Prolate Clouds Research Articles

Maser flares driven by variations in pumping and background radiation

ABSTRACT We simulate maser flares by varying either the pump rate or the background level of radiation in a 3D model of a maser cloud. We investigate the effect of different cloud shapes, saturation levels, and viewpoints. Results are considered for clouds with both uniform and internally variable unsaturated inversion. Pumping and background variations are represented by several different driving functions, some of which are light curves drawn from observations. We summarize the pumping variability results in terms of three observable parameters: the maximum flux density achieved, a variability index, and duty cycle. We demonstrate typical ranges of the flux density that may result from viewing an aspherical object from random viewpoints. The best object for a flare is a prolate cloud, viewed close to its long axis and driven from unsaturated conditions to at least modest saturation. Results for variation of the background level are qualitatively different from the variable pumping results in that they tend to produce short intervals of low flux density under conditions of moderate saturation and sufficient variability to be consistent with strong flaring. Variable background models typically have a significantly higher duty cycle than those with variable pumping.

Maser flare simulations from oblate and prolate clouds

We investigated, through numerical models, the flaring variability that may arise from the rotation of maser clouds of approximately spheroidal geometry, ranging from strongly oblate to strongly prolate examples. Inversion solutions were obtained for each of these examples over a range of saturation levels from unsaturated to highly saturated. Formal solutions were computed for rotating clouds with many randomly chosen rotation axes, and corresponding averaged maser light curves plotted with statistical information. The dependence of results on the level of saturation and on the degree of deformation from the spherical case were investigated in terms of a variability index and duty cycle. It may be possible to distinguish observationally between flares from oblate and prolate objects. Maser flares from rotation are limited to long timescales (at least a few years) and modest values of the variability index ($\lesssim 100$), and can be aperiodic or quasi-periodic. Rotation is therefore not a good model for H$_2$O variability on timescales of weeks to months, or of truly periodic flares.

Evolution of prolate molecular clouds at H ii boundaries – II. Formation of BRCs of asymmetrical morphology

A systematic investigation on the evolution of a prolate cloud at an Hii boundary is conducted using Smoothed Particle Hydrodynamics (SPH) in order to understand the mechanism for a variety of irregular morphological structures found at the boundaries of various Hii regions. The prolate molecular clouds in this investigation are set with their semi-major axes at inclinations between 0 and 90 degrees to a plane parallel ionizing radiation flux. A set of 4 parameters, the number density n, the ratio of major to minor axis gamma, the inclination angle phi and the incident flux F_EUV, are used to define the initial state of the simulated clouds. The dependence of the evolution of a prolate cloud under Radiation Driven Implosion (RDI) on each of the four parameters is investigated. It is found that: i) in addition to the well studied standard type A, B or C Bright Rimmed Clouds (BRCs), many other types such as asymmetrical BRCs, filamentary structures and irregular horse-head structures could also be developed at Hii boundaries with only simple initial conditions; ii) the final morphological structures are very sensitive to the 4 initial parameters, especially to the initial density and the inclination; iii) The previously defined ionizing radiation penetration depth can still be used as a good indicator of the final morphology. Based on the simulation results, the efficiency of the RDI triggered star formation from clouds of different initial conditions is also estimated. Finally a unified mechanism for the various morphological structures found in many different Hii boundaries is suggested.

