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Volume density is a key physical quantity controlling the evolution of the interstellar medium (ISM) and star formation, but it cannot be accessed directly by observations of molecular clouds. We aim at estimating the volume density distribution in nearby molecular clouds, to measure the relation between column and volume densities and to determine their roles as predictors of star formation. We develop an inverse modelling method to estimate the volume density distributions of molecular clouds. We apply this method to 24 nearby molecular clouds for which column densities have been derived using Herschel observations and for which star formation efficiencies (SFE) have been derived using observations with the Spitzer space telescope. We then compare the relationships of several column- and volume-density based descriptors of dense gas with the SFE of the clouds. We derive volume density distributions for 24 nearby molecular clouds, which represents the most complete sample of such distributions to date. The relationship between column densities and peak volume densities in these clouds is a piece-wise power-law relation that changes its slope at a column density of $5-10\times 10^{22}$ H$_2$cm$^{-2}$. We interpret this as a signature of hierarchical fragmentation in the dense ISM. We find that the volume-density based dense gas fraction is the best predictor of star formation in the clouds, and in particular, it is as anticipated a better predictor than the column-density based dense gas fraction. We also derive a volume density threshold density for star formation of $2\times 10^4$ H$_2$cm$^{-3}$., Comment: 23 pages, 22 figures, accepted for publication in Astronomy and Astrophysics, supplementary online material at https://zenodo.org/records/14360623

Context. The availability of large bandwidth receivers for millimeter radio telescopes allows the acquisition of position-position-frequency data cubes over a wide field of view and a broad frequency coverage. These cubes contain much information on the physical, chemical, and kinematical properties of the emitting gas. However, their large size coupled with inhomogenous signal-to-noise ratio (SNR) are major challenges for consistent analysis and interpretation.Aims. We search for a denoising method of the low SNR regions of the studied data cubes that would allow to recover the low SNR emission without distorting the signals with high SNR.Methods. We perform an in-depth data analysis of the 13 CO and C 17 O (1 -- 0) data cubes obtained as part of the ORION-B large program performed at the IRAM 30m telescope. We analyse the statistical properties of the noise and the evolution of the correlation of the signal in a given frequency channel with that of the adjacent channels. This allows us to propose significant improvements of typical autoassociative neural networks, often used to denoise hyperspectral Earth remote sensing data. Applying this method to the 13 CO (1 -- 0) cube, we compare the denoised data with those derived with the multiple Gaussian fitting algorithm ROHSA, considered as the state of the art procedure for data line cubes.Results. The nature of astronomical spectral data cubes is distinct from that of the hyperspectral data usually studied in the Earth remote sensing literature because the observed intensities become statistically independent beyond a short channel separation. This lack of redundancy in data has led us to adapt the method, notably by taking into account the sparsity of the signal along the spectral axis. The application of the proposed algorithm leads to an increase of the SNR in voxels with weak signal, while preserving the spectral shape of the data in high SNR voxels.Conclusions. The proposed algorithm that combines a detailed analysis of the noise statistics with an innovative autoencoder architecture is a promising path to denoise radio-astronomy line data cubes. In the future, exploring whether a better use of the spatial correlations of the noise may further improve the denoising performances seems a promising avenue. In addition

Understanding the initial properties of star-forming material and how they affect the star formation process is key. From an observational point of view, the feedback from young high-mass stars on future star formation properties is still poorly constrained. In the framework of the IRAM 30m ORION-B large program, we obtained observations of the translucent and moderately dense gas, which we used to analyze the kinematics over a field of 5 deg^2 around the filamentary structures. We used the ROHSA algorithm to decompose and de-noise the C18O(1-0) and 13CO(1-0) signals by taking the spatial coherence of the emission into account. We produced gas column density and mean velocity maps to estimate the relative orientation of their spatial gradients. We identified three cloud velocity layers at different systemic velocities and extracted the filaments in each velocity layer. The filaments are preferentially located in regions of low centroid velocity gradients. By comparing the relative orientation between the column density and velocity gradients of each layer from the ORION-B observations and synthetic observations from 3D kinematic toy models, we distinguish two types of behavior in the dynamics around filaments: (i) radial flows perpendicular to the filament axis that can be either inflows (increasing the filament mass) or outflows and (ii) longitudinal flows along the filament axis. The former case is seen in the Orion B data, while the latter is not identified. We have also identified asymmetrical flow patterns, usually associated with filaments located at the edge of an HII region. This is the first observational study to highlight feedback from HII regions on filament formation and, thus, on star formation in the Orion B cloud. This simple statistical method can be used for any molecular cloud to obtain coherent information on the kinematics., Comment: 45 pages. Abridged abstract. Accepted by Astronomy and Astrophysics

Dust extinction is one of the most reliable tracers of the gas distribution in the Milky Way. The near-infrared (NIR) Vista Variables in the Via Lactea (VVV) survey enables extinction mapping based on stellar photometry over a large area in the Galactic plane. We devise a novel extinction mapping approach, XPNICER, by bringing together VVV photometric catalogs, stellar parameter data from StarHorse catalogs, and previously published Xpercentile and PNICER extinction mapping techniques. We apply the approach to the VVV survey area, resulting in an extinction map that covers the Galactic disk between 295 and 350 degrees at longitude and -2 to 2 degrees at latitude, and the Galactic bulge between -10 and 5 degrees at latitude. The map has 30 arcseconds spatial resolution and it traces extinctions typically up to about 10-20 mag of visual extinction and maximally up to Av~30 mag. We compare our map to previous dust based maps, concluding that it provides a high-fidelity extinction-based map, especially in its ability to recover both the diffuse dust component of the Galaxy and moderately extincted giant molecular cloud regions. The map is especially useful as independent, extinction-based data on the Galactic dust distribution and applicable for a wide range of studies from individual molecular clouds to the studies of the Galactic stellar populations., Comment: accepted by MNRAS, 37 pages

