Star-forming Molecular Clouds Research Articles

Tearing-mediated Reconnection in Magnetohydrodynamic Poorly Ionized Plasmas. I. Onset and Linear Evolution

In high-Lundquist-number plasmas, reconnection proceeds via the onset of tearing, followed by a nonlinear phase during which plasmoids continuously form, merge, and are ejected from the current sheet (CS). This process is understood in fully ionized, magnetohydrodynamic plasmas. However, many plasma environments, such as star-forming molecular clouds and the solar chromosphere, are poorly ionized. We use theory and computation to study tearing-mediated reconnection in such poorly ionized systems. In this paper, we focus on the onset and linear evolution of this process. In poorly ionized plasmas, magnetic nulls on scales below v A,n0/ν ni0, with v A,n0 the neutral Alfvén speed and ν ni0 the neutral–ion collision frequency, will self-sharpen via ambipolar diffusion. This sharpening occurs at an increasing rate, inhibiting the onset of reconnection. Once the CS becomes thin enough, however, ions decouple from neutrals and the thinning of the CS slows, allowing the onset of tearing in a time of order νni0−1 . We find that the wavelength and growth rate of the mode that first disrupts the forming sheet can be predicted from a poorly ionized tearing dispersion relation; as the plasma recombination rate increases and ionization fraction decreases, the growth rate becomes an increasing multiple of ν ni0 and the wavelength becomes a decreasing fraction of v A,n0/ν ni0.

What is the Role of Gravity, Turbulence and Magnetic Fields in High-mass Star Formation Clouds?

To explore the potential role of gravity, turbulence and magnetic fields in high-mass star formation in molecular clouds, this study revisits the velocity dispersion–size (σ–L) and density–size (ρ–L) scalings and the associated turbulent energy spectrum using an extensive data sample. The sample includes various hierarchical density structures in high-mass star formation clouds, across scales of 0.01–100 pc. We observe σ ∝ L 0.26 and ρ ∝ L −1.54 scalings, converging toward a virial equilibrium state. A nearly flat virial parameter–mass (α vir−M) distribution is seen across all density scales, with α vir values centered around unity, suggesting a global equilibrium maintained by the interplay between gravity and turbulence across multiple scales. Our turbulent energy spectrum (E(k)) analysis, based on the σ–L and ρ–L scalings, yields a characteristic E(k) ∝ k −1.52. These findings indicate the potential significance of gravity, turbulence, and possibly magnetic fields in regulating dynamics of molecular clouds and high-mass star formation therein.

A Consistent Explanation for the Unusual Initial Mass Function and Star Formation Rate in the Central Molecular Zone (CMZ)

We examine various physical processes that may explain the shallow high-mass slope of the initial mass function (IMF), as well as the low star formation rate (SFR) in star-forming molecular clouds (MCs) in the Central Molecular Zone (CMZ). We show that the strong tidal field and shear experienced by the CMZ have opposite effects on the collapse of density fluctuations and cannot explain these properties. Similarly, we show that the intense magnetic field in the CMZ provides a negligible pressure support and, for the high densities at play, should not modify the probability density function of the turbulent gas flow, thus affecting negligibly the IMF. However, we show that, in contrast to the MCs in the Galactic disk, the ones in the CMZ experience only one single episode of turbulence cascade. Indeed, their rather short lifetime, due to their high mean densities, is similar to one typical turbulence crossing time. Consequently, according to the Hennebelle–Chabrier theory of star formation, within this “single turbulence cascade episode,” the cloud experiences one single field of turbulence-induced density fluctuations, leading eventually to gravitationally unstable cores. As shown in Hennebelle & Chabrier (2013), this yields a shallower IMF than usual and leads to the correct observed slope for the CMZ star-forming clouds. Similarly, this single large-scale turbulence event within the cloud lifetime yields a 5–6 times lower SFR than under usual conditions, in agreement with the observed values. Therefore, we suggest that this “single turbulence cascade” scenario can explain both the shallow IMF and low SFR of clouds in the CMZ.

