Contraction and Fragmentation of Magnetized Rotating Clouds and Formation of Binary Systems

Using three-dimensional (3D) magnetohydrodynamical (MHD) nested-grid simulations, the fragmentation of a rotating magnetized molecular cloud core is studied. An isothermal rotating magnetized cylindrical cloud in hydrostatic balance is considered. We studied non-axisymmetric evolution of the cloud. It is found that non-axisymmetry hardly evolves in the early phase, but it begins to grow after the gas contracts and forms a thin disk. The disk formation and thus growth of non-axisymmetric perturbation are strongly promoted by rotation and magnetic field strength. We found two types of fragmentations: fragmentation from a ring and that from a bar. These two types of fragmentations occur in thin adiabatic cores with the thickness being smaller than 1/4 of the radial size. For the fragments to survive, they should be formed in a heavily elongated barred core or a flat round disk. In the models showing fragmentation, outflows from respective fragments are found as well as that driven by the rotating bar or the disk.     

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.     

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.     

Specific angular momentum of disc merger remnants and the λR-parameter

We use two-dimensional kinematic maps of simulated binary disc mergers to investigate the  λ_R  -parameter, which is a luminosity-weighted measure of projected angular momentum per unit mass. This parameter was introduced to subdivide the SAURON sample of early-type galaxies in so-called fast  λ_R > 0.1  and slow rotators  λ_R < 0.1  . Tests on merger remnants reveal that  λ_R  is a robust indicator of the true angular momentum content in elliptical galaxies. We find the same range of  λ_R  values in our merger remnants as in the SAURON galaxies. The merger mass ratio is decisive in transforming fast rotators into slow rotators in a single binary merger, the latter being created mostly in an equal-mass merger. Slow rotators have a  λ_R  which does not vary with projection. The confusion rate with face-on fast rotators is very small. Mergers with a gas component form slow rotators with smaller ellipticities than collisionless merger remnants have, and are in much better agreement with the SAURON slow rotators. Remergers of merger remnants are slow rotators, but tend to have too high ellipticities. Fast rotators maintain the angular momentum content from the progenitor disc galaxy if merger mass ratio is high. Some SAURON galaxies have values of  λ _R   as high as our progenitor disc galaxies.     

Binary formation with different metallicities: dependence on initial conditions

The fragmentation process in collapsing clouds with various metallicities is studied using three-dimensional nested-grid hydrodynamics. Initial clouds are specified by three parameters: cloud metallicity, initial rotation energy and initial cloud shape. For different combinations of these parameters, we calculate 480 models in total and study cloud evolution, fragmentation conditions, orbital separation and binary frequency. For the cloud to fragment during collapse, the initial angular momentum must be higher than a threshold value, which decreases with decreasing metallicity. Although the exact fragmentation conditions depend also on the initial cloud shape, this dependence is only modest. Our results indicate a higher binary frequency in lower metallicity gas. In particular, with the same median rotation parameter as in the solar neighbourhood, a majority of stars are born as members of binary/multiple systems for  <10⁻⁴ Z_⊙  . With initial mass  <0.1 M_⊙  , if fragments are ejected in embryo from the host clouds by multibody interaction, they evolve to substellar-mass objects. This provides a formation channel for low-mass stars in zero- or low-metallicity environments.     

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density which travels at a relevant radial group speed C _g. The wave energy surface density and the wave angular momentum surface density are related to by = and = m respectively, where is the angular frequency in an inertial frame of reference and the integer m , proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discussed.     

Mass and spin co-evolution during the alignment of a black hole in a warped accretion disc

In this paper, we explore the gravitomagnetic interaction of a black hole (BH) with a misaligned accretion disc to study BH spin precession and alignment jointly with BH mass M _BH and spin parameter a evolution, under the assumption that the disc is continually fed, in its outer region, by matter with angular momentum fixed on a given direction     . We develop an iterative scheme based on the adiabatic approximation to study the BH–disc co-evolution: in this approach, the accretion disc transits through a sequence of quasi-steady warped states (Bardeen–Petterson effect) and interacts with the BH until the spin   J _BH  aligns with     . For a BH aligning with a corotating disc, the fractional increase in mass is typically less than a few per cent, while the spin modulus can increase up to a few tens of per cent. The alignment time-scale     is of  ∼10⁵–10⁶ yr  for a maximally rotating BH accreting at the Eddington rate. BH–disc alignment from an initially counter-rotating disc tends to be more efficient compared to the specular corotating case due to the asymmetry seeded in the Kerr metric: counter-rotating matter carries a larger and opposite angular momentum when crossing the innermost stable orbit, so that the spin modulus decreases faster and so the relative inclination angle.     

