We use detailed numerical simulations of the coupled chemical, thermal and dynamical evolution of the gas in a turbulent molecular cloud to study the usefulness of the [CI] 609 micron and 370 micron fine structure emission lines as tracers of cloud structure. Emission from these lines is observed throughout molecular clouds, and yet the question of what we can learn from them about the physics of the clouds remains largely unexplored.
We show that the fact that [CI] emission is widespread within molecular clouds is a simple consequence of the fact that the clouds are dominated by turbulent motions. Turbulence creates large density inhomogeneities, allowing radiation to penetrate deeply into the clouds. As a result, [CI] emitting gas is found throughout the cloud, rather than being concentrated at the edges. We examine how well we can use [CI] emission to trace the structure of the cloud, and show that the integrated intensity of the 609 micron line traces column density accurately over a wide range of visual extinctions. For extinctions greater than a few, [CI] and 13CO both perform well, but [CI] becomes a superior tracer of column densities for visual extinctions A_V <= 3
We have also studied the distribution of [CI] excitation temperatures in the gas, and show that these are typically smaller than the kinetic temperature, indicating that most of the carbon atoms are not in local thermodynamic equilibrium. We discuss how best to determine T_ex from observations of the [CI] lines, and how to use these values to estimate the column density of neutral atomic carbon. We show that even in the best case, we tend to systematically underestimate the atomic carbon content of the gas. Our results suggest that observationally-derived estimates of the atomic carbon content of real GMCs could be in error by as much as a factor of two.
Here we present a simple, but nevertheless, instructive model for the star formation efficiency in turbulent molecular clouds. The model is based on the assumption of log-normal density distribution which reflects the turbulent nature of the interstellar medium (ISM). Together with the number count of cloud cores, which follows a Salpeter-like core mass function (CMF), and the minimum mass for the collapse of individual cloud cores, given by the local Jeans mass, we are able to derive the SFE for clouds as a function of their Jeans masses. We find a very generic power-law, SFE \propto (M_cloud…
We present a set of numerical experiments designed to systematically investigate how turbulence and magnetic fields influence the morphology, energetics, and dynamics of filaments produced in wind-cloud interactions. We cover 3D magnetohydrodynamic systems of supersonic winds impacting clouds with turbulent density, velocity, and magnetic fields. We find that log-normal density distributions aid shock propagation through clouds, increasing their velocity dispersion and producing filaments with expanded cross sections and highly-magnetised knots and sub-filaments. In self-consistently turbulent…
To date, most numerical simulations of molecular clouds, and star formation within them, assume a uniform density sphere or box with an imposed turbulent velocity field. In this work, we select molecular clouds from galactic scale simulations as initial conditions, increase their resolution, and re-simulate them using the SPH code Gadget2. Our approach provides clouds with morphologies, internal structures, and kinematics that constitute more consistent and realistic initial conditions for simulations of star formation. We perform comparisons between molecular clouds derived from a galactic si…
Clustering and dynamics of nano-sized particles (nano dust) is investigated using high-resolution ($1024^3$) simulations of compressible isothermal hydrodynamic turbulence, intended to mimic the conditions inside cold molecular clouds in the interstellar medium. Nano-sized grains may cluster in a turbulent flow (small-scale clustering), which increases the local grain density significantly. Together with the increased interaction rate due to turbulent motions, aggregation of interstellar nano-dust may be plausible.
