Column Density Probability Distribution Function Research Articles

Molecular cloud matching in CO and dust in M33

This study is aimed to contribute to a more comprehensive understanding of the molecular hydrogen distribution in the galaxy M33 by introducing novel methods for generating high angular resolution (18.2″, equivalent to 75 pc for a distance of 847 kpc) column density maps of molecular hydrogen (NH2). M33 is a local group galaxy that has been observed with Herschel in the far-infrared (FIR) wavelength range from 70 to 500 μm. Previous studies have presented total hydrogen column density maps (NH), using these FIR data (partly combined with mid-IR maps), employing various methods. We first performed a spectral energy distribution (SED) fit to the 160, 250, 350, and 500 μm continuum data obtain NH, using a technique similar to one previously reported in the literature. We also use a second method which involves translating only the 250 μm map into a NH map at the same angular resolution of 18.2″. An NH2 map via each method is then obtained by subtracting the H I component. Distinguishing our study from previous ones, we adopt a more versatile approach by considering a variable emissivity index, β, and dust absorption coefficient, κ0. This choice enables us to construct a κ0 map, thereby enhancing the depth and accuracy of our investigation of the hydrogen column density. We address the inherent biases and challenges within both methods (which give similar results) and compare them with existing maps available in the literature. Moreover, we calculate a map of the carbon monoxide CO(1 − 0)-to-molecular hydrogen (H2) conversion factor (XCO factor), which shows a strong dispersion around an average value of 1.8 × 1020 cm−2/(K km s−1) throughout the disk. We obtain column density probability distribution functions (N-PDFs) from the NH, NH2, and NH I maps and discuss their shape, consisting of several log-normal and power-law tail components.

CO Mapping of Cygnus-X—Volume Density Distribution

We present CO(2-1) and 13CO(2-1) maps of the Cygnus-X molecular cloud complex using the 10 m Heinrich Hertz Submillimeter Telescope. The maps cover the southern portion of the complex, which is strongly impacted by the feedback from the Cygnus OB2 association. Combining CO(1-0) and 13CO(1-0) maps from the Nobeyama 45 m Cygnus-X CO Survey, we carry out a multitransition molecular line analysis with RADEX and derive the volume density of velocity-coherent gas components. We select those components with a column density in the power-law tail part of the column density probability distribution function (N-PDF) and assemble their volume density into a volume density PDF (ρ-PDF). The ρ-PDF exhibits a power-law shape in the range of 104.5 cm−3 105.5 cm−3 with a fitted slope of α = −1.12 ± 0.05. The slope is shallower than what is predicted by simulations of rotationally supported structures or those undergoing gravitational collapse. Applying the same analysis to synthetic observations with feedback may help identify the cause of the shallow slope. The ρ-PDF provides another useful benchmark for testing models of molecular cloud formation and evolution.

Multilognormal density structure in Cygnus-X molecular clouds: a fitting for N-PDF without power law

ABSTRACT We studied the H2 column density probability distribution function (N-PDF) based on molecular emission lines using the Nobeyama 45-m Cygnus X CO survey data. Using the DENDROGRAM and SCIMES algorithms, we identified 124 molecular clouds in the 13CO data. From these identified molecular clouds, an N-PDF was constructed for 11 molecular clouds with an extent of more than 0.4 deg2. From the fitting of the N-PDF, we found that the N-PDF could be well fitted with one or two lognormal distributions. These fitting results provided an alternative density structure for molecular clouds from a conventional picture. We investigated the column density, dense molecular cloud cores, and radio continuum source distributions in each cloud and found that the N-PDF shape was less correlated with the star-forming activity over a whole cloud. Furthermore, we found that the lognormal N-PDF parameters obtained from the fitting showed two impressive features. First, the lognormal distribution at the low-density part had the same mean column density (∼1021.5 cm−2) for almost all the molecular clouds. Second, the width of the lognormal distribution tended to decrease with an increasing mean density of the structures. These correlations suggest that the shape of the N-PDF reflects the relationship between the density and turbulent structure of the whole molecular cloud but is less affected by star-forming activities.