The kinematics of molecular gas are crucial for setting the stage for star formation. One key question related to the kinematic properties of gas is how they depend on the spatial scale. We aim to describe the CO spectra, velocity dispersions, and especially the linewidth-size relation, of molecular gas from cloud (parsec-) scales to kiloparsec scales in a complete region within the Milky Way disk. We utilise the census of molecular clouds within 2 kpc from our earlier work, together with CO emission data for them from the literature. We study the kinematics and the Larson's relations for the sample of individual clouds. We also mimic a face-on view of the Milky Way and analyse the kinematics of the clouds within apertures of 0.25-2 kpc in size. In this way, we describe the scale-dependency of the CO gas kinematics and Larson's relations. We describe the spectra of CO gas at cloud scales and in apertures between 0.25-2 kpc in our survey area. The spectra within the apertures are relatively symmetric but show non-Gaussian high-velocity wings. At cloud-scales, our sample shows a linewidth-size relation \sigma_v=1.5*R^{0.3\pm0.1} with a large scatter. The mass-size relation in the sample of clouds is M_{CO}= 794*R^{1.5\pm0.5}. The relations are also present for the apertures at kpc-scales. A suggestive dependency on galactic environment is seen, with apertures closer to the Galactic centre and the Sagittarius spiral arm having slightly higher velocity dispersions. We explore the possible effect of a diffuse component in the survey area, and find that such a component would widen the CO spectra and could flatten the linewidth-size relation. Understanding the nature of the possible diffuse CO component and its effects on observations is crucial for connecting Galactic and extragalactic data., Comment: 8 pages, 10 figures, accepted for publication in Astronomy & Astrophysics

The new Gaia data release (EDR3) with improved astrometry has opened a new era in studying our Milky Way in fine detail. We use Gaia EDR3 astrometry together with 2MASS and WISE photometry to study two of the most massive molecular clouds in the solar vicinity: Orion A and California. Despite having remarkable similarities in the plane of the sky in terms of shape, size, and extinction, California has an order of magnitude lower star formation efficiency. We use our state-of-the-art dust mapping technique to derive the detailed three-dimensional (3D) structure of the two clouds, taking into account both distance and extinction uncertainties, and a full 3D spatial correlation between neighbouring points. We discover that, despite the apparent filamentary structure in the plane of the sky, California is a flat 120-pc-long sheet extending from 410 to 530 $pc$. We show that not only Orion A and California differ substantially in their 3D shapes, but also Orion A has considerably higher density substructures in 3D than California. This result presents a compelling reason why the two clouds have different star formation activities. We also demonstrate how the viewing angle of California can substantially change the cloud's position in the Kennicutt-Schmidt relation. This underlines the importance of 3D information in interpreting star formation relations and challenges studies that rely solely on the column density thresholds to determine star formation activities in molecular clouds. Finally, we provide accurate distance estimates to multiple lines of sight towards various parts of the two clouds., Comment: Accepted for publication in ApJ Letters

The Gaia data give us an unprecedented view to the 3-dimensional (3D) structure of molecular clouds in the Solar neighbourhood. We study how the projected areas and masses of clouds, and consequently the Kennicutt-Schmidt relation (KS-relation), depend on the viewing angle. We derive the probability distributions of the projected areas and masses for nine clouds within 400 pc from the Sun using 3D dust distribution data from the literature. We find that the viewing angle can have a dramatic effect on the observed areas and masses of individual clouds. The joint probability distributions of the areas and masses are strongly correlated, relatively flat, and can show multiple peaks. The typical ranges and 50% quartiles of the distributions are roughly 100-200% and 20-80% of the median value, respectively, making viewing angle effects important for all individual clouds. The threshold value used to define the cloud areas is also important; our analysis suggests that the clouds become more anisotropic for smaller thresholds (larger scales). On average, the areas and masses of the plane-of-the-sky and face-on projections agree, albeit with a large scatter. This suggests that sample averages of areas and masses are relatively free of viewing angle effects, which is important to facilitate comparisons of extragalactic and galactic data. Ultimately, our results demonstrate that a cloud's location in the KS-relation is affected by viewing angle in a non-trivial manner. However, the KS-relation of our sample as a whole is not strongly affected by these effects, because the co-variance of the areas and masses causes the observed mean column density to remain relatively constant., Comment: Accepted to A&A Letters, 15 pages including appendices

Describing how the properties of the interstellar medium combine across size-scales is crucial for understanding star formation scaling laws and connecting Galactic and extragalactic data of molecular clouds. We describe how the statistical structure of clouds, and its connection to star formation, changes from sub-parsec to kiloparsec scales in a complete region within the Milky Way disk. We build a census of molecular clouds within 2 kpc from the Sun using literature. We examine the dust-based column density probability distributions (N-PDFs) of the clouds and their relation to star formation traced by young stellar objects (YSOs). We then examine our survey region from the outside, within apertures of varying sizes, and describe how the N-PDFs and their relation to star formation changes with the size-scale. The N-PDFs of the clouds are not well described by any single simple model; use of any single model may bias the interpretation of the N-PDFs. The top-heaviness of the N-PDFs correlates with star formation activity, and the correlation changes with Galactic environment (spiral-/inter-arm regions). We find that the density contrast of clouds may be more intimately linked to star formation than the dense gas mass fraction. The aperture-averaged N-PDFs vary with the size-scale and are more top-heavy for larger apertures. The top-heaviness of the aperture N-PDFs correlates with star formation activity up to roughly 0.5 kpc size-scale, depending on the environment. Our results suggest that the relations between cloud structure and star formation are environment specific and best captured by relative quantities (e.g., the density contrast). Finally, we show how the density structures of individual clouds give rise to a kpc-scale Kennicutt-Schmidt relationship as a combination of sampling effects and blending of different galactic environments., Comment: 19 pages and 19 figures in main text. Accepted for publication in A&A

Molecular hydrogen being unobservable in cold molecular clouds, the column density measurements of molecular gas currently rely either on dust emission observation in the far-IR or on star counting. (Sub-)millimeter observations of numerous trace molecules are effective from ground based telescopes, but the relationships between the emission of one molecular line and the H2 column density (NH2) is non-linear and sensitive to excitation conditions, optical depths, abundance variations due to the underlying physico-chemistry. We aim to use multi-molecule line emission to infer NH2 from radio observations. We propose a data-driven approach to determine NH2 from radio molecular line observations. We use supervised machine learning methods (Random Forests) on wide-field hyperspectral IRAM-30m observations of the Orion B molecular cloud to train a predictor of NH2, using a limited set of molecular lines as input, and the Herschel-based dust-derived NH2 as ground truth output. For conditions similar to the Orion B molecular cloud, we obtain predictions of NH2 within a typical factor of 1.2 from the Herschel-based estimates. An analysis of the contributions of the different lines to the predictions show that the most important lines are $^{13}$CO(1-0), $^{12}$CO(1-0), C$^{18}$O(1-0), and HCO$^+$(1-0). A detailed analysis distinguishing between diffuse, translucent, filamentary, and dense core conditions show that the importance of these four lines depends on the regime, and that it is recommended to add the N$_2$H$^+$(1-0) and CH$_3$OH(20-10) lines for the prediction of NH2 in dense core conditions. This article opens a promising avenue to directly infer important physical parameters from the molecular line emission in the millimeter domain. The next step will be to try to infer several parameters simultaneously (e.g., NH2 and far-UV illumination field) to further test the method. [Abridged], Comment: Accepted for publication in A&A

