Self-gravitating Molecular Clouds Research Articles

Protoplanetary Disk Formation in a Self-gravitating Molecular Cloud

Protoplanetary Disk Formation in a Self-gravitating Molecular Cloud

The Dense Gas Mass Fraction and the Relationship to Star Formation in M51

Observations of 12CO J = 1 – 0 and HCN J = 1 – 0 emission from NGC 5194 (M51) made with the 50 m Large Millimeter Telescope and the SEQUOIA focal plane array are presented. Using the HCN-to-CO ratio, we examine the dense gas mass fraction over a range of environmental conditions within the galaxy. Within the disk, the dense gas mass fraction varies along the spiral arms but the average value over all spiral arms is comparable to the mean value of interarm regions. We suggest that the near-constant dense gas mass fraction throughout the disk arises from a population of density-stratified, self-gravitating molecular clouds and the required density threshold to detect each spectral line. The measured dense gas fraction significantly increases in the central bulge in response to the effective pressure, P e , from the weight of the stellar and gas components. This pressure modifies the dynamical state of the molecular cloud population and, possibly, the HCN-emitting regions in the central bulge from self-gravitating to diffuse configurations in which P e is greater than the gravitational energy density of individual clouds. Diffuse molecular clouds comprise a significant fraction of the molecular gas mass in the central bulge, which may account for the measured sublinear relationships between the surface densities of the star formation rate and molecular and dense gas.

Velocity Anisotropy in Self-gravitating Molecular Clouds. II. Observation

Abstract The view on velocity structures in molecular clouds and their relationship with magnetic fields (B field) has evolved during the past decade from almost no correlation to highly parallel. Our numerical simulations suggest a more nuanced picture: Depending on whether the self-gravity is dynamically dominant, the velocity field can be governed by either contraction (at high densities) or turbulence (at low densities), and their anisotropies will tend to be either perpendicular or parallel, respectively, to the B fields. High-density regions are always embedded in the low-density fore/background, so the velocity behaviors from lines of sight (LOSs) with high column densities will be a mixture of orthogonal anisotropies, which can be hard to interpret and necessitates zooming in onto certain LOS scales to better characterize localized behaviors. We tested and confirmed the above prediction with CO observations of the Taurus molecular cloud.

Photodissociation region diagnostics across galactic environments

ABSTRACT We present three-dimensional astrochemical simulations and synthetic observations of magnetized, turbulent, self-gravitating molecular clouds. We explore various galactic interstellar medium environments, including cosmic ray ionization rates in the range of ζCR = 10−17–$10^{-14}\, {\rm s}^{-1}$, far-UV intensities in the range of G0 = 1–103 and metallicities in the range of Z = 0.1–$2\, {\rm Z}_{\odot }$. The simulations also probe a range of densities and levels of turbulence, including cases where the gas has undergone recent compression due to cloud–cloud collisions. We examine: (i) the column densities of carbon species across the cycle of C ii, C i, and CO, along with O i, in relation to the H i-to-H2 transition; (ii) the velocity-integrated emission of [C ii] 158 μm, [13C ii] 158 μm, [C i] 609 μm and 370 μm, [O i] 63 μm and 146 μm, and of the first ten 12CO rotational transitions; (iii) the corresponding Spectral Line Energy Distributions; (iv) the usage of [C ii] and [O i] 63 μm to describe the dynamical state of the clouds; (v) the behaviour of the most commonly used ratios between transitions of CO and [C i]; and (vi) the conversion factors for using CO and C i as H2-gas tracers. We find that enhanced cosmic ray energy densities enhance all aforementioned line intensities. At low metallicities, the emission of [C ii] is well connected with the H2 column, making it a promising new H2 tracer in metal-poor environments. The conversion factors of XCO and XC i depend on metallicity and the cosmic ray ionization rate, but not on FUV intensity. In the era of ALMA, SOFIA, and the forthcoming CCAT-prime telescope, our results can be used to understand better the behaviour of systems in a wide range of galactic and extragalactic environments.