The Star Formation–Gas Density Relation in Four Galactic GMCs: Effects of Stellar Feedback

We present maps of four Galactic giant molecular clouds (GMCs) in the J = 2-1 emission of both CO and 13CO. We use an LTE analysis to derive maps of the CO excitation temperature and column density and the distribution of total molecular gas column density, Σgas. The depletion of CO by freeze-out onto cold dust grains is accounted for by an approximation to the results of Lewis et al., which were derived from far-IR observations with Herschel. The surface density of young stellar objects (YSOs) is obtained from published catalogs. The mean YSO surface density exhibits a power-law dependence on Σgas, with exponents in the range 0.9–1.9. Gas column density probability distribution functions show power-law tails extending to high column densities. The distributions of sonic Mach number, M S , are sharply peaked at MS ∼ 5–8 for 3 GMCs; a fourth has a broad distribution up to M S = 30, possibly a result of feedback effects from multiple OB stars. An analysis following the methodology of Pokhrel et al. finds that our sample of GMCs shows power-law relations that are somewhat shallower than those found by Pokhrel et al. for the star formation rate versus 〈Σgas〉 and versus 〈Σgas〉/t ff in a different sample of clouds. We discuss possible differences in the two samples of star-forming clouds and the effects of stellar feedback on the relation between gas density and star formation rate.

Can Turbulent, High-density Gas Form Stars in Molecular Clouds: A Case Study in Ophiuchus

Star formation is governed by the interplay between gravity and turbulence in most of molecular clouds. Recent theoretical works assume that dense gas, whose column density is above a critical value in the column density probability distribution function (N-PDF), where gravity starts to overcome turbulence, becomes star-forming gas and will collapse to form stars. However, these high-density gases will include some very turbulent areas in the clouds. Will these dense but turbulent gases also form stars? We test this scenario in Ophiuchus molecular cloud using N-PDF analysis and find that at least in some regions, the turbulent, dense gas is not forming stars. We identified two isolated high-density structures in Ophiuchus, which are gravitationally unbound and show no sign of star formation. Their high densities may come from turbulence.

Molecular Clouds in the Second Quadrant of the Milky Way Midplane from l = 104.°75 to l = 119.°75 and b = −5.°25 to b = 5.°25

Abstract In this work, we study the properties of molecular clouds in the second quadrant of the Milky Way Midplane, from l = 104.°75 to l = 119.°75, and b = −5.°25 to b = 5.°25, using the 12CO, 13CO, and C18O J = 1 − 0 emission line data from the Milky Way Imaging Scroll Painting project. We identify 857 and 300 clouds in the 12CO and 13CO spectral cubes, respectively, using the DENDROGRAM + SCIMES algorithms. The distances of the molecular clouds are estimated, and physical properties such as the mass, size, and surface densities of the clouds are tabulated. The molecular clouds in the Perseus Arm are about 30−50 times more massive, and 4−6 times larger than the clouds in the Local Arm. This result, however, is likely to be biased by distance selection effects. The surface densities of the clouds are enhanced in the Perseus Arm, with an average value of ∼100 M ⊙ pc−2. Here. we select the 40 most extended (>0.35 arcdeg2) molecular clouds from the 12CO catalog to build the H2 column density probability distribution function (N-PDF). Some 78% of the N-PDFs of the selected molecular clouds are well fitted with log-normal functions with only small deviations at high densities, corresponding to star-forming regions with scales of ∼1–5 pc in the Local Arm, and ∼5–10 pc in the Perseus Arm. About 18% of the selected molecular clouds have power-law N-PDFs at high densities. In these molecular clouds, the majority of the regions fitted with the power law correspond to molecular clumps at sizes of ∼1 pc, or filaments at widths of ∼1 pc.

On the shape and completeness of the column density probability distribution function of molecular clouds

Both observational and theoretical research over the past decade has demonstrated that the probability distribution function (PDF) of the gas density in turbulent molecular clouds is a key ingredient for understanding star formation. It has recently been argued that the PDF of molecular clouds is a pure power-law distribution. It has been claimed that the log-normal part is ruled out when using only the part of the PDF up/down to which it is complete, that is where the column density contours are still closed. By using the results from high-resolution magnetohydrodynamical simulations of molecular cloud formation and evolution, we find that the column density PDF is indeed composed of a log-normal and, if including self-gravity, a power-law part. We show that insufficient sampling of a molecular cloud results in closed contours that cut off the log-normal part. In contrast, systematically increasing the field of view and sampling the entire cloud yields a completeness limit at the lower column densities, which also recovers the log-normal part. This demonstrates that the field of view must be sufficiently large for the PDF to be complete down to its log-normal part, which has important implications for predictions of star-formation activity based on the PDF.

