Fragmentation Of Molecular Clouds Research Articles

The formation of a star cluster: predicting the properties of stars and brown dwarfs

We present results from the largest numerical simulation of star formation to resolve the fragmentation process down to the opacity limit. The simulation follows the collapse and fragmentation of a large-scale turbulent molecular cloud to form a stellar cluster and, simultaneously, the formation of circumstellar discs and binary stars. This large range of scales enables us to predict a wide variety of stellar properties for comparison with observations. The calculation clearly demonstrates that star formation is a highly-dynamic and chaotic process. Star-disc encounters form binaries and truncate discs. Stellar encounters disrupt bound multiple systems. The cloud produces roughly equal numbers of stars and brown dwarfs, with masses down to the opacity limit for fragmentation (~5 Jupiter masses). The initial mass function is consistent with a Salpeter slope (Gamma=-1.35) above 0.5 Msun, a roughly flat distribution (Gamma=0) in the range 0.006-0.5 Msun, and a sharp cutoff below ~0.005 Msun. This is consistent with recent observational surveys. The brown dwarfs form by the dynamical ejection of low-mass fragments from dynamically unstable multiple systems before the fragments have been able to accrete to stellar masses. Close binary systems (with separations <10 AU) are not formed by fragmentation in situ. Rather, they are produced by hardening of initially wider multiple systems through a combination of dynamical encounters, gas accretion, and/or the interaction with circumbinary and circumtriple discs. Finally, we find that the majority of circumstellar discs have radii less than 20 AU due to truncation in dynamical encounters. This is consistent with observations of the Orion Trapezium Cluster and implies that most stars and brown dwarfs do not form large planetary systems.

The formation mechanism of brown dwarfs

We present results from the first hydrodynamical star formation calculation to demonstrate that brown dwarfs are a natural and frequent product of the collapse and fragmentation of a turbulent molecular cloud. The brown dwarfs form via the fragmentation of dense molecular gas in unstable multiple systems and are ejected from the dense gas before they have been able to accrete to stellar masses. Thus, they can be viewed as 'failed stars'. Approximately three-quarters of the brown dwarfs form in gravitationally unstable circumstellar discs while the remainder form in collapsing filaments of molecular gas. These formation mechanisms are very efficient, producing roughly the same number of brown dwarfs as stars, in agreement with recent observations. However, because close dynamical interactions are involved in their formation, we find a very low frequency of binary brown dwarf systems (≤5 per cent) and that those binary brown dwarf systems that do exist must be close, ≤ 10 au. Similarly, we find that young brown dwarfs with large circumstellar discs (radii ≥ 10 au) are rare ( 5 per cent).

The Intrinsic Shapes of Molecular Cloud Fragments over a Range of Length Scales

We decipher intrinsic three-dimensional shape distributions of molecular clouds, cloud cores, Bok globules, and condensations using recently compiled catalogs of observed axis ratios for these objects mapped in carbon monoxide, in ammonia, through optical selection, or in continuum dust emission. We apply statistical techniques to compare assumed intrinsic axis ratio distributions with observed projected axis ratio distributions. Intrinsically triaxial shapes produce projected distributions that agree with observations. Molecular clouds mapped in 12CO are intrinsically triaxial but more nearly prolate than oblate, while the smaller cloud cores, Bok globules, and condensations are also intrinsically triaxial but more nearly oblate than prolate.

High‐Mass Protostellar Candidates. II. Density Structure from Dust Continuum and CS Emission