Turbulence in a Self-gravitating Molecular Cloud Core

Abstract Externally driven interstellar turbulence plays an important role in shaping the density structure in molecular clouds. Here we study the dynamical role of internally driven turbulence in a self-gravitating molecular cloud core. Depending on the initial conditions and evolutionary stages, we find that a self-gravitating core in the presence of gravity-driven turbulence can undergo constant, decelerated, and accelerated infall, and thus has various radial velocity profiles. In the gravity-dominated central region, a higher level of turbulence results in a lower infall velocity, a higher density, and a lower mass accretion rate. As an important implication of this study, efficient reconnection diffusion of magnetic fields against the gravitational drag naturally occurs due to the gravity-driven turbulence, without invoking externally driven turbulence.

Star Formation in Self-Gravitating Molecular Cloud: The Critical Mass and the Core Accretion Rate

Understanding how stars form in molecular clouds is one of the ongoing research areas in astrophysics. Star formation is the fundamental process to which our current understanding remains incomplete due to the complexity of the physics that drives their formation within molecular clouds. In this article theoretical modelling of the lowest possible mass of the cloud needed for collapse and the core accretion rate has been presented for the molecular cloud collapsing under its gravity. In many of previous studies the critical mass of star forming cloud under its gravity has been modelled using kinetic energy and gravitational potential energy. However, we test the effect of thermodynamic efficiency factor together with other physical processes in describing the critical mass, and controlling or triggering the rate of mass falling onto the central core. Assuming that, the ratio of radiation luminosity to gravitational energy released per unit time of the collapsing MC is less than unity. Following this conceptual framework we have formulated the critical mass and the core accretion rate of the self-gravitating molecular cloud.

Tracing Magnetic Field Morphology Using the Velocity Gradient Technique in the Presence of CO Self-absorption

Abstract Probing magnetic fields in self-gravitating molecular clouds is generally difficult, even with the use of polarimetry. Based on the properties of magnetohydrodynamic turbulence and turbulent reconnection, the velocity gradient technique (VGT) provides a new way of tracing magnetic field orientation and strength based on spectroscopic data. Our study tests the applicability of VGT in various molecular tracers, e.g., 12CO, 13CO, and C18O. By inspecting synthetic molecular-line maps of CO isotopologs generated through radiative transfer calculations, we show that the VGT can be successfully applied in probing the magnetic field direction in the diffuse interstellar medium, as well as in self-gravitating molecular clouds.

Star cluster formation from turbulent clumps. II. Gradual star cluster formation

We investigate the dynamical evolution of star clusters during their formation, assuming that they are born from a turbulent starless clump of a given mass that is embedded within a parent self-gravitating molecular cloud characterized by a particular mass surface density. In contrast to the standard practice of most $N$-body studies, we do not assume that all stars are formed at once. Rather, we explore the effects of different star formation rates on the global structure and evolution of young embedded star clusters, also considering various primordial binary fractions and mass segregation levels. Our fiducial clumps studied in this paper have initial masses of $M_{\rm cl} = 3000\,M_\odot$, are embedded in ambient cloud environments of $\Sigma_{\rm cloud} = 0.1$ and 1 g cm$^{-2}$, and gradually form stars with an overall efficiency of 50% until the gas is exhausted. We investigate star formation efficiencies per free-fall time in the range $\epsilon_{\rm ff}=0.01$ to 1, and also compare to the instantaneous case ($\epsilon_{\rm ff}=\infty$) of Paper I. We show that most of the interesting dynamical processes that determine the future of the cluster, happen during the early formation phase. In particular, the ejected stellar population is sensitive to the duration of star cluster formation: for example, clusters with longer formation times produce more runaway stars, since these clusters remain in a dense state for longer, thus favouring occurrence of dynamical ejections. We also show that the presence of radial age gradients in star clusters depends sensitively on the star formation efficiency per free fall time, with observed values being matched best by our slowest forming clusters with $\epsilon_{\rm ff}\lesssim0.03$.

