The approach to collapse of molecular clouds

The dense molecular cloud cores that form stars, like other self-gravitating objects, undergo bulk oscillations. Just at the point of gravitational instability, their fundamental oscillation mode has zero frequency. We study, using perturbation theory, the evolution of a spherical cloud that possesses such a frozen mode. We find that the cloud undergoes a prolonged epoch of subsonic, accelerating contraction. This slow contraction occurs whether the cloud is initially inflated or compressed by the oscillation. The subsonic motion described here could underlie the spectral infall signature observed in many starless dense cores.     

On the radial distributions of molecular clouds in galaxies

The dynamics of the interstellar gas (the IS gas) driven by the viscous torque of a system of giant molecular clouds (the MC gas) is considered with the infinitesimally thin disk layer approximation. The flow explains the radial distributions of molecules observed in galaxies.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–26 October, 1984.     

On the origin of stellar aggregates in molecular clouds

A method which provides the possibility to connect the global characteristics of the interstellar medium with that of the young stellar population of the Galaxy is proposed.     

On the outer boundary of the sunspot penumbra

Comparison of photographic observations and vector-magnetograph measurements demonstrate that the outer boundary of the sunspot penumbra – even in complex sunspot groups – closely follows the 0.075 T iso-gauss line of the total value of the magnetic field, corresponding approximately to the equipartition value in the photosphere. Radio observations also show this feature. The thick penumbra model with interchange convection (Jahn and Schmidt, 1994) gives the best explanation of the penumbral structure. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1020985530075     

Interaction between the north-eastern boundary of Sgr A East and giant molecular clouds

We have detected the   v = 1 → 0 S(1) (λ= 2.1218 μm)  and   v = 2 → 1 S(1) (λ= 2.2477 μm)  lines of H₂ in the Galactic Centre, in a  90 × 27 arcsec²  region between the north-eastern boundary of the non-thermal source Sgr A East, and the giant molecular cloud (GMC)  M−0.02 − 0.07  . The detected  H₂ v = 1 → 0  S(1) emission has an intensity of  1.6–21 × 10⁻¹⁸ W m⁻² arcsec⁻²  and is present over most of the region. Along with the high intensity, the large linewidths  (FWHM = 40–70 km s⁻¹)  and the  H₂ v = 2 → 1 S(1)  to   v = 1 → 0 S(1)  line ratios (0.3–0.5) can be best explained by a combination of C-type shocks and fluorescence. The detection of shocked H₂ is clear evidence that Sgr A East is driving material into the surrounding adjacent cool molecular gas. The H₂ emission lines have two velocity components at ∼+50 and  ∼0 km s⁻¹  , which are also present in the NH₃(3, 3) emission mapped by McGary, Coil & Ho. This two-velocity structure can be explained if Sgr A East is driving C-type shocks into both the  GMC M−0.02 − 0.07  and the northern ridge of McGary et al.     

Radiation–hydrodynamical collapse of pre-galactic clouds in the ultraviolet background

To explain the effects of the ultraviolet (UV) background radiation on the collapse of pre-galactic clouds, we implement a radiation–hydrodynamical calculation, combining one-dimensional spherical hydrodynamics with an accurate treatment of the radiative transfer of ionizing photons. Both absorption and scattering of UV photons are explicitly taken into account. It turns out that a gas cloud contracting within the dark matter potential does not settle into hydrostatic equilibrium, but undergoes run-away collapse even under the presence of the external UV field. The cloud centre is shown to become self-shielded against ionizing photons by radiative transfer effects before shrinking to the rotation barrier. Based on our simulation results, we further discuss the possibility of H₂ cooling and subsequent star formation in a run-away collapsing core. The present results are closely relevant to the survival of subgalactic Population III objects as well as to metal injection into intergalactic space.     

The collapse of self-gravitating clouds of pure hydrogen

Exploratory models of the collapse of spherical self-gravitating clouds are studied in relation to the problem of the formation of first generation star-systems. The masses which were considered are in the range of 83 to 5.2×10¹⁰ M _⊙. For simplicity, the assumed composition includes hydrogen only, which could be in the form of H, H₂, H⁺ or H^?. Since the physical conditions that might have prevailed in a primeval nebula are not well known, rather simple initial conditions were chosen: The gas starts from rest and has initially a uniform temperature. We consider the case of rather cool (T ₀～100 K) neutral clouds with different initial ionization degrees. Some of the initial density-distributions here considered are uniform while others are decreasing from the center outwards. The assumed initial values for the densities are ～10^?24 g cm^?3, except for one of the models, for which it is ～10^?26 g cm^?3. Several atomic processes within the gas, including physical-chemical reactions and the evaluation of radiative emission coefficients are considered. A system of differential equations is set up in order to evaluate the concentrationsn _H,n _{H 2},n _H ⁺,n _H ^? andn _e as a function of time. The treatment makes possible the study of the cooling and heating properties of the gas. Furthermore, the dynamical, thermal and chemical evolution of the cloud can be followed during the collapse. The computations apply only to the optically thin stages. The models show the importance of a correct evaluation of the chemical reactions and dissipative mechanisms, which cannot be ignored in a realistic treatment of the collapse of self-gravitating clouds. The influence of the initial conditions on the dynamical and thermal properties during evolution are also analysed.     