The Anatomy of the Column Density Probability Distribution Function (N-PDF)

Abstract The column density probability distribution function (N-PDF) of Giant Molecular Clouds (GMCs) has been used as a diagnostic of star formation. Simulations and analytic predictions have suggested that the N-PDF is composed of a low-density lognormal component and a high-density power-law component tracing turbulence and gravitational collapse, respectively. In this paper, we study how various properties of the true 2D column density distribution create the shape, or “anatomy,” of the PDF. We test our ideas and analytic approaches using both a real, observed PDF based on Herschel observations of dust emission and a simulation that uses the ENZO code. Using a dendrogram analysis, we examine the three main components of the N-PDF: the lognormal component, the power-law component, and the transition point between these two components. We find that the power-law component of an N-PDF is the summation of N-PDFs of power-law substructures identified by the dendrogram algorithm. We also find that the analytic solution to the transition point between lognormal and power-law components proposed by Burkhart et al. is applicable when tested on observations and simulations, within the uncertainties. Based on the resulting anatomy of the N-PDF, we suggest applying the N-PDF analysis in combination with the dendrogram algorithm to obtain a more complete picture of the global and local environments and their effects on the density structures.

The effect of magnetic fields and ambipolar diffusion on the column density probability distribution function in molecular clouds

Simulations generally show that non-self-gravitating clouds have a lognormal column density ($\Sigma$) probability distribution function (PDF), while self-gravitating clouds with active star formation develop a distinct power-law tail at high column density. Although the growth of the power law can be attributed to gravitational contraction leading to the formation of condensed cores, it is often debated if an observed lognormal shape is a direct consequence of supersonic turbulence alone, or even if it is really observed in molecular clouds. In this paper we run three-dimensional magnetohydrodynamic simulations including ambipolar diffusion with different initial conditions to see the effect of strong magnetic fields and nonlinear initial velocity perturbations on the evolution of the column density PDFs. Our simulations show that column density PDFs of clouds with supercritical mass-to-flux ratio, with either linear perturbations or nonlinear turbulence, quickly develop a power-law tail such that $dN/d \log \Sigma \propto \Sigma^{-\alpha}$ with index $\alpha \simeq 2$. Interestingly, clouds with subcritical mass-to-flux ratio also proceed directly to a power-law PDF, but with a much steeper index $\alpha \simeq 4$. This is a result of gravitationally-driven ambipolar diffusion. However, for nonlinear perturbations with a turbulent spectrum ($v_{k}^{2} \propto k^{-4}$), the column density PDFs of subcritical clouds do retain a lognormal shape for a major part of the cloud evolution, and only develop a distinct power-law tail with index $\alpha \simeq 2$ at greater column density when supercritical pockets are formed.

HP2 survey

We present new high resolution and dynamic range dust column density and temperature maps of the California Molecular Cloud derived from a combination of Planck and Herschel dust-emission maps, and 2MASS NIR dust-extinction maps. We used these data to determine the ratio of the 2.2 micron extinction coefficient to the 850 micron opacity and found the value to be close to that found in similar studies of the Orion B and Perseus clouds but higher than that characterizing the Orion A cloud, indicating that variations in the fundamental optical properties of dust may exist between local clouds. We show that over a wide range of extinction, the column density probability distribution function (PDF$_N$) of the cloud can be well described by a simple power law with an index that represents a steeper decline with column density than found in similar studies of the Orion and Perseus clouds. Using only the protostellar population of the cloud and our extinction maps we investigate the Schmidt relation within the cloud. We show that the protostellar surface density, $\Sigma_*$, is directly proportional to the ratio of the protostellar and cloud pdfs. We use the cumulative distribution of protostars to infer the functional forms for both $\Sigma_*$ and PDF$_*$. We find that $\Sigma_*$ is best described by two power-law functions with steeper indicies than found in other local GMCs. We find that the protostellar pdf is a declining function of extinction also best described by two power-laws whose behavior mirrors that of $\Sigma_*$. Our observations suggest that variations both in the slope of the Schmidt relation and in the sizes of the protostellar populations between GMCs are largely driven by variations in the slope of the cloud pdf. This confirms earlier studies suggesting that cloud structure plays a major role in setting the global star formation rates in GMCs.