COLLAPSE AND FRAGMENTATION OF MAGNETIC MOLECULAR CLOUD CORES WITH THE Enzo AMR MHD CODE. II. PROLATE AND OBLATE CORES

We present the results of a large suite of three-dimensional (3D) models of the collapse of magnetic molecular cloud cores using the adaptive mesh refinement (AMR) code Enzo2.2 in the ideal magnetohydrodynamics (MHD) approximation. The cloud cores are initially either prolate or oblate, centrally condensed clouds with masses of 1.73 or 2.73 $M_\odot$, respectively. The radial density profiles are Gaussian, with central densities 20 times higher than boundary densities. A barotropic equation of state is used to represent the transition from low density, isothermal phases, to high density, optically thick phases. The initial magnetic field strength ranges from 6.3 to 100 $\mu$G, corresponding to clouds that are strongly to marginally supercritical, respectively, in terms of the mass to magnetic flux ratio. The magnetic field is initially uniform and aligned with the clouds' rotation axes, with initial ratios of rotational to gravitational energy ranging from $10^{-4}$ to 0.1. Two significantly different outcomes for collapse result: (1) formation of single protostars with spiral arms, and (2) fragmentation into multiple protostar systems. The transition between these two outcomes depends primarily on the initial magnetic field strength, with fragmentation occurring for mass to flux ratios greater than about 14 times the critical ratio for prolate clouds. Oblate clouds typically fragment into several times more clumps than prolate clouds. Multiple, rather than binary, system formation is the general rule in either case, suggesting that binary stars are primarily the result of the orbital dissolution of multiple protostar systems.

Evolution of prolate molecular clouds at H舁ii boundaries – I. Formation of fragment-core structures

The evolution of a prolate cloud at an Hii boundary is investigated using Smoothed Particle Hydrodynamics (SPH). The prolate molecular clouds in our investigation are set with their semi-major axis perpendicular to the radiative direction of a plane parallel ionising Extreme Ultraviolet (EUV) flux. Simulations on three high mass prolate clouds reveal that EUV radiation can trigger distinctive high density core formation embedded in a final linear structure. This contrasts with results of the previous work in which only an isotropic Far Ultraviolet (FUV) interstellar background flux was applied. A systematic investigation on a group of prolate clouds of equal mass but different initial densities and geometric shapes finds that the distribution of the cores over the final linear structure changes with the initial conditions of the prolate cloud and the strength of the EUV radiation flux. These highly condensed cores may either scatter over the full length of the final linear structure or form two groups of high density cores at two foci, depending on the value of the ionising radiation penetration depth d_EUV, the ratio of the physical ionising radiation penetration depth to the minor axis of the cloud. Data anlysis on the total mass of the high density cores and the core formation time finds that the potential for EUV radiation triggered star formation efficiency is higher in prolate clouds with shallow ionisation penetration depth and intermediate major to minor axial ratio, for the physical environments investigated. Finally, it is suggested that the various fragment-core structures observed at Hii boundaries may result from the interaction between ionising radiation and pre-existing prolate clouds of different initial geometrical and physical conditions.

Forming misaligned stellar disks around a massive black hole: cloud infall in the Galactic center

AbstractThe innermost parsec around Sgr A* has been found to play host to two disks or streamers of O and W-R stars. They are misaligned by an angle approaching 90°. That the stars are approximately coeval indicates that they formed in the same event rather than independently. We have performed smoothed particle hydrodynamic simulations of the infall of a single prolate cloud towards a massive black hole. As the cloud is disrupted, the large spread in angular momentum can, if conditions allow, lead to the creation of misaligned gas disks. In turn, stars may form within those disks. We are now investigating the origins of these clouds in the Galactic center (GC) region.

