Simulations Of Molecular Clouds Research Articles

The origin and evolution of the CII deficit in HII regions and star-forming molecular clouds

We analyse synthetic emission maps of the CII 158 mu m line and far-infrared (FIR) continuum of simulated molecular clouds (MCs) within the SILCC-Zoom project to study the origin of the observed CII deficit, that is, the drop in the CII /FIR intensity ratio caused by stellar activity. All simulations include stellar radiative feedback and the on-the-fly chemical evolution of hydrogen species, CO, and C$^+$. We also account for further ionisation of C$^+$ into C$^ $ inside HII regions, which is crucial to obtain reliable results. Studying individual HII regions, we show that $I_ FIR $ is initially high in the vicinity of newly born stars, and then moderately decreases over time as the gas is compressed into dense and cool shells. In contrast, there is a large drop in $I_ CII $ over time, to which the second ionisation of C$^+$ into C$^ $ contributes significantly. This leads to a large drop in deficit inside HII regions, with deficit decreasing from 10$^ $ at scales above 10 pc to around 10$^ $ at scales below 2 pc. However, projection effects can significantly affect the radial profile of $I_ CII $, $I_ FIR $, and their ratio, and can create apparent HII regions without any stars. Considering the evolution on MC scales, we show that the luminosity ratio, deficitl , decreases from values of gtrsim 10$^ $ in MCs without star formation to values of around $ $ in MCs with star formation. We attribute this decrease and thus the origin of the CII deficit to two main contributors: (i) the saturation of the CII line and (ii) the conversion of C$^+$ into C$^ $ by stellar radiation. The drop in the deficitl ratio can be divided into two phases: (i) During the early evolution of HII regions, the saturation of CII and the further ionisation of C$^+$ limit the increase in $L_ CII $, while $L_ FIR $ increases rapidly, leading to the initial decline of deficitl . (ii) In more evolved HII regions, $L_ CII $ stagnates and even partially drops over time due to the aforementioned reasons. $L_ FIR $ also stagnates as the gas gets pushed into the cooler shells surrounding the HII region. In combination, this keeps the global deficitl ratio at low values of $

Impact of ice growth on the physical and chemical properties of dense cloud cores

We investigated the effect of time-dependent ice growth on dust grains on the opacity and hence on the dust temperature in a collapsing molecular cloud core, with the aim of quantifying the effect of the dust temperature variations on ice abundances as well as the evolution of the collapse. To perform the simulations, we employed a one-dimensional collapse model that self-consistently and time-dependently combines hydrodynamics with chemical and radiative transfer simulations. The dust opacity was updated on the fly based on the ice growth as a function of the location in the core. The results of the fully dynamical model were compared against simulations run with different values of fixed ice thickness. We found that the ice thickness increases quickly and reaches a saturation value (as a result of a balance between adsorption and desorption) of approximately 90 monolayers in the central core (volume density ~104 cm−3), and several tens of monolayers at a volume density of ~103 cm−3, after only a few 105 yr of evolution. The results thus exclude the adoption of thin (approximately ten monolayer) ices in molecular cloud simulations except at very short timescales. However, the differences in abundances and the dust temperature between the fully dynamic simulation and those with a fixed dust opacity are small; abundances change between the solutions generally within a factor of two only. The assumptions on the dust opacity do have an effect on the collapse dynamics through the influence of the photoelectric effect on the gas temperature, and the simulations take a different time to reach a common central density. This effect is, however, small as well. In conclusion, carrying out chemical simulations using a dust temperature corresponding to a fixed opacity seems to be a good approximation. Still, although at least in the present case its effect on the overall results is limited – as long as the grains are monodisperse – ice growth should be considered to obtain the most accurate representation of the collapse dynamics. We have found in a previous work that considering a grain size distribution leads to a complicated ice composition that depends on the grain size nonlinearly. With this in mind, we will carry out a follow-up study where the influence of the grain size on the present simulation setup is investigated.