Implication of the Velocity Dispersion Scalings on High-mass Star Formation in Molecular Clouds

This paper is aimed at exploring the implications of velocity-dispersion scalings on high-mass star formation in molecular clouds, including the scalings of Larson’s linewidth–size (σ– R) and ratio–mass surface density ( L – Σ; here L = σ/R 0.5). We have systematically analyzed the σ parameter of well-selected 221 massive clumps, complemented with published samples of other hierarchical density structures of molecular clouds over spatial scales of 0.01–10 pc. Those massive clumps are classified into four phases: quiescent, protostellar, H ii region, and PDR clumps in an evolutionary sequence. The velocity dispersion of clumps increases overall with the evolutionary sequence, reflecting enhanced stellar feedback in more evolved phases. The relations of σ– R and L – Σ are weak with the clump sample alone, but become evident when combined with others spanning a much wider spatial scales. For σ– R, its tight relation indicates a kinematic connection between hierarchical density structures, supporting theoretical models of multiscale high-mass star formation. From the L – Σ relation, cloud structures can be found to transition from overvirial state (α vir > 2) to subvirial state (α vir < 2) as they become smaller and denser, indicating a possible shift in the governing force from turbulence to gravity. This implies that the multiscale physical process of high-mass star formation hinges on the self-gravity of subvirial molecular clouds. However, the influence of turbulence may not be dismissed until large-scale clouds attain a subvirial state. This is pending confirmation from future multiscale kinematic observations of molecular clouds with uniform observing settings.

An Ensemble Study of Turbulence in Extended QSO Nebulae at z ≈ 0.5–1

Turbulent motions in the circumgalactic medium play a critical role in regulating the evolution of galaxies, yet their detailed characterization remains elusive. Using two-dimensional velocity maps constructed from spatially extended [O ii] and [O iii] emission, Chen et al. measured the velocity structure functions (VSFs) of four quasar nebulae at z ≈ 0.5–1.1. One of these exhibits a spectacular Kolmogorov relation. Here, we carry out an ensemble study using an expanded sample incorporating four new nebulae from three additional quasi-stellar object (QSO) fields. The VSFs measured for all eight nebulae are best explained by subsonic turbulence revealed by the line-emitting gas, which in turn strongly suggests that the cool gas (T ∼ 104 K) is dynamically coupled to the hot ambient medium. Previous work demonstrates that the largest nebulae in our sample reside in group environments with clear signs of tidal interactions, suggesting that environmental effects are vital in seeding and enhancing the turbulence within the gaseous halos, ultimately promoting the formation of the extended nebulae. No discernible differences are observed in the VSF properties between radio-loud and radio-quiet QSO fields. We estimate the turbulent heating rate per unit volume, Q turb, in the QSO nebulae to be ∼10−26–10−22 erg cm−3 s−1 for the cool phase and ∼10−28–10−25 erg cm−3 s−1 for the hot phase. This range aligns with measurements in the intracluster medium and star-forming molecular clouds but is ∼103 times higher than the Q turb observed inside cool gas clumps on scales ≲1 kpc using absorption-line techniques. We discuss the prospect of bridging the gap between emission and absorption studies by pushing the emission-based VSF measurements to below ≈10 kpc.

Dynamics in Star-forming Cores (DiSCo): project overview and the first look towards the B1 and NGC 1333 regions in Perseus

ABSTRACT The internal velocity structure within dense gaseous cores plays a crucial role in providing the initial conditions for star formation in molecular clouds. However, the kinematic properties of dense gas at core scales (∼0.01−0.1 pc) has not been extensively characterized because of instrument limitations until the unique capabilities of GBT-Argus became available. The ongoing GBT-Argus Large Program, Dynamics in Star-forming Cores (DiSCo) thus aims to investigate the origin and distribution of angular momentum of star-forming cores. DiSCo will survey all starless cores and Class 0 protostellar cores in the Perseus molecular complex down to ∼0.01 pc scales with &amp;lt;0.05 km s−1 velocity resolution using the dense gas tracer N2H+. Here, we present the first data sets from DiSCo towards the B1 and NGC 1333 regions in Perseus. Our results suggest that a dense core’s internal velocity structure has little correlation with other core-scale properties, indicating these gas motions may be originated externally from cloud-scale turbulence. These first data sets also reaffirm the ability of GBT-Argus for studying dense core velocity structure and provided an empirical basis for future studies that address the angular momentum problem with a statistically broad sample.

