS COMPARISON PROJECT. II. ISOLATED DISK TEST

ABSTRACT Using an isolated Milky Way-mass galaxy simulation, we compare results from nine state-of-the-art gravito-hydrodynamics codes widely used in the numerical community. We utilize the infrastructure we have built for the AGORA High-resolution Galaxy Simulations Comparison Project. This includes the common disk initial conditions, common physics models (e.g., radiative cooling and UV background by the standardized package Grackle) and common analysis toolkit yt, all of which are publicly available. Subgrid physics models such as Jeans pressure floor, star formation, supernova feedback energy, and metal production are carefully constrained across code platforms. With numerical accuracy that resolves the disk scale height, we find that the codes overall agree well with one another in many dimensions including: gas and stellar surface densities, rotation curves, velocity dispersions, density and temperature distribution functions, disk vertical heights, stellar clumps, star formation rates, and Kennicutt–Schmidt relations. Quantities such as velocity dispersions are very robust (agreement within a few tens of percent at all radii) while measures like newly formed stellar clump mass functions show more significant variation (difference by up to a factor of ∼3). Systematic differences exist, for example, between mesh-based and particle-based codes in the low-density region, and between more diffusive and less diffusive schemes in the high-density tail of the density distribution. Yet intrinsic code differences are generally small compared to the variations in numerical implementations of the common subgrid physics such as supernova feedback. Our experiment reassures that, if adequately designed in accordance with our proposed common parameters, results of a modern high-resolution galaxy formation simulation are more sensitive to input physics than to intrinsic differences in numerical schemes.

LINKING DENSE GAS FROM THE MILKY WAY TO EXTERNAL GALAXIES

ABSTRACT In a survey of 65 galaxies, Gao & Solomon found a tight linear relation between the infrared luminosity (L IR, a proxy for the star formation rate) and the HCN(1–0) luminosity ( ). Wu et al. found that this relation extends from these galaxies to the much less luminous Galactic molecular high-mass star-forming clumps (∼1 pc scales), and posited that there exists a characteristic ratio L IR/ for high-mass star-forming clumps. The Gao–Solomon relation for galaxies could then be explained as a summation of large numbers of high-mass star-forming clumps, resulting in the same L IR/ ratio for galaxies. We test this explanation and other possible origins of the Gao–Solomon relation using high-density tracers (including HCN(1–0), N2H+(1–0), HCO+(1–0), HNC(1–0), HC3N(10–9), and C2H(1–0)) for ∼300 Galactic clumps from the Millimetre Astronomy Legacy Team 90 GHz (MALT90) survey. The MALT90 data show that the Gao–Solomon relation in galaxies cannot be satisfactorily explained by the blending of large numbers of high-mass clumps in the telescope beam. Not only do the clumps have a large scatter in the L IR/ ratio, but also far too many high-mass clumps are required to account for the Galactic IR and HCN luminosities. We suggest that the scatter in the L IR/ ratio converges to the scatter of the Gao–Solomon relation at some size-scale ≳1 kpc. We suggest that the Gao–Solomon relation could instead result from of a universal large-scale star formation efficiency, initial mass function, core mass function, and clump mass function.