We present a detailed 1.2 mm continuum and CS spectral line study of a large sample of 69 massive star forming regions in very early stages of evolution, most of them prior to building up an ultracompact H II region. The continuum data show a zoo of different morphologies and give detailed information on the spatial distributions, masses, column densities, and average densities of the whole sample. Fitting the radial intensity profiles shows that three parameters are needed to describe the spatial distribution of the sources: constant emission from the center out to a few arcseconds radius followed by a first power-law intensity distribution, which steepens farther outside into a second power-law distribution. The inner flat region is possibly caused by fragmentation of the large-scale cores into smaller subsources, whereas the steeper outer power-law distributions indicate finite sizes of the cores. Separating the sources into subsamples suggests that in the earliest stages prior to the onset of massive star formation, the intensity radial distributions are rather flat, resembling the structure of intensity peaks in more quiescent molecular clouds. Then in the subsequent collapse and accretion phase the intensity distributions become centrally peaked, with steep power-law indices. In this evolutionary stage the sources show also the broadest C34S line width. During the following phase, when ultracompact H II regions evolve, the intensity power-law radial distributions flatten out again. This is probably caused by the ignited massive stars in the center which disrupt the surrounding cores. The mean inner power-law intensity index mi (I ~ r) is 1.2, corresponding to density indices p (n ~ r-p) of 1.6. In total, the density distributions of our massive star formation sites seem to be not too different from their low-mass counterparts, but we show that setting tight constrains on the density indices is very difficult and subject to many possible errors. The local densities we derive from CS calculations are higher (up to 1 order of magnitude) than the mean densities we find via the millimeter continuum. Such inhomogeneous density distribution reflects most likely the ubiquitous phenomenon of clumping and fragmentation in molecular clouds. Line width-mass relations show a departure from virial equilibrium in the stages of strongly collapsing cores.

Noble Gases in the Solar System

This chapter provides an overview of available noble gas data for solar system bodies apart from the Earth, Mars, and asteroids. Besides the Sun, the Moon, and the giant planets, we will also discuss data for the tenuous atmospheres of Mercury and the Moon, comets, interplanetary dust particles and elementary particles in the interplanetary medium and beyond. In addition, we summarize the scarce data base for the Venusian atmosphere. The extensive meteorite data from Mars and asteroidal sources are discussed in chapters in this volume by Ott (2002), Swindle (2002a,b) and Wieler (2002). Data from the Venusian and Martian atmospheres are discussed in more detail in chapters by Pepin and Porcelli (2002) and Swindle (2002b). Where appropriate, we will also present some data for other highly volatile elements such as H or N. The solar system formed from a molecular cloud fragment—traditionally called the solar nebula—that was rather well mixed. Therefore, isotopic abundances in almost all available solar system materials are very similar to each other, and elemental abundances in primitive meteorites are also similar to the values in the Sun. The major exceptions to this rule are the noble gases. Because they are chemically inert and volatile, they are very strongly depleted in solid matter. As a consequence, numerous noble gas “components” can be recognized throughout the solar system which are not necessarily related to the composition of the bulk nebula. Still, one major question in cosmochemistry is to what extent planetary bodies contain reservoirs that reflect the noble gas composition in the nebula or the presolar cloud. To discuss this, we first need a proxy for the nebula composition. The obvious choice is the bulk Sun, except for He, which has been produced in the Sun throughout its history. We will discuss the …

Formation of Planetary-Mass Objects by Protostellar Collapse and Fragmentation

Searches for very low mass objects in young star clusters have uncovered evidence for free-floating objects with inferred masses possibly as low as 5-15 Jupiter masses (MJup), similar to the masses of several extrasolar planets. We show here that the process that forms single and multiple protostars, namely, collapse and fragmentation of molecular clouds, might be able to produce self-gravitating objects with initial masses less than ~1 MJup, provided that magnetic field tension effects are important and can be represented approximately by diluting the gravitational field. If such fragments can be ejected from an unstable quadruple protostar system, prior to gaining significantly more mass, protostellar collapse might then be able to explain the formation of free-floating objects with masses below 13 MJup. These objects might then be best termed sub-brown dwarf stars.

Massive Black Holes as Population III Remnants

Recent numerical simulations of the fragmentation of primordial molecular clouds in hierarchical cosmogonies have suggested that the very first stars (the so-called Population III) may have been rather massive. Here we point out that a numerous population of massive black holes (MBHs)—with masses intermediate between those of stellar and supermassive holes—may be the end product of such an episode of pregalactic star formation. If only one MBH with m• 150 M☉ formed in each of the minihalos collapsing at z ≈ 20 from 3 σ fluctuations, then the mass density of Population III MBHs would be comparable to that of the supermassive variety observed in the nuclei of galaxies. Since they form in high-σ rare density peaks, relic MBHs are predicted to cluster in the bulges of present-day galaxies as they become incorporated through a series of mergers into larger and larger systems. Dynamical friction would cause 50 (m•/150 M☉)1/2 such objects to sink toward the center. The presence of a small cluster of MBHs in galaxy nuclei may have several interesting consequences associated with it, such as tidal captures of ordinary stars (likely followed by disruption), MBH capture by the central supermassive black hole, and gravitational wave radiation from such coalescences. Accreting pregalactic MBHs may be detectable as ultraluminous, off-nuclear X-ray sources.