Molecular clouds are essentially made up of atomic and molecular hydrogen, which in spite of being the simplest molecule in the ISM plays a key role in the chemical evolution of molecular clouds. Since its formation time is very long, the H2 molecules can be transported by the turbulent motions within the cloud toward low density and warm regions, where its enhanced abundance can boost the abundances of molecules with high endothermicities. We present high resolution simulations where we include the evolution of the molecular gas under the effect of the dynamics, and we analyze its impact on t…
In this paper we continue to investigate the energy conservation equation obtained in our previous work. We set ourselves three new goals. The first one is to rewrite the main equations in terms of density profile in order to give more physical insight. The second one is to investigate the significance of two new terms in the energy conservation equation. They originate from the gravity of the outer shells of cloud and the masses outer to the cloud, respectively. The third goal is to investigate the main equation in the case when the kinetic turbulent term scales according to Larson's law and …
Stars form in highly-magnetised, supersonic turbulent molecular clouds. Many of the tools and models that we use to carry out star formation studies rely upon the assumption of cloud isotropy. However, structures like high-density filaments in the presence of magnetic fields, and magnetosonic striations introduce anisotropies into the cloud. In this study we use the two-dimensional (2D) power spectrum to perform a systematic analysis of the anisotropies in the column density for a range of Alfvén Mach numbers ($\mathcal{M}_A=0.1$--$10$) and turbulent Mach numbers ($\mathcal{M}=2$--$20$), with …
We present a study of the impact of photoionization feedback from young massive stars on the turbulent statistics of star-forming molecular clouds. This feedback is expected to alter the density structure of molecular clouds and affect future star formation. Using the AMUN- Rad code, we first generate a converged isothermal forced turbulent density structure inside a periodic box. We then insert an ionizing source in this box and inject photoionization energy using a two-temperature pseudo-isothermal equation of state. We study the impact of sources at different locations in the box and of dif…
Complex turbulent motions of magnetized gas are ubiquitous in the interstellar medium. The source of this turbulence, however, is still poorly understood. Previous work suggests that compression caused by supernova shockwaves, gravity, or cloud collisions, may drive the turbulence to some extent. In this work, we present three-dimensional (3D) magnetohydrodynamic (MHD) simulations of contraction in turbulent, magnetized clouds from the warm neutral medium (WNM) of the ISM to the formation of cold dense molecular clouds, including radiative heating and cooling. We study different contraction ra…
In order to understand the origin of observed molecular cloud properties, it is critical to understand how clouds interact with their environments during their formation, growth, and collapse. It has been suggested that accretion-driven turbulence can maintain clouds in a highly turbulent state, preventing runaway collapse, and explaining the observed non-thermal velocity dispersions. We present 3D, AMR, MHD simulations of a kiloparsec-scale, stratified, supernova-driven, self-gravitating, interstellar medium, including diffuse heating and radiative cooling. These simulations model the formati…
A stochastic model of fragmentation of molecular clouds has been developed for studying the resulting Initial Mass Function (IMF) where the number of fragments, inter-occurrence time of fragmentation, masses and velocities of the fragments are random variables. Here two turbulent patterns of the velocities of the fragments have been considered, namely, Gaussian and Gamma distributions. It is found that for Gaussian distribution of the turbulent velocity, the IMFs are shallower in general compared to Salpeter mass function. On the contrary, a skewed distribution for turbulent velocity leads to …
In a companion paper, we develop a theory for the evolution of stellar wind driven bubbles in dense, turbulent clouds. This theory proposes that turbulent mixing at a fractal bubble-shell interface leads to highly efficient cooling, in which the vast majority of the input wind energy is radiated away. This energy loss renders the majority of the bubble evolution momentum-driven rather than energy-driven, with expansion velocities and pressures orders of magnitude lower than in the classical Weaver77 solution. In this paper, we validate our theory with three-dimensional, hydrodynamic simulation…
Observations of interstellar gas clouds are typically limited to two-dimensional (2D) projections of the intrinsically three-dimensional (3D) structure of the clouds. In this study, we present a novel method for relating the 2D projected fractal dimension ($\mathcal{D}_{\text{p}}$) to the 3D fractal dimension ($\mathcal{D}_{\text{3D}}$) of turbulent clouds. We do this by computing the fractal dimension of clouds over two orders of magnitude in turbulent Mach number $(\mathcal{M} = 1-100)$, corresponding to seven orders of magnitude in spatial scales within the clouds. This provides us with the…