The ionization fraction plays a key role in the physics and chemistry of the neutral interstellar medium, from controlling the coupling of the gas to the magnetic field to allowing fast ion-neutral reactions that drive interstellar chemistry. Most estimations of the ionization fraction have relied on deuterated species such as DCO+, whose detection is limited to dense cores representing an extremely small fraction of the volume of the giant molecular clouds they are part of. As large field-of-view hyperspectral maps become available, new tracers may be found. We search for the best observable tracers of the ionization fraction based on a grid of astrochemical models. We build grids of models that sample randomly a large space of physical conditions (unobservable quantities such as gas density, temperature, etc.) and compute the corresponding observables (line intensities, column densities) and the ionization fraction. We estimate the predictive power of each potential tracer by training a Random Forest model to predict the ionization fraction from that tracer, based on these model grids. In both translucent medium and cold dense medium conditions, several observable tracers with very good predictive power for the ionization fraction are found. Several tracers in cold dense medium conditions are found to be better and more widely applicable than the traditional DCO+/HCO+ ratio. We also provide simpler analytical fits for estimating the ionization fraction from the best tracers, and for estimating the associated uncertainties. We discuss the limitations of the present study and select a few recommended tracers in both types of conditions. The method presented here is very general and can be applied to the measurement of any other quantity of interest (cosmic ray flux, elemental abundances, etc.) from any type of model (PDR models, time-dependent chemical models, etc.). (abridged), Comment: 29 pages, 15 figures. Accepted for publication in A&A

CO isotopologue transitions are routinely observed in molecular clouds to probe the column density of the gas, the elemental ratios of carbon and oxygen, and to trace the kinematics of the environment. We aim at estimating the abundances, excitation temperatures, velocity field and velocity dispersions of the three main CO isotopologues towards a subset of the Orion B molecular cloud. We use the Cramer Rao Bound (CRB) technique to analyze and estimate the precision of the physical parameters in the framework of local-thermodynamic-equilibrium excitation and radiative transfer with an additive white Gaussian noise. We propose a maximum likelihood estimator to infer the physical conditions from the 1-0 and 2-1 transitions of CO isotopologues. Simulations show that this estimator is unbiased and efficient for a common range of excitation temperatures and column densities (Tex > 6 K, N > 1e14 - 1e15 cm-2). Contrary to the general assumptions, the different CO isotopologues have distinct excitation temperatures, and the line intensity ratios between different isotopologues do not accurately reflect the column density ratios. We find mean fractional abundances that are consistent with previous determinations towards other molecular clouds. However, significant local deviations are inferred, not only in regions exposed to UV radiation field but also in shielded regions. These deviations result from the competition between selective photodissociation, chemical fractionation, and depletion on grain surfaces. We observe that the velocity dispersion of the C18O emission is 10% smaller than that of 13CO. The substantial gain resulting from the simultaneous analysis of two different rotational transitions of the same species is rigorously quantified. The CRB technique is a promising avenue for analyzing the estimation of physical parameters from the fit of spectral lines., Comment: 27 pages, 23 PDF figures. Accepted for publication in A&A. Uses aa latex macro

The Vista Variables in the Via Lactea (VVV) survey has performed a multi-epoch near-infrared imaging of the inner Galactic plane. High-fidelity photometric catalogs are needed to utilize the data. We aim at producing a deep, point-spread-function (PSF) photometric catalog for the VVV survey J, H, and Ks band data. Specifically, we aim at taking advantage of all the epochs of the survey to reach high limiting magnitudes. We develop an automatic PSF-fitting pipeline based on the DaoPHOT algorithm and perform photometry on the stacked VVV images in J, H, and Ks bands. We present a PSF photometric catalog in the Vega system that contains about 926 million sources in the J, H, and Ks filters. About 10% of the sources are flagged as possible spurious detections. The 5 sigma limiting magnitudes of the sources with high reliability are about 20.8, 19.5, and 18.7 mag in the J, H, and Ks band, respectively, depending on the local crowding condition. Our photometric catalog reaches on average about one magnitude deeper than the previously released PSF DoPHOT photometric catalog. It also includes less spurious detections. There are significant differences in the brightnesses of faint sources between our catalog and the previously released one. The likely origin of these differences is in the different photometric algorithms that are utilized; it is not straightforward to assess which catalog is more accurate in which situations. Our new catalog is beneficial especially for science goals that require high limiting magnitudes; our catalog reaches such in fields that have a relatively uniform source number density. Overall, the limiting magnitudes and completeness are different in the fields with different crowding conditions., Comment: 19 pages, 22 figures, and 2 tables. Accepted by A&A

Our understanding of the dynamics of the interstellar medium is informed by the study of the detailed velocity structure of emission line observations. One approach to study the velocity structure is to decompose the spectra into individual velocity components; this leads to a description of the dataset that is significantly reduced in complexity. However, this decomposition requires full automation lest it becomes prohibitive for large datasets, such as Galactic plane surveys. We developed GaussPy+, a fully automated Gaussian decomposition package that can be applied to emission line datasets, especially large surveys of HI and isotopologues of CO. We built our package upon the existing GaussPy algorithm and significantly improved its performance for noisy data. New functionalities of GaussPy+ include: i) automated preparatory steps, such as an accurate noise estimation, which can also be used as standalone applications; ii) an improved fitting routine; iii) an automated spatial refitting routine that can add spatial coherence to the decomposition results by refitting spectra based on neighbouring fit solutions. We thoroughly tested the performance of GaussPy+ on synthetic spectra and a test field from the Galactic Ring Survey. We found that GaussPy+ can deal with cases of complex emission and even low to moderate signal-to-noise values., Comment: Accepted for publication in A&A. 36 pages, 33 figures (main text: 23 pages, 18 figures; Appendix: 13 pages, 15 figures). The GaussPy+ package is written in Python 3 and is freely available at GitHub under https://github.com/mriener/gausspyplus