Resolved Kennicutt–Schmidt law in two strongly lensed star-forming galaxies at redshift 1

We study the star formation rate (SFR) vs. molecular gas mass (Mmol) scaling relation from hundreds to thousands of parsec in two strongly lensed galaxies at redshift z ∼ 1, the Cosmic Snake and A521. We trace the SFR using extinction-corrected rest-frame UV observations with the Hubble Space Telescope (HST), and Mmol using detections of the CO(4–3) line with the Atacama Large Millimeter/submillimeter Array (ALMA). The similar angular resolutions of our HST and ALMA observations of 0.15 − 0.2″ combined with magnifications reaching μ &gt; 20 enable us to resolve structures in the galaxies of sizes lower than 100 pc. These resolutions are close to those of studies of nearby galaxies. This allows us to investigate for the first time the Kennicutt–Schmidt (KS) law (SFR–Mmol surface densities) at different spatial scales, from galactic scales to ∼100 pc scales, in galaxies at z ∼ 1. At integrated scales we find that both galaxies satisfy the KS law defined by galaxies at redshifts between 1 and 2.5. We test the resolved KS (rKS) law in cells of sizes down to 200 pc in the two galaxies. We observe that this relationship generally holds in these z ∼ 1 galaxies, although its scatter increases significantly with decreasing spatial scales. We check the scale dependence of the spatial correlation between the surface densities of SFR and Mmol by focusing on apertures centred on individual star-forming regions and molecular clouds. We conclude that star-forming regions and molecular clouds become spatially de-correlated at ≲1 kpc in the Cosmic Snake, whereas they appear de-correlated at all spatial scales (from 400 pc to 6 kpc) in A521.

Predicting reliable H2 column density maps from molecular line data using machine learning

ABSTRACT The total mass estimate of molecular clouds suffers from the uncertainty in the H2-CO conversion factor, the so-called XCO factor, which is used to convert the 12CO (1–0) integrated intensity to the H2 column density. We demonstrate the machine learning’s ability to predict the H2 column density from the 12CO, 13CO, and C18O (1–0) data set of four star-forming molecular clouds: Orion A, Orion B, Aquila, and M17. When the training is performed on a subset of each cloud, the overall distribution of the predicted column density is consistent with that of the Herschel column density. The total column density predicted and observed is consistent within 10 per cent, suggesting that the machine learning prediction provides a reasonable total mass estimate of each cloud. However, the distribution of the column density for values &amp;gt;∼2 × 1022 cm−2, which corresponds to the dense gas, could not be predicted well. This indicates that molecular line observations tracing the dense gas are required for the training. We also found a significant difference between the predicted and observed column density when we created the model after training the data on different clouds. This highlights the presence of different XCO factors between the clouds, and further training in various clouds is required to correct for these variations. We also demonstrated that this method could predict the column density towards the area not observed by Herschel if the molecular line and column density maps are available for the small portion, and the molecular line data are available for the larger areas.

Significance mode analysis (SigMA) for hierarchical structures

We present a new clustering method, significance mode analysis (SigMA), for extracting co-spatial and co-moving stellar populations from large-scale surveys such as ESA Gaia. The method studies the topological properties of the density field in the multidimensional phase space. We validated SigMA on simulated clusters and find that it outperforms competing methods, especially in cases where many clusters are closely spaced. We applied the new method to Gaia DR3 data of the closest OB association to Earth, Scorpio-Centaurus (Sco-Cen), and find more than 13 000 co-moving young objects, about 19% of which have a substellar mass. SigMA finds 37 co-moving clusters in Sco-Cen. These clusters are independently validated by their narrow Hertzsprung-Russell diagram sequences and, to a certain extent, by their association with massive stars too bright for Gaia, and are hence unknown to SigMA. We compared our results with similar recent work and find that the SigMA algorithm recovers richer populations, is able to distinguish clusters with velocity differences down to about 0.5 km s−1, and reaches cluster volume densities as low as 0.01 sources pc−3. The 3D distribution of these 37 coeval clusters implies a larger extent and volume for the Sco-Cen OB association than typically assumed in the literature. Additionally, we find the association more actively star-forming and dynamically complex than previously thought. We confirm that the star-forming molecular clouds in the Sco-Cen region, namely, Ophiuchus, L134/L183, Pipe Nebula, Corona Australis, Lupus, and Chamaeleon, are part of the Sco-Cen association. The application of SigMA to Sco-Cen demonstrates that advanced machine learning tools applied to the superb Gaia data allows an accurate census of the young populations to be constructed, which in turn allows us to quantify their dynamics and recreate the recent star formation history of the local Milky Way.