TRIGGERED STAR FORMATION IN A BRIGHT-RIMMED CLOUD (BRC 5) OF IC 1805

We report recent optical, near-infrared (NIR), and millimeter observations which have revealed some new features of the bright-rimmed cloud BRC 5 associated with W4. With slitless spectroscopy, we detected 17 Hα emission stars around the cloud; 4 are near the surface of the cloud, and 1 is toward IRAS 02252+6120. NIR photometry shows that the central Hα emission star, together with one bright infrared source, has large NIR excesses and Class I spectral energy distributions. These two Class I objects are associated with the 2.9 mm continuum peaks and with a bipolar outflow, and are in between two separate, elongated C18O(J = 1-0) cores. The C18O cores and the two Class I sources are aligned along a line at position angle ~240°, somewhat less than perpendicular to the direction of UV radiation from the OB stars. Most of the detected Hα emission stars, all T Tauri candidates, are located within ~3' of the cloud on the exciting star side. An estimate of the age of the stars based on a color-magnitude diagram suggests that these T Tauri candidates have ages of ~1 Myr or less, but are more evolved objects than the central young stellar objects. This age sequence suggests sequential star formation within the BRC 5 cloud. The 13CO(J = 1-0) emission shows three elongated structures, which indicates the asymmetric structure toward the UV incident axis. We present our exploratory simulation results by using a smoothed particle hydrodynamic code that suggests that the asymmetrical BRC 5 structure could possibly result from the evolution of a preexisting prolate molecular cloud subject to radiation-driven implosion (RDI). Our best-fit prolate cloud has an initial mass of ~400 M ☉, an axial ratio of ~1.7, and a semi-major axis of ~1.6 pc, pointing away from the ionization flux by an angle of 15°. The simulated cloud structure not only closely matches the observed asymmetric morphological structure of BRC 5, but also reveals the possibility of the development of two major cores at the head of BRC 5. For the first time, the possibility of forming two stars by an RDI mechanism in a BRC is investigated.

Misaligned streamers around a Galactic Centre black hole from a single cloud's infall

We follow the near radial infall of a prolate cloud on to a 4 × 106 M⊙ supermassive black hole in the Galactic Centre using smoothed particle hydrodynamics. We show that a prolate cloud oriented perpendicular to its orbital plane naturally produces a spread in angular momenta in the gas which can translate into misaligned discs as is seen in the young stars orbiting Sagittarius A*. A turbulent or otherwise highly structured cloud is necessary to avoid cancelling too much angular momentum through shocks at closest approach. Our standard model of a 2 × 104 M⊙ gas cloud brought about the formation of a disc within 0.3 pc from the black hole and a larger, misaligned streamer at 0.5 pc. A total of 1.5 × 104 M⊙ of gas formed these structures. Our exploration of the simulation parameter space showed that when star formation occurred, it resulted in top-heavy initial mass functions with stars on eccentric orbits with semi-major axes 0.02–0.3 pc and inclinations following the gas discs and streamers. We suggest that the single event of an infalling prolate cloud can explain the occurrence of multiple misaligned discs of young stars.

THE EQUILIBRIUM STRUCTURE OF PROLATE MAGNETIZED MOLECULAR CORES

The structure of molecular cloud cores supported by thermal pressure and a poloidal magnetic field is reinvestigated in the magnetohydrostatic and axisymmetric approximation. In addition to oblate configurations found in earlier work, solutions yielding prolate spheroidal shapes have also been obtained for a reference state described by a uniform sphere threaded by a uniform background magnetic field. The solutions for prolate configurations are found to be relevant for lower masses than for their oblate counterparts. Of particular importance is the result that the prolate cloud cores have radii less than a maximum given by $0.25 pc (a/0.2km/s)^2 (P_{\rm ext}/10^{-12} dyne/cm^2)^{-1/2}$, where $a$ is the sound speed and $P_{\rm ext}$ is the external pressure of the background medium. The existence of such solutions obviates the presence of toroidal fields in such modeled structures.

Two‐dimensional Axisymmetric Collapse of Thermally Unstable Primordial Clouds

We have performed two-dimensional hydrodynamic simulations of the collapse of isolated axisymmetric clouds condensing via radiative cooling in a primordial background gas. In order to study the development of the so-called shape instability, we have considered two types of axisymmetric clouds, oblate and prolate clouds of various sizes and with axial ratios of 0.5 ≤ Rc,R/Rc,z ≤ 2. We find that the degree of oblateness or prolateness is enhanced during the initial cooling phase. However, it can be reversed later, if the initial contrast in cooling times between the cloud gas and the background gas is much greater than 1. In such cases an oblate cloud collapses to a structure composed of an outer thin disk and a central prolate component. A prolate cloud, on the other hand, becomes a thin cigar-shaped structure with a central dense oblate component. The reversal of shape in the central part of the cooled clouds is due to supersonic motions either along the disk plane in the case of oblate clouds or along the symmetry axis in the case of prolate clouds. For a background gas of Th = 1.7 × 106 K and nh = 0.1 cm-3 in a protogalactic halo environment, the mean density of the cloud gas that has cooled to 104 K increases to 100nh or so in our simulations where nonequilibrium cooling is adopted and the background gas cools too. The spherical Jeans mass of such gas is estimated to be about MJ ~ 5 × 107 M☉. In order for cloud mass to exceed the Jeans mass and at the same time in order for the thermal instability to operate, the initial cloud size should be around 1lcool-1.5lcool, where lcool is the cooling length.