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  .     

Chemical evolution with radial mixing

Models of the chemical evolution of our Galaxy are extended to include radial migration of stars and flow of gas through the disc. The models track the production of both iron and α-elements. A model is chosen that provides an excellent fit to the metallicity distribution of stars in the Geneva–Copenhagen survey (GCS) of the solar neighbourhood and a good fit to the local Hess diagram. The model provides a good fit to the distribution of GCS stars in the age–metallicity plane, although this plane was not used in the fitting process. Although this model's star formation rate is monotonically declining, its disc naturally splits into an α-enhanced thick disc and a normal thin disc. In particular, the model's distribution of stars in the ([O/Fe], [Fe/H]) plane resembles that of Galactic stars in displaying a ridge line for each disc. The thin-disc's ridge line is entirely due to stellar migration, and there is the characteristic variation of stellar angular momentum along it that has been noted by Haywood in survey data. Radial mixing of stellar populations with high  σ _z   from inner regions of the disc to the solar neighbourhood provides a natural explanation of why measurements yield a steeper increase of  σ _z   with age than predicted by theory. The metallicity gradient in the interstellar medium is predicted to be steeper than in earlier models, but appears to be in good agreement with data for both our Galaxy and external galaxies. The models are inconsistent with a cut-off in the star formation rate at low gas surface densities. The absolute magnitude of the disc is given as a function of time in several photometric bands, and radial colour profiles are plotted for representative times.     

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.     

Rotation and activity in the solar-type stars of NGC 2547

We present high-resolution spectroscopy of a sample of 24 solar-type stars in the young (15–40 Myr), open cluster NGC 2547. We use our spectra to confirm cluster membership in 23 of these stars, to determine projected equatorial velocities and chromospheric activity, and to search for the presence of accretion discs. We find examples of both fast ( v _e sin  i >50 km s⁻¹) and slow ( v _e sin  i <10 km s⁻¹) rotators, but no evidence for active accretion in any of the sample. The distribution of projected rotation velocities is indistinguishable from the slightly older IC 2391 and IC 2602 clusters, implying similar initial angular momentum distributions and circumstellar disc lifetimes. The presence of very slow rotators indicates either that long (10–40 Myr) disc lifetimes or internal differential rotation are needed, or that NGC 2547 (and IC 2391/2602) were born with more slowly rotating stars than are presently seen in even younger clusters and associations. The solar-type stars in NGC 2547 follow a similar rotation–activity relationship to that seen in older clusters. X-ray activity increases until a saturation level is reached for v _e sin  i >15–20 km s⁻¹. We are unable to explain why this saturation level, of log( L _x L _bol)≃−3.3, is a factor of 2 lower than in other clusters, but rule out anomalously slow rotation rates or uncertainties in X-ray flux calculations.     

H i and dark matter in the windy starburst dwarf galaxy NGC 1705

We present 21-cm H  i line observations of the blue compact dwarf galaxy NGC 1705. Previous optical observations show a strong outflow powered by an ongoing starburst dominating the H  ii morphology and kinematics. In contrast, most of the H  i lies in a rotating disc. An extraplanar H  i spur accounts for ∼8 per cent of the total H  i mass, and is possibly associated with the H  ii outflow. The inferred mass loss rate out of the core of the galaxy is significant, ∼0.2 − 2 M_⊙ yr⁻¹, but does not dominate the H  i dynamics. Mass model fits to the rotation curve show that the dark matter (DM) halo is dominant at nearly all radii and has a central density ρ₀ ≈ 0.1 M_⊙ pc⁻³: ten times higher than typically found in dwarf irregular galaxies, but similar to the only other mass-modelled blue compact dwarf, NGC 2915. This large difference strongly indicates that there is little evolution between dwarf irregular and blue compact dwarf types. Instead, dominant DM haloes may regulate the morphology of dwarf galaxies by setting the critical surface density for disc star formation. Neither our data nor catalogue searches reveal any likely external trigger to the starburst in NGC 1705.     