HYACINTH: HYdrogen And Carbon chemistry in the INTerstellar medium in Hydro simulations

Aims. We present a new sub-grid model, HYACINTH – HYdrogen And Carbon chemistry in the INTerstellar medium in Hydro simulations – for computing the non-equilibrium abundances of H2 and its carbon-based tracers, namely CO, C, and C+, in cosmological simulations of galaxy formation. Methods. The model accounts for the unresolved density structure in simulations using a variable probability distribution function of sub-grid densities and a temperature-density relation. Included is a simplified chemical network that has been tailored for hydrogen and carbon chemistry within molecular clouds and easily integrated into large-scale simulations with minimal computational overhead. As an example, we applied HYACINTH to a simulated galaxy at redshift z ~ 2.5 in post-processing and compared the resulting abundances with observations. Results. The chemical predictions from HYACINTH are in reasonable agreement with high-resolution molecular-cloud simulations at different metallicities. By post-processing a galaxy simulation with HYACINTH, we reproduced the H I − H2 transition as a function of the hydrogen column density NH for both Milky-Way-like and Large-Magellanic-Cloud-like conditions. We also matched the NCO versus NH2 relation inferred from absorption measurements towards Milky-Way molecular clouds, although most of our post-processed regions occupy the same region as (optically) dark molecular clouds in the NCO – NH2 plane. Column density maps reveal that CO is concentrated in the peaks of the H2 distribution, while atomic carbon more broadly traces the bulk of H2 in our post-processed galaxy. Based on both the column density maps and the surface density profiles oŕ the different gas species in the post-processed galaxy, we find that C+ maintains a substantially high surŕace density out to ~10 kpc as opposed to other components that exhibit a higher central concentration. This is similar to the extended [C II] emission ŕound in some recent observations at high redshifts.

Decaying turbulence in molecular clouds: how does it affect filament networks and star formation?

ABSTRACT The fragmentation of gas to form stars in molecular clouds is intrinsically linked to the turbulence within them. These internal motions are set at the birth of the cloud and may vary with galactic environment and as the cloud evolves. In this paper, we introduce a new suite of 15 high-resolution 3D molecular cloud simulations using the moving mesh code arepo to investigate the role of different decaying turbulent modes (mixed, compressive, and solenoidal) and virial ratios on the evolution of a $10^4\, \mathrm{M}_{\odot }$ molecular cloud. We find that diffuse regions maintain a strong relic of the initial turbulent mode, whereas the initial gravitational potential dominates dense regions. Solenoidal seeded models thus give rise to a diffuse cloud with filament-like morphology, and an excess of brown dwarf mass fragments. Compressive seeded models have an early onset of star-formation, centrally condensed morphologies and a higher accretion rate, along with overbound clouds. 3D filaments identified using disperse and analysed through a new python toolkit we develop and make publicly available with this work called fiesta, show no clear trend in lengths, masses and densities between initial turbulent modes. Overbound clouds, however, produce more filaments and thus have more mass in filaments. The hubs formed by converging filaments are found to favour star-formation, with surprisingly similar mass distributions independent of the number of filaments connecting the hub.

On the evolution of the observed mass-to-length relationship for star-forming filaments

ABSTRACT The interstellar medium is threaded by a hierarchy of filaments from large scales (∼100 pc) to small scales (∼0.1 pc). The masses and lengths of these nested structures may reveal important constraints for cloud formation and evolution, but it is difficult to investigate from an evolutionary perspective using single observations. In this work, we extract simulated molecular clouds from the ‘Cloud Factory’ galactic-scale ISM suite in combination with 3D Monte Carlo radiative transfer code polaris to investigate how filamentary structure evolves over time. We produce synthetic dust continuum observations in three regions with a series of snapshots and use the filfinder algorithm to identify filaments in the dust derived column density maps. When the synthetic filaments mass and length are plotted on an mass–length (M–L) plot, we see a scaling relation of L ∝ M0.45 similar to that seen in observations, and find that the filaments are thermally supercritical. Projection effects systematically affect the masses and lengths measured for the filaments, and are particularly severe in crowded regions. In the filament M–L diagram we identify three main evolutionary mechanisms: accretion, segmentation, and dispersal. In particular we find that the filaments typically evolve from smaller to larger masses in the observational M–L plane, indicating the dominant role of accretion in filament evolution. Moreover, we find a potential correlation between line mass and filament growth rate. Once filaments are actively star forming they then segment into smaller sections, or are dispersed by internal or external forces.