What Sets the Star Formation Rate of Molecular Clouds? The Density Distribution as a Fingerprint of Compression and Expansion Rates

We use a suite of 3D simulations of star-forming molecular clouds, with and without stellar feedback, magnetic fields, and driven turbulence, to study the compression and expansion rates of the gas as functions of density. We show that, around the mean density, supersonic turbulence promotes rough equilibrium between the amounts of compressing and expanding gas, consistent with continuous gas cycling between high- and low-density states. We find that the inclusion of protostellar jets produces rapidly expanding and compressing low-density gas. We find that the gas mass flux peaks at the transition between the lognormal and power-law forms of the density probability distribution function (PDF). This is consistent with the transition density tracking the post-shock density, which promotes an enhancement of mass at this density (i.e., shock compression and filament formation). At high densities, the gas dynamics are dominated by self-gravity: the compression rate in all of our runs matches the rate of the run with only gravity, suggesting that processes other than self-gravity have little effect at these densities. The net gas mass flux becomes constant at a density below the sink formation threshold, where it equals the star formation rate. The density at which the net gas mass flux equals the star formation rate is one order of magnitude lower than our sink threshold density, corresponds to the formation of the second power-law tail in the density PDF, and sets the overall star formation rates of these simulations.

Extragalactic Magnetism with SOFIA (SALSA Legacy Program). V. First Results on the Magnetic Field Orientation of Galaxies

We present the analysis of the magnetic field (B-field) structure of galaxies measured with far-infrared (FIR) and radio (3 and 6 cm) polarimetric observations. We use the first data release of the Survey of extragALactic magnetiSm with SOFIA of 14 nearby ( Mpc) galaxies with resolved ( 90 pc–1 kpc) imaging polarimetric observations using SOFIA/HAWC+ from 53 to 214 μm. We compute the magnetic pitch-angle () profiles as a function of the galactocentric radius. We introduce a new magnetic alignment parameter (ζ) to estimate the disordered-to-ordered ratio of spiral B-fields. We find FIR and radio wavelengths to not generally trace the same B-field morphology in galaxies. The profiles tend to be more ordered across all galactocentric radii in radio () than in FIR (). For spiral galaxies, FIR B-fields are 2%–75% more turbulent than the radio B-fields. For starburst galaxies, we find that FIR polarization is a better tracer of the B-fields along the galactic outflows than radio polarization. Our results suggest that the B-fields associated with dense, dusty, turbulent star-forming regions (those traced at FIR) are less ordered than warmer, less dense regions (those traced at radio) of the interstellar medium. The FIR B-fields seem to be more sensitive to the activity of the star-forming regions and molecular clouds within a vertical height of a few hundred parsecs in the disk of spiral galaxies than the radio B-fields.

Properties of the dense cores and filamentary structures in the Vela C molecular cloud

The initial and boundary conditions of the Galactic star formation in molecular clouds are not well understood. In an effort to shed new light on this long-standing problem, we measured the properties of dense cores and filamentary structures in the Vela C molecular cloud, observed with Herschel. We used the hires algorithm to create high-resolution surface densities (11.7″) from the Herschel multiwavelength dust continuum. We applied the getsf extraction method to separate the components of sources and filaments from each other and their backgrounds before detecting, measuring, and cataloging the structures. The cores and filamentary structures constitute 40% of the total mass of Vela C; most of the material is in the low-density molecular background cloud. We selected 570 reliable cores, of which 149 are the protostellar cores and 421 are the starless cores. Almost 78% (329 of 421) of the starless cores were identified with the gravitationally bound prestellar cores. The exponent of the CMF (α = 1.35) is identical to that of the Salpeter IMF. The high-resolution surface density image helped us determine and subtract backgrounds and measure the sizes of the structures. We selected 68 filaments with at least one side that appeared not blended with adjacent structures. The filament widths are in the range from 0.15 pc to 0.63 pc, and have a median value of W = 0.3 ± 0.11 pc. The surface densities of filaments are well correlated with their contrasts and linear densities. Within uncertainties of the filament instability criterion, many filaments (39) may be both supercritical and subcritical. A large fraction of filaments (29), in which are found 94 prestellar cores, 83 protostellar cores, and only 1 unbound starless core, can definitely be considered supercritical. Taking into account the uncertainties, the supercritical filaments contain only prestellar and protostellar cores. Our findings support the idea that there is a direct relationship between the CMF and IMF and that filaments play a key role in the formation of prestellar cores, which is consistent with the previous Herschel results.