Most detected neutral atomic hydrogen (HI) at low redshift is associated with optically bright galaxies. However, a handful of HI clouds are known which appear to be optically dark and have no nearby potential progenitor galaxies, making tidal debris an unlikely explanation. In particular, 6 clouds identified by the Arecibo Galaxy Environment Survey are interesting due to the combination of their small size, isolation, and especially their broad line widths atypical of other such clouds. A recent suggestion is that these clouds exist in pressure equilibrium with the intracluster medium, with t…
It is speculated that the high star-formation efficiency observed in spiral-arm molecular clouds is linked to the prevalence of compressive (curl-free) turbulent modes, while the shear-driven solenoidal (divergence-free) modes appear to be the main cause of the low star-formation efficiency that characterises clouds in the Central Molecular Zone. Similarly, analysis of the Orion B molecular cloud has confirmed that, although turbulent modes vary locally and at different scales within the cloud, the dominant solenoidal turbulence is compatible with its low star formation rate. This evidence poi…
Winds from massive stars have velocities of 1000 km/s or more, and produce hot, high pressure gas when they shock. We develop a theory for the evolution of bubbles driven by the collective winds from star clusters early in their lifetimes, which involves interaction with the turbulent, dense interstellar medium of the surrounding natal molecular cloud. A key feature is the fractal nature of the hot bubble's surface. The large area of this interface with surrounding denser gas strongly enhances energy losses from the hot interior, enabled by turbulent mixing and subsequent cooling at temperatur…
Filamentary structures are ubiquitous in observations of real molecular clouds, and also in simulations of turbulent, self-gravitating gas. However, making comparisons between observations and simulations is complicated by the difficulty of estimating volume-densities observationally. Here, we have post-processed hydrodynamical simulations of a turbulent isothermal molecular cloud, using a full time-dependent chemical network. We have then run radiative transfer models to obtain synthetic line and continuum intensities that can be compared directly with those observed. We find that filaments h…
We present 3D hydrodynamic simulations of the adiabatic interaction of a shock with a dense, spherical cloud. We compare how the nature of the interaction changes with the Mach number of the shock, $M$, and the density contrast of the cloud, $χ$. We examine the differences with 2D axisymmetric calculations, perform detailed resolution tests, and compare "inviscid" results to those obtained with the inclusion of a $k$-$ε$ subgrid turbulence model. Resolutions of 32-64 cells per cloud radius are the minimum necessary to capture the dominant dynamical processes in 3D simulations, while the 3D inv…
Molecular clouds are to a great extent influenced by turbulent motions in the gas. Numerical and observational studies indicate that the star formation rate and efficiency crucially depend on the mixture of solenoidal and compressive modes in the turbulent acceleration field, which can be quantified by the turbulent driving parameter b. For purely solenoidal (divergence-free) driving previous studies showed that b=1/3 and for entirely compressive (curl-free) driving b=1. In this study, we determine the evolution of the turbulent driving parameter b in magnetohydrodynamical simulations of molec…
We present a new set of analytic models for the expansion of HII regions powered by UV photoionisation from massive stars and compare them to a new suite of radiative magnetohydrodynamic simulations of turbulent, self-gravitating molecular clouds. To perform these simulations we use the Eulerian adaptive mesh magnetohydrodynamics code RAMSES-RT, including radiative transfer of UV photons. Our analytic models successfully predict the global behaviour of the HII region provided the density and velocity structure of the cloud is known. We give estimates for the HII region behaviour based on a pow…
Momentum deposition by radiation pressure from young, massive stars may help to destroy molecular clouds and unbind stellar clusters by driving large-scale outflows. We extend our previous numerical radiation hydrodynamic study of turbulent, star-forming clouds to analyze the detailed interaction between non-ionizing UV radiation and the cloud material. Our simulations trace the evolution of gas and star particles through self-gravitating collapse, star formation, and cloud destruction via radiation-driven outflows. These models are idealized in that we include only radiation feedback and adop…
Context: Star clusters form within giant molecular clouds that are strongly altered by the feedback action of the massive stars, but the cluster still remains embedded in a dense, highly turbulent medium and interactions with ambient structures may modify its dynamical evolution from that expected if it were isolated. Aims: We aim to study coupling mechanisms between the dynamical evolution of the cluster, accelerated by the mass segregation process, with harassment effects caused by the gaseous environment. Methods: We simulated the cluster dynamical evolution combining $N$-body and hydrodyna…