NEATH – II. N2H+ as a tracer of imminent star formation in quiescent high-density gas

ABSTRACT Star formation activity in molecular clouds is often found to be correlated with the amount of material above a column density threshold of ${\sim} 10^{22} \, {\rm cm}^{-2}$. Attempts to connect this column density threshold to a volume density above which star formation can occur are limited by the fact that the volume density of gas is difficult to reliably measure from observations. We post-process hydrodynamical simulations of molecular clouds with a time-dependent chemical network, and investigate the connection between commonly observed molecular species and star formation activity. We find that many molecules widely assumed to specifically trace the dense, star-forming component of molecular clouds (e.g. HCN, HCO+, CS) actually also exist in substantial quantities in material only transiently enhanced in density, which will eventually return to a more diffuse state without forming any stars. By contrast, N2H+ only exists in detectable quantities above a volume density of $10^4 \, {\rm cm}^{-3}$, the point at which CO, which reacts destructively with N2H+, begins to deplete out of the gas phase on to grain surfaces. This density threshold for detectable quantities of N2H+ corresponds very closely to the volume density at which gas becomes irreversibly gravitationally bound in the simulations: the material traced by N2H+ never reverts to lower densities, and quiescent regions of molecular clouds with visible N2H+ emission are destined to eventually form stars. The N2H+ line intensity is likely to directly correlate with the star formation rate averaged over time-scales of around a Myr.

CO and [C ii] line emission of molecular clouds: the impact of stellar feedback and non-equilibrium chemistry

ABSTRACT We analyse synthetic 12CO, 13CO, and [C ii] emission maps of molecular cloud (MC) simulations from the SILCC-Zoom project. We present radiation, magnetohydrodynamic zoom-in simulations of individual clouds, both with and without radiative stellar feedback, forming in a turbulent multiphase interstellar medium following on-the-fly the evolution of e.g. H2, CO, and C+. We introduce a novel post-processing routine based on cloudy which accounts for higher ionization states of carbon due to stellar radiation in H ii regions. Synthetic emission maps of [C ii] in and around feedback bubbles show that the bubbles are largely devoid of [C ii], as recently found in observations, which we attribute to the further ionization of C+ into C2+. For both 12CO and 13CO, the cloud-averaged luminosity ratio, $L_\rm {CO}/L_\rm {[C\, \small {II}]}$, can neither be used as a reliable measure of the H2 mass fraction nor of the evolutionary stage of the clouds. We note a relation between the $I_\rm {CO}/I_\rm {[C\, \small {II}]}$ intensity ratio and the H2 mass fraction for individual pixels of our synthetic maps. The scatter, however, is too large to reliably infer the H2 mass fraction. Finally, the assumption of chemical equilibrium overestimates H2 and CO masses by up to 150 and 50 per cent, respectively, and $L_\rm {CO}$ by up to 60 per cent. The masses of H and C+ would be underestimated by 65 and 30 per cent, respectively, and $L_\rm {[C\, \small {II}]}$ by up to 35 per cent. Hence, the assumption of chemical equilibrium in MC simulations introduces intrinsic errors of a factor of 2 in chemical abundances, luminosities, and luminosity ratios.

Non-Equilibrium Abundances Treated Holistically (NEATH): the molecular composition of star-forming clouds

ABSTRACT Much of what we know about molecular clouds, and by extension star formation, comes from molecular line observations. Interpreting these correctly requires knowledge of the underlying molecular abundances. Simulations of molecular clouds typically only model species that are important for the gas thermodynamics, which tend to be poor tracers of the denser material where stars form. We construct a framework for post-processing these simulations with a full time-dependent chemical network, allowing us to model the behaviour of observationally important species not present in the reduced network used for the thermodynamics. We use this to investigate the chemical evolution of molecular gas under realistic physical conditions. We find that molecules can be divided into those that reach peak abundances at moderate densities ($10^3 \, {\rm cm}^{-3}$) and decline sharply thereafter (such as CO and HCN), and those that peak at higher densities and then remain roughly constant (e.g. NH3, N2H+). Evolving the chemistry with physical properties held constant at their final values results in a significant overestimation of gas-phase abundances for all molecules, and does not capture the drastic variations in abundance caused by different evolutionary histories. The dynamical evolution of molecular gas cannot be neglected when modelling its chemistry.