The changing interstellar medium of massive elliptical galaxies and cosmic evolution of radio galaxies and quasars

The recently discovered apparent dramatic expansion in the effective radii of massive elliptical galaxies from   z ≃ 2  to ≃0.1 has been interpreted in terms of either galaxy mergers or the rapid loss of cold gas due to active galactic nuclei (AGN) feedback. In examining the latter case, we have quantified the extent of the expansion, which is uncertain observationally, in terms of the star formation parameters and time of the expulsion of the cold gas. In either case, the large global decrease in stellar density should translate into a major drop in the interstellar medium density and pressure with cosmic epoch. These cosmological changes are expected to have a major influence on the gas accretion mode, which will shift from 'cold' thin disc accretion at high redshifts towards 'hot' Bondi fed Advection Dominated Accretion Flow (ADAF) accretion at low redshifts. The decline of angular momentum inflow would then lead to a spin down of the black hole, for which we have calculated more precise time-scales; a value of about 0.2 Gyr is typical for a  10⁹ M_⊙  central black hole. These results have implications for the different cosmological evolutionary patterns found for the luminosity functions of powerful and weak radio galaxies.     

Discs and haloes in pre-main-sequence stars

We study the infrared (IR) emission from flared discs with and without additional optically thin haloes. Flux calculations of a flared disc in vacuum can be considered a special case of the more general family of models in which the disc is imbedded in an optically thin halo. In the absence of such a halo, flux measurements can never rule out its existence because the disc flaring surface defines a mathematically equivalent halo that produces the exact same flux at all IR wavelengths. When a flared disc with height H at its outer radius R is imbedded in a halo whose optical depth at visual wavelengths is  τ_halo  , the system IR flux is dominated by the halo whenever  τ_halo > (1/4) H / R   . Even when its optical depth is much smaller, the halo can still have a significant effect on the disc temperature profile. Imaging is the only way to rule out the existence of a potential halo, and we identify a decisive test that extracts a signature unique to flared discs from imaging observations.     

Kelvin–Helmholtz driven propeller in AE Aquarii: A unified model for thermal and non-thermal flares

In this paper, an attempt is made to integrate the propeller ejection of material by the fast rotating white dwarf in AE Aquarii with the highly transient thermal and non-thermal emission in a single unifying model. It has been shown that the violent interaction between the fast rotating magnetosphere and a clumpy fragmented stream, in AE Aquarii specifically, may result in the growth of unstable modes of the Kelvin–Helmholtz instability and associated turbulence over length scales comparable to the stream radius on time-scales  τ_K-H ∼  t _dyn (∼ 600 s  ). For all conversion efficiencies of magnetohydrodynamic (MHD) power to mechanical energy ε≥ 0.1, these instabilities result in the effective azimuthal acceleration of the gas parcels to the escape velocity over time-scales   t _acc≤ 1000 s (∼ t _dyn)  . Further, it has been shown that the turbulence in the flow will cascade down to the dissipative level over time-scales  τ_cas∼ 3 h  . If released through dissipative shocks, this reservoir can drive a luminosity of   L ∼ 10³³ erg s⁻¹  , which can significantly contribute to the total emission when blobs collide in the exit stream, resulting in shock heating and associated flares. During the propeller process, particles can also be accelerated to high energies, which may be the driving mechanism behind the non-thermal radio to mid-infrared emission. The confluence of these ejected magnetized clouds may result in radio remnant surrounding AE Aquarii, which is optically thin between frequencies ν≥ 100 MHz–1 GHz.     

Stability of accretion discs threaded by a strong magnetic field

We study the stability of poloidal magnetic fields anchored in a thin accretion disc. The two-dimensional hydrodynamics in the disc plane is followed by a grid-based numerical simulation including the vertically integrated magnetic forces. The three-dimensional magnetic field outside the disc is calculated in a potential field approximation from the magnetic flux density distribution in the disc. For uniformly rotating discs we confirm numerically the existence of the interchange instability as predicted by Spruit, Stehle & Papaloizou . In agreement with predictions from the shearing sheet model, discs with Keplerian rotation are found to be stabilized by the shear, as long as the contribution of magnetic forces to support against gravity is small. When this support becomes significant, we find a global instability which transports angular momentum outwardly and allows mass to accrete inwardly. The instability takes the form of a m =1 rotating 'crescent', reminiscent of the purely hydrodynamic non-linear instability previously found in pressure-supported discs. A model where the initial surface mass density Σ( r ) and B _z ( r ) decrease with radius as power laws shows transient mass accretion during about six orbital periods, and settles into a state with surface density and field strength decreasing approximately exponentially with radius. We argue that this instability is likely to be the main angular momentum transport mechanism in discs with a poloidal magnetic field sufficiently strong to suppress magnetic turbulence. It may be especially relevant in jet-producing discs.     