We report the detection of a wing component in NH$_3$ emission toward the starless core TUKH122 with subthermal turbulence in the Orion A cloud. This NH$_3$ core is suggested to be on the verge of star formation because the turbulence inside the NH$_3$ core is almost completely dissipated, and also because it is surrounded by CCS, which resembles the prestellar core L1544 in Taurus showing infall motions. Observations were carried out with the Nobeyama 45 m telescope at 0.05 km s$^{-1}$ velocity resolution. We find that the NH$_3$ line profile consists of two components. The quiescent main com…
Radiation feedback from stellar clusters is expected to play a key role in setting the rate and efficiency of star formation in giant molecular clouds (GMCs). To investigate how radiation forces influence realistic turbulent systems, we have conducted a series of numerical simulations employing the {\it Hyperion} radiation hydrodynamics solver, considering the regime that is optically thick to ultraviolet (UV) and optically thin to infrared (IR) radiation. Our model clouds cover initial surface densities between $Σ_{\rm cl,0} \sim 10-300~M_{\odot}~{\rm pc^{-2}}$, with varying initial turbulenc…
We developed methods for mapping spatial variations of the spatial power spectrum (SPS) and structure function (SF) slopes, with a goal of connecting neutral hydrogen (HI) statistical properties with the turbulent drivers. The new methods were applied on the HI observations of the Small and Large Magellanic Clouds (SMC and LMC). In the case of the SMC, we find highly uniform turbulent properties of HI, with no evidence for local enhancements of turbulence due to stellar feedback. Such properties could be caused by a significant turbulent driving on large-scales. Alternatively, a significant li…
The character of star formation is intimately related to the supersonic magnetohydrodynamic (MHD) turbulent dynamics of the molecular clouds in which stars form. A significant amount of the turbulent energy dissipates in low velocity shocks. Fast and slow MHD shocks differ in how they compress and heat the molecular gas, and so their radiative signatures reveal distinct physical conditions. We use a two-fluid model to compare one-dimensional fast and slow MHD shocks propagating at low speeds (a few km/s). Fast shocks are magnetically driven, forcing ion species to stream through the neutral ga…
We (Li et al. 2009; Paper-I) compared the magnetic field directions inferred from polarimetry data obtained from 100-pc scale inter-cloud media (ICM) and from sub-pc scale molecular cloud cores. The highly correlated result led us to conclude that cloud turbulence must be sub-Alfvenic. Here we extend the study with 0.01-pc cores observed by interferometers. The inferred field directions at this scale significantly deviate from that of the surrounding ICM. An obvious question to ask is whether this high-resolution result contradicts the sub-Alfvenic picture concluded earlier. We performed MHD s…
Radiation feedback from young star clusters embedded in giant molecular clouds (GMCs) is believed to be important to the control of star formation. For the most massive and dense clouds, including those in which super star clusters (SSCs) are born, pressure from reprocessed radiation exerted on dust grains may disperse a significant portion of the cloud mass back into the interstellar medium (ISM). Using our radiaton hydrodynamics (RHD) code, Hyperion, we conduct a series of numerical simulations to test this idea. Our models follow the evolution of self-gravitating, strongly turbulent clouds …
We carried out synthetic observations of a theoretical model of interstellar carbon in CO, C I and C II including H2 formation. The theoretical model based on numerical simulations of H I gas converging at a velocity of 20 km/s by Inoue & Inutsuka (2012) is employed in the present study. The gas model, which is fairy realistic and consistent with the observations of the local gas located at high b, is turbulent and inhomogeneous with magnetic field. We focus on the evolution of the rare species, CO, C I and C II from 0.3 Myr to 9 Myr since the converging flows collided. In the early phase with…
We create a photoionization model embedded in the turbulent ISM by using the state-of-the-art Messenger Monte-Carlo MAPPINGS~V code (M$^3$) in conjunction with the CMFGEN stellar atmosphere model. We show that the turbulent ISM causes the inhomogeneity of electron temperature and density within the nebula. The fluctuation in the turbulent ISM creates complex ionization structures seen in nearby nebulae. The inhomogeneous density distribution within the nebula creates a significant scatter on the spatially-resolved standard optical diagnostic diagrams, which cannot be represented by the spheric…
We obtain an equation for the density profile in a self-gravitating polytropic spherically symmetric turbulent fluid with an equation of state $p_{\rm gas}\propto ρ^Γ$. This is done in the framework of ensembles of molecular clouds represented by single abstract objects as introduced by Donkov et al. (2017). The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state changes from isothermal (in the outer cloud layers) with $Γ=1$ to one of `hard polytrope' with exponent $Γ>1$. On the assumption of steady state, as the accreting matte…
