Collapse and fragmentation of rotating magnetized clouds – II. Binary formation and fragmentation of first cores

Subsequent to Paper I, the evolution and fragmentation of a rotating magnetized cloud are studied with use of three-dimensional magnetohydrodynamic nested grid simulations. After the isothermal runaway collapse, an adiabatic gas forms a protostellar first core at the centre of the cloud. When the isothermal gas is stable for fragmentation in a contracting disc, the adiabatic core often breaks into several fragments. Conditions for fragmentation and binary formation are studied. All the cores which show fragmentation are geometrically thin, as the diameter-to-thickness ratio is larger than 3. Two patterns of fragmentation are found. (1) When a thin disc is supported by centrifugal force, the disc fragments into a ring configuration (ring fragmentation). This is realized in a rapidly rotating adiabatic core as  Ω > 0.2τ⁻¹_ff  , where Ω and  τ_ff  represent the angular rotation speed and the free-fall time of the core, respectively. (2) On the other hand, the disc is deformed to an elongated bar in the isothermal stage for a strongly magnetized or rapidly rotating cloud. The bar breaks into 2–4 fragments (bar fragmentation). Even if a disc is thin, the disc dominated by the magnetic force or thermal pressure is stable and forms a single compact body. In either ring or bar fragmentation mode, the fragments contract and a pair of outflows is ejected from the vicinities of the compact cores. The orbital angular momentum is larger than the spin angular momentum in the ring fragmentation. On the other hand, fragments often quickly merge in the bar fragmentation, since the orbital angular momentum is smaller than the spin angular momentum in this case. Comparison with observations is also shown.     

Fragmentation of a Molecular Cloud Core versus Fragmentation of the Massive Protoplanetary Disk in the Main Accretion Phase

We present three-dimensional numerical simulations on binary formation through fragmentation. The simulations follow gravitational collapse of a molecular cloud core up to growth of the first core by accretion. At the initial stage, the gravity is only slightly dominant over the gas pressure. We made various models by changing initial velocity distribution (rotation speed, rotation law, and bar-mode perturbation). The cloud fragments whenever the cloud rotates sufficiently slowly to allow collapse but faster enough to form a disk before first-core formation. The latter condition is equivalent to Ω₀ t _ff ? 0.05, where Ω₀ and t _ff f denote the initial central angular velocity and the freefall time measured from the central density, and the condition is independent of the initial rotation law and bar-mode perturbation. Fragmentation is classified into six types. When the initial cloud rotates rigidly the cloud collapses to form a adiabatic disk supported by rotation. When the bar-mode perturbation is very minor, the disk deforms to a rotating bar, and the bar fragments. Otherwise, the adiabatic disk evolves into a central core surrounded by a circumstellar disk, and the the circumstellar disk fragments. When the initial cloud rotates differentially, the cloud deforms to a ring or bar in the isothermal collapse phase. The ring fragments into free or more cores, while the bar fragments into only two cores. In the latter case, the core merges due to low orbital angular momentum and new satellite cores form in the later stages.     

Can newly-forming stars act like Mini-QSOs?

The birth of stars takes place inside dense molecular clouds and is therefore difficult to observe with optical telescopes. Yet some stars form at the edges of clouds, and combined radio, infrared, optical and X-ray observations have recently revealed a great deal of structure: over a wide range of luminosities one observes high mass-outflow rates from pre-Main-Sequence and T Tauri-stars, with wind momenta exceeding the radiation momenta by large factors. The mass flows take the shape of two highly supersonic jets, perpendicular to a circumstellar disk. The jets have knotlike condensations, show strong linear polarization along the flow direction, and are often seen to reconverge. They resemble the twin-jets from the nuclei of active galaxies and may be driven by a similar type of engine. They may even hold a clue to the problem of how stars like our Sun got rid of the enormous angular momentum of their progenitor cloud. I propose that in both phenomena, the central engine is the maximally rotating core of a massive disk which produces a pair of thin, antipodal, magnetized relativistic jets.     

Collimation of astrophysical MHD outflows

We explain in simple terms why a rotating and magnetized outflow forms a core with a jet and show numerical simulations which substantiate this argument. The outflow from a solar-type inefficient magnetic rotator is found to be very weakly collimated while the outflow from a ten times faster rotating YSO is shown to produce a tightly collimated jet. This gives rise to an evolutionary scenario for stellar outflows. We also propose a two-component model consisting of a wind outflow from a central object and a faster rotating outflow launched from a surrounding accretion disk which plays the role of the flow collimator.     