The evolution of HCO+ in molecular clouds using a novel chemical post-processing algorithm

ABSTRACT Modelling the chemistry of molecular clouds is critical to accurately simulating their evolution. To reduce computational cost, 3D simulations generally restrict their chemistry to species with strong heating and cooling effects. Time-dependent information about the evolution of other species is therefore often neglected. We address this gap by post-processing tracer particles in the SILCC-Zoom molecular cloud simulations. Using a chemical network of 39 species and 301 reactions (including freeze-out of CO and H2O) and a novel algorithm to reconstruct a density grid from sparse tracer particle data, we produce time-dependent density distributions for various species. We focus upon the evolution of HCO+, which is a critical formation reactant of CO but is not typically modelled on the fly. We find that ∼ 90 per cent of the HCO+ content of the cold molecular gas forms in situ around nHCO+ ∼ 103–104 cm−3, over a time-scale of approximately 1 Myr. The remaining ∼ 10 per cent forms at high extinction sites, with minimal turbulent mixing out into the less dense gas. We further show that the dominant HCO+ formation pathway is dependent on the visual extinction, with the reaction H3+ + CO contributing 90 per cent of the total HCO+ production above AV, 3D = 3. We produce the very first maps of the HCO+ column density, N(HCO+), and show that it reaches values as high as 1015 cm−2. We find that 50 per cent of the HCO+ mass is located within AV ∼ 10–30 in a density range of 103.5–104.5 cm−3. Our maps of N(HCO+) are shown to be in good agreement with recent observations of the W49A star-forming region.

Massive pre-stellar cores in radiation-magneto-turbulent simulations of molecular clouds

ABSTRACT We simulate the formation and collapse of pre-stellar cores at few-au resolution in a set of radiation-magnetohydrodynamic simulations of giant molecular clouds (GMCs) using the grid-based code RAMSES-RT. We adopt, for the first time to our best knowledge, realistic initial/boundary conditions by zooming in on to individual massive pre-stellar cores within the GMC. We identify two distinct modes of fragmentation: ‘quasi-spherical’ and ‘filamentary’. In both modes, the fragments eventually become embedded in a quasi-steady accretion disc or toroid with radii ∼500–5000 au and opening angles H/R ∼ 0.5 − 1. The discs/toroids are Toomre stable but the accreted pre-existing fragments are found orbiting the outer disc, appearing as disc fragmentation. Each core converts nearly 100 per cent of the gas mass into a few massive stars forming near the disc centre. Large and massive discs around high-mass stars are supported by magnetic pressure in the outer disc, at radii >200–1000 au, and turbulent pressure in the inner disc. The most massive core accretes several times more mass than its initial mass, forming a cluster of 8 massive (proto)stars enshrouded by a toroid, suggesting a competitive accretion scenario for the formation of stars above ∼30 M⊙. We also find that the H ii regions produced by a single massive star remain trapped in the dense circumstellar discs for a few hundred kiloyears, while the dynamic motions of massive stars in wide binaries or multiple systems displace the stars from the densest parts of the disc, allowing UV radiation to escape producing steady or pulsating bipolar H ii regions.

Tree-based solvers for adaptive mesh refinement code flash – IV. An X-ray radiation scheme to couple discrete and diffuse X-ray emission sources to the thermochemistry of the interstellar medium

ABSTRACT X-ray radiation, in particular radiation between 0.1 and 10 keV, is evident from both point-like sources, such as compact objects and T-Tauri young stellar objects, and extended emission from hot, cooling gas, such as in supernova remnants. The X-ray radiation is absorbed by nearby gas, providing a source of both heating and ionization. While protoplanetary chemistry models now often include X-ray emission from the central young stellar object, simulations of star-forming regions have yet to include X-ray emission coupled to the chemo-dynamical evolution of the gas. We present an extension of the treeray reverse ray trace algorithm implemented in the flash magnetohydrodynamic code which enables the inclusion of X-ray radiation from 0.1 keV < Eγ < 100 keV, dubbed xraythespot. xraythespot allows for the use of an arbitrary number of bins, minimum and maximum energies, and both temperature-independent and temperature-dependent user-defined cross-sections, along with the ability to include both point and extended diffuse emission and is coupled to the thermochemical evolution. We demonstrate the method with several multibin benchmarks testing the radiation transfer solution and coupling to the thermochemistry. Finally, we show two example star formation science cases for this module: X-ray emission from protostellar accretion irradiating an accretion disc and simulations of molecular clouds with active chemistry, radiation pressure, and protostellar radiation feedback from infrared to X-ray radiation.