We investigate giant molecular cloud (GMCs) collisions and their ability to induce gravitational instability and thus star formation. This mechanism may be a major driver of star formation activity in galactic disks. We carry out a series of three dimensional, magnetohydrodynamics (MHD), adaptive mesh refinement (AMR) simulations to study how cloud collisions trigger formation of dense filaments and clumps. Heating and cooling functions are implemented based on photo-dissociation region (PDR) models that span the atomic to molecular transition and can return detailed diagnostic information. Th…
We have set ourselves the task of obtaining the probability distribution function of the mass density of a self-gravitating isothermal compressible turbulent fluid from its physics. We have done this in the context of a new notion: the molecular clouds ensemble. We have applied a new approach that takes into account the fractal nature of the fluid. Using the medium equations, under the assumption of steady state, we show that the total energy per unit mass is an invariant with respect to the fractal scales. As a next step we obtain a nonlinear integral equation for the dimensionless scale Q wh…
In the present work we apply virial analysis to the model of self-gravitating turbulent cloud ensembles introduced by Donkov \& Stefanov in two previous papers, clarifying some aspects of turbulence and extending the model to account not only for supersonic flows but for trans- and subsonic ones as well. Make use of the Eulerian virial theorem at an arbitrary scale, far from the cloud core, we derive an equation for the density profile and solve it in approximate way. The result confirms the solution $\varrho(\ell)=\ell^{-2}$ found in the previous papers. This solution corresponds to three pos…
We investigate spatial variations of turbulent properties in the Small Magellanic Cloud (SMC) by using neutral hydrogen HI observations. With the goal of testing the importance of stellar feedback on HI turbulence, we define central and outer SMC regions based on the star formation rate (SFR) surface density, as well as the HI integrated intensity. We use the structure function and the Velocity Channel Analysis (VCA) to calculate the power-law index (gamma) for both underlying density and velocity fields in these regions. In all cases, our results show essentially no difference in gamma betwee…
Previous studies have shown that star formation depends on the driving of molecular cloud turbulence, and differences in the driving can produce an order of magnitude difference in the star formation rate. The turbulent driving is characterised by the parameter $ζ$, with $ζ=0$ for compressive, curl-free driving (e.g. accretion or supernova explosions), and $ζ=1$ for solenoidal, divergence-free driving (e.g. Galactic shear). Here we develop a new method to measure $ζ$ from observations of synchrotron emission from molecular clouds. We calculate statistics of mock synchrotron intensity images pr…
Many studies have considered the roles of clouds, outflows, and turbulence in producing the broad emission and absorption lines in the spectra of active galactic nuclei (AGNs). However, these are often treated as separate or even competing models. Here, we consider the possibility that AGN clouds are condensations formed within the thermally unstable zones of outflows and then compare the typical sizes of such condensations with the injection scale $k_0^{-1} \sim L_0$ of turbulence, where $L_0$ is assumed to be the scale height of a representative global outflow model. We find that for broad l…
We investigate the physical mechanism that decides the saturation level of turbulence in collapsing gas clouds. We perform a suite of high-resolution numerical simulations following the collapse of turbulent gas clouds with various effective polytropic exponents $γ_{\rm eff}$, initial Mach numbers $\mathcal{M}_0$, and initial turbulent seeds. Equating the energy injection rate by gravitational contraction and the dissipation rate of turbulence, we obtain an analytic expression of the saturation level of turbulence, and compare it with the numerical results. Consequently, the numerical results …
The formation of stars occurs in the dense molecular cloud phase of the interstellar medium. Observations and numerical simulations of molecular clouds have shown that supersonic magnetised turbulence plays a key role for the formation of stars. Simulations have also shown that a large fraction of the turbulent energy dissipates in shock waves. The three families of MHD shocks --- fast, intermediate and slow --- distinctly compress and heat up the molecular gas, and so provide an important probe of the physical conditions within a turbulent cloud. Here we introduce the publicly available algor…
The kinetic energy of supersonic turbulence within interstellar clouds is subject to cooling by dissipation in shocks and subsequent line radiation. The clouds are therefore susceptible to a condensation process controlled by the specific entropy. In a form analogous to the thermodynamic entropy, the entropy for supersonic turbulence is proportional to the log of the product of the mean turbulent velocity and the size scale. We derive a dispersion relation for the growth of entropic instabilities in a spherical self-gravitating cloud and find that there is a critical maximum dissipation time s…