The distribution of the warm and dense molecular gas around Cepheus A HW 2

We present VLA observations of the ( J , K )=(1, 1), (2, 2), (3, 3) and (4, 4) inversion transitions of NH₃ toward the HW 2 object in Cepheus A, with 1-arcsec angular resolution. Emission is detected in the main hyperfine line of the first three transitions. The NH₃(2, 2) emission shows a non-uniform 'ring' structure, which is more extended (3 arcsec) and intense than the emission seen in the (1, 1) and (3, 3) lines. A rotational temperature of ∼ 30–50 K and a lower limit to the mass of ∼ 1 ( X _NH3/10⁻⁸)⁻¹ M_⊙ are derived for the ring structure. The spatio-kinematical distribution of the NH₃ emission does not seem to be consistent with a simple circumstellar disc around the HW 2 thermal biconical radio jet. We suggest that it represents the remnant of the parental core from which both the inner 300-au (0.4 arcsec) disc, traced by the water maser spots previously found in the region, and the central object have formed. The complex velocity field of this core is probably produced from bound motions (similar to those of the inner disc) and from interaction with outflowing material.     

The neutral carbon distribution in a bipolar outflow/molecular disc source configuration: G35.2−0.74N

Maps are presented of ³ P ₁→³ P ₀[C  i ] and J =2→1 C¹⁸O line emission from the interstellar molecular cloud G35.2−0.74N. The maps are interpreted with reference to a previous model for the structure of the cloud in which opposing jets from a central object, embedded in a rotating interstellar disc, precess and drive a bipolar molecular outflow. The C¹⁸O emission traces the rotating interstellar disc, but the [C  i ] emission shows several features. An unresolved component is observed which probably results from dissociation of CO in the centre of the disc by UV radiation from the central source. Background [C  i ] emission is also observed which shares the rotation of the disc on larger scales. The C  i /CO ratio in these components is typically a few per cent. High-velocity [C  i ] emission, where C  i /CO is high (>0.1–0.4), is observed between the CO molecular outflow and the cavity exacavated by the jet. This material has probably been accelerated by the jet but dissociated by far-UV radiation propagating through the cavity. The C  i /CO ratio falls as the shocked outflow later sweeps up CO.     

The emission and kinematic structures of the bipolar planetary nebula M 1-8

We have undertaken echelle spectroscopy and narrow-band line imaging of the bipolar planetary nebula M 1-8. This has permitted us to map the outflow in [N  ii ]λλ 6548+6583 Å, Hα, and in the v = 1–0 S(1) transition of H₂ at λ 2.122 μm. It has also permitted us to acquire high-resolution spectra for [N  ii ]λ 6583 Å, Hα and He  ii λ 6560 Å. Our observations support the results of a previous 2MASS analysis by two of the authors (J. P. Phillips and G. Ramos-Larios), and confirm that there is strong H₂ emission outside of the ionized zone, as well as along the major axis of the outflow. Finally, we have investigated the spatial structure of the outflow in low and high excitation lines, and noted evidence for strong ionization stratification within the envelope of the source. We also note that major axis spectra show asymmetries attributable to outflow along the lobes, oriented at an angle i ∼ 35°–40° to the line of sight. Asymmetries along the minor axis, by contrast, appear to be associated with the central collimating disc, and may be interpretable in terms of asymmetries in disc structure, or rotation at an angular velocity of Ω∼ 1.4 10⁻¹² rad s⁻¹. If the disc arises due to common-envelope evolution, then it seems that angular momentum constraints must be relatively tight, and can only be satisfied given fairly extreme physical assumptions (such as low disc mass, high primary star mass, a low distance to the source and so forth).