Observations have discovered numerous giant molecular filaments (GMFs) in the Milky Way. However, their role in the Galactic star formation and Galaxy-scale evolution of dense gas is still unknown. We investigate systematically the star-forming content of all currently known GMFs. This allows us to estimate the star formation rates (SFRs) of the GMFs and to establish relationships between the SFRs and the GMF properties. We identify and classify the young stellar object (YSO) population of each GMF using multi-wavelength photometry from near- to far-infrared. We estimate the total SFRs assuming a universal and fully sampled initial mass function and luminosity function. We uniformly estimate the physical properties of 57 GMFs. The GMFs show correlations between the 13CO line width, mass, and size, similar to Larson's relations. We identify 36 394 infrared excess sources in 57 GMFs and obtain SFRs for 46 GMFs. The median SFR surface density (Sigma_SFR) and star formation efficiency (SFE) of GMFs are 0.62 Msun Myr-1 pc-2 and 1%, similar to the nearby star-forming clouds. The star formation rate per free-fall time of GMFs is between 0.002-0.05 with the median value of 0.02. We also find a strong correlation between SFR and dense gas mass that is defined as gas mass above a visual extinction of 7 mag, which suggests that the SFRs of the GMFs scale similarly with dense gas as those of nearby molecular clouds. We also find a strong correlation between the mean SFR per unit length and dense gas mass per unit length. The origin of this scaling remains unknown, calling for further studies that can link the structure of GMFs to their SF activity and explore the differences between GMFs and other molecular clouds, Comment: 74 pages, 91 figures, 7 appendix, accepted for publication in A&A

An increasing number of hundred-parsec scale, high line-mass filaments have been detected in the Galaxy. Their evolutionary path, including fragmentation towards star formation, is virtually unknown. We characterize the fragmentation within the Nessie filament, covering size-scales between $\sim$ 0.1-100 pc. We also connect the small-scale fragments to the star-forming potential of the cloud. We combine near-infrared data from the VVV survey with mid-infrared GLIMPSE data to derive a high-resolution dust extinction map and apply a wavelet decomposition technique on it to analyze the fragmentation characteristics of the cloud, which are compared with predictions from fragmentation models. We compare the detected objects to those identified in $\sim$ 10 times coarser resolution from ATLASGAL data. We present a high-resolution extinction map of Nessie. We estimate the mean line-mass of Nessie to be $\sim$ 627 M$_\odot$/pc and the distance to be $\sim$ 3.5 kpc. We find that Nessie shows fragmentation at multiple size scales. The nearest-neighbour separations of the fragments at all scales are within a factor of 2 of the Jeans' length at that scale. However, the relationship between the mean densities of the fragments and their separations is significantly shallower than expected for Jeans' fragmentation. The relationship is similar to the one predicted for a filament that exhibits a Larson-like scaling between size-scale and velocity dispersion; such a scaling may result from turbulent support. Based on the number of YSOs in Nessie, we estimate that the star formation rate is $\sim$ 371 M$_\odot$/Myr; similar values result if using the number of dense cores, or the amount of dense gas, as the proxy of star formation. The star formation efficiency is 0.017. These numbers indicate that Nessie's star-forming content is comparable to the Solar neighborhood giant molecular clouds like Orion A.

[abridged] We determine the relationship between turbulence energy and gas density variance for 15 molecular clouds in the Solar neighbourhood. We use the linewidths of the CO molecule as the probe of the turbulence energy (sonic Mach number, $\cal{M}_\mathrm{s}$) and three-dimensional models to reconstruct the density probability distribution function ($\rho$-PDF) of the clouds, derived using near-infrared extinction and Herschel dust emission data, as the probe of the density variance ($\sigma_\mathrm{s}$). We find no significant correlation between $\cal{M}_\mathrm{s}$ and $\sigma_\mathrm{s}$ among the studied clouds, however, we also cannot rule out a weak correlation. In the context of turbulence-dominated gas, the range of the $\cal{M}_\mathrm{s}$ and $\sigma_\mathrm{s}$ values corresponds with the model predictions. The data cannot constrain whether or not the turbulence driving parameter, $b$, and/or thermal-to-magnetic pressure ratio, $\beta$, vary among the sample clouds. Most clouds are not in agreement with field strengths stronger than given by $\beta \lesssim 0.05$. A model with $b^2 \beta / (\beta+1) = 0.30 \pm 0.06$ provides an adequate fit to the cloud sample as a whole. When considering the average behaviour of the sample, we can rule out three regimes: (i) strong compression combined with a weak magnetic field ($b \gtrsim 0.7$ and $\beta \gtrsim 3$), (ii) weak compression ($b \lesssim 0.35$), and (iii) strong magnetic field ($\beta \lesssim 0.1$). Including independent magnetic field strength estimates to the analysis, the data rule out solenoidal driving ($b < 0.4$) for the majority of the Solar neighbourhood clouds. However, most clouds have $b$ parameters larger than unity, which indicates a discrepancy with the turbulence-dominated picture; we discuss the possible reasons for this., Comment: Accepted for publication in Astronomy & Astrophysics

We determine the physical properties and turbulence driving mode of molecular clouds formed in numerical simulations of a Milky Way-type disc galaxy with parsec-scale resolution. The clouds form through gravitational fragmentation of the gas, leading to average values for mass, radii and velocity dispersion in good agreement with observations of Milky Way clouds. The driving parameter (b) for the turbulence within each cloud is characterised by the ratio of the density contrast (sigma_rho) to the average Mach number (Mach) within the cloud, b = sigma_rho/Mach. As shown in previous works, b ~ 1/3 indicates solenoidal (divergence-free) driving and b ~ 1 indicates compressive (curl-free) driving. We find that the average b value of all the clouds formed in the simulations has a lower limit of b > 0.2. Importantly, we find that b has a broad distribution, covering values from purely solenoidal to purely compressive driving. Tracking the evolution of individual clouds reveals that the b value for each cloud does not vary significantly over their lifetime. Finally, we perform a resolution study with minimum cell sizes of 8, 4, 2 and 1 pc and find that the average b value increases with increasing resolution. Therefore, we conclude that our measured b values are strictly lower limits and that a resolution better than 1 pc is required for convergence. However, regardless of the resolution, we find that b varies by factors of a few in all cases, which means that the effective driving mode alters significantly from cloud to cloud., Comment: 12 pages, 11 figures, accepted for publication in MNRAS, more info: https://www.mso.anu.edu.au/~chfeder/pubs/turb_driv_gal/turb_driv_gal.html