Infrared dust bubble CS51 and its interaction with the surrounding interstellar medium

A multiwavelength investigation of the southern infrared dust bubble CS51 is presented in this paper. We probe the associated ionized, cold dust, molecular and stellar components. Radio continuum emission mapped at 610 and 1300 MHz, using the Giant Metrewave Radio Telescope, India, reveal the presence of three compact emission components (A, B, and C) apart from large-scale diffuse emission within the bubble interior. Radio spectral index map show the coexistence of thermal and non-thermal emission components. Modified blackbody fits to the thermal dust emission using Herschel PACS and SPIRE data is performed to generate dust temperature and column density maps. We identify five dust clumps associated with CS51 with masses and radius in the range 810 - 4600 M{\sun} and 1.0 - 1.9 pc, respectively. We further construct the column density probability distribution functions of the surrounding cold dust which display the impact of ionization feedback from high-mass stars. The estimated dynamical and fragmentation timescales indicate the possibility of collect and collapse mechanism in play at the bubble border. Molecular line emission from the MALT90 survey is used to understand the nature of two clumps which show signatures of expansion of CS51.

The relation between the column density structures and the magnetic field orientation in the Vela C molecular complex

We statistically evaluated the relative orientation between gas column density structures, inferred from Herschel submillimetre observations, and the magnetic field projected on the plane of sky, inferred from polarized thermal emission of Galactic dust observed by the Balloon-borne Large-Aperture Submillimetre Telescope for Polarimetry (BLASTPol) at 250, 350, and 500 μm, towards the Vela C molecular complex. First, we find very good agreement between the polarization orientations in the three wavelength-bands, suggesting that, at the considered common angular resolution of 3.́0 that corresponds to a physical scale of approximately 0.61 pc, the inferred magnetic field orientation is not significantly affected by temperature or dust grain alignment effects. Second, we find that the relative orientation between gas column density structures and the magnetic field changes progressively with increasing gas column density, from mostly parallel or having no preferred orientation at low column densities to mostly perpendicular at the highest column densities. This observation is in agreement with previous studies by the Planck collaboration towards more nearby molecular clouds. Finally, we find a correspondencebetween (a) the trends in relative orientation between the column density structures and the projected magnetic field; and (b) the shape of the column density probability distribution functions (PDFs). In the sub-regions of Vela C dominated by one clear filamentary structure, or “ridges”, where the high-column density tails of the PDFs are flatter, we find a sharp transition from preferentially parallel or having no preferred relative orientation at low column densities to preferentially perpendicular at highest column densities. In the sub-regions of Vela C dominated by several filamentary structures with multiple orientations, or “nests”, where the maximum values of the column density are smaller than in the ridge-like sub-regions and the high-column density tails of the PDFs are steeper, such a transition is also present, but it is clearly less sharp than in the ridge-like sub-regions. Both of these results suggest that the magnetic field is dynamically important for the formation of density structures in this region.

Cloud Structure of Three Galactic Infrared Dark Star-forming Regions from Combining Ground- and Space-based Bolometric Observations