Collapse and Fragmentation of Molecular Cloud Cores. VII. Magnetic Fields and Multiple Protostar Formation

Recent observations of star-forming regions suggest that binary and multiple young stars are the rule rather than the exception and implicate fragmentation as the likely mechanism for their formation. Most numerical hydrodynamic calculations of fragmentation have neglected the possibly deleterious effects of magnetic fields, despite ample evidence for the importance of magnetic support of precollapse clouds. We present here the first numerical hydrodynamic survey of the collapse and fragmentation of initially magnetically supported clouds that takes into account several magnetic field effects in an approximate manner. The models are calculated with a three-dimensional, finite differences code that solves the equations of hydrodynamics, gravitation, and radiative transfer in the Eddington and diffusion approximations. Magnetic field effects are included through two simple approximations: magnetic pressure is added to the gas pressure, and magnetic tension is approximated by gravity dilution once collapse is well underway. Ambipolar diffusion of the magnetic field leading to cloud collapse is treated approximately as well. Models are calculated for a variety of initial cloud density profiles, shapes, and rotation rates. We find that in spite of the inclusion of magnetic field effects, dense cloud cores are capable of fragmenting into binary and multiple protostar systems. Initially prolate clouds tend to fragment into binary protostars, while initially oblate clouds tend to fragment into multiple protostar systems containing a small number (of the order of 4) of fragments. The latter are likely to be subject to rapid orbital evolution, with close encounters possibly leading to the ejection of fragments. Contrary to expectation, magnetic tension effects appear to enhance fragmentation, allowing lower mass fragments to form than would otherwise be possible, because magnetic tension helps to prevent a central density singularity from forming and producing a dominant single object. Magnetically supported dense cloud cores thus seem to be capable of collapsing and fragmenting into sufficient numbers of binary and multiple protostar systems to be compatible with observations of the relative rarity of single protostars.

Protostellar collapse models of prolate molecular cloud cores

The continued detection of binary systems among pre-main-sequence stars suggests that fragmenta- tion is a very frequent process during the early stages of star formation. However, the fragmentation hypothesis rests only upon the results of three-dimensional hydrodynamics code calculations. The validity of isothermal frag- mentation calculations was questioned by the results of Truelove et al. (1997), and more recently, of Boss et al. (2000), who found, working at very high spatial resolution, that a particular Gaussian cloud model collapsed isothermally to form a singular lament rather than a binary or quadruple protostellar system as predicted by previous calculations. Suciently high spatial resolution is necessary to resolve the Jeans length and hence avoid articial fragmentation in isothermal collapse calculations. Here we use an adaptive, spherical-coordinate hydro- dynamics code based on the \zooming coordinates to investigate the isothermal collapse of centrally condensed (Gaussian), prolate (2:1 axial ratio) cloud core models, with thermal energy 0:22 and varied rotational energy (0:246 0:00025), to discern whether they will still undergo fragmentation into a protostellar binary system, as found in most previous prolate cloud collapse calculations, or condense all the way into a thin lament, as suggested by the linear analysis of Inutsuka & Miyama (1992) and the ndings of Truelove et al. and Boss et al. for the spherical, Gaussian cloud model. The prolate clouds all collapsed self-similarly to produce an intermediate barlike core, which then shrank indenetely into a singular lament without fragmenting. Collapse of the bar into a thin lament also occurred self-similarly, with the forming laments being much longer than the Jeans length. Since the laments form at maximum densities that are typical of the transition from the isothermal to the nonisothermal phase, gradual heating may retard the collapse and allow fragmentation of the lament into a binary or multiple protostellar core, as required to explain the high frequency of binary stars.