VISIONS: the VISTA Star Formation Atlas

VISIONS is an ESO public survey of five nearby (d &lt; 500 pc) star-forming molecular cloud complexes that are canonically associated with the constellations of Chamaeleon, Corona Australis, Lupus, Ophiuchus, and Orion. The survey was carried out with the Visible and Infrared Survey Telescope for Astronomy (VISTA), using the VISTA Infrared Camera (VIRCAM), and collected data in the near-infrared passbands J (1.25 μm), H (1.65 μm), and KS (2.15 μm). With a total on-sky exposure time of 49.4h VISIONS covers an area of 650 deg2, it is designed to build an infrared legacy archive with a structure and content similar to the Two Micron All Sky Survey (2MASS) for the screened star-forming regions. Taking place between April 2017 and March 2022, the observations yielded approximately 1.15 million images, which comprise 19 TB of raw data. The observations undertaken within the survey are grouped into three different subsurveys. First, the wide subsurvey comprises shallow, large-scale observations and it has revisited the star-forming complexes six times over the course of its execution. Second, the deep subsurvey of dedicated high-sensitivity observations has collected data on areas with the largest amounts of dust extinction. Third, the control subsurvey includes observations of areas of low-to-negligible dust extinction. Using this strategy, the VISIONS observation program offers multi-epoch position measurements, with the ability to access deeply embedded objects, and it provides a baseline for statistical comparisons and sample completeness – all at the same time. In particular, VISIONS is designed to measure the proper motions of point sources, with a precision of 1 mas yr−1 or better, when complemented with data from the VISTA Hemisphere Survey (VHS). In this way, VISIONS can provide proper motions of complete ensembles of embedded and low-mass objects, including sources inaccessible to the optical ESA Gaia mission. VISIONS will enable the community to address a variety of research topics from a more informed perspective, including the 3D distribution and motion of embedded stars and the nearby interstellar medium, the identification and characterization of young stellar objects, the formation and evolution of embedded stellar clusters and their initial mass function, as well as the characteristics of interstellar dust and the reddening law.

Magnetic fields do not suppress global star formation in low metallicity dwarf galaxies

ABSTRACT Many studies concluded that magnetic fields suppress star formation in molecular clouds and Milky Way like galaxies. However, most of these studies are based on fully developed fields that have reached the saturation level, with little work on investigating how an initial weak primordial field affects star formation in low metallicity environments. In this paper, we investigate the impact of a weak initial field on low metallicity dwarf galaxies. We perform high-resolution arepo simulations of five isolated dwarf galaxies. Two models are hydrodynamical, two start with a primordial magnetic field of 10$^{-6} \, \mu$G and different sub-solar metallicities, and one starts with a saturated field of 10$^{-2} \, \mu$G. All models include a non-equilibrium, time-dependent chemical network that includes the effects of gas shielding from the ambient ultraviolet field. Sink particles form directly from the gravitational collapse of gas and are treated as star-forming clumps that can accrete gas. We vary the ambient uniform far ultraviolet field, and cosmic ray ionization rate between 1 per cent and 10 per cent of solar values. We find that the magnetic field has little impact on the global star formation rate (SFR), which is in tension with some previously published results. We further find that the initial field strength has little impact on the global SFR. We show that an increase in the mass fractions of both molecular hydrogen and cold gas, along with changes in the perpendicular gas velocity dispersion and the magnetic field acting in the weak-field model, overcome the expected suppression in star formation.

Effects of the environment on the multiplicity properties of stars in the STARFORGE simulations

ABSTRACT Most observed stars are part of a multiple star system, but the formation of such systems and the role of environment and various physical processes is still poorly understood. We present a suite of radiation-magnetohydrodynamic simulations of star-forming molecular clouds from the STARFORGE project that include stellar feedback with varied initial surface density, magnetic fields, level of turbulence, metallicity, interstellar radiation field, simulation geometry and turbulent driving. In our fiducial cloud, the raw simulation data reproduces the observed multiplicity fractions for Solar-type and higher mass stars, similar to previous works. However, after correcting for observational incompleteness the simulation underpredicts these values. The discrepancy is likely due to the lack of disc fragmentation, as the simulation only resolves multiples that form either through capture or core fragmentation. The raw mass distribution of companions is consistent with randomly drawing from the initial mass function for the companions of $\gt 1\, \mathrm{M}_{\rm \odot }$ stars. However, accounting for observational incompleteness produces a flatter distribution similar to observations. We show that stellar multiplicity changes as the cloud evolves and anticorrelates with stellar density. This relationship also explains most multiplicity variations between runs, i.e. variations in the initial conditions that increase stellar density (increased surface density, reduced turbulence) also act to decrease multiplicity. While other parameters, such as metallicity, interstellar radiation, and geometry significantly affect the star formation history or the IMF, varying them produces no clear trend in stellar multiplicity properties.