Abstract We have modified the iterative procedure introduced by Lin et al., to systematically combine the submillimeter images taken from ground-based (e.g., CSO, JCMT, APEX) and space (e.g., Herschel, Planck) telescopes. We applied the updated procedure to observations of three well-studied Infrared Dark Clouds (IRDCs): G11.11−0.12, G14.225−0.506, and G28.34+0.06, and then performed single-component, modified blackbody fits to each pixel to derive ∼10″ resolution dust temperature and column density maps. The derived column density maps show that these three IRDCs exhibit complex filamentary structures embedded with rich clumps/cores. We compared the column density probability distribution functions (N-PDFs) and two-point correlation (2PT) functions of the column density field between these IRDCs with several OB-cluster-forming regions. Based on the observed correlation between the luminosity-to-mass ratio and the power-law index of the N-PDF, and complementary hydrodynamical simulations for a 104 molecular cloud, we hypothesize that cloud evolution can be better characterized by the evolution of the (column) density distribution function and the relative power of dense structures as a function of spatial scales, rather than merely based on the presence of star-forming activity. An important component of our approach is to provide a model-independent quantification of cloud evolution. Based on the small analyzed sample, we propose four evolutionary stages, namely, cloud integration, stellar assembly, cloud pre-dispersal, and dispersed cloud. The initial cloud integration stage and the final dispersed cloud stage may be distinguished from the two intermediate stages by a steeper than −4 power-law index of the N-PDF. The cloud integration stage and the subsequent stellar assembly stage are further distinguished from each other by the larger luminosity-to-mass ratio (>40 ) of the latter. A future large survey of molecular clouds with high angular resolution may establish more precise evolutionary tracks in the parameter space of N-PDF, 2PT function, and luminosity-to-mass ratio.

CLOUD STRUCTURE OF GALACTIC OB CLUSTER-FORMING REGIONS FROM COMBINING GROUND- AND SPACE-BASED BOLOMETRIC OBSERVATIONS

ABSTRACT We have developed an iterative procedure to systematically combine the millimeter and submillimeter images of OB cluster-forming molecular clouds, which were taken by ground-based (CSO, JCMT, APEX, and IRAM-30 m) and space telescopes (Herschel and Planck). For the seven luminous ( L ⊙) Galactic OB cluster-forming molecular clouds selected for our analyses, namely W49A, W43-Main, W43-South, W33, G10.6-0.4, G10.2-0.3, and G10.3-0.1, we have performed single-component, modified blackbody fits to each pixel of the combined (sub)millimeter images, and the Herschel PACS and SPIRE images at shorter wavelengths. The ∼10″ resolution dust column density and temperature maps of these sources revealed dramatically different morphologies, indicating very different modes of OB cluster-formation, or parent molecular cloud structures in different evolutionary stages. The molecular clouds W49A, W33, and G10.6-0.4 show centrally concentrated massive molecular clumps that are connected with approximately radially orientated molecular gas filaments. The W43-Main and W43-South molecular cloud complexes, which are located at the intersection of the Galactic near 3 kpc (or Scutum) arm and the Galactic bar, show a widely scattered distribution of dense molecular clumps/cores over the observed ∼10 pc spatial scale. The relatively evolved sources G10.2-0.3 and G10.3-0.1 appear to be affected by stellar feedback, and show a complicated cloud morphology embedded with abundant dense molecular clumps/cores. We find that with the high angular resolution we achieved, our visual classification of cloud morphology can be linked to the systematically derived statistical quantities (i.e., the enclosed mass profile, the column density probability distribution function (N-PDF), the two-point correlation function of column density, and the probability distribution function of clump/core separations). In particular, the massive molecular gas clumps located at the center of G10.6-0.4 and W49A, which contribute to a considerable fraction of their overall cloud masses, may be special OB cluster-forming environments as a direct consequence of global cloud collapse. These centralized massive molecular gas clumps also uniquely occupy much higher column densities than what is determined by the overall fit of power-law N-PDF. We have made efforts to archive the derived statistical quantities of individual target sources, to permit comparisons with theoretical frameworks, numerical simulations, and other observations in the future.

Constructing multiscale gravitational energy spectra from molecular cloud surface density PDF – interplay between turbulence and gravity