Properties of massive star-forming clumps with infall motions

In this work, we aim to characterise high-mass clumps with infall motions. We selected 327 clumps from the Millimetre Astronomy Legacy Team 90-GHz (MALT90) survey, and identified 100 infall candidates. Combined with the results of He et al. (2015), we obtained a sample of 732 high-mass clumps, including 231 massive infall candidates and 501 clumps where infall is not detected. Objects in our sample were classified as pre-stellar, proto-stellar, HII or photo-dissociation region (PDR). The detection rates of the infall candidates in the pre-stellar, proto-stellar, HII and PDR stages are 41.2%, 36.6%, 30.6% and 12.7%, respectively. The infall candidates have a higher H$_{2}$ column density and volume density compared with the clumps where infall is not detected at every stage. For the infall candidates, the median values of the infall rates at the pre-stellar, proto-stellar, HII and PDR stages are 2.6$\times$10$^{-3}$, 7.0$\times$10$^{-3}$, 6.5$\times$10$^{-3}$ and 5.5$\times$10$^{-3}$ M$_\odot$ yr$^{-1}$, respectively. These values indicate that infall candidates at later evolutionary stages are still accumulating material efficiently. It is interesting to find that both infall candidates and clumps where infall is not detected show a clear trend of increasing mass from the pre-stellar to proto-stellar, and to the HII stages. The power indices of the clump mass function (ClMF) are 2.04$\pm$0.16 and 2.17$\pm$0.31 for the infall candidates and clumps where infall is not detected, respectively, which agree well with the power index of the stellar initial mass function (2.35) and the cold Planck cores (2.0).

Probing the clumping structure of giant molecular clouds through the spectrum, polarisation and morphology of X-ray reflection nebulae

We suggest a method for probing global properties of clump populations in Giant Molecular Clouds (GMCs) in the case where these act as X-ray reflection nebulae (XRNe), based on the study of the clumping's overall effect on the reflected X-ray signal, in particular on the Fe K-alpha line's shoulder. We consider the particular case of Sgr B2, one of the brightest and most massive XRN in our Galaxy. We parametrise the gas distribution inside the cloud using a simple clumping model, with the slope of the clump mass function (alpha), the minimum clump mass (m_{min}), the fraction of the cloud's mass contained in clumps (f_{DGMF}), and the mass-size relation of individual clumps as free parameters, and investigate how these affect the reflected X-ray spectrum. In the case of very dense clumps, similar to those presently observed in Sgr B2, these occupy a small volume of the cloud and present a small projected area to the incoming X-ray radiation. We find that these contribute negligibly to the scattered X-rays. Clump populations with volume filling factors of > 10^{-3}, do leave observational signatures, that are sensitive to the clump model parameters, in the reflected spectrum and polarisation. Future high-resolution X-ray observations could therefore complement the traditional optical and radio observations of these GMCs, and prove to be a powerful probe in the study of their internal structure. Finally, clumps in GMCs should be visible both as bright spots and regions of heavy absorption in high resolution X-ray observations. We therefore further study the time-evolution of the X-ray morphology, under illumination by a transient source, as a probe of the 3d distribution and column density of individual clumps by future X-ray observatories.

The Central Molecular Zone in H13CO+ and thermal SiO emission lines

Abstract We present results from a high-resolution wide-field imaging observation of the Central Molecular Zone (CMZ) in H13CO+J = 1–0 and SiO v = 0, J = 2–1 emission lines using the 45-m telescope at the Nobeyama Radio Observatory in order to depict the high-density molecular gas mass distribution and explore molecular gas affected by interstellar shocks. By using the clumpfind algorithm we identify 114 molecular clumps in the H13CO+ data cube. The clump mass function (CMF) can be described by a power law (dN/dM ∝ M−γ, with γ ≃ 2) in the range of 5 × 103 < Mclump < 2 × 104 M⊙. The brightness temperature ratio RT = T(SiO)/T(H13CO+) indicates the strength of the shock. The Sgr B2 complex has several expanding shell-like structures with a large velocity-width (ΔV > 50 km s−1). They correspond to the high brightness temperature ratio area (RT ≲ 8). A Large Velocity Gradient model analysis with the RADEX program confirms the enhancement of SiO molecules in the shells. On the other hand, there is no such large shell with a high ratio in the Sgr A complex. A hollow hemispherical structure is found in the l–b–v data cube of the Sgr B2 complex. The central part of the structure has a high ratio (RT ≲ 8). The ratio decreases with proximity to the outer area. The properties are consistent with those expected from simulations of cloud–cloud collisions. The structure is probably a site of ongoing cloud–cloud collision.