Do simulated molecular clouds look like real ones?

ABSTRACT Simulations of molecular clouds often begin from highly idealized initial conditions, such as a uniform-density sphere with an artificially imposed turbulent velocity field. While the resulting structures may appear qualitatively similar to those detected in continuum and line observations, it is unclear whether they are genuinely representative of real molecular clouds. Recent observational work has discovered a tight, often close-to-linear relationship between the integrated intensity of molecular lines and the total column density of the cloud material. We combine magnetohydrodynamical simulations, time-dependent chemistry, and radiative transfer to produce synthetic molecular line observations of model clouds. We find similarly tight correlations between line intensity and column density to those observed, although the linear behaviour is only seen in isolated (as opposed to colliding) model clouds. This linear relationship is not due to optically thin emission; all lines investigated have high optical depths, and the increase in integrated intensity with column density is due to higher velocity dispersion along the line of sight. Overall, the idealized models commonly used in the literature appear to be reasonably accurate representations of real molecular clouds.

Modelling star cluster formation: Mergers

Abstract Star cluster formation in giant molecular clouds involves the local collapse of the cloud into small gas-rich subclusters, which can then subsequently collide and merge to build up the final star cluster(s). In this paper, we simulate collisions between these subclusters, using coupled smooth particle hydrodynamics for the gas and N-body dynamics for the stars. We are guided by previous radiation hydrodynamics simulations of molecular cloud collapse which provide the global properties of the colliding clusters, such as their stellar and gas masses, and their initial positions and velocities. The subclusters in the original simulation were treated as sink particles which immediately merged into a single entity after the collision. We show that the more detailed treatment provides a more complex picture. At collisional velocities above ≈ 10 km/s, the stellar components of the cluster do not form a monolithic cluster within 3 Myr, although the gas may do so. At lower velocities, the clusters do eventually merge but over timescales that may be longer than the time for a subsequent collision. The structure of the resultant cluster is not well-fit by any standard density distribution, and the clusters are not in equilibrium but continue to expand over our simulation time. We conclude that the simple sink particle treatment of subcluster mergers in large-scale giant molecular cloud simulations provides an upper limit on the final cluster properties.

The impact of cosmic-ray attenuation on the carbon cycle emission in molecular clouds

Context. Observations of the emission of the carbon cycle species (C, C+, CO) are commonly used to diagnose gas properties in the interstellar medium, but they are significantly sensitive to the cosmic-ray ionization rate. The carbon-cycle chemistry is known to be quite sensitive to the cosmic-ray ionization rate, ζ, controlled by the flux of low-energy cosmic rays which get attenuated through molecular clouds. However, astrochemical models commonly assume a constant cosmic-ray ionization rate in the clouds. Aims. We investigate the effect of cosmic-ray attenuation on the emission of carbon cycle species from molecular clouds, in particular the [CII] 158 μm, [CI] 609 μm, and CO (J = 1–0) 115.27 GHz lines. Methods. We used a post-processed chemical model of diffuse and dense simulated molecular clouds and quantified the variation in both column densities and velocity-integrated line emission of the carbon cycle with different cosmic-ray ionization rate models. Results. We find that the abundances and column densities of carbon cycle species are significantly impacted by the chosen cosmic-ray ionization rate model: no single constant ionization rate can reproduce the abundances modeled with an attenuated cosmic-ray model. Further, we show that constant ionization rate models fail to simultaneously reproduce the integrated emission of the lines we consider, and their deviations from a physically derived cosmic-ray attenuation model is too complex to be simply corrected. We demonstrate that the two clouds we modeled exhibit a similar average AV,eff – nH relationship, resulting in an average relation between the cosmic-ray ionization rate and density ζ(nH). Conclusions. We conclude by providing a number of implementation recommendations for cosmic rays in astrochemical models, but emphasize the necessity for column-dependent cosmic-ray ionization rate prescriptions.