Formation of ultra-compact dwarf galaxies from supergiant molecular clouds

The origin of ultra-compact dwarf galaxies (UCDs) is not yet clear. One possible formation path of UCDs is the threshing of a nucleated elliptical dwarf galaxy (dE, N), however, it remains unclear how such massive nuclear stellar systems were formed in dwarf galaxies. To better establish the early history of UCDs, we investigate the formation of UCD progenitor clusters from super giant molecular clouds (SGMCs), using hydrodynamical simulations. In this study we focus on SGMCs with masses $10^{7} - 10^{8} \rm M_{\odot}$ that can form massive star clusters that display physical properties similar to UCDs. We find that the clusters have extended star formation histories with two phases, producing multiple distinct stellar populations, and that the star formation rate is dependent on the feedback effects of SNe and AGB stars. The later generations of stars formed in these clusters are more compact, leading to a clearly nested structure, and these stars will be more He-rich than those of the first generation, leading to a slight colour gradient. The simulated clusters demonstrate scaling relations between $R_{\rm eff}$ and $M$ and $\sigma_{v}$ and $M$ consistent with those observed in UCDs and strongly consistent with those of the original SGMC. We discuss whether SGMCs such as these can be formed through merging of self-gravitating molecular clouds in galaxies at high-z.

Pulsational instability of complex charge-fluctuating magnetized turbulent astroclouds

We develop a theoretic model to study the linear stability behaviour of pulsational (gravito-electrostatic) mode in a self-gravitating, magnetized, collisional, turbulent and unbounded dust molecular cloud (DMC). The analytic model consists of lighter electrons and ions; and massive charged dust grains with partial ionization over the geometrically infinite extension. The semi-empirically obtained Larson logatropic equation of state, correlating all the thermo-turbo-magnetic pressures concurrently, is included afresh to model the constituent fluid turbulence pressures arising because of multiple randomized aperiodic flow scales of space and time. A linear normal mode analysis over the slightly perturbed composite cloud, relative to the defined homogeneous hydrostatic equilibrium, results in a unique mathematical construct of generalized polynomial (octic) dispersion relation with different coefficients sensitively dependent upon the diversified equilibrium cloud parameters. The main features of the modified pulsational mode dynamics are numerically explored over a commodious window of parametric values. It is shown and established that the grain mass introduces a dispersive stabilizing effect to the mode (with enhancement in phase speed), and vice-versa. A spatiotemporal illustrative tapestry is also portrayed for further confirmation of the dispersive mode with sporadic properties. The tentative application of our findings in different space and astrophysical circumstances is briefly outlined.

Kiloparsec-scale Simulations of Star Formation in Disk Galaxies. IV. Regulation of Galactic Star Formation Rates by Stellar Feedback

Abstract Star formation from the interstellar medium of galactic disks is a basic process controlling the evolution of galaxies. Understanding the star formation rate (SFR) in a local patch of a disk with a given gas mass is thus an important challenge for theoretical models. Here we simulate a kiloparsec region of a disk, following the evolution of self-gravitating molecular clouds down to subparsec scales, as they form stars that then inject feedback energy by dissociating and ionizing UV photons and supernova explosions. We assess the relative importance of each feedback mechanism. We find that H2-dissociating feedback results in the largest absolute reduction in star formation compared to the run with no feedback. Subsequently adding photoionization feedback produces a more modest reduction. Our fiducial models that combine all three feedback mechanisms yield, without fine-tuning, SFRs that are in excellent agreement with observations, with H2-dissociating photons playing a crucial role. Models that only include supernova feedback—a common method in galaxy evolution simulations—settle to similar SFRs, but with very different temperatures and chemical states of the gas, and with very different spatial distributions of young stars.

Star Cluster Formation from Turbulent Clumps. I. The Fast Formation Limit

Abstract We investigate the formation and early evolution of star clusters, assuming that they form from a turbulent starless clump of a given mass bounded inside a parent self-gravitating molecular cloud characterized by a particular mass surface density. As a first step, we assume instantaneous star cluster formation and gas expulsion. We draw our initial conditions from observed properties of starless clumps. We follow the early evolution of the clusters up to 20 Myr, investigating the effects of different star formation efficiencies, primordial binary fractions and eccentricities, and primordial mass segregation levels. We investigate clumps with initial masses of embedded in ambient cloud environments with mass surface densities and . We show that these models of fast star cluster formation result, in the fiducial case, in clusters that expand rapidly, even considering only the bound members. Clusters formed from higher environments tend to expand more quickly and thus are soon larger than clusters born from lower conditions. To form a young cluster of a given age, stellar mass, and mass surface density, these models need to assume a parent molecular clump that is many times denser, which is unrealistic compared to observed systems. We also show that, in these models, the initial binary properties are only slightly modified by interactions, meaning that the binary properties, e.g., at 20 Myr, are very similar to those at birth. With this study, we set up the foundation for future work, where we will investigate more realistic models of star formation compared to this instantaneous, baseline case.