Collapse and fragmentation of rotating magnetized clouds – I. Magnetic flux–spin relation

We discuss the evolution of the magnetic flux density and angular velocity in a molecular cloud core, on the basis of three-dimensional numerical simulations, in which a rotating magnetized cloud fragments and collapses to form a very dense optically thick core of  >5 × 10¹⁰ cm⁻³  . As the density increases towards the formation of the optically thick core, the magnetic flux density and angular velocity converge towards a single relationship between the two quantities. If the core is magnetically dominated its magnetic flux density approaches  1.5( n /5 × 10¹⁰ cm⁻³)^1/2 mG  , while if the core is rotationally dominated the angular velocity approaches  2.57 × 10⁻³ ( n /5 × 10¹⁰ cm⁻³)^1/2 yr⁻¹  , where n is the density of the gas. We also find that the ratio of the angular velocity to the magnetic flux density remains nearly constant until the density exceeds  5 × 10¹⁰ cm⁻³  . Fragmentation of the very dense core and emergence of outflows from fragments will be shown in the subsequent paper.     

Collapse of a Magnetized Rotating Cloud2D Numerical Simulations

We present results of the 2D simulations of magnetorotational mechanism for the rotating magnetized cloud. It was found that amplification of the toroidal magnetic field leads to the transformation of the part of the rotational energy of the cloud to the kinetic energy of radial motion. A compression wave appearing in the transition region between the core of the cloud and the envelope transforms soon to the MHD shock wave and pushes away part of the envelope of the cloud. Time evolution of the thrown away mass and energy are given. Simulations have been made on the base of the conservative implicit Lagrangian scheme on triangular grid with grid reconstruction. This revised version was published online in July 2006 with corrections to the Cover Date.     

Low T/|W| dynamical instability in differentially rotating stars: diagnosis with canonical angular momentum

We study the nature of non-axisymmetric dynamical instabilities in differentially rotating stars with both linear eigenmode analysis and hydrodynamic simulations in Newtonian gravity. We especially investigate the following three types of instability; the one-armed spiral instability, the low   T /| W |  bar instability, and the high   T /| W |  bar instability, where T is the rotational kinetic energy and W is the gravitational potential energy. The nature of the dynamical instabilities is clarified by using a canonical angular momentum as a diagnostic. We find that the one-armed spiral and the low   T /| W |  bar instabilities occur around the corotation radius, and they grow through the inflow of canonical angular momentum around the corotation radius. The result is a clear contrast to that of a classical dynamical bar instability in high   T /| W |  . We also discuss the feature of gravitational waves generated from these three types of instability.     

Collapse of primordial clouds and the formation of a central core

The collapse of rotating clouds is investigated using three-dimensional self-gravitating hydrodynamical simulations. We take into account the detailed non-equilibrium chemical reactions for primordial gas that consists of pure hydrogen. The parameters of the collapse and the condition of the fragmentation are compared with those of isothermal clouds. It is shown that the geometrical flatness of the central region of the disc is a good indicator for predicting whether the clouds fragment or not. If the flatness is greater than the critical value, ∼ 4π, a cloud fragments into filaments and blobs. On the other hand, if the flatness is smaller than the critical value, fragmentation is not expected before the central core formation even if the cooling is efficient and the total mass becomes much greater than the local Jeans mass at the centre. The critical mass is found to be 3 × 10⁶ M_⊙ for a typical initial condition. If the initial cloud mass is smaller than this critical value, fragmentation before the central core formation is not expected. For a typically estimated first collapsing cosmological baryonic object, M ≲ 10⁶ M_⊙, central core formation is expected and will have a significant effect on the later evolution of the whole system. This revised version was published online in July 2006 with corrections to the Cover Date.     

