First, equilibrium structure and maximum mass of a rotating isothermal cloud are described. Second, growth rate of fragmentation instability in an infinite disk and filament is presented. Finally, results of 2D and 3D simulations of collapse and fragmentation of rotating isothermal clouds are reviewed and comments are given.

The problem of gravitational collapse and star formation is entirely different when the ratio of the mass of a molecular cloud Mcl to its magnetic flux Φ is high than when it is low. Magnetically-diluted overall collapse of a large dense core and the formation of an OB association or a bound cluster are the likely outcomes in the former case; quasi-static contraction of many small cores and their ultimate collapse to form a T association, in the latter. In our picture, the birth of a T association in a dark cloud like Taurus proceeds by ambipolar diffusion on a time-scale of ∼ 107 years. As magnetic and turbulent support is gradually lost from a small condensing core, it approaches a state resembling a slowly rotating singular isothermal sphere which, when it passes the brink of instability, collapses from “inside-out,” building up a central protostar and nebular disk. The emergent spectral energy distributions of theoretical models in this stage of protostellar evolution resemble closely those of recently found sources with steep spectra in the infrared. The protostellar phase is ended by the reversal of the infall by an intense stellar wind, whose ultimate source of energy derived from the differential rotation of the star. We argue that the initial breakout is likely to occur along the rotational poles, leading to collimated jets and bipolar outflows. The stellar jet eventually widens to sweep out gas in nearly all 4π steradian, revealing at the center a T Tauri star and a remnant nebular disk. We give rough scaling relations which must apply if an analogous process is to succeed for producing high mass stars.

The gravitational instabilities are investigated for rigidly rotating isothermal gaseous disks with a magnetic field whose mean direction is parallel (case A) and perpendicular (case B) to the rotation axis. The linearized equation for the perturbation becomes an eigen value problem which is solved numerically. The stability depends on two non-dimensional parameters p2 ≡ B20/(4π2Gσ20) and q2 ≡ Ω20/(π Gρ0c) where B0, σ0, Ω0 and ρ0c are the magnetic field strength, the column density of the disk, the uniform angular velocity and the central density, respectively.

A theory for the sequential formation of OB stars in dense molecular clouds was first quantitatively investigated by Elmegreen and Lada (1976). The model was one-dimensional in nature and assumed shock propagation into homogeneous clouds. This picture has provided a successful explanation of the morphology of the Ori OB1 association.

Cloud-cloud collision has been regarded as one of the important mechanisms which triggers star formation. But a detailed analysis on the change of the critical mass has been absent due to the poor resolution of numerical experiments or limited by the assumption of a geometrical symmetry. We simulate the collisions between isothermal interstellar clouds using a three-dimensional hydrodynamic code (Smoothed Particle Method). The simulation in three dimensions gives us not only the criterion for the trigger of star formation but also the information about the origin of the interstellar cloud rotation and its initial distribution of angular momentum.

Accretion is a dominant factor in the early evolution of stars. The first time an accretion regime settles in is when a dusty opaque core forms. The mass of adiabatically contracting core inside the isothermally collapsing envelope depends only on the optical properties of dust. Spherically symmetric models of dusty cores were constructed using the Henyey technique with accretion boundary conditions (Menshchikov 1986). It appears that all protostars with normal chemical composition should pass through the stage of a quasistatic dusty core. The evolution of dusty cores is similar to that of “normal” young stars with accretion. One could distinguish convective, radiative and central core contraction phases. The life-time tc of the core depends on the core mass Mc and the accretion rate Ṁ (for Mc = 0.01 M⊙ and Ṁ = 1.6x10−6, 1.6x10−5 M⊙/year tc = 1.2x104, 3x103 yrs consequently). After dust exhaustion in the core it collapses and a central ionized quasistatic region grows in several tens of years. A flash of infrared radiation at the moment is not excluded.

The extended cloud complex containing members of the Gem OB1 association, the supernova remnant IC443, and the H II region S249 has been studied with IRAS observations at 12,25,60 and 100 microns and WSRT observations at 327 and 1400 MHz and in the 21-cm H I line. A skeleton-like framework of cool dust delineates the boundaries of the region, and physical parameters have been derived for the entire complex, individual H II regions and the shocked and recombined gas within IC443 using the radio and infrared data. IC443 is shown to consist of three interconnected, roughly spherical subshells of vastly different radii and centroids. The geometry is fully constrained by the structural and kinematic data. Two of the subshells together define the usually assumed boundaries of IC443, while the third includes the optical filaments which extend beyond the northeastern rim and which are shown to have well-correlated nonthermal radio components. The available evidence implies that the SNR shock has encountered a pre-existing high density shell. It is shown that the system of subshells is fully consistent with formation by stellar wind driven bubbles generated by association members within the inhomogeneous environment of the complex.

An analytical, theoretical, time-dependent initial mass function is derived for the objects created in the fragmentation of a gravitationally unstable gas protocloud. The mass spectrum depends on the chemical-dynamical-radiative evolution of the protocloud and it peaks at a mass slightly greater than the minimum Jeans mass attained throughout the evolution. A fragmentation rate mass spectrum is also analytically derived.

We propose a hierarchical model of large molecular complexes (mean density ∼ 10 cm−3, masses larger than 105 M⊙ relevant to their “cold phase”) which preceeds the formation of massive stars and H II regions, and investigate the gravitational stability of the different scales.