PHIBSS: exploring the dependence of the CO–H2 conversion factor on total mass surface density at z<1.5

We present an analysis of the relationship between the CO-H$_{2}$ conversion factor ($\alpha_{\rm CO}$) and total mass surface density ($\Sigma_{\rm tot}$) in star-forming galaxies at $z < 1.5$. Our sample, which is drawn from the IRAM Plateau de Bure HIgh-$z$ Blue Sequence Survey (PHIBSS) and the CO Legacy Database for GASS (COLD GASS), includes 'normal,' massive star-forming galaxies that dominate the evolution of the cosmic star formation rate (SFR) at this epoch and probe the $\Sigma_{\rm tot}$ regime where the strongest variation in $\alpha_{\rm CO}$ is observed. We constrain $\alpha_{\rm CO}$ via existing CO observations, measurements of the star formation rate, and an assumed molecular gas depletion time ($t_{\rm dep}$=$M_{\rm gas}$/SFR) --- the latter two of which establish the total molecular gas mass independent of the observed CO luminosity. For a broad range of adopted depletion times, we find that $\alpha_{\rm CO}$ is independent of total mass surface density, with little deviation from the canonical Milky Way value. This runs contrary to a scenario in which $\alpha_{\rm CO}$ decreases as surface density increases within the extended clouds of molecular gas that potentially fuel clumps of star formation in $z\sim1$ galaxies, similar to those observed in local ULIRGs. Instead, our results suggest that molecular gas, both at $z\sim0$ and $z\sim1$, is primarily in the form of self-gravitating molecular clouds. While CO observations suggest a factor of $\sim3$ reduction in the average molecular gas depletion time between $z \sim 0$ and $z\sim1$, we find that, for typical galaxies, the structure of molecular gas and the process of star formation at $z \sim 1$ is otherwise remarkably similar to that observed in local star-forming systems.

Velocity Anisotropy in Self-gravitating Molecular Clouds. I. Simulation

Abstract The complex interplay between turbulence, magnetic fields, and self-gravity leads to the formation of molecular clouds out of the diffuse interstellar medium (ISM). One avenue of studying this interplay is by analyzing statistical features derived from observations, where the interpretation of these features is greatly facilitated by comparisons with numerical simulations. Here we focus on the statistical anisotropy present in synthetic maps of velocity centroid data, which we derive from three-dimensional magnetohydrodynamic simulations of a turbulent, magnetized, self-gravitating patch of ISM. We study how the orientation and magnitude of the velocity anisotropy correlate with the magnetic field and with the structures generated by gravitational collapse. Motivated by recent observational constraints, our simulations focus on the supersonic (sonic Mach number  ≈ 2 – 17 ) but sub- to trans-alfvénic (alfvénic Mach number  A ≈ 0.2 – 1.2 ) turbulence regime, and we consider clouds that are barely to mildly magnetically supercritical (mass-to-flux ratio equal to once or twice the critical value). Additionally we explore the impact of the turbulence driving mechanism (solenoidal or compressive) on the velocity anisotropy. While we confirm previous findings that the velocity anisotropy generally aligns well with the plane-of-sky magnetic field, our inclusion of the effects of self-gravity reveals that in regions of higher column density, the velocity anisotropy may be destroyed or even reoriented to align with the gravitationally formed structures. We provide evidence that this effect is not necessarily due to the increase of  A inside the high-density regions.