含粘滞和磁场的薄吸积盘不稳定性

本文采用微扰方法导出色散方程，并在四种情况下详细讨论了薄吸积盘的不稳定性。结果表明：在纯粘滞和纯磁场盘中都存在脉动不稳定性。而且在吸积盘内同时考虑粘滞和磁场时，存在两种不稳定性，一种是脉动不稳定性，另一种是单调不稳定性。同时数值计算还表明，脉动不稳定性更可能存在于盘的内区，而单调不稳定性则只在盘的外区，对短波扰动才有意义。这些结果为解释ＢＬＬａｃ天体、Ｓｅｙｆｅｒｔ星系及类星体等活动星系核的光变现象进一步提供了理论依据。     

Molecular Cloud Collapse

Theoretical models of star formation from the collapse of molecular cloud cores have been evolving in complexity for many years. This work describes the evolution of models from the nonrotating, nonmagnetized singular isothermal sphere to rotating, magnetized singular isothermal toroids. Four members of the same family are studied–the four combinations of nonrotation/rotation and nonmagnetization/magnetization. It is found that although rotation alone can hinder collapse to a pointmass, addition of braking from a magnetic field can transport away much of the angular momentum upward in a low-velocity outflow during the collapse phase. For all magnetized cases, accretion proceeds at a constant rate similar to that of the isothermal sphere.     

磁化黑洞吸积盘的演化及放能效率

采用等效电路模型讨论了两种不同类型的磁场对黑洞的旋转能量和角动量的提取机制；Blandford-Znajek(BZ)过程和磁耦合过程，在研究磁化吸积盘中心黑洞自转参量演化特征的基础上，详细比较了纯吸积过程，BZ过程和磁耦合过程对黑洞吸积盘放能效率的贡献，结果表明，磁耦合过程是提取黑洞旋转能量重要的新机制，其放能效率与BZ过程几乎相等，在黑洞自转不是特别大的情况，纯吸积过程的放能效率高于BZ过程和磁耦合过程的放能效率，但是当黑洞自转接近极端Kerr黑洞的自转状态时，放能效率主要由BZ过程和磁耦合过程贡献。     

Large-scale structure of molecular gas in Heiles Cloud 2: a remarkable rotating ring

We have mapped the J = 1 --> 0 transition of 13CO over a 3 deg2 region in Heiles Cloud 2 using the Five College Radio Astronomy Observatory 14 m telescope. The complete map contains 3600 individual spectra of which 2400 were sampled with 1' spacing. The map suggest that the structure of Heiles Cloud 2 is dominated by a quasi equilibrium rotating ring similar to those found in numerical calculations of the gravitational collapse of a rotating cloud. Within this ring, several dense condensations have been identified and partially mapped in C18O. These subcondensations, among which is the dense filament TMC-1, probably result from the instability of the ring to fragmentation and have masses on the order of the Jeans mass. Thus, they are marginally unstable to further collapse and may be the precursors of fragments that will eventually form stars.     

Dynamical evolution of fragmenting gas clouds

Previous numerical simulations have shown that under certain conditions rotating gas clouds break up in two equal parts. We explore the consequences, if this process continues and a planar, equal mass four-body system forms. The results of the four-body calculations are used in Monte Carlo simulation of fragmentation of a rotating gas cloud in a galactic nucleus. Then it appears possible that clusters of large numbers of objects form; the dynamical evolution of these clusters have been calculated. The results were applied to ejection of supermassive objects from galactic nuclei. We find that several statistical properties of double radio sources may be understood as resulting from the fragmentation process.     

Oligarchic growth with migration and fragmentation

In the core-accretion model, giant-planet cores form by oligarchic growth from a population of planetesimals prior to the dispersal of the disk gas. Once a core reaches a critical mass of roughly 10 Earth masses, it begins to accrete a gaseous envelope, forming a giant planet. Collisions between planetesimals cause fragmentation. Planetesimal fragments are more easily captured by cores, speeding up growth, but fragments are also lost by radial drift, reducing the total solid mass in the disk. Interaction with the gas causes cores to undergo inward type-I migration. Migration allows a core to accrete planetesimals from a larger region, but migrating cores may be lost if they reach the star. Thus, migration and fragmentation have both a positive and a negative impact on core formation. Here we describe results of new simulations of oligarchic growth that include fragmentation and/or migration. In the absence of migration, cores grow until they reach their isolation mass, which increases with distance from the star, or until the disk gas disperses. Fragmentation increases the maximum core mass by increasing growth rates in the outer disk, allowing objects to reach their isolation mass during the disk lifetime. When migration is present, cores migrate inwards rapidly when they approach 1 Earth mass. Most migrating cores are lost. Migrating cores gain little extra mass since they are passing through regions that have been depleted by earlier generations of cores. For a disk viscosity parameter alpha=1e−3 and planetesimal radius = 10 km, the maximum core mass is roughly 4 and 0.5 Earth masses with/without fragmentation, respectively, with little dependence on the disk mass. Formation and survival of 10-Earth-mass cores, in the presence of migration, requires large alpha (1e−2) and a massive disk (0.1 solar masses). When alpha is large, type-I migration rates decrease rapidly with time, allowing large, late-forming cores to survive. The addition of a stochastic (random-walk) migration component makes little difference to the outcome, provided that stochastic migration affects only cores larger than 0.01 Earth masses. Stochastic migration becomes increasingly important if it also affects lower-mass objects.     