(Abridged) We derive an analytical formula which provides estimates on multiscale gravitational energy distribution using the observed surface density PDF. Our analytical formalism also enables one to convert the observed column density PDF into an estimated volume density PDF, and to obtain average radial density profile $\rho(r)$. For a region with $N_{\rm col} \sim N^{-\gamma_{\rm N}}$, the gravitational energy spectra is $E_{\rm p}(k)\sim k^{-4(1 - 1/\gamma_{\rm N})}$. We apply the formula to observations of molecular clouds, and find that a scaling index of $-2$ of the surface density PDF implies that $\rho \sim r^{-2}$ and $E_{\rm p}(k) \sim k^{-2}$. The results are valid from the cloud scale (a few parsec) to around $\sim 0.1 \;\rm pc$. Because of the resemblance the scaling index of the gravitational energy spectrum and the that of the kinetic energy power spectrum of the Burgers turbulence (where $E\sim k^{-2}$), our result indicates that gravity can act effectively against turbulence over a multitude of physical scales. This is the critical scaling index which divides molecular clouds into two categories: clouds like Orion and Ophiuchus have shallower power laws, and the amount of gravitational energy is too large for turbulence to be effective inside the cloud. Because gravity dominates, we call this type of cloud g-type clouds. On the other hand, clouds like the California molecular cloud and the Pipe nebula have steeper power laws, and turbulence can overcome gravity if it can cascade effectively from the large scale. We call this type of cloud t-type clouds. The analytical formula can be used to determine if gravity is dominating cloud evolution when the column density probability distribution function (PDF) can be reliably determined.

The reliability of observational measurements of column density probability distribution functions

Probability distribution functions (PDFs) of column densities are an established tool to characterize the evolutionary state of interstellar clouds. Using simulations, we show to what degree their determination is affected by noise, line-of-sight contamination, field selection, and the incomplete sampling in interferometric measurements. We solve the integrals that describe the convolution of a cloud PDF with contaminating sources and study the impact of missing information on the measured column density PDF. The effect of observational noise can be easily estimated and corrected for if the root mean square (rms) of the noise is known. For $\sigma_{noise}$ values below 40% of the typical cloud column density, $N_{peak}$, this involves almost no degradation of the accuracy of the PDF parameters. For higher noise levels and narrow cloud PDFs the width of the PDF becomes increasingly uncertain. A contamination by turbulent foreground or background clouds can be removed as a constant shield if the PDF of the contamination peaks at a lower column or is narrower than that of the observed cloud. Uncertainties in the definition of the cloud boundaries mainly affect the low-column density part of the PDF and the mean density. As long as more than 50% of a cloud are covered, the impact on the PDF parameters is negligible. In contrast, the incomplete sampling of the uv plane in interferometric observations leads to uncorrectable distortions of the PDF of the produced maps. An extension of ALMA's capabilities would allow us to recover the high-column density tail of the PDF but we found no way to measure the intermediate and low column density part of the underlying cloud PDF in interferometric observations.

THE LOGNORMAL PROBABILITY DISTRIBUTION FUNCTION OF THE PERSEUS MOLECULAR CLOUD: A COMPARISON OF HI AND DUST

The shape of the probability distribution function (PDF) of molecular clouds is an important ingredient for modern theories of star formation and turbulence. Recently, several studies have pointed out observational difficulties with constraining the low column density (i.e. Av <1) PDF using dust tracers. In order to constrain the shape and properties of the low column density probability distribution function, we investigate the PDF of multiphase atomic gas in the Perseus molecular cloud using opacity-corrected GALFA-HI data and compare the PDF shape and properties to the total gas PDF and the N(H2) PDF. We find that the shape of the PDF in the atomic medium of Perseus is well described by a lognormal distribution, and not by a power-law or bimodal distribution. The peak of the atomic gas PDF in and around Perseus lies at the HI-H2 transition column density for this cloud, past which the N(H2) PDF takes on a powerlaw form. We find that the PDF of the atomic gas is narrow and at column densities larger than the HI-H2 transition the HI rapidly depletes, suggesting that the HI PDF may be used to find the HI-H2 transition column density. We also calculate the sonic Mach number of the atomic gas by using HI absorption line data, which yields a median value of Ms=4.0 for the CNM, while the HI emission PDF, which traces both the WNM and CNM, has a width more consistent with transonic turbulence.