Photoionization feedback in a self-gravitating, magnetized, turbulent cloud

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 power law fit to the density field assuming that the system is virialised. We give a radius at which the ionisation front should stop expanding ("stall"). If this radius is smaller than the distance to the edge of the cloud, the HII region will be trapped by the cloud. This effect is more severe in collapsing clouds than in virialised clouds, since the density in the former increases dramatically over time, with much larger photon emission rates needed for the HII region to escape a collapsing cloud. We also measure the response of Jeans unstable gas to the HII regions to predict the impact of UV radiation on star formation in the cloud. We find that the mass in unstable gas can be explained by a model in which the clouds are evaporated by UV photons, suggesting that the net feedback on star formation should be negative

Thermal condensation modes of an expanding medium including self-gravity and diffusion mechanisms

Thermal instability of a self-gravitating magnetic molecular cloud is investigated by means of a linear perturbation analysis, when the unperturbed background is expanding uniformly. The previous studies did not precisely consider the effect of Hall diffusion, since they supposed that the electrons and ions move together. Then, we revisit the effect of Hall diffusion on the growth of the thermal instability. Our results indicate that the non-ideal effects highly reduce the stabilizing role of the magnetic field in a thermally unstable medium. With increasing the diffusion parameters, the profile of the growth rate tends to the non-magnetized case. Thus, thermal instability in the presence of the diffusion mechanisms can explain the formation of low-mass condensations in molecular clouds. The wavenumber of the perturbations corresponding to the maximum growth rate also shifts to the smaller values (longer wavelengths) as the nondimensional diffusion parameters become large. We find that self-gravity shifts the growth rate of a system without self-gravity to the higher values, while the growth rate of such a medium is reduced because of the existence of expansion. Therefore the expanding motions within the molecular clouds cause a more stable system. But the diffusion mechanisms can enhance the growth rate and speed up the rate of structure formation in molecular clouds.

Mutual influence of supernovae and molecular clouds

Context. Molecular clouds are known to be turbulent and strongly affected by stellar feedback. Moreover, stellar feedback is believed to drive turbulence at large scales in galaxies. Aims. We study the role played by supernovae in molecular clouds and the influence of the magnetic field on this process. Methods. We performed three-dimensional numerical simulations of supernova explosions, in and near turbulent self-gravitating molecular clouds. In order to study the influence of the magnetic field, we performed both hydrodynamical and magnetohydrodynamical simulations. We also ran a series of simple uniform density medium simulations and developed a simple analytical model. Results. We find that the total amount of momentum that is delivered during supernova explosions typically varies by a factor of about 2, even when the gas density changes by 3 orders of magnitude. However, the amount of momentum delivered to the dense gas varies by almost a factor of 10 if the supernova explodes within or outside the molecular cloud. The magnetic field has little influence on the total amount of momentum injected by the supernova explosions but increases the momentum injected into the dense gas. Conclusions. Supernovae that explode inside molecular clouds remove a significant fraction of the cloud mass. Supernovae that explode outside have a limited influence on the cloud. It is thus essential to know sufficiently well the correlation between supernovae and the surrounding dense material in order to know whether supernovae can regulate star formation effectively.

THE ANGULAR MOMENTUM OF MAGNETIZED MOLECULAR CLOUD CORES: A TWO-DIMENSIONAL-THREE-DIMENSIONAL COMPARISON

We study the rotational properties of magnetized and self-gravitating molecular cloud cores formed in 2 very high resolution 3D molecular cloud simulations.The simulations have been performed using the code RAMSES at an effective resolution of 4096^3.One simulation represents a mildly magnetically-supercritical cloud and the other a strongly magnetically-supercritical cloud.A noticeable difference between the 2 simulations is the core formation efficiency (CFE) of the high density cores.In the strongly supercritical simulations the CFE is ~33 % per free-fall time of the cloud tff,cl, whereas in the mildly supercritical simulations this value goes down to ~6%/tff,cl. A comparison of the intrinsic specific angular momentum j3D distributions of the cores with the distribitions of j2D derived using synthetic 2D velocity maps of the cores,shows that the synthetic observations tend to overestimate the true value of j by a factor of ~10.The origin of this discrepancy lies in the fact that contrary to the intrinsic determination which sums up the individual gas parcels contributions to j, the determination of j using the observational procedure which is based on a measurement on the global velocity gradient under the hypothesis of uniform rotation smoothes out the complex fluctuations present in the 3D velocity field. Our results provide a natural explanation for the discrepancy by a factor ~10 observed between the intrinsic 3D distributions of j and the corresponding distributions derived in real observations.We suggest that measurements of j which are based on the measurement of the observed global velocity gradients may need to be reduced by a factor of ~10 in order to derive a more accurate estimate of j in the cores.