ATLASGAL – Kinematic distances and the dense gas mass distribution of the inner Galaxy

The formation of high mass stars and clusters occurs in giant molecular clouds. Objects in evolved stages of massive star formation such as protostars, hot molecular cores, and ultracompact HII regions have been studied in more detail than earlier, colder objects. With this in mind, the APEX Telescope Large Area Survey of the whole inner Galactic plane at 870 micron (ATLASGAL) has been carried out to provide a global view of cold dust and star formation at submillimetre wavelengths. To derive kinematic distances to a large sample of ATLASGAL clumps we divided them into groups of sources, which are located close together, mostly within a radius of 2 pc, and have velocities in a similar range with a median velocity dispersion of ~ 1 km/s. Using NH3, N2H+ and CS velocities we calculate near and far kinematic distances to 296 groups of ATLASGAL sources in the first quadrant and 393 groups in the fourth quadrant. We analyse HI self-absorption and HI absorption to resolve the kinematic distance ambiguity. We obtain a scale height of ~ 28+/-2 pc and displacement below the Galactic midplane of ~ -7+/-1 pc. Within distances from 2 to 18 kpc ATLASGAL clumps have a broad range of gas masses with a median of 1050 solar masses and a wide distribution of radii with a median of 0.4 pc. Their distribution in galactocentric radii is correlated with spiral arms. Using a statistically significant ATLASGAL sample we derive a power-law exponent of -2.2+/-0.1 of the clump mass function. This is consistent with the slope derived for clusters and with that of the stellar initial mass function. Examining the power-law index for different galactocentric distances and various source samples shows that it is independent of environment and evolutionary phase. Fitting the mass-size relationship by a power law gives a slope of 1.76+/-0.01 for cold sources such as IRDCs and warm clumps associated with HII regions.

CHARACTERIZING THE STRUCTURE OF DIFFUSE EMISSION IN Hi-GAL MAPS

We present a study of the structure of the Galactic interstellar medium through the Delta-variance technique, related to the power spectrum and the fractal properties of infrared/sub-mm maps. Through this method, it is possible to provide quantitative parameters which are useful to characterize different morphological and physical conditions, and to better constrain the theoretical models. In this respect, the Herschel Infrared Galactic Plane Survey carried out at five photometric bands from 70 to 500 \mu m constitutes an unique database for applying statistical tools to a variety of regions across the Milky Way. In this paper, we derive a robust estimate of the power-law portion of the power spectrum of four contiguous 2{\deg}x2{\deg} Hi-GAL tiles located in the third Galactic quadrant (217{\deg} < l < 225{\deg}, -2{\deg} < b < 0{\deg}). The low level of confusion along the line of sight testified by CO observations makes this region an ideal case. We find very different values of the power spectrum slope from tile to tile but also from wavelength to wavelength (2 < \beta < 3), with similarities between fields attributable to components located at the same distance. Thanks to the comparison with models of turbulence, an explanation of the determined slopes in terms of the fractal geometry is also provided, and possible relations with the underlying physics are investigated. In particular, an anti-correlation between ISM fractal dimension and star formation efficiency is found for the two main distance components observed in these fields. A possible link between the fractal properties of the diffuse emission and the resulting clump mass function is discussed.

On the shape of the mass-function of dense clumps in the Hi-GAL fields

Context. Stars form in dense, dusty clumps of molecular clouds, but little is known about their origin, their evolution, and their detailed physical properties. In particular, the relationship between the mass distribution of these clumps (also known as the “clump mass function”, or CMF) and the stellar initial mass function (IMF) is still poorly understood.

Clump mass function at an early stage of molecular cloud evolution – II. Galactic cloud complexes

The statistical approach for derivation of the clump mass function (ClMF) developed by Donkov, Veltchev & Klessen is put to observational test through comparison with mass distributions of clumps from molecular emission and dust continuum maps of Galactic cloud complexes, obtained by various authors. The results indicate gravitational boundedness of the dominant clump population, with or without taking into account the contribution of their thermal and magnetic energy. The ClMF can be presented by combination of two power-law functions separated by a characteristic mass from about ten to hundreds solar masses. The slope of the intermediate-mass ClMF is shallow and nearly constant (-0.25 \gtrsim \Gamma_{IM} \gtrsim -0.55) while the high-mass part is fitted by models that imply gravitationally unstable clumps and exhibit slopes in a broader range (-0.9 \gtrsim \Gamma_{IM} \gtrsim -1.6), centered at the value of the stellar initial mass function (\Gamma_{HM} \gtreqless -1.3).