Evolution of column density distributions within Orion A

We compare the structure of star-forming molecular clouds in different regions of Orion A to determine how the column density probability distribution function (N-PDF) varies with environmental conditions such as the fraction of young protostars. A correlation between the N-PDF slope and Class 0 protostar fraction has been previously observed in a low-mass star-formation region (Perseus) by Sadavoy; here we test if a similar correlation is observed in a high-mass star-forming region. We use Herschel data to derive a column density map of Orion A. We use the Herschel Orion Protostar Survey catalog for accurate identification and classification of the Orion A young stellar object (YSO) content, including the short-lived Class 0 protostars (with a $\sim$ 0.14 Myr lifetime). We divide Orion A into eight independent 13.5 pc$^2$ regions; in each region we fit the N-PDF distribution with a power-law, and we measure the fraction of Class 0 protostars. We use a maximum likelihood method to measure the N-PDF power-law index without binning. We find that the Class 0 fraction is higher in regions with flatter column density distributions. We test the effects of incompleteness, YSO misclassification, resolution, and pixel-scale. We show that these effects cannot account for the observed trend. Our observations demonstrate an association between the slope of the power-law N-PDF and the Class 0 fractions within Orion A. Various interpretations are discussed including timescales based on the Class 0 protostar fraction assuming a constant star-formation rate. The observed relation suggests that the N-PDF can be related to an "evolutionary state" of the gas. If universal, such a relation permits an evaluation of the evolutionary state from the N-PDF power-law index at much greater distances than those accesible with protostar counts. (abridged)

STAR FORMATION IN TURBULENT MOLECULAR CLOUDS WITH COLLIDING FLOW

Using self-gravitational hydrodynamical numerical simulations, we investigated the evolution of high-density turbulent molecular clouds swept by a colliding flow. The interaction of shock waves due to turbulence produces networks of thin filamentary clouds with a sub-parsec width. The colliding flow accumulates the filamentary clouds into a sheet cloud and promotes active star formation for initially high-density clouds. Clouds with a colliding flow exhibit a finer filamentary network than clouds without a colliding flow. The probability distribution functions (PDFs) for the density and column density can be fitted by lognormal functions for clouds without colliding flow. When the initial turbulence is weak, the column density PDF has a power-law wing at high column densities. The colliding flow considerably deforms the PDF, such that the PDF exhibits a double peak. The stellar mass distributions reproduced here are consistent with the classical initial mass function with a power-law index of $-1.35$ when the initial clouds have a high density. The distribution of stellar velocities agrees with the gas velocity distribution, which can be fitted by Gaussian functions for clouds without colliding flow. For clouds with colliding flow, the velocity dispersion of gas tends to be larger than the stellar velocity dispersion. The signatures of colliding flows and turbulence appear in channel maps reconstructed from the simulation data. Clouds without colliding flow exhibit a cloud-scale velocity shear due to the turbulence. In contrast, clouds with colliding flow show a prominent anti-correlated distribution of thin filaments between the different velocity channels, suggesting collisions between the filamentary clouds.

Understanding star formation in molecular clouds

Column-density maps of molecular clouds are one of the most important observables in the context of molecular cloud- and star-formation (SF) studies. With the Herschel satellite it is now possible to determine the column density from dust emission. We use observations and simulations to demonstrate how LOS contamination affects the column density probability distribution function (PDF). We apply a first-order approximation (removing a constant level) to the molecular clouds of Auriga, Maddalena, Carina and NGC3603. In perfect agreement with the simulations, we find that the PDFs become broader, the peak shifts to lower column densities, and the power-law tail of the PDF flattens after correction. All PDFs have a lognormal part for low column densities with a peak at Av~2, a deviation point (DP) from the lognormal at Av(DP)~4-5, and a power-law tail for higher column densities. Assuming a density distribution rho~r^-alpha, the slopes of the power-law tails correspond to alpha(PDF)=1.8, 1.75, and 2.5 for Auriga, Carina, and NGC3603 (alpha~1.5-2 is consistent gravitational collapse). We find that low-mass and high-mass SF clouds display differences in the overall column density structure. Massive clouds assemble more gas in smaller cloud volumes than low-mass SF ones. However, for both cloud types, the transition of the PDF from lognormal shape into power-law tail is found at the same column density (at Av~4-5 mag). Low-mass and high-mass SF clouds then have the same low column density distribution, most likely dominated by supersonic turbulence. At higher column densities, collapse and external pressure can form the power-law tail. The relative importance of the two processes can vary between clouds and thus lead to the observed differences in PDF and column density structure.