Problems on gravitational collapse of interstellar gas clouds

The gravitational collapse of a spherically symmetric interstellar gas cloud has been investigated following the non-linear discontinuity waves propagation theory. It has been pointed out that macroscopic phenomena, such as the process of fragmentation, can arise (shock wave formation)-even in the case of spherical symmetry- at times smaller than the free-fall timet _ff, provided the initial data of the Cauchy problem be discontinuous within a sphere of radius (caustic cases). It has also been proved that strong discontinuities outside the mentioned sphere may generate critical timest _cr<t _ff (depending on the typical non-linear structure of the differential system). The cooling-heating function plays an important role in contrasting the formation of shock waves.     

Axisymmetric gravitational collapse of rotating interstellar gas clouds

Numerical calculations have been made of the gravitational axisymmetric collapse of isothermal gas clouds endowed with angular momentum. The evolutionary study is based on the so-called Fluid-in-Cell method coupled to an efficient algebraic algorithm which allows the Poisson equation to be integrated by means of block tri-diagonal matrices. The results, at ages slight larger than the initial free-fall time, indicate that flattened disk-shaped structures are formed in the central region of the clouds-in good agreement with the previous analytical results predicted by the authors.     

Comet formation in molecular clouds

The observed properties of the long-period comet system, and its periodic disturbance by galactic forces manifesting as terrestrial impact episodes, may be indicative of a comet capture/escape cycle as the Solar System orbits the Galaxy. A mean number density of comets in molecular clouds of ～10^?1±1 AU^?3 is implied. This is sufficient to deplete metals from the gaseous component of the interstellar medium, as observed, but leads to the problem of how stars are formed nevertheless with solar metal abundances. Formation of comets prior to stars in dense systems of near-zero energy may be indicated, and isotope signatures in cometary particles may be diagnostic of conditions in young spiral arm material.     

Turbulent motions in molecular clouds

We have studied the behavior of the inner motions of OH, H₂CO, and CO molecular clouds. This study shows the existence of two main components of these clouds: the narrow one, associated to dense small clouds and a wide one representing the large diffuse clouds seen in neutral hydrogen, the large clouds are the vortex and intermediate state between turbulent and hydrodynamic motions in the Galaxy.For the dense clouds with sizesd<10 pc we have found a relationship d ^0.38 consistent with the Kolmogorov law of turbulence; the densities and sizes of these clouds behave asnd ^–1. This last relation for these molecular clouds is compared with theHII one. Also, we discuss the effects of the inner magnetic field in these clouds.     

Small-scale clumping in molecular clouds

Summary This review consists of five sections. In the introduction, we briefly review the development of the study of molecular clouds. In the second section, we review the theories of molecular cloud structure and compare these predictions with the statistical properties of the clouds. In Sect. 3 we give an overview of current approaches to determinations of mass and local density in clouds. In the fourth part, we discuss the observations of a selected sample of individual sources. The emphasis here is on high resolution studies of regions of star formation. The final section contains a discussion of instrumental limitations and mentions some future developments.     

Evolution of collapse nonuniformity for rotating magnetic interstellar clouds

We investigate the formation and evolution of isothermal collapse nonuniformity for rotating magnetic interstellar clouds. The initial and boundary conditions correspond to the statement of the problem of homogeneous cloud contraction from a pressure equilibrium with the external medium. The initial uniform magnetic field is collinear with the angular velocity. Fast and slow magnetosonic rarefaction waves are shown to be formed and propagate from the boundary of the cloud toward its center in the early collapse stages. The front of the fast rarefaction wave divides the gas mass into two parts. The density, angular velocity, and magnetic field remain uniform in the inner region and have nonuniform profiles in the outer region. The rarefaction wave front surface can take both prolate and oblate shapes along the rotation axis, depending on the relationship between the initial angular velocity and magnetic field. We derive a criterion that separates the two regimes of rarefaction wave dynamics with the dominant role of electromagnetic and centrifugal forces. Based on analytical estimations and numerical calculations, we discuss possible scenarios for the evolution of collapse nonuniformity for rotating magnetic interstellar clouds.     

Gravitational collapse of polytropic, magnetized, filamentary clouds

For the case in which the gas of a magnetized filamentary cloud obeys a polytropic equation of state, gravitational collapse of the cloud is studied using a simplified model. We concentrate on the radial distribution and restrict ourselves to a purely toroidal magnetic field. If the axial motions and poloidal magnetic fields are sufficiently weak, we could reasonably expect our solutions to be a good approximation. We show that while the filament experiences gravitational condensation and the density at the centre increases, the toroidal flux-to-mass ratio remains constant. A series of spatial profiles of density, velocity and magnetic field for several values of the toroidal flux-to-mass ratio and the polytropic index, is obtained numerically and discussed.     

The formation of molecular clouds

In a recent paper, Elmegreen has made a cogent case, from an observational point of view, that the lifetimes of molecular clouds are comparable to their dynamical time-scales. If so, this has important implications for the mechanisms by which molecular clouds form. In particular, we consider the hypothesis that molecular clouds may form not by in situ cooling of atomic gas, but rather by the agglomeration of the dense phase of the interstellar medium, much, if not most, of which is already in molecular form.