Three-dimensional simulations of molecular cloud fragmentation regulated by magnetic fields and ambipolar diffusion

We employ the first fully three-dimensional simulation to study the role of magnetic fields and ion–neutral friction in regulating gravitationally driven fragmentation of molecular clouds. The cores in an initially subcritical cloud develop gradually over an ambipolar diffusion time while the cores in an initially supercritical cloud develop in a dynamical time. The infalling speeds on to cores are subsonic in the case of an initially subcritical cloud, while an extended (≳0.1 pc) region of supersonic infall exists in the case of an initially supercritical cloud. These results are consistent with previous two-dimensional simulations. We also found that a snapshot of the relation between density (ρ) and the strength of the magnetic field ( B ) at different spatial points of the cloud coincides with the evolutionary track of an individual core. When the density becomes large, both the relations tend to   B ∝ρ^0.5  .     

A turbulent MHD model for molecular clouds and a new method of accretion on to star-forming cores

We describe the results of a sequence of simulations of gravitational collapse in a turbulent magnetized region. The parameters are chosen to be representative of molecular cloud material. We find that several protostellar cores and filamentary structures of higher than average density form. The filaments inter connect the high-density cores. Furthermore, the magnetic field strengths are found to correlate positively with the density, in agreement with recent observations. We make synthetic channel maps of the simulations, and show that material accreting on to the cores is channelled along the magnetized filamentary structures. This is compared with recent observations of S106, and shown to be consistent with these data. We postulate that this mechanism of accretion along filaments may provide a means for molecular cloud cores to grow to the point where they become gravitationally unstable and collapse to form stars.     

Molecular collisions in circumstellar discs

Inelastic molecular collisions are incorporated into the statistical model for turbulent circumstellar discs (Hämeen-Anttila, 1991; Verronenet al., 1993), and are found to provide a more effective cooling mechanism than molecule-grain impacts. Examination of the viscous evolution of the disc shows that the chemical composition and the coefficient of viscosity are crucial for determining the existence and properties of a state of equilibrium. A detailed study is carried out for carbon monoxide and hydroxyl. Abundances as small as 10^–5 for CO and 10^–8 for OH are sufficient to balance the disc against the viscous production of heat. The disc is usually non-convective. Near the equilibrium state the dust layer becomes thin enough to be gravitationally unstable. Infall of interstellar material is not expected to change the occurrence of instability, since the disc was not found to be convective even in the homogeneous circumstances. The results also remain unaltered even if the abundances of coolants are reduced by several orders of magnitude.     

Explosion-triggered star formation in the central region of the Galaxy

The role of shock waves generated by explosions in the nucleus of a galaxy and propagating through the surrounding gas, on the efficiency of star formation in this region, is investigated. It is found that if the gas in the shock-compressed layer follows polytropic changes in the density and temperature, a very wide range of masses of the fragments can be formed. Calculation shows that under suitable physical conditions a burst of star formation is actually realized.     

Chondrules born in plasma? Simulation of gas–grain interaction using plasma arcs with applications to chondrule and cosmic spherule formation

We are investigating chondrule formation by nebular shock waves, using hot plasma as an analog of the heated gas produced by a shock wave as it passes through the protoplanetary environment. Precursor material (mainly silicates, plus metal, and sulfide) was dropped through the plasma in a basic experimental set‐up designed to simulate gas–grain collisions in an unconstrained spatial environment (i.e., no interaction with furnace walls during formation). These experiments were undertaken in air (at atmospheric pressure), to act as a “proof‐of‐principle”—could chondrules, or chondrule‐analog objects (CAO), be formed by gas–grain interaction initiated by shock fronts? Our results showed that if accelerating material through a fixed plasma field is a valid simulation of a supersonic shock wave traveling through a cloud of gas and dust, then CAO certainly could be formed by this process. Melting of and mixing between starting materials occurred, indicating temperatures of at least 1266 °C (the olivine‐feldspar eutectic). The production of CAO with mixed mineralogy from monomineralic starting materials also shows that collisions between particles are an important mechanism within the chondrule formation process, such that dust aggregates are not necessarily required as chondrule precursors. Not surprisingly, there were significant differences between the synthetic CAO and natural chondrules, presumably mainly because of the oxidizing conditions of the experiment. Results also show similarity to features of micrometeorites like cosmic spherules, particularly the dendritic pattern of iron oxide crystallites produced on micrometeorites by oxidation during atmospheric entry and the formation of vesicles by evaporation of sulfides.     