A resolution criterion based on characteristic time-scales for MHD simulations of molecular clouds

ABSTRACT We investigate the effect of numerical magnetic diffusion in magnetohydrodynamic (MHD) simulations of magnetically supported molecular clouds. To this end, we have performed numerical studies on adaptive mesh isothermal simulations of marginally subcritical molecular clouds. We find that simulations with low and intermediate resolutions collapse, contrary to what is theoretically expected. However, the simulation with the highest numerical resolution oscillates around an equilibrium state without collapsing. In order to quantify the numerical diffusion of the magnetic field, we ran a second suit of current-sheet simulations in which the numerical magnetic diffusion coefficient can be directly measured and computed the corresponding diffusion times at various numerical resolutions. On this basis, we propose a criterion for the resolution of magnetic fields in MHD simulations based on requiring that the diffusion time to be larger than the characteristic time-scale of the physical process responsible for the dynamic evolution of the structure.

Grouped star formation: converting sink particles to stars in hydrodynamical simulations

ABSTRACT Modelling star formation and resolving individual stars in numerical simulations of molecular clouds and galaxies is highly challenging. Simulations on very small scales can be sufficiently well resolved to consistently follow the formation of individual stars, whilst on larger scales sinks that have masses sufficient to fully sample the IMF can be converted into realistic stellar populations. However, as yet, these methods do not work for intermediate scale resolutions whereby sinks are more massive compared to individual stars but do not fully sample the IMF. In this paper, we introduce the grouped star formation prescription, whereby sinks are first grouped according to their positions, velocities, and ages, then stars are formed by sampling the IMF using the mass of the groups. We test our grouped star formation method in simulations of various physical scales, from sub-parsec to kilo-parsec, and from static isolated clouds to colliding clouds. With suitable grouping parameters, this star formation prescription can form stars that follow the IMF and approximately mimic the original stellar distribution and velocity dispersion. Each group has properties that are consistent with a star-forming region. We show that our grouped star formation prescription is robust and can be adapted in simulations with varying physical scales and resolution. Such methods are likely to become more important as galactic or even cosmological scale simulations begin to probe sub-parsec scales.

HAWC+/SOFIA Polarimetry in L1688: Relative Orientation of Magnetic Field and Elongated Cloud Structure

Abstract We present a study of the relative orientation between the magnetic field and elongated cloud structures for the ρ Oph A and ρ Oph E regions in L1688 in the Ophiuchus molecular cloud. Combining inferred magnetic field orientation from HAWC+ 154 μm observations of polarized thermal emission with column density maps created using Herschel submillimeter observations, we find consistent perpendicular relative alignment at scales of 0.02 pc (33.″6 at d ≈ 137 pc) using the histogram of relative orientations (HRO) technique. This supports the conclusions of previous work using Planck polarimetry and extends the results to higher column densities. Combining this HAWC+ HRO analysis with a new Planck HRO analysis of L1688, the transition from parallel to perpendicular alignment in L1688 is observed to occur at a molecular hydrogen column density of approximately 1021.7 cm−2. This value for the alignment transition column density agrees well with values found for nearby clouds via previous studies using only Planck observations. Using existing turbulent, magnetohydrodynamic simulations of molecular clouds formed by colliding flows as a model for L1688, we conclude that the molecular hydrogen volume density associated with this transition is approximately ∼104 cm−3. We discuss the limitations of our analysis, including incomplete sampling of the dense regions in L1688 by HAWC+.

Dust polarization studies on MHD simulations of molecular clouds: comparison of methods for the relative-orientation analysis