The Formation of Stellar Clusters: Mass Spectra from Turbulent Molecular Cloud Fragmentation

Turbulent fragmentation determines where and when protostellar cores form, and how they contract and grow in mass from the surrounding cloud material. This process is investigated, using numerical models of self-gravitating molecular cloud dynamics. Molecular cloud regions without turbulent driving sources, or where turbulence is driven on large scales, exhibit rapid and efficient star formation in a clustered mode, whereas interstellar turbulence that carries most energy on small scales results in isolated star formation with low efficiency. The clump mass spectrum of shock-generated density fluctuations in pure hydrodynamic, supersonic turbulence is not well fit by a power law, and it is too steep at the high-mass end to be in agreement with the observational data. When gravity is included in the turbulence models, local collapse occurs, and the spectrum extends towards larger masses as clumps merge together, a power-law description dN/dM ~ M^nu becomes possible with slope nu < -2. In the case of pure gravitational contraction, i.e. in regions without turbulent support, the clump mass spectrum is shallower with nu = -3/2. The mass spectrum of protostellar cores in regions without turbulent support and where turbulence is replenished on large-scales, however, is well described by a log-normal or by multiple power laws, similar to the stellar IMF at low and intermediate masses. In the case of small-scale turbulence, the core mass spectrum is too flat compared to the IMF for all masses.

Instabilities in a Nonuniform Partially Ionized Isothermal Magnetoplasma

Electromagnetic modes and associated instabilities in a partially ionized, self-gravitating, nonuniform, isothermal, initially static magnetoplasma are theoretically investigated. The effects of the neutral fluid dynamics, the inhomogeneities in the external magnetic field and the background plasma number density, the self-gravitational field, the drag forces, the ionization and recombination, etc., on the dispersion properties of electromagnetic waves for different frequency regimes of interest are examined. It is shown that new types of instabilities, the first type of which is due to the combined effects of the self-gravitational and the drag forces, the second type of which is due to the combined effects of the plasma and the neutral fluid dynamics, and the third type of which is due to the drifting of electrons, exist in such a magnetoplasma. Furthermore, the effects of the external magnetic field and its inhomogeneity, the neutral fluid temperature, collisions of electrons or ions with neutrals, and the ionization play the stabilizing role, whereas the effects of the neutral fluid mass density, the plasma number density inhomogeneity, collisions of neutrals with electrons or ions, and the recombination play the destabilizing role. It is suggested that such instabilities could be responsible for the fragmentation of molecular clouds into substructures that in turn may fail to be supported against the self-gravity and may collapse to form the stars.

The Turbulent Shock Origin of Proto–Stellar Cores

The fragmentation of molecular clouds (MC) into proto-stellar cores is a central aspect of the process of star formation. Because of the turbulent nature of supersonic motions in MCs, it has been suggested that dense structures such as filaments and clumps are formed by shocks in a turbulent flow. In this work we present strong evidence in favor of the turbulent origin of the fragmentation of MCs. The most generic result of turbulent fragmentation is that dense postshock gas traces a gas component with a smaller velocity dispersion than lower density gas, since shocks correspond to regions of converging flows, where the kinetic energy of the turbulent motion is dissipated. Using synthetic maps of spectra of molecular transitions, computed from the results of numerical simulations of supersonic turbulence, we show that the dependence of velocity dispersion on gas density generates an observable relation between the rms velocity centroid and the integrated intensity (column density), σ(V0)-I, which is indeed found in the observational data. The comparison between the theoretical model (maps of synthetic 13CO spectra) with 13CO maps from the Perseus, Rosette, and Taurus MC complexes shows excellent agreement in the σ(V0)-I relation. The σ(V0)-I relation of different observational maps with the same total rms velocity are remarkably similar, which is a strong indication of their origin from a very general property of the fluid equations, such as the turbulent fragmentation process.