A Global Model of MHD Wave Support of a Stratified Molecular Cloud

We perform numerical simulations of nonlinear MHD waves in a gravitationally stratified molecular cloud that is bounded by a hot and tenuous external medium, within a 1.5-dimensional approximation. Under the influence of a driving source of Alfvénic disturbances, the cloud is lifted up by the pressure of MHD waves and reaches a steady state characterized by oscillations about a new time-averaged equilibrium state. The nonlinear effect results in the generation of longitudinal motions and many shock waves. Models of an ensemble of clouds show that, for various strengths of the input energy, the velocity dispersion in the cloud σ ∝ Z ^0.5, where Z is a characteristic size of the cloud. Furthermore, σ is always comparable to the mean Alfvén velocity of the cloud, consistent with observational results.     

Electrostatic ion cyclotron waves in an anisotropic plasma

In the solar wind, electrostatic ion cyclotron waves can be excited, by electrons or ions when the flow velocity becomes supersonic. The instability of these waves is investigated for a situation in which ions are streaming in opposite directions along the interplanetary magnetic field in a uniform background of relatively stationary electrons. Many modes become unstable under the existing conditions. It is conjectured that the excitation of this instability may lead to a steady state electrostatic turbulence in the solar wind.     

Gravitational instability of partially-ionized plasma in an oblique magnetic field

The effects of Hall currents, finite conductivity, and collision with neutrals have been studied on the gravitational instability of a partially-ionized plasma. It is assumed that plasma is permeated by an oblique magnetic field. The dispersion relation has been obtained and numerical calculations have been performed to obtain the dependence of the growth rate of the gravitationally unstable mode on the various physical parameters involved. It is found that Jeans's criterion remains unchanged in the presence of Hall currents, finite conductivity, and collisions. The Hall currents, finite conductivity, and collisions have destabilizing influence on the unstable mode of wave propagation of a gravitational instability of partially-ionized plasma.     

On the overtaking interaction of typical shock waves in the solar wind flow

The interaction of traveling fast solar shock waves with other fast shock waves generated previously is considered in terms of magnetohydrodynamics for various solar wind parameters. The shocks are not piston ones and move freely in the flow. The magnetic structure in the interplanetary magnetic field emerging after the shock interaction is shown to correspond to the well-known magnetic configuration commonly observed on spacecraft or the classical Hundhausen R model. A head-on collision of solar shock waves with the boundary of a magnetic cloud is considered. It is pointed out that a slow shockwave refracted into the magnetic cloud can appear at an oblique collision of the shock with the cloud boundary. The results clarify our understanding of the available spacecraft data.     

Helicoidal magneto-electron waves in interstellar molecular clouds

We investigate the evolution of the magnetic flux density in a magnetically supported molecular cloud driven by Hall and Ohmic components of the electric field generated by the flows of thermal electrons. Particular attention is given to the wave transport of the magnetic field in a cloud whose gas dynamics is dominated by electron flows; the mobility of neutrals and ions is regarded as heavily suppressed. It is shown that electromagnetic waves penetrating such a cloud can be converted into helicons – weakly damped, circularly polarized waves in which the densities of the magnetic flux and the electron current undergo coherent oscillations. These waves are interesting in their own right, because for electron magnetohydrodynamics the low-frequency helicoidal waves have the same physical significance as the transverse Alfvén waves do for a single-component magnetohydrodynamics. The latter, as is known, are considered to be responsible for the widths of molecular lines detected in dark, magnetically supported clouds. From our numerical estimates for the group velocity and the rate of dissipation of helicons it follows that a possible contribution of these waves to the broadening of molecular lines is consistent with the conditions typical of dark molecular clouds.     

Nonlinear thin shell instabilities in molecular clouds

Observations of molecular clouds point to the existence of supersonic, turbulent flows. Therefore, any theory which attempts to describe molecular cloud evolution and star formation must include a consideration of the dynamics of colliding flows. Previous studies have considered the collision of supersonic streams or clouds. The resultant instabilities provide a mechanism which may give rise to observable cloud morphologies and enhance the star formation rate. One such instability is the nonlinear thin shell instability (NTSI) of a shock-bounded slab. This process is driven by ram pressure and efficient cooling. In this study, I use numerical simulations to examine the head-on collision of supersonic gas streams in a cold, molecular gas. A dense slab forms in the collision midplane and is prone to a number of instabilities, including the NTSI. The thermodynamic processes involved are found to have a controlling influence upon the instability and fragmentation of the slab. Although some minimal amount of cooling is needed to drive the instability, too rapid a cooling rate gives rise to smaller wavelength instabilities which wipe out the NTSI. The growth rate of the NTSI in a gas undergoing molecular cooling corresponds to a timescale of order 10¹² s, in general agreement with the theoretical value for an isothermal gas. The NTSI may provide a viable mechanism for the instigation of rapid star formation.     