A Hi-GAL study of the high-mass star-forming region G29.96–0.02

Context. G29.96-0.02 is a high-mass star-forming cloud observed at 70, 160, 250, 350, and 500 microns as part of the Herschel survey of the Galactic Plane during the Science Demonstration Phase. Aims. We wish to conduct a far-infrared study of the sources associated with this star-forming region by estimating their physical properties and evolutionary stage, and investigating the clump mass function, the star formation efficiency and rate in the cloud. Methods. We have identified the Hi-GAL sources associated with the cloud, searched for possible counterparts at centimeter and infrared wavelengths, fitted their spectral energy distribution and estimated their physical parameters. Results. A total of 198 sources have been detected in all 5 Hi-GAL bands, 117 of which are associated with 24 microns emission and 87 of which are not associated with 24 microns emission. We called the former sources 24 microns-bright and the latter ones 24 microns-dark. The [70-160] color of the 24 microns-dark sources is smaller than that of the 24 microns-bright ones. The 24 microns-dark sources have lower L_bol and L_bol/M_env than the 24 microns-bright ones for similar M_env, which suggests that they are in an earlier evolutionary phase. The G29-SFR cloud is associated with 10 NVSS sources and with extended centimeter continuum emission well correlated with the 70 microns emission. Most of the NVSS sources appear to be early B or late O-type stars. The most massive and luminous Hi-GAL sources in the cloud are located close to the G29-UC region, which suggests that there is a privileged area for massive star formation towards the center of the G29-SFR cloud. Almost all the Hi-GAL sources have masses well above the Jeans mass but only 5% have masses above the virial mass, which indicates that most of the sources are stable against gravitational collapse. The sources with M_env > M_virial and that ...

On the shape of the mass-function of dense clumps in the Hi-GAL fields

Stars form in dense, dusty clumps of molecular clouds, but little is known about their origin and evolution. In particular, the relationship between the mass distribution of these clumps (also known as the "clump mass function", or CMF) and the stellar initial mass function (IMF), is still poorly understood. In order to discern the "true" shape of the CMF and to better understand how the CMF may evolve toward the IMF, large samples of bona-fide pre- and proto-stellar clumps are required. The sensitive observations of the Herschel Space Observatory (HSO) are now allowing us to look at large clump populations in various clouds with different physical conditions. We analyse two fields in the Galactic plane mapped by HSO during its science demonstration phase, as part of the more complete and unbiased Herschel infrared GALactic Plane Survey (Hi-GAL). These fields undergo a source-extraction and flux-estimation pipeline, which allows us to obtain a sample with thousands of clumps. Starless and proto-stellar clumps are separated using both color and positional criteria to find those coincident with MIPS 24 micron sources. We describe the probability density functions of the power-law and lognormal models that are used to fit the CMFs, and we then find their best-fit parameters. For the lognormal model we apply several statistical techniques to the data and compare their results. The CMFs of the two SDP fields show very similar shapes, but very different mass scales. This similarity is confirmed by the values of the best-fit parameters of either the power-law or lognormal model. The power-law model leads to almost identical CMF slopes, whereas the lognormal model shows that the CMFs have similar widths. The similar CMF shape but different mass scale represents an evidence that the overall process of star formation in the two regions is very different.