Magnetic Fields and the Triaxiality of Molecular Cloud Cores

We make the hypothesis that molecular cloud fragments are triaxial bodies with a large scale magnetic field oriented along the short axis. While consistent with theoretical expectations, this idea is supported by magnetic field strength data, which show strong evidence for flattening along the direction of the mean magnetic field. It is also consistent with early submillimeter polarization data, which show that the projected direction of the magnetic field is often slightly misaligned with the projected minor axis of a molecular cloud core, i.e., the offset angle $\Psi$ is nonzero. We calculate distributions of $\Psi$ for various triaxial bodies, when viewed from a random set of viewing angles. The highest viewing probability always corresponds to $\Psi=0^{\circ}$, but there is a finite probability of viewing all nonzero $\Psi$, including even $\Psi =90^{\circ}$; the average offset typically falls in the range $10^{\circ}-30^{\circ}$ for triaxial bodies most likely to satisfy observational and theoretical constraints.

Instabilities of self-gravitating dusty clouds in magnetized plasmas

A rigorous theoretical investigation has been made of electromagnetic modes and associated filamentational instabilities in a nonuniform, partially ionized, self-gravitating, dusty magnetoplasma, taking into account the effects of the neutral fluid dynamics, inhomogeneities in the external magnetic field and the plasma density, the drag forces, the ionization and recombination, etc. It is found that there exist two new types of filamentational instabilities; one type is due to the combined effects of collisions of dust particles or ions with stationary neutrals and the self-gravitational force, and the other type is due to the combined effects of the dusty plasma and the neutral fluid dynamics. Furthermore, the effects of the external magnetic field and its inhomogeneity, the neutral fluid temperature, collisions of dust particles with neutrals, and the ionization play the stabilizing role, whereas the effects of the neutral fluid mass density, the plasma number density inhomogeneity, collisions of ions with neutrals, and the recombination play the destabilizing role. The newly found instabilities may be responsible for the formation of stars in galaxies via fragmentation or filamentation of interstellar dense molecular clouds.

The Formation and Fragmentation of Primordial Molecular Clouds

Many questions in physical cosmology regarding the thermal history of the intergalactic medium, chemical enrichment, reionization, etc. are thought to be intimately related to the nature and evolution of pregalactic structure. In particular the efficiency of primordial star formation and the primordial IMF are of special interest. We present results from high resolution three-dimensional adaptive mesh refinement simulations that follow the collapse of primordial molecular clouds and their subsequent fragmentation within a cosmologically representative volume. Comoving scales from 128 kpc down to 0.5 pc are followed accurately. Dark matter dynamics, hydrodynamics and all relevant chemical and radiative processes (cooling) are followed self-consistently for a cluster normalized CDM structure formation model. Primordial molecular clouds with ~100,000 solar masses are assembled by mergers of multiple objects that have formed hydrogen molecules in the gas phase with a fractional abundance of 100,000/cm^3 are found. We find that less than 1% of the primordial gas in such small scale structures cools and collapses to sufficiently high densities to be available for primordial star formation. Furthermore, our results indicate that the formation of very massive objects, massive black holes, fragmentation of a large fraction of baryons into brown dwars or Jupiter size fragments seems, in contrast to various claims in the literature, very unlikely. The expected escape fraction of UV photons with (h nu) > 11eV is very small.

Fragmentation instability of molecular clouds

It is found that a strong coupling between the neutral fluid and self-gravitating, partially ionized, nonuniform magnetoplasmas leads to a novel Jeans-type instability involving short wavelength (in comparison with the Jean's critical wavelength) electromagnetic perturbations. The analysis of the new dispersion relation derived here reveals the excitation of short wavelength electromagnetic modes when the coupling between the neutral fluid and the plasma is taken into consideration. The newly found instability is responsible for the fragmentation of dense molecular interstellar clouds, and subsequent formation of stars.

Star formation with 3-D adaptive mesh refinement: the collapse and fragmentation of molecular clouds

We describe a powerful methodology for numerical solution of 3-D self-gravitational hydrodynamics problems with unprecendented resolution. This code utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids at multiple levels of resolution. These grids are automatically and dynamically added and removed as necessary to maintain adequate resolution. This technology allows solution of problems that would be prohibitively expensive with methods using fixed resolution, and it is more versatile and efficient than competing methods of achieving variable resolution. The application of this technique to simulate the collapse and fragmentation of a molecular cloud, a key step in star formation is discussed. The simulation involves many orders of magnitude of variation in length scale as fragments form. In this paper we describe the methodology and present illustrative applications for both isothermal and nonisothermal cloud collapse. We describe the numerical Jeans condition, a new criterion for stability of self-gravitational gas dynamic problems. We find that the uniformly rotating, spherical clouds treated here first collapse to disks in the equatorial plane and then, in the presence of applied perturbations, form filamentary singularities that do not fragment while isothermal. As the collapse enters the non-isothermal phase, we show the evolutionary sequence that leads to the formation of a binary system consisting of protostellar cores surrounded by distinct protostellar disks. The scale of the disks, of order 100 AU, is consistent with observations of gaseous disks surrounding single T-Tauri stars and debris disks surrounding systems such as Beta Pictoris.