Grain destruction in interstellar shock waves

Interstellar shock waves can erode and destroy grains present in the shocked gas, primarily as the result of sputtering and grain-grain collisions. Uncertainties in current estimates of sputtering yields are reviewed. Results are presented for the simple case of sputtering of fast grains being stopped in cold gas. An upper limit is derived for sputtering of refractory grains in C-type MHD shocks: shock speedsv _s 50 km s^–1 are required for return of more than 30% of the silicate to the gas phase. Sputtering can also be important for removing molecular ice mantles from grains in two-fluid MHD shock waves in molecular gas. Recent estimates of refractory grain lifetimes against destruction in shock waves are summarized, and the implications of these short lifetimes are discussed.     

Magnetic draping of merging cores and radio bubbles in clusters of galaxies

Sharp fronts observed by the Chandra satellite between dense cool cluster cores moving with near-sonic velocity through the hotter intergalactic gas, require strong suppression of thermal conductivity across the boundary. This may be due to magnetic fields tangential to the contact surface separating the two plasma components. We point out that a super-Alfvenic motion of a plasma cloud (a core of a merging galaxy) through a weakly magnetized intercluster medium leads to 'magnetic draping', formation of a thin, strongly magnetized boundary layer with a tangential magnetic field. For supersonic cloud motion,   M _s≥ 1  , magnetic field inside the layer reaches near-equipartition values with thermal pressure. Typical thickness of the layer is  ∼ L / M ²_A≪ L   , where L is the size of the obstacle (plasma cloud) moving with Alfvén Mach number   M _A≫ 1  . To a various degree, magnetic draping occurs for both subsonic and supersonic flows, random and ordered magnetic fields and it does not require plasma compressibility. The strongly magnetized layer will thermally isolate the two media and may contribute to the Kelvin–Helmholtz stability of the interface. Similar effects occur for radio bubbles, quasi-spherical expanding cavities blown up by active galactic nucleus jets; in this case, the thickness of the external magnetized layer is smaller,  ∼ L / M ³_A≪ L   .     

Galactic magnetic fields and their interactions with the gas and cosmic rays

(i) The controversy of dynamo or primordial origin of galactic magnetic fields is summarized and extended to show that the dynamo theory appears to fail. However, much more important than their origin are the characteristics of the fields and their interactions with the gas and cosmic rays. (ii) A passive magnetic field frozen into a turbulent plasma is not dissipated like a cloud of smoke (turbulent or eddy diffusion) as believed previously. On the contrary it is amplified exponentially until, within a few eddy periods, either the growing magnetic stresses halt the turbulence or the field becomes chaotic. Even if the Petschek reconnection mechanism operates, the field is always disordered to a scale <0.1L, whereL is the eddy dimension. The investigation may at last provide a semi-quantitative deductive theory of hydromagnetic eddies. (iii) It is concluded that the gas motions observed in our Galaxy are not convective but are mainly hydromagnetic waves or oscillations, with the magnetic field in control. The significance of this result is discussed in connection with the overall gas velocity field, the creation of stars and stellar systems, and with the origin and distribution of cosmic rays.     

Binary formation in stellar clusters

We consider how the tidal potential of a stellar cluster or a dense molecular cloud affects the fragmentation of gravitationally unstable molecular cloud cores. We find that molecular cloud cores which would collapse to form a single star in the absence of tidal shear, can be forced to fragment if they are subjected to tides. This may enhance the frequency of binaries in star-forming regions such as Ophiuchus and the frequency of binaries with separations ≲100 au in the Orion Trapezium Cluster. We also find that clouds which collapse to form binary systems in the absence of a tidal potential will form bound binary systems if exposed to weak tidal shear. However, if the tidal shear is sufficiently strong, even though the cloud still collapses to form two fragments, the fragments are pulled apart while they are forming by the tidal shear and two single stars are formed. This sets an upper limit for the separation of binaries that form near dense molecular clouds or in stellar clusters.     