The Structure and Evolution of Magnetized Cloud Cores in a Zero‐Density Background

Molecular-line observations of star-forming cloud cores indicate that they are not the flattened structures traditionally considered by theory. Rather, they are elongated, perhaps in the direction of their internal magnetic field. We are thus motivated to consider the structure and evolution of axisymmetric, magnetized clouds that start from a variety of initial states, both flattened (oblate) and elongated (prolate). We devise a new technique, dubbed the $q$-method, that allows us to construct magnetostatic equilibria of any specified shape. We find, in agreement with previous authors, that the field lines in oblate clouds bend inward. However, those in prolate clouds bow outward, confining the structures through magnetic tension. We next follow the quasi-static evolution of these clouds via ambipolar diffusion, under the assumption of constant core mass. An oblate cloud either relaxes to a magnetically force-free sphere or, if sufficiently massive, flattens along its polar axis as its central density runs away. A prolate cloud always relaxes to a sphere of modest central density. We finally consider the evolution of an initially spherical cloud subject to the tidal gravity of neighboring bodies. Although the structure constricts equatorially, it also shortens along the pole, so that it ultimately flattens on the way to collapse. In summary, none of our initial states can evolve to the point of collapse while maintaining an elongated shape. We speculate that this situation will change once we allow the cloud to gain mass from its environment.

Impact of Magnetic Fields on Fragmentation

Fragmentation is the leading explanation for the formation of binary and multiple stars. However, nearly all three dimensional calculations of the collapse and fragmentation of dense molecular cloud cores have ignored the effects of magnetic fields, whereas magnetic fields are generally regarded to be a dominant force in molecular clouds. Three dimensional models of the collapse of clouds with frozen-in magnetic fields have shown that such clouds cannot fragment for a range of initial conditions. However, calculations that allow for magnetic field loss by am-bipolar diffusion have shown that fragmentation is possible for initially prolate or oblate, rotating, magnetically-supported cloud cores. The latter calculations rely on approximations that should be verified by more detailed, traditional magnetohydrodynamical codes. The most obvious effect of magnetic fields is to delay the onset of the collapse phase, but once collapse begins in earnest, fragmentation proceeds in much the same manner as in nonmagnetic clouds, with initially prolate clouds tending to form binary protostars, and with initially oblate clouds tending to form multiple protostars.

Formation of an Infalling Disklike Envelope around a Protostar

We examined the gravitational contraction of isothermal molecular cloud cores with slow rotation by means of two-dimensional numerical simulations. Applying a sink-cell method, we followed the evolution of the cloud cores up to the stages at which most of the matter accretes onto the central region (i.e., a protostar and a rotationally supported circumstellar disk). We show that both an infalling disklike envelope and a rotationally supported disk around the central star are natural outcomes of the gravitational contraction of a prolate cloud core with slow rotation. The early evolution of infalling envelopes resembles sheet models recently proposed by Hartmann and coworkers. In the infalling disklike envelope, the radial profiles of density, radial velocity, and azimuthal velocity can be approximated by ρ ∝ r-1.5, vr ∝ r-0.5, and v ∝ r-1, respectively. The fate of infalling envelopes is also discussed.

Collapse and Fragmentation Models of Oblate Molecular Cloud Cores. III. Formation of Small Protostellar Clusters