On the formation of protostellar disks

An analysis is presented of the hydrodynamic aspects of the growth of protostellar disks from the accretion (or collapse) of a rotating gas cloud. The size, mass, and radiative properties of protostellar disks are determined by the distribution of mass and angular momentum in the clouds from which they are formed, as well as from the dissipative processes within the disks themselves. The angular momentum of the infalling cloud is redistributed by the action of turbulent viscosity on a shear layer near the surface of the disk (downstream of the accretion shock) and on the radial shear across cylindrical surfaces parallel to the rotation axis. The fraction of gas that is fed into a central core (protostar) during accretion depends on the ratio of the rate of viscous diffusion of angular momentum to the accretion rate; rapid viscous diffusion (or a low accretion rate) promotes a large core-to-disk mass ratio. The continuum radiation spectrum of a highly viscous disk is similar to that of a steady-state accretion disk without mass addition. It is possible to construct models of the primitive solar nebula as an accretion disk, formed by the collapse of a slowly rotating protostellar cloud, and containing the minimum mass required to account for the planets. Other models with more massive disks are also possible.     

Unipolar induction of a magnetized accretion disk around a black hole

The structure and magnitude of the electromagnetic field produced by a rotating accretion disk around a black hole were determined. The disk matter is assumed to be a magnetized plasma with a frozenin poloidal magnetic field. The vacuum approximation is used outside the disk.     

The gravitational-wave spectrum of a non-axisymmetric torus around a rapidly spinning black hole

The gravitational-wave spectrum emitted by a non-axisymmetric torus rotating at an angular velocity Ω_T, is derived in terms of a structure function representing a combination of sausage-tilt modes in the torus in the limit of an incompressible fluid. The analysis of the gravitational-wave spectrum is then applied to a model proposed recently, in which a highly magnetized torus interacts with a stellar mass, Kerr black hole via poloidal field lines that connect the torus and the horizon. The deformation of the torus results from global magnetic instabilities when the magnetic field strength inside the torus exceeds a few times 10¹⁵ Gauss. The dynamics of the system is illustrated using a non-MHD toy model. It is found that, quite generally, most of the gravitational-wave energy emitted is in the frequency range of sensitivity of LIGO and Virgo.     

Weak Elliptical Distortion of the Milky Way Potential traced by Open Clusters

From photometric observations and star counts, the existence of a bar in the cen-tral few kpc of the Galaxy is suggested. It is generally thought that our Galaxy is surrounded by a massive invisible halo. The gravitational potential of the Galaxy is therefore made non-axisymmetric generated by the central tfiaxial bar, by the outer triaxial halo, and/or by the spiral structures. Selecting nearly 300 open clusters with complete spatial velocity measure-ments and ages, we were able to construct the rotation curve of the Milky Way within a range of 3 kpc of the Sun. Using a dynamic model for an assumed elliptical disk, a clear weak el-liptical potential of the disk with ellipticity of ε(R0) = 0.060 ± 0.012 is detected, the Sun is found to be near the minor axis, displaced by 30°± 3°. The motion of the clusters is suggested to be on an oval orbit rather than on a circular one.     

Two-stage fragmentation in a rotating protostellar cloud

We discuss the problem of fragmentation in a rotating cloud, showing that different physical models can result in widely different results. We also show that results of our turbulent-rotation model agree qualitatively with those of numerical calculations by Larson (1978a) and suggest that fragmentation in a rotating nebula takes place at two different stages.