The clump mass function of the dense clouds in the Carina nebula complex

We want to characterize the properties of the cold dust clumps in the Carina Nebula Complex (CNC), which shows a very high level of massive star feedback. We derive the Clump Mass Function (ClMF), explore the reliability of different clump extraction algorithms, and investigate the influence of the temperatures within the clouds on the resulting shape of the ClMF. We analyze a 1.25x1.25 deg^2 wide-field sub-mm map obtained with LABOCA (APEX), which provides the first spatially complete survey of the clouds in the CNC. We use the three clump-finding algorithms CLUMPFIND (CF), GAUSSCLUMPS (GC) and SExtractor (SE) to identify individual clumps and determine their total fluxes. In addition to assuming a common `typical' temperature for all clouds, we also employ an empirical relation between cloud column densities and temperature to determine an estimate of the individual clump temperatures, and use this to determine individual clump masses. While the ClMF based on the CF extraction is very well described by a power-law, the ClMFs based on GC and SE are better represented by a log-normal distribution. We also find that the use of individual clump temperatures leads to a shallower ClMF slope than the assumption of a common temperature (e.g. 20 K) of all clumps. The power-law of dN/dM \propto M^-1.95 we find for the CF sample is in good agreement with ClMF slopes found in previous studies of other regions. The dependence of the ClMF shape (power-law vs. log-normal distribution) on the employed extraction method suggests that observational determinations of the ClMF shape yields only very limited information about the true structure of the cloud. Interpretations of log-normal ClMF shape as a signature of turbulent pre-stellar clouds vs. power-law ClMFs as a signature of star-forming clouds may be taken with caution for a single extraction algorithm without additional information.

CONNECTING THE DOTS: ANALYZING SYNTHETIC OBSERVATIONS OF STAR-FORMING CLUMPS IN MOLECULAR CLOUDS

In this paper, we investigate the extent to which observations of molecular clouds can correctly identify and measure star-forming clumps. We produced a synthetic column density map and a synthetic spectral-line data cube from the simulated collapse of a 5000 M$_{\odot}$ molecular cloud. By correlating the clumps found in the simulation to those found in the synthetic observations, clump masses derived from spectral-line data cubes were found to be quite close to the true physical properties of the clumps. We also find that the `observed' clump mass function derived from the column density map is shifted by a factor of ~ 3 higher than the true clump mass function, due to projection of low-density material along the line of sight. Alves et al. (2007) first proposed that a shift of a clump mass function to higher masses by a factor of 3 can be attributed to a star formation efficiency of 30 %. Our results indicate that this finding may instead be due to an overestimate of clump masses determined from column density observations.

Gravitational fragmentation of the Carina Flare supershell

AbstractWe study the gravitational fragmentation of a thick shell comparing the analytical theory to 3D hydrodynamic simulations and to observations of the Carina Flare supershell. We use both grid-based (AMR) and particle-based (SPH) codes to follow the idealised model of the fragmenting shell and found an excellent agreement between the two codes. Growth rates of fragments at different wavelength are well described by the pressure assisted gravitational instability (PAGI) - a new theory of the thick shell fragmentation. Using the APEX telescope we observe a part of the surface of the Carina Flare supershell (GSH287+04-17) in the 13CO(2–1) line. We apply a new clump-finding algorithm DENDROFIND to identify 50 clumps. We determine the clump mass function and we construct the minimum spanning tree connecting clumps positions to estimate the typical distance among clumps. We conclude that the observed masses and distances correspond well to the prediction of PAGI.

Clump mass function at an early stage of molecular cloud evolution - I. A statistical approach

We derive the mass function of condensations (clumps) which were formed through a turbulent cascade over a range of spatial scales $L\le20$ pc during early, predominantly turbulent evolution of a molecular cloud. The approach rests upon the assumption of a statistical clump mass-density relationship $n\propto m^x$ with a scale dependence of the exponent $x$ obtained from equipartition relations between various forms of energy of clumps. The derived clump mass function (ClMF) could be represented by series of 2 or 3 power laws, depending on the chosen equipartition relation, the velocity scaling index and the type of turbulent forcing. The high-mass ClMF exhibits an average slope $\Gamma\simeq-1$, typical for fractal clouds, whereas its intermediate-mass part is shallower or flattened, in agreement with some observational studies.