OMC-2 FIR 4 under the microscope: Shocks, filaments, and a highly collimated jet at 100 au scales

Context. Star-forming molecular clouds are characterised by the ubiquity of intertwined filaments. The filaments have been observed in both high- and low-mass star-forming regions, and they are thought to split into collections of sonic fibres. The locations where filaments converge are termed hubs, and these are associated with the young stellar clusters. However, the observations of filamentary structures within hubs at distances of 75–300 pc require a high angular resolution &lt;2″ (~ 150–600 au) that limits the number of such studies conducted so far. Aims. The integral shaped filament (ISF) of the Orion A molecular cloud is noted for harbouring several hubs within which no filamentary structures have been observed so far. The goal of our study is to investigate the nature of the filamentary structures within one of these hubs, which is the chemically rich hub OMC-2 FIR 4, and to analyse their emission with high density and shock tracers. Methods. We observed the OMC-2 FIR 4 proto-cluster using Band 6 of the Atacama Large (sub-)Millimetre Array (ALMA) in Cycle 4 with an angular resolution of ~0.26″ (100 au). We analysed the spatial distribution of dust, the shock tracer SiO, and dense gas tracers (i.e., CH3OH, CS, and H13CN). We also studied the gas kinematics using SiO and CH3OH maps. Results. Our observations for the first time reveal interwoven filamentary structures within OMC-2 FIR 4 that are probed by several tracers. Each filamentary structure is characterised by a distinct velocity as seen from the emission peak of CH3OH lines. They also show transonic and supersonic motions. SiO is associated with filaments and also with multiple bow-shock features. The bow-shock features have sizes between ~500 and 2700 au and are likely produced by the outflow from HOPS-370. Their dynamical ages are &lt;800 yr. In addition, for the first time, we reveal a highly collimated SiO jet (~1°) with a projected length of ~5200 au from the embedded protostar VLA 15. Conclusions. Our study unveiled the previously unresolved filamentary structures as well as the shocks within OMC-2 FIR 4. The kinematics of the filamentary structures might be altered by external and/or internal mechanisms such as the wind from H II regions, the precessing jet from the protostellar source HOPS-370, or the jet from VLA 15. While the complexity of the region, coupled with the limited number of molecular lines in our dataset, makes any clear association with these mechanisms challenging, our study shows that multi-scale observations of these regions are crucial for understanding the accretion processes and flow of material that shape star formation.

Understanding star formation in molecular clouds

Probability distribution functions of the total hydrogen column density (N-PDFs) are a valuable tool for distinguishing between the various processes (turbulence, gravity, radiative feedback, magnetic fields) governing the morphological and dynamical structure of the interstellar medium. We present N-PDFs of 29 Galactic regions obtained from Herschel imaging at high angular resolution (18″), covering diffuse and quiescent clouds, and those showing low-, intermediate-, and high-mass star formation (SF), and characterize the cloud structure using the ∆-variance tool. The N-PDFs show a large variety of morphologies. They are all double-log-normal at low column densities, and display one or two power law tails (PLTs) at higher column densities. For diffuse, quiescent, and low-mass SF clouds, we propose that the two log-normals arise from the atomic and molecular phase, respectively. For massive clouds, we suggest that the first log-normal is built up by turbulently mixed H2 and the second one by compressed (via stellar feedback) molecular gas. Nearly all clouds have two PLTs with slopes consistent with self-gravity, where the second one can be flatter or steeper than the first one. A flatter PLT could be caused by stellar feedback or other physical processes that slow down collapse and reduce the flow of mass toward higher densities. The steeper slope could arise if the magnetic field is oriented perpendicular to the LOS column density distribution. The first deviation point (DP), where the N-PDF turns from log-normal into a PLT, shows a clustering around values of a visual extinction of AV (DP1) ~ 2–5. The second DP, which defines the break between the two PLTs, varies strongly. In contrast, the width of the N-PDFs is the most stable parameter, with values of σ between ~0.5 and 0.6. Using the ∆-variance tool, we observe that the AV value, where the slope changes between the first and second PLT, increases with the characteristic size scale in the ∆-variance spectrum. We conclude that at low column densities, atomic and molecular gas is turbulently mixed, while at high column densities, the gas is fully molecular and dominated by self-gravity. The best fitting model N-PDFs of molecular clouds is thus one with log-normal low column density distributions, followed by one or two PLTs.

Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field

ABSTRACT Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study, we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $\delta {\boldsymbol{B}}$ , and large-scale, ${\boldsymbol{B}}_0$, fields, ${\left\langle (\delta \mathrm{{\boldsymbol {\mathit {B}}}}\cdot {\mathrm{{\boldsymbol {\mathit {B}}}}_0})^{2} \right\rangle ^{1/2}_{\mathcal {V}}}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfvénic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible magnetohydrodynamic (MHD) turbulence. Furthermore, we explore the relation between the turbulent mean field and total Alfvén Mach numbers, and demonstrate that sub-Alfvénic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfvénic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfvénic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetized ISM.

J-comb: An image fusion algorithm to combine observations covering different spatial frequency ranges

Ground-based, high-resolution bolometric (sub)millimeter continuum mapping observations on spatially extended target sources are often subject to significant missing fluxes. This hampers accurate quantitative analyses. Missing flux can be recovered by fusing high-resolution images with observations that preserve extended structures. However, the commonly adopted image fusion approaches do not maintain the simplicity of the beam response function and do not try to elaborate the details of the yielded beam response functions. These make the comparison of the observations at multiple wavelengths not straightforward. We present a new algorithm, J-comb, which combines the high and low-resolution images linearly. By applying a taper function to the low-pass filtered image and combining it with a high-pass filtered image using proper weights, the beam response functions of our combined images are guaranteed to have near-Gaussian shapes. This makes it easy to convolve the observations at multiple wavelengths to share the same beam response functions. Moreover, we introduce a strategy to tackle the specific problem that the imaging at 850 um from the present-date ground-based bolometric instrument and that taken with the Planck satellite do not overlap in the Fourier domain. We benchmarked our method against two other widely-used image combination algorithms, CASA-feather and MIRIAD-immerge, with mock observations of star-forming molecular clouds. We demonstrate that the performance of the J-comb algorithm is superior to those of the other two algorithms. We applied the J-comb algorithm to real observational data of the Orion A star-forming region. We successfully produced dust temperature and column density maps with ~10" angular resolution, unveiling much greater details than the previous results.

Statistical properties and correlation length in star-forming molecular clouds

Observations of molecular clouds (MCs) show that their properties exhibit large fluctuations. The proper characterization of the general statistical behavior of these fluctuations, from a limited sample of observations or simulations, is of prime importance to understand the process of star formation. In this article, we use the ergodic theory for any random field of fluctuations, as commonly used in statistical physics, to derive rigorous statistical results. We outline how to evaluate the autocovariance function (ACF) and the characteristic correlation length of these fluctuations. We then apply this statistical approach to astrophysical systems characterized by a field of density fluctuations, notably star-forming clouds. When it is difficult to determine the correlation length from the empirical ACF, we show alternative ways to estimate the correlation length. Notably, we give a way to determine the correlation length of density fluctuations from the estimation of the variance of the volume and column-density fields. We show that the statistics of the column-density field is hampered by biases introduced by integration effects along the line of sight and we explain how to reduce these biases. The statistics of the probability density function (PDF) ergodic estimator also yields the derivation of the proper statistical error bars. We provide a method that can be used by observers and numerical simulation specialists to determine the latter. We show that they (i) cannot be derived from simple Poisson statistics and (ii) become increasingly large for increasing density contrasts, severely hampering the accuracy of the high end part of the PDF because of a sample size that is too small. As templates of various stages of star formation in MCs, we then examine the case of the Polaris and Orion B clouds in detail. We calculate, from the observations, the ACF and the correlation length in these clouds and show that the latter is on the order of ~1% of the size of the cloud. This justifies the assumption of statistical homogeneity when studying the PDF of star-forming clouds. These calculations provide a rigorous framework for the analysis of the global properties of star-forming clouds from limited statistical observations of their density and surface properties.