Self‐gravitational Hydrodynamics with Three‐dimensional Adaptive Mesh Refinement: Methodology and Applications to Molecular Cloud Collapse and Fragmentation

We describe a new code for numerical solution of three-dimensional self-gravitational hydrodynamics problems. This code utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids at multiple levels of resolution and automatically and dynamically adding and removing these grids as necessary to maintain adequate resolution. This technology allows solution of problems that would be prohibitively expensive with a code using fixed resolution, and it is more versatile and efficient than competing methods of achieving variable resolution. In particular, we apply this technique to simulate the collapse and fragmentation of a molecular cloud, a key step in star formation. The simulation involves many orders of magnitude of variation in length scale as fragments form at positions that are not a priori discernible from general initial conditions. In this paper, we describe the methodology behind this new code and present several illustrative applications. The criterion that guides the degree of adaptive mesh refinement is critical to the success of the scheme, and, for the isothermal problems considered here, we employ the Jeans condition for this purpose. By maintaining resolution finer than the local Jeans length, we set new benchmarks of accuracy by which to measure other codes on each problem we consider, including the uniform collapse of a finite pressured cloud. We find that the uniformly rotating, spherical clouds treated here first collapse to disks in the equatorial plane and then, in the presence of applied perturbations, form filamentary singularities that do not fragment while isothermal. Our results provide numerical confirmation of recent work by Inutsuka & Miyama on this scenario of isothermal filament formation.

Jeans Instability in Collisional Dusty Plasmas

It is shown that dust-neutral and ion-neutral drags can produce instabilities of electrostatic waves in multicomponent self-gravitating dusty plasmas. Explicit expressions for the growth rates of the instabilities are presented. The relevance of our investigation to fragmentation of molecular dust clouds is discussed.

Resolution requirements for smoothed particle hydrodynamics calculations with self-gravity

We determine a new resolution requirement for the smoothed particle hydrodynamics (SPH) numerical method when self-gravity is included. Comparison calculations between an SPH code and an Eulerian grid code are performed. The calculations are of a computationally demanding molecular cloud collapse and fragmentation problem. We demonstrate that the results given by the two different hydrodynamic methods are in good agreement, so long as the minimum resolvable mass in the SPH calculations is always less than the Jeans mass. If this criterion is not satisfied, SPH may give incorrect results, with the stability of near-Jeans-mass clumps depending on the details of how the SPH code is implemented rather than on physical processes. We give examples, from the literature, of problems that have been encountered in simulations of star, galaxy and cosmological-structure formation where this resolution requirement is ignored.

GRAPESPH with fully periodic boundary conditions: fragmentation of molecular clouds

A method of adapting smoothed particle hydrodynamics (SPH) with periodic boundary conditions for use with the special purpose device GRAPE is presented. GRAPE (GRAvity PipE) solves the Poisson and force equations for an N-body system by direct summation on a specially designed chip and in addition returns the neighbour list for each particle. Due to its design, GRAPE cannot treat periodic particle distributions directly. This limitation of GRAPESPH can be overcome by computing a correction force for each particle due to periodicity (Ewald correction) on the host computer using a PM-like method. This scheme is applied to study the fragmentation process in giant molecular clouds. Assuming a pure isothermal model, we follow the dynamical evolution in the interior of a molecular cloud starting from an Gaussian initial density distribution to the formation of selfgravitating clumps until most of the gas is consumed in these dense cores. Despite its simplicity, this model can reproduce some fundamental properties of observed molecular clouds, like a clump mass distribution of the form $dN/dm \propto m^n$, with $n ~ -1.5$.

Fragmentation of filamentary molecular clouds with longitudinal magnetic fields: Formation of disks and their collapse

Fragmentation of filamentary molecular clouds with longitudinal magnetic fields: Formation of disks and their collapse