We study the probability distribution function (PDF) of mass surface densities, $\Sigma$, of infrared dark cloud (IRDC) G028.37+00.07 and its surrounding giant molecular cloud. This PDF constrains the physical processes, such as turbulence, magnetic fields and self-gravity, that are expected to be controlling cloud structure and star formation activity. The chosen IRDC is of particular interest since it has almost 100,000 solar masses within a radius of 8 parsecs, making it one of the most massive, dense molecular structures known and is thus a potential site for the formation of a "super star cluster." We study $\Sigma$ in two ways. First, we use a combination of NIR and MIR extinction maps that are able to probe the bulk of the cloud structure up to $\Sigma\sim1\:{\rm{g\:cm}^{-2}}\:$($A_V\simeq200$ mag). Second, we study the FIR and sub-mm dust continuum emission from the cloud utilizing Herschel PACS and SPIRE images and paying careful attention to the effects of foreground and background contamination. We find that the PDFs from both methods, applied over a $\sim20^\prime$(30 pc)-sized region that contains $\simeq1.5\times10^5\:M_\odot$ and encloses a minimum closed contour with $\Sigma\simeq0.013\:{\rm{g\:cm}^{-2}}\:$($A_V\simeq3$ mag), shows a log-normal shape with the peak measured at $\Sigma\simeq0.021\:{\rm{g\:cm}^{-2}}\:$($A_V\simeq4.7$ mag). There is tentative evidence for the presence of a high-$\Sigma$ power law tail that contains from $\sim3\%$ to 8\% of the mass of the cloud material. We discuss the implications of these results for the physical processes occurring in this cloud., Comment: Accepted for publication in the ApJL. 9 pages, 5 figures

We study the fragmentation of the nearest high line-mass filament, the integral shaped filament (ISF, line-mass $\sim$ 400 M$_\odot$ pc$^{-1}$) in the Orion A molecular cloud. We have observed a 1.6 pc long section of the ISF with the Atacama Large Millimetre/submillimeter Array (ALMA) at 3 mm continuum emission, at a resolution of $\sim$3" (1 200 AU). We identify from the region 43 dense cores with masses about a solar mass. 60% of the ALMA cores are protostellar and 40\% are starless. The nearest neighbour separations of the cores do not show a preferred fragmentation scale; the frequency of short separations increases down to 1 200 AU. We apply a two-point correlation analysis on the dense core separations and show that the ALMA cores are significantly grouped at separations below $\sim$17 000 AU and strongly grouped below $\sim$6 000 AU. The protostellar and starless cores are grouped differently: only the starless cores group strongly below $\sim$6 000 AU. In addition, the spatial distribution of the cores indicates periodic grouping of the cores into groups of $\sim$30 000 AU in size, separated by $\sim$50 000 AU. The groups coincide with dust column density peaks detected by Herschel. These results show hierarchical, two-mode fragmentation in which the maternal filament periodically fragments into groups of dense cores. Critically, our results indicate that the fragmentation models for lower line-mass filaments ($\sim$ 16 M$_\odot$ pc$^{-1}$) fail to capture the observed properties of the ISF. We also find that the protostars identified with Spitzer and Herschel in the ISF are grouped at separations below $\sim$17 000 AU. In contrast, young stars with disks do not show significant grouping. This suggests that the grouping of dense cores is partially retained over the protostar lifetime, but not over the lifetime of stars with disks., Comment: Accepted to A&A

Orion A hosts the nearest massive star factory, thus offering a unique opportunity to resolve the processes connected with the formation of both low- and high-mass stars. Here we present the most detailed and sensitive near-infrared (NIR) observations of the entire molecular cloud to date. With the unique combination of high image quality, survey coverage, and sensitivity, our NIR survey of Orion A aims at establishing a solid empirical foundation for further studies of this important cloud. In this first paper we present the observations, data reduction, and source catalog generation. To demonstrate the data quality, we present a first application of our catalog to estimate the number of stars currently forming inside Orion A and to verify the existence of a more evolved young foreground population. We used the European Southern Observatory's (ESO) Visible and Infrared Survey Telescope for Astronomy (VISTA) to survey the entire Orion A molecular cloud in the NIR $J, H$, and $K_S$ bands, covering a total of $\sim$18.3 deg$^2$. We implemented all data reduction recipes independently of the ESO pipeline. Estimates of the young populations toward Orion A are derived via the $K_S$-band luminosity function. Our catalog (799995 sources) increases the source counts compared to the Two Micron All Sky Survey by about an order of magnitude. The 90% completeness limits are 20.4, 19.9, and 19.0 mag in $J, H$, and $K_S$, respectively. The reduced images have 20% better resolution on average compared to pipeline products. We find between 2300 and 3000 embedded objects in Orion A and confirm that there is an extended foreground population above the Galactic field, in agreement with previous work. The Orion A VISTA catalog represents the most detailed NIR view of the nearest massive star-forming region and provides a fundamental basis for future studies of star formation processes toward Orion., Comment: Accepted for publication in A&A, high-quality version available at http://homepage.univie.ac.at/stefan.meingast/vision.pdf

Filamentary structures are common in molecular clouds. Explaining how they fragment to dense cores is a missing step in understanding their role in star formation. We perform a case study of whether low-mass filaments are close-to hydrostatic prior to their fragmentation, and whether their fragmentation agrees with gravitational fragmentation models. For this, we study the 6.5 pc long Musca molecular cloud that is an ideal candidate for a filament at an early stage of fragmentation. We employ dust extinction mapping in conjunction with near-infrared data from the NEWFIRM instrument, and 870 um dust continuum emission data from the LABOCA instrument, to estimate column densities. We use the data to identify fragments from the cloud and to determine the radial density distribution of its filamentary part. We compare the cloud's morphology with 13CO and C18O line emission observed with the APEX/SHeFI instrument. The Musca cloud is pronouncedly fragmented at its ends, but harbours a remarkably well-defined, 1.6 pc long filament in its Center region. The line mass of the filament is 21-31 Ms pc^-1 and FWHM 0.07 pc. Its radial profile can be fitted with a Plummer profile that has the power-index of 2.6 \pm 11%, flatter than that of an infinite hydrostatic filament. The profile can also be fitted with a hydrostatic cylinder truncated by external pressure. These models imply a central density of 5-10 x 10^4 cm^-3. The fragments in the cloud have a mean separation of 0.4 pc, in agreement with gravitational fragmentation. These properties, together with the subsonic and velocity-coherent nature of the cloud, suggest a scenario in which an initially hydrostatic cloud is currently gravitationally fragmenting. The fragmentation has started a few tenths of a Myr ago from the cloud ends, leaving its center yet relatively non-fragmented, possibly because of gravitational focusing in a finite geometry., Comment: 14 pages, 7 figures, accepted for publication in A&A