Supersonic turbulent motion of gas plays a significant role in the dynamics and physics of a cosmic gas cloud. One of the most important effects of the supersonic turbulence is a strong compression of the gas by shock waves, that may trigger the gravitational instability of the shock-compressed layer leading to the formation of stars.

The hydrogen molecule would work as an efficient coolant in a pre-galactic medium which is free from heavy elements. It is shown by linear perturbation analysis that molecular reactions lead to a thermal instability of condensation mode (Sabano and Yoshii 1977, Yoshii and Sabano 1979, Silk 1983). In the present paper we study the nonlinear growth of perturbations by a one-dimensional simulation of gas dynamics, which includes molecular reactions as well as an energy equation. We numerically follow the time-evolution of a spherically symmetric perturbation, which is superposed on initially uniform medium under free-fall contraction, by a Lagrangian hydrodynamical programme with an artificial viscosity (Richtmyer and Morton 1967).

In the light of the growing interest for the modes of formation of various astronomical objects, a relevant amount of data were collected and treated to obtain mass spectra. Statistical comparisons of the data suggest that a single process drives the formation of the various self-gravitating objects.

Growth of perturbations and fragmentation of isothermal sheet-like clouds are computed three dimensionally. An initial cloud is a self-gravitating equilibrium gas layer with small fluctuations, which have the form ei(kxk+kyy). The simulations of models with various values of kx and ky are performed.

Detailed calculations show that the two most important dynamical problems in the formulation of a theory of star formation (namely, the angular momentum and magnetic flux problems) can be resolved in that order by magnetic braking and ambipolar diffusion, respectively, relatively early during the collapse of an interstellar cloud or fragment. Although the physical processes involved are complicated and highly nonlinear and the formal solutions are mathematically nontrivial, they can often be elucidated by exact analogies with small-amplitude, transverse waves on strings, by a mechanical (or quantum mechanical) “leaky” system of N coupled oscillators, and by spinning coaxial metal disks joined by rubber bands and sharing (as well as losing to an external medium) energy and angular momentum (see Mouschovias and Morton 1985a, Astrophys. J. 298, 190; 1985b, Astrophys. J. 298, 205, Mouschovias and Paleologuo 1979, Astrophys. J. 230, 204; 1980, Astrophys. J. 237, 877).

The magnetic flux to mass ratio of an interstellar cloud is 104 to 105 times the ratio in a typical magnetic star with a surface field of 1kG, and is at least several hundred times the ratio in most strongly magnetic stars. This excess magnetic flux must be lost in some stage of star formation. The dominant process of magnetic flux loss in ordinary clouds is the drift of charged particles and magnetic fields in the sea of neutral particles (plasma drift, also called ambipolar diffusion). However, even this process is inefficient in a cloud of hydrogen number density nH ≲ 1010 cm−3.

The hypothesis that density waves trigger star formation is critically examined. Much of the former evidence in favor of the hypothesis is shown to be inconsistent with modern observations. A comparison between galaxies with and without density waves reveals no significant difference in their star formation rates. A new role for density waves in the context of star formation might be based on four principles: 1. density waves are intrinsically strong, 2. the gas is compressed more than the stars in the wave, 3. star formation follows the gas, with no preferential trigger related to the wave itself, and 4. regions of star formation are larger in the spiral arms than they are between the arms. This new role for density waves is primarily one of organization: the waves place most of the gas in the arms, so most of the star formation is in the arms too. The waves also promote the coagulation of small clouds into large cloud complexes, or superclouds, by what appears to be a combination of collisional agglomeration and large-scale gravitational instabilities. Special regions where density waves do trigger a true excess of star formation are discussed, and possible reasons for the difference between these triggering waves and the more common, organizing, waves are mentioned. Other aspects of large-scale star formation, such as the occurrence of kiloparsec-size regions of activity and kiloparsec-range propagation, are illustrated with numerous examples. The importance of these largest scales to the overall mechanism of star formation in galaxies is emphasized.

A variety of observations of molecular clouds outside the solar circle (mostly around R = 14 kpc) are reported. Maps of CO, 13CO (J = 1 → 0) and CO (J = 2 → 1) emission are discussed. Cloud sizes and masses range up to the GMC class. However, envelope kinetic temperatures are lower than those in GMCs in the molecular ring. Continuum observations, using the VLA at 6 cm and 20 cm, and far infrared observations, taken on the Kuiper Airborne Observatory, suggest the presence of newly formed late O and early B stars.

We present a galactic survey which to date consists of 47,000 positions covering −3° < l < 122°, −1° < b < 1°, observed in the J= 1→ 0 line of 13CO to an rms noise level of 0.15 K in 0.68 km s−1 channels, using the 7 m antenna at Crawford Hill. Maps made from the survey data show a clear difference between spiral arm and interarm regions. The signature of spiral structure on kiloparsec scales is the presence in galactic survey data of voids in l, b, v space which contain many times fewer Giant Molecular Clouds (GMCs) than do adjacent regions of similar size. The difference between arm and interarm regions in the inner galaxy is manifested only in the GMCs — small clouds are present throughout. These results are based on catalogs of clouds and their estimated sizes in 13CO. We suggest that GMCs are formed as interstellar