Recent near-infrared imaging surveys of the giant molecular cloud L1641 have revealed the existence of small clusters consisting of on the order of 10-50 young stars. While these observations suggest that stars may actually form in a range of stellar densities, the multiplicity of pre-main-sequence stars, along with the emerging evidence for protostellar condensations, indicate that stars may ultimately form through fragmentation of collapsing molecular cloud cores. Previous collapse calculations have shown that prolate cloud models are highly susceptible to fragmentation into protostellar binaries. While these results apply to star formation in an isolated environment, small cluster formation may require starting the collapse from oblate, rather than prolate, shapes. Here we use a smoothed-particle hydrodynamics code to further investigate the gravitational collapse and fragmentation of centrally condensed (Gaussian), oblate molecular clouds with varied thermal energy (α) and axial ratios of 2:1, 4:1, and 8:1. All models start with uniform rotation and ratios of rotational to gravitational energy β ≈ 0.02. Because of the oblate geometry, the clouds first collapse down to their equatorial plane, forming a rotationally unbalanced, intermediate central core that may be spherical, oblate spheroidal, or disklike, depending on the value of α. The evolution proceeds with the central core collapsing radially inward while becoming progressively flatter. During this phase, a rotationally supported, thin pancake forms, which quickly becomes gravitationally unstable to the point of fragmentation. The results indicate that the 2:1 clouds all produced low-order protostellar systems consisting of 2-3 clumps for 0.18 ≤ α ≤ 0.48. Similarly, the 4:1 and 8:1 clouds formed low-order systems of 3-5 clumps for α ≥ 0.37 and α = 0.48, respectively. Formation of small clusters of ~10 protostars occurred only in the 4:1 clouds for α = 0.18 and in the 8:1 clouds for α ≤ 0.37. Thus, increasing the degree of cloud oblateness extends the range of α values for which fragmentation into a larger number of clumps is allowed. Since extreme axial ratios of 4:1 and 8:1 are consistent with the observations, the results may have implications for understanding the formation of the small clusters observed in L1641.

Collapse and fragmentation of rotating, prolate clouds

We present the results of collapse calculations for uniformly rotating, prolate clouds performed using the numerical method: smoothed particle hydrodynamics (SPH). The clouds considered are isothermal, prolate spheroids with different axial ratios (a/b), and with different values of β, the ratio of the rotational to gravitational energy. Small density perturbations are added to the clouds, and different initial perturbation spectra are studied. All of the clouds considered are strongly unstable to gravitational contraction, and so collapse to form a spindle configuration. Such a linear structure is unstable to fragmentation, so that the clouds break up into a number of subcondensations. The long-term evolution of the system is then determined by the angular momentum possessed by these fragments. It is found that a number of the calculations performed result in the formation of orbitally stable binary systems, composed of two rotationally supported discs in orbit about their common centre of mass. Tidal interactions during closest approach, close three-body interactions and the continued accretion of material with high specific angular momentum are all found to increase the orbital separation during these calculations, ensuring that the systems do not merge at later times. The calculations are therefore relevant to the problem of binary star formation, though the systems produced tend to have large orbital separations and periods. One of the strong points of the models presented, however, is their ability to produce systems with a range of mass ratios and orbital eccentricities, without the explicit inclusion of biases in the initial conditions.

Collapse and Fragmentation Models of Prolate Molecular Cloud Cores. II. Initial Differential Rotation

The prevalence of companions to pre-main-sequence stars and the emerging observational evidence for binary and multiple protostellar condensations suggest that fragmentation during protostellar collapse is a mechanism that may occur frequently in the star formation process. Here a second-order accurate hydrodynamic code has been used to investigate the gravitational (postmagnetic) collapse and fragmentation of low-mass (~1 M☉), small (~0.05 pc) molecular cloud cores, starting from moderately centrally condensed (Gaussian), prolate (2:1 and 4:1 axial ratios) configurations with varying thermal energies (α) and degrees of differential rotation (ν = 1/3 and 2/3). To facilitate comparisons with previous collapse calculations of uniformly rotating prolate cloud cores (Sigalotti & Klapp), all the models were made to start with a ratio of rotational to gravitational energy of β ≈ 0.036. The results indicate that prolate clouds are highly susceptible to binary fragmentation and that with respect to uniformly rotating initial conditions, differential rotation plays no role in either determining or enhancing fragmentation in initially slowly rotating clouds. In contrast to the fragmentation criteria previously established by Boss and Myhill, the results also indicate that clouds with α = 0.56 and varied prolateness collapse in a similar fashion, producing intermediate central condensations of oblate spheroidal shape before fragmenting into either a binary (2:1 clouds) or multiple protostellar core (4:1 clouds). The models with α ≤ 0.45 all produced binary systems after having formed intermediate central condensations, which might be of prolate ellipsoidal (2:1 clouds) or narrow cylindrical (4:1 clouds) shape. The mass and separation of the binary fragments increase with decreasing α and with an increase of both the degree of differential rotation and the cloud elongation. The results imply that for initial low β, the degree of cloud prolateness has a greater effect on the outcome than does differential rotation.