The formation of stars shapes the structure and evolution of entire galaxies. The rate and efficiency of this process are affected substantially by the density structure of the individual molecular clouds in which stars form. The most fundamental measure of this structure is the probability density function of volume densities (rho-PDF), which determines the star formation rates predicted with analytical models. This function has remained unconstrained by observations. We have developed an approach to quantify rho-PDFs and establish their relation to star formation. The rho-PDFs instigate a density threshold of star formation and allow us to quantify the star formation efficiency above it. The rho-PDFs provide new constraints for star formation theories and correctly predict several key properties of the star-forming interstellar medium., Comment: Science (2014) vol. 345. 34 pages

Throughout the Milky Way, molecular clouds typically appear filamentary, and mounting evidence indicates that this morphology plays an important role in star formation. What is not known is to what extent the dense filaments most closely associated with star formation are connected to the surrounding diffuse clouds up to arbitrarily large scales. How are these cradles of star formation linked to the Milky Way's spiral structure? Using archival Galactic plane survey data, we have used multiple datasets in search of large-scale, velocity-coherent filaments in the Galactic plane. In this paper, we present our methods employed to identify coherent filamentary structures first in extinction and confirmed using Galactic Ring Survey data. We present a sample of seven Giant Molecular Filaments (GMFs) that have lengths of order $\sim$100 pc, total masses of 10$^4$ - 10$^5$ M$_{\odot}$, and exhibit velocity coherence over their full length. The GMFs we study appear to be inter-arm clouds and may be the Milky Way analogues to spurs observed in nearby spiral galaxies. We find that between 2 and 12% of the total mass (above $\sim$10$^{20}$ cm$^{-2}$) is "dense" (above 10$^{22}$ cm$^{-2}$), where filaments near spiral arms in the Galactic midplane tend to have higher dense gas mass fractions than those further from the arms., Comment: 22 pages, 16 figures. Accepted to A&A

We study how the estimation of the sonic Mach number ($M_s$) from $^{13}$CO linewidths relates to the actual 3D sonic Mach number. For this purpose we analyze MHD simulations which include post-processing to take radiative transfer effects into account. As expected, we find very good agreement between the linewidth estimated sonic Mach number and the actual sonic Mach number of the simulations for optically thin tracers. However, we find that opacity broadening causes $M_s$ to be overestimated by a factor of ~ 1.16 - 1.3 when calculated from optically thick $^{13}$CO lines. We also find that there is a dependency on the magnetic field: super-Alfv\'enic turbulence shows increased line broadening as compared with sub-Alfv\'enic turbulence for all values of optical depth for supersonic turbulence. Our results have implications for the observationally derived sonic Mach number--density standard deviation ($\sigma_{\rho/<\rho>}$) relationship, $\sigma^2_{\rho/<\rho>}=b^2M_s^2$, and the related column density standard deviation ($\sigma_{N/}$) sonic Mach number relationship. In particular, we find that the parameter b, as an indicator of solenoidal vs. compressive driving, will be underestimated as a result of opacity broadening. We compare the $\sigma_{N/}-M_s$ relation derived from synthetic dust extinction maps and $^{13}$CO linewidths with recent observational studies and find that solenoidally driven MHD turbulence simulations have values of $\sigma_{N/}$ which are lower than real molecular clouds. This may be due to the influence of self-gravity which should be included in simulations of molecular cloud dynamics., Comment: 10 pages, 3 figures, 2 tables, accepted on ApJL

We use deep $8\:\mu m$ Spitzer-IRAC imaging of a massive Infrared Dark Cloud (IRDC) G028.37+00.07 to construct a Mid-Infrared (MIR) extinction map that probes mass surface densities up to $\Sigma\:\sim 1\:\rm{g~cm^{-2}}$ ($A_V\sim200\:$mag), amongst the highest values yet probed by extinction mapping. Merging with a NIR extinction map of the region, creates a high dynamic range map that reveals structures down to $A_V\sim1\:$mag. We utilize the map to: (1) Measure a cloud mass $\sim7\times10^4\:M_\odot$ within a radius of $\sim8\:$pc. $^{13}$CO kinematics indicate that the cloud is gravitationally bound. It thus has the potential to form one of the most massive young star clusters known in the Galaxy. (2) Characterize the structures of 16 massive cores within the IRDC, finding they can be fit by singular polytropic spheres with $\rho\propto{r}^{-k_\rho}$ and $k_\rho=1.3\pm0.3$. They have $\overline{\Sigma}\simeq0.1-0.4\:\rm{g~cm^{-2}}$ --- relatively low values that, along with their measured cold temperatures, suggest magnetic fields, rather than accretion-powered radiative heating, are important for controlling fragmentation of these cores. (3) Determine the $\Sigma$ (equivalently column density or $A_V$) probability distribution function (PDF) for a region that is near complete for $A_V>3\:$mag. The PDF is well fit by a single log-normal with mean $\overline{A}_V\simeq9\:$mag, high compared to other known clouds. It does not exhibit a separate high-end power law tail, which has been claimed to indicate the importance of self-gravity. However, we suggest that the PDF does result from a self-similar, self-gravitating hierarchy of structure being present over a wide range of scales in the cloud., Comment: 6 pages, 3 figures, 1 table, accepted to ApJL