Chondrule collisions in shock waves

Abstract— Detailed numerical models have shown that solar nebula shock waves would be able to thermally process chondrules in a way that is consistent with experimental constraints. However, it has recently been argued that the high relative velocities that would be generated between chondrules of different sizes immediately behind the shock front would lead to energetic collisions that would destroy the chondrules as they were processed rather than preserving them for incorporation into meteorite parent bodies. Here the outcome of these collisions is quantitatively explored using a simple analytic expression for the viscous dissipation of collisional energy in a liquid layer. It is shown that molten chondrules can survive collisions at velocities as high as a few hundred meters per second. It is also shown that the thermal evolution of chondrules in a given shock wave varies with chondrule size, which may allow chondrules of different textures to form in a given shock wave. While experiments are needed to further constrain the parameters used in this work, these calculations show that the expected outcomes from collisions behind shock waves are consistent with what is observed in meteorites.     

Enhanced Cloud Disruption by Magnetic Field Interaction

We present results from the first three-dimensional numerical simulations of moderately supersonic cloud motion through a tenuous, magnetized medium. We show that the interaction of the cloud with a magnetic field perpendicular to its motion has a great dynamical impact on the development of instabilities at the cloud surface. Even for initially spherical clouds, magnetic field lines become trapped in surface deformations and undergo stretching. The consequent field amplification that occurs there and, in particular, its variation across the cloud face then dramatically enhance the growth rate of Rayleigh-Taylor unstable modes, hastening the cloud disruption.     

Influence of magnetic clouds on cosmic ray intensity variation

The data from a high counting rate neutron monitor has been analysed to study the nature of galactic cosmic-ray transient modulation associated with three classes of magnetic clouds, i.e., clouds associated with shock, stream interface and cold magnetic enhancement.It is found that the decreases in cosmic-ray intensity which are associated with clouds preceded by a shock, are very high (Forbush-type) and these decreases start earlier than the arrival of the cloud at the Earth. From the study of the time profile of these decreases it is found that the onset time of a Forbush-type decrease produced by a shock-associated cloud starts nearly at the time of arrival of the shock front at the Earth and the recovery is almost complete within a week.The decreases in cosmic-ray intensity associated with clouds followed by a stream interface are smaller in magnitude and larger in duration. The depression starts on the day of the arrival of the cloud.The decreases associated with the third category of clouds, i.e., clouds associated with cold magnetic enhancement (a region in which plasma temperature is anomalously low and the magnetic field strength is enhanced) are of still smaller amplitude and duration. The decrease in this case starts on the day the cloud arrives at the Earth.It seems that the Forbush decrease modulating region consists of a shock front followed by a plasma sheath in which the field intensity is high and turbulent. The amplitude of decrease is related to the field magnitude and the speed of the cloud. Both shocked plasma and the magnetic cloud are influential in determining the time profile of these decreases. In our view it is not the magnetic field strength or the topology alone which is responsible for the cosmic-ray depression. The most likely additional effect is the increased degree of turbulence.     

On the Stability of Colliding Flows: Radiative Shocks, ThinShells, and Supersonic Turbulence

High-resolution numerical simulations reveal the turbulent character of the interaction zone of colliding, radiative, hypersonic flows. As the shocked gas cools radiatively, the cooled matter is squeezed into thin, high density shells. The remaining kinetic energy causes supersonic turbulence within these shells, before it is finally dissipated by internal shocks and vortex cascades. The density is far from homogeneous. High density filaments and large voids coexist. Its mean value is significantly below the stationary value. Similarly, areas with supersonic velocities are found next to subsonic regions. The mean velocity is slightly below or above the sound speed. While quasi uniform flow motions are observed on smaller scales the large scale velocity distribution is isotropic. Part of the turbulent shell is occupied by relatively uniform flow-patches, resembling coherent structures. Astronomical implications of the turbulent interaction zone are multifarious. It probably drives the X-ray variability in colliding wind binaries as well as the surprising dust formation on orbital scales in some WR-binaries. It lets us understand the knotty appearance of wind-driven structures as planetary and WR-ring nebulae, symbiotics, supernova remnants, galactic supperbubbles. Also, WR and other radiatively driven, clumpy winds, advection dominated accretion, cooling flows and molecular cloud dynamics in star-forming regions may carry its stamp This revised version was published online in July 2006 with corrections to the Cover Date.