Collapse and Fragmentation of Molecular Cloud Cores. IV. Oblate Clouds and Small Cluster Formation

view Abstract Citations (40) References (53) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Collapse and Fragmentation of Molecular Cloud Cores. IV. Oblate Clouds and Small Cluster Formation Boss, Alan P. Abstract Binary and multiple stars are believed to form primarily by the gravitational collapse of dense molecular cloud cores and by the fragmentation of the clouds into systems of protostars. Previous numerical calculations have shown that initially prolate (or cylindrical) cloud cores may collapse and fragment into binary or higher order protostellar systems. Observations of precollapse clouds are consistent with a significant fraction being oblate as well as prolate, yet the collapse of oblate clouds has not been investigated to date with a three-dimensional hydrodynamics code. We present here three-dimensional calculations of the isothermal collapse of oblate cloud cores, with initial axial ratios of 2:1 and uniform or centrally condensed (Gaussian) radial density profiles. The calculations are performed with a spatially and temporally second-order accurate hydrodynamics code with relatively high resolution in the azimuthal direction (Nφ = 128). Oblate clouds with moderate solid-body rotation rates collapse in two steps. First, the clouds collapse along their short axes to form thin pancakes, which are unsupported by centrifugal effects. Second, the pancakes collapse radially inward along their midplanes until centrifugal support is achieved in their inner regions. During the second phase, the surface density of the pancakes becomes so high [σ(r) > σζ(r) ≍(c2sπ/(Gr)] that the inner regions of the pancakes fragment into multiple protostars. Fragmentation occurs when the initial ratio of thermal to gravitational energy (αι) is about 0.4 or less. Varying the ratio of rotational to gravitational energy (βι) from 0.14 to 0.018 has relatively little effect, because the highly fragmentable pancakes are formed primarily as a result of the oblate geometry of the initial clouds rather than by rotational flattening. The most dramatic result is that oblate clouds appear to fragment into a larger number of protostars than do prolate clouds with similar values of αι and βι. The models imply that centrally condensed, oblate cloud cores close to virial equilibrium (α ≍ ½) should collapse and fragment into small clusters containing on the order of 10 protostars. Publication: The Astrophysical Journal Pub Date: September 1996 DOI: 10.1086/177686 Bibcode: 1996ApJ...468..231B Keywords: HYDRODYNAMICS; ISM: CLOUDS; ISM: MOLECULES; STARS: FORMATION; GALAXY: OPEN CLUSTERS AND ASSOCIATIONS: GENERAL full text sources ADS | data products SIMBAD (10) Related Materials (9) Part 1: 1993ApJ...410..157B Part 2: 1995ApJ...439..224B Part 2: 1997ApJ...483..309B Part 3: 1995ApJ...451..218B Part 3: 1999ApJ...520..744B Part 7: 2002ApJ...568..743B Part 8: 2005ApJ...622..393B Part 9: 2007ApJ...658.1136B Part 10: 2009ApJ...697.1940B

Three-dimensional hydrodynamic simulations of collapsing prolate clouds

We present the results of collapse calculations for elongated clouds performed using the numerical method of smoothed particle hydrodynamics (SPH). The clouds considered are isothermal, prolate spheroids with different axial ratios (a/b). Results are obtained for different values of a/b and , the mean mass per unit length. It is found that initially uniform clouds undergo fragmentation when the collapse is preferentially down on to the major axis, due to the intrinsic instability of a linear configuration. This occurs when the value of is sufficiently large. A criterion for elongated clouds to undergo linear collapse is derived using the tensor virial theorem, and it is found that the numerically obtained value of for which fragmentation occurs corresponds closely to that expected from analytical considerations