The orientations of filamentary molecular clouds in the Gould Belt and their local ICM (inter-cloud media) magnetic fields are studied using near-infrared dust extinction maps and optical stellar polarimetry data. These filamentary clouds are a few-to-ten parsecs in length, and we find that their orientations tend to be either parallel or perpendicular to the mean field directions of the local ICM. This bimodal distribution is not found in cloud simulations with super-Alfvenic turbulence, in which the cloud orientations should be random. ICM magnetic fields that are dynamically important compared to inertial-range turbulence and self-gravity can readily explain both field-filament configurations. Previous studies commonly recognize that strong magnetic fields can guide gravitational contraction and result in filaments perpendicular to them, but few discuss the fact that magnetic fields can also channel sub-Alfvenic turbulence to form filaments aligned with them. This strong-field scenario of cloud formation is also consistent with the constant field strength observed from ICM to clouds (Crutcher et al. 2010) and is possible to explain the "hub-filament" cloud structure (Myers 2009) and the density threshold of cloud gravitational contraction (Kainulainen et al. 2009)., Comment: 26 pages, 7 figures, accepted by MNRAS

We examine the physical parameters that affect the accumulation of gas in molecular clouds to high column densities where the formation of stars takes place. In particular, we analyze the dense gas mass fraction (DGMF) in a set of self-gravitating, isothermal, magnetohydrodynamic turbulence simulations including sink particles to model star formation. We find that the simulations predict close to exponential DGMFs over the column density range N(H2) = 3-25 x 10^{21} cm^{-2} that can be easily probed via, e.g., dust extinction measurements. The exponential slopes correlate with the type of turbulence driving and also with the star formation efficiency. They are almost uncorrelated with the sonic Mach number and magnetic-field strength. The slopes at early stages of cloud evolution are steeper than at the later stages. A comparison of these predictions with observations shows that only simulations with relatively non-compressive driving (b ~< 0.4) agree with the DGMFs of nearby molecular clouds. Massive infrared dark clouds can show DGMFs that are in agreement with more compressive driving. The DGMFs of molecular clouds can be significantly affected by how compressive the turbulence is on average. Variations in the level of compression can cause scatter to the DGMF slopes, and some variation is indeed necessary to explain the spread of the observed DGMF slopes. The observed DGMF slopes can also be affected by the clouds' star formation activities and statistical cloud-to-cloud variations., Comment: 7 pages, 7 figures, accepted to A&A Letters

We present a spectral investigation of X-ray binaries in NGC 5128 (Cen A), using six 100 ks Chandra observations taken over two months in 2007. We divide our sample into thermally and non-thermally dominated states based on the behavior of the fitted absorption column, and present the spectral parameters of sources with L >2x10^37 erg/s. The majority of sources are consistent with being neutron star low mass X-ray binaries (NS LMXBs) and we identify three transient black hole (BH) LMXB candidates coincident with the dust lane, which is the remnant of a small late-type galaxy. Our results also provide tentative support for the apparent `gap' in the mass distribution of compact objects between ~2-5 Msol. We propose that BH LMXBs are preferentially found in the dust lane, and suggest this is because of the younger stellar population. The majority (~70-80%) of potential Roche-lobe filling donors in the Cen A halo are >12 Gyr old, while BH LMXBs require donors >1 Msol to produce the observed peak luminosities. This requirement for more massive donors may also explain recent results that claim a steepening of the X-ray luminosity function with age at Lx >= 5x10^38 erg/s for the XB population of early-type galaxies; for older stellar populations, there are fewer stars >1 Msol, which are required to form the more luminous sources., Comment: Accepted for publication in ApJ

Measuring the mass distribution of infrared dark clouds (IRDCs) over the wide dynamic range of their column densities is a fundamental obstacle in determining the initial conditions of high-mass star formation and star cluster formation. We present a new technique to derive high-dynamic-range, arcsecond-scale resolution column density data for IRDCs and demonstrate the potential of such data in measuring the density variance - sonic Mach number relation in molecular clouds. We combine near-infrared data from the UKIDSS/Galactic Plane Survey with mid-infrared data from the Spitzer/GLIMPSE survey to derive dust extinction maps for a sample of ten IRDCs. We then examine the linewidths of the IRDCs using 13CO line emission data from the FCRAO/Galactic Ring Survey and derive a column density - sonic Mach number relation for them. For comparison, we also examine the relation in a sample of nearby molecular clouds. The presented column density mapping technique provides a very capable, temperature independent tool for mapping IRDCs over the column density range equivalent to A_V=1-100 mag at a resolution of 2". Using the data provided by the technique, we present the first direct measurement of the relationship between the column density dispersion, \sigma_{N/}, and sonic Mach number, M_s, in molecular clouds. We detect correlation between the variables with about 3-sigma confidence. We derive the relation \sigma_{N/} = (0.047 \pm 0.016) Ms, which is suggestive of the correlation coefficient between the volume density and sonic Mach number, \sigma_{\rho/<\rho>} = (0.20^{+0.37}_{-0.22}) Ms, in which the quoted uncertainties indicate the 3-sigma range. When coupled with the results of recent numerical works, the existence of the correlation supports the picture of weak correlation between the magnetic field strength and density in molecular clouds (i.e., B ~ \rho^{0.5})., Comment: Accepted for publication in A&A. 29 pages. Download the version with full-resolution figures from http://www.mpia-hd.mpg.de/homes/jtkainul/NexusI/PaperII_arxiv.pdf.gz

The initial conditions of massive star and star cluster formation are expected to be cold, dense and high column density regions of the interstellar medium, which can reveal themselves via near, mid and even far-infrared absorption as Infrared Dark Clouds (IRDCs). Elucidating the dynamical state of IRDCs thus constrains theoretical models of these complex processes. In particular, it is important to assess whether IRDCs have reached virial equilibrium, where the internal pressure balances that due to the self-gravitating weight of the cloud plus the pressure of the external environmental. We study this question for the filamentary IRDC G035.39-00.33 by deriving mass from combined NIR & MIR extinction maps and velocity dispersion from C18O (1-0) & (2-1) line emission. In contrast to our previous moderately super-virial results based on 13CO emission and MIR-only extinction mapping, with improved mass measurements we now find that the filament is consistent with being in virial equilibrium, at least in its central parsec-wide region where ~1000 M_Sun snakes along several parsecs. This equilibrium state does not require large-scale net support or confinement by magnetic fields., Comment: 4 pages, 2 figures, Accepted to ApJL