Context. The all-sky survey from the Planck space telescope has revealed that thermal emission from Galactic dust is polarized on scales ranging from the whole sky down to the inner regions of molecular clouds. Polarized dust emission can therefore be used as a probe for magnetic fields on different scales. In particular, the analysis of the relative orientation between the density structures and the magnetic field projected on the plane of the sky can provide information on the role of magnetic fields in shaping the structure of molecular clouds where star formation takes place. Aims. The orientation of the magnetic field with respect to the density structures has been investigated using different methods. The goal of this paper is to explicitly compare two of these: the Rolling Hough Transform (RHT) and the gradient technique (GRAD). Methods. We generated synthetic surface brightness maps at 353 GHz (850 μm) via magnetohydrodynamic simulations. We applied RHT and GRAD to two morphologically different regions identified in our maps. Region 1 is dominated by a dense and thick filamentary structure with some branches, while Region 2 includes a thinner filament with denser knots immersed in a more tenuous medium. Both methods derive the relative orientation between the magnetic field and the density structures, to which we applied two statistics, the histogram of relative orientation and the projected Rayleigh statistic, to quantify the variations of the relative orientation as a function of column density. Results. Both methods find areas with significant signal, and these areas are substantially different. In terms of relative orientations, in all our considered cases the predominant orientation of the density structures is perpendicular to the direction of the magnetic field. When the methods are applied to the same selected areas the results are consistent with each other in Region 2 but show some noticeable differences in Region 1. In Region 1, RHT globally finds the relative orientation becoming more perpendicular for increasing column density, while GRAD, applied at the same resolution as RHT, gives the opposite trend. These disparities are caused by the intrinsic differences in the methods and in the structures that they select. Conclusions. Our results indicate that the interpretation of the relative orientation between the magnetic field and density structures should take into account the specificity of the methods used to determine such orientation. The combined use of complementary techniques such as RHT and GRAD provides more complete information, which can be advantageously used to better understand the physical mechanisms operating in magnetized molecular clouds.

Striations, integrals, hourglasses, and collapse – thermal instability driven magnetic simulations of molecular clouds

ABSTRACT The MHD version of the adaptive mesh refinement (AMR) code, MG, has been employed to study the interaction of thermal instability, magnetic fields, and gravity through 3D simulations of the formation of collapsing cold clumps on the scale of a few parsecs, inside a larger molecular cloud. The diffuse atomic initial condition consists of a stationary, thermally unstable, spherical cloud in pressure equilibrium with lower density surroundings and threaded by a uniform magnetic field. This cloud was seeded with 10 per cent density perturbations at the finest initial grid level around n = 1.1 cm−3 and evolved with self-gravity included from the outset. Several cloud diameters were considered (100, 200, and 400 pc) equating to several cloud masses (17 000, 136 000, and 1.1 × 106 M⊙). Low-density magnetic-field-aligned striations were observed as the clouds collapse along the field lines into disc-like structures. The induced flow along field lines leads to oscillations of the sheet about the gravitational minimum and an integral-shaped appearance. When magnetically supercritical, the clouds then collapse and generate hourglass magnetic field configurations with strongly intensified magnetic fields, reproducing observational behaviour. Resimulation of a region of the highest mass cloud at higher resolution forms gravitationally bound collapsing clumps within the sheet that contain clump-frame supersonic (M ∼ 5) and super-Alfvénic (MA ∼ 4) velocities. Observationally realistic density and velocity power spectra of the cloud and densest clump are obtained. Future work will use these realistic initial conditions to study individual star and cluster feedback.

Understanding biases in measurements of molecular cloud kinematics using line emission

ABSTRACT Molecular line observations using a variety of tracers are often used to investigate the kinematic structure of molecular clouds. However, measurements of cloud velocity dispersions with different lines, even in the same region, often yield inconsistent results. The reasons for this disagreement are not entirely clear, since molecular line observations are subject to a number of biases. In this paper, we untangle and investigate various factors that drive linewidth measurement biases by constructing synthetic position–position–velocity cubes for a variety of tracers from a suite of self-gravitating magnetohydrodynamic simulations of molecular clouds. We compare linewidths derived from synthetic observations of these data cubes to the true values in the simulations. We find that differences in linewidth as measured by different tracers are driven by a combination of density-dependent excitation, whereby tracers that are sensitive to higher densities sample smaller regions with smaller velocity dispersions, opacity broadening, especially for highly optically thick tracers such as CO, and finite resolution and sensitivity, which suppress the wings of emission lines. We find that, at fixed signal-to-noise ratio, three commonly used tracers, the J = 4 → 3 line of CO, the J = 1 → 0 line of C18O, and the (1,1) inversion transition of NH3, generally offer the best compromise between these competing biases, and produce estimates of the velocity dispersion that reflect the true kinematics of a molecular cloud to an accuracy of $\approx 10{{\ \rm per\ cent}}$ regardless of the cloud magnetic field strengths, evolutionary state, or orientations of the line of sight relative to the magnetic field. Tracers excited primarily in gas denser than that traced by NH3 tend to underestimate the true velocity dispersion by $\approx 20{{\ \rm per\ cent}}$ on average, while low-density tracers that are highly optically thick tend to have biases of comparable size in the opposite direction.