The non-isothermal stage of magnetic star formation - II. Results

In a previous paper we formulated the problem of the formation and evolution of fragments (or cores) in magnetically-supported, self-gravitating molecular clouds in axisymmetric geometry, accounting for the effects of ambipolar diffusion and Ohmic dissipation, grain chemistry and dynamics, and radiative transfer. Here we present results of star formation simulations that accurately track the evolution of a protostellar fragment over eleven orders of magnitude in density (from 300 cm^-3 to \approx 10^14 cm^-3), i.e., from the early ambipolar-diffusion--initiated fragmentation phase, through the magnetically supercritical, dynamical-contraction phase and the subsequent magnetic decoupling stage, to the formation of a protostellar core in near hydrostatic equilibrium. As found by Fiedler & Mouschovias (1993), gravitationally-driven ambipolar diffusion leads to the formation and subsequent dynamic contraction of a magnetically supercritical core. Moreover, we find that ambipolar diffusion, not Ohmic dissipation, is responsible for decoupling all the species except the electrons from the magnetic field, by a density \approx 3 x 10^12 cm^-3. Magnetic decoupling precedes the formation of a central stellar object and ultimately gives rise to a concentration of magnetic flux (a `magnetic wall') outside the hydrostatic core --- as also found by Tassis & Mouschovias (2005a,b) through a different approach. At approximately the same density at which Ohmic dissipation becomes more important than ambipolar diffusion (\gtrsim 7 x 10^12 cm^-3), the grains carry most of the electric charge as well as the electric current. The prestellar core remains disclike down to radii ~ 10 AU, inside which thermal pressure becomes important. The magnetic flux problem of star formation is resolved for at least strongly magnetic newborn stars by this stage of the evolution, i.e., by a central density \approx 10^14 cm^-3. The hydrostatic core has radius \approx 2 AU, density \approx 10^14 cm^-3, temperature \approx 300 K, magnetic field strength \approx 0.2 G, magnetic flux \approx 5 x 10^18 Wb, luminosity ~ 10^-3 L_\odot, and mass ~ 10^-2 M_\odot.

ERRATUM: “THE NONISOTHERMAL STAGE OF MAGNETIC STAR FORMATION. I. FORMULATION OF THE PROBLEM AND METHOD OF SOLUTION” (2009, APJ, 693, 1895)

We formulate the problem of the formation and subsequent evolution of fragments (or cores) in magnetically-supported, self-gravitating molecular clouds in two spatial dimensions. The six-fluid (neutrals, electrons, molecular and atomic ions, positively-charged, negatively-charged, and neutral grains) physical system is governed by the radiative, nonideal magnetohydrodynamic (RMHD) equations. The magnetic flux is not assumed to be frozen in any of the charged species. Its evolution is determined by a newly-derived generalized Ohm's law, which accounts for the contributions of both elastic and inelastic collisions to ambipolar diffusion and Ohmic dissipation. The species abundances are calculated using an extensive chemical-equilibrium network. Both MRN and uniform grain size distributions are considered. The thermal evolution of the protostellar core and its effect on the dynamics are followed by employing the grey flux-limited diffusion approximation. Realistic temperature-dependent grain opacities are used that account for a variety of grain compositions. We have augmented the publicly-available Zeus-MP code to take into consideration all these effects and have modified several of its algorithms to improve convergence, accuracy and efficiency. Results of magnetic star formation simulations that accurately track the evolution of a protostellar fragment from a density ~10^3 cm^-3 to a density ~10^15 cm^-3, while rigorously accounting for both nonideal MHD processes and radiative transfer, are presented in a separate paper.