We report the discovery of a bright X-ray transient, CXOU J132527.6-430023, in the nearby early-type galaxy NGC 5128. The source was first detected over the course of five Chandra observations in 2007, reaching an unabsorbed outburst luminosity of 1-2*10^38 erg/s in the 0.5-7.0 keV band before returning to quiescence. Such luminosities are possible for both stellar-mass black hole and neutron star X-ray binary transients. Here, we attempt to characterize the nature of the compact object. No counterpart has been detected in the optical or radio sky, but the proximity of the source to the dust lanes allows for the possibility of an obscured companion. The brightness of the source after a >100 fold increase in X-ray flux makes it either the first confirmed transient non-ULX black hole system in outburst to be subject to detailed spectral modeling outside the Local Group, or a bright (>10^38 erg/s) transient neutron star X-ray binary, which are very rare. Such a large increase in flux would appear to lend weight to the view that this is a black hole transient. X-ray spectral fitting of an absorbed power law yielded unphysical photon indices, while the parameters of the best-fit absorbed disc blackbody model are typical of an accreting ~10 Msol black hole in the thermally dominant state., Comment: 8 pages, 6 figures, accepted for publication in ApJ

We present new optical spectroscopy with FLAMES/VLT, near-IR imaging with HAWK-I/VLT, and 870 micron mapping with APEX/LABOCA of the Coronet cluster. The optical data allow to estimate spectral types, extinction and the presence of accretion in 6 more M-type members, in addition to the 12 that we had previously studied. The submillimeter maps and near-IR data reveal the presence of nebular structures and high extinction regions, which are in some cases associated to known IR, optical, and X-ray sources. Most star formation is associated to two elongated structures crossing in the central part of the cluster. Placing all the 18 objects with known spectral types and extinction in the HR diagram suggests that the cluster is younger than previously thought (<2 Myr, and probably ~0.5-1 Myr). The new age estimate is in agreement with the evolutionary status of the various protostars in the region and with its compactness (<1.3 pc across), but results in a conflict with the low disk and accretion fraction (only 50-65% of low-mass stars appear to have protoplanetary disks, and most transitional and homologously depleted disks are consistent with no accretion) and with the evolutionary features observed in the mid-IR spectra and spectral energy distributions of the disks., Comment: 30 pages, 9 figures, 6 tables, ApJ in press

We present a study of dense structures in the L1495 filament in the Taurus Molecular Cloud and examine its star-forming properties. In particular we construct a dust extinction map of the filament using deep near-infrared observations, exposing its small-scale structure in unprecedented detail. The filament shows highly fragmented substructures and a high mass-per-length value of M_line=17 Msun/pc, reflecting star-forming potential in all parts of it. However, a part of the filament, namely B211, is remarkably devoid of young stellar objects. We argue that in this region the initial filament collapse and fragmentation is still taking place and star formation is yet to occur. In the star-forming part of the filament, we identify 39 cores with masses from 0.4...10 Msun and preferred separations in agreement with the local Jeans length. Most of these cores exceed the Bonnor-Ebert critical mass, and are therefore likely to collapse and form stars. The Dense Core Mass Function follows a power law with exponent Gamma=1.2, a form commonly observed in star-forming regions., Comment: 11 pages, 13 figures, accepted for publication in ApJ

The present work aims at performing a comprehensive census and characterisation of the pre-main sequence (PMS) population in the cometary cloud L1615/L1616, in order to assess the significance of the triggered star formation scenario and investigate the impact of massive stars on its star formation history and mass spectrum. Our study is based on UBVRcIc and JHKs photometry, as well as optical multi-object spectroscopy. We performed a physical parametrisation of the young stellar population in L1615/L1616. We identified 25 new T Tauri stars mainly projected on the dense head of the cometary cloud, almost doubling the current number of known members. We studied the spatial distribution of the cloud members as a function of the age and H$\alpha$ emission. The star formation efficiency in the cloud is about 7-8 %, as expected for molecular clouds in the vicinity of OB associations. The slope of the initial mass function (IMF), in the mass range 0.1

[Abridged] We describe the near-infrared reddening signature of giant molecular clouds (GMCs) in external galaxies. In particular, we examine the E(J-H) and E(H-K) color-excesses, and the effective extinction law observed in discrete GMC regions. We also study the effect of the relative scale height of the GMC distribution to the color-excesses, and to the observed mass function of GMCs. We perform Monte Carlo radiative transfer simulations with 3D models of stellar radiation and clumpy dust distributions, resembling a face-on geometry. The scattered light is included in the models, and near-infrared color maps are calculated from the simulated data. The effective near-infrared reddening law, i.e. the ratio E(J-H)/E(H-K), has a value close to unity in GMC regions. The ratio depends on the relative scale height of GMCs, xi, and for xi values 0.1...0.75 we find the typical ratios of 0.6...1.1. The effective extinction law turns out to be very flat in GMC regions. We find the ratios of apparent extinctions of A(H)/A(K)=1.35...1.55 and A(J)/A(H)=1.15. The effect of the scattered flux on the effective reddening law, as well as on the effective extinction law, is significant. Regarding the GMC mass function, we find no correlation between the input and observed slopes of the mass functions. Rather, the observed slope reflects the parameter $\xi$ and the dynamical range of the mass function. We estimate that only a fraction of 10...20 % of the total mass of GMCs is recovered, if the observed color-excess values are transformed to masses using the Galactic reddening law. In the case of individual clouds the fraction can vary between ~0...50 %., Comment: 8 pages, 10 figures, accepted for publication in A&A. Added missing histograms in Fig. 5

[Abridged] The giant molecular clouds (GMCs) of external galaxies can be mapped with sub-arcsecond resolution using multiband observations in the near-infrared. However, the interpretation of the observed features, and their transformation into physical quantities, is greatly hampered by the effects arising from the unknown geometry and the scattering of light by dust particles. We examine the relation between the observed NIR reddening and the column density of the dust clouds. In this paper we particularly assess the feasibility of deriving the mass function of GMCs from NIR color-excess data. We perform Monte Carlo radiative transfer simulations with 3D models of stellar radiation and clumpy dust distributions. We include the scattered light in the models and calculate NIR color maps from the simulated data. We extract clumps from the color maps and compare the observed mass function to the true mass function. For the physical configuration chosen in this study, essentially a face-on geometry, the observed mass function is a non-trivial function of the true mass function. The dynamical range of the observed mass function is confined to ~10^3.5... 10^5.5 M_\odot regardless of the dynamical range of the true mass function. The color maps are more sensitive in detecting the high-mass end of the mass function, and on average the masses of clouds are underestimated by a factor of ~10. The simulations show that the cloud mass function derived from JHK color excess data using simple foreground screening geometry cannot be regarded as a one-to-one tracer of the underlying mass function., Comment: 5 pages, 3 figures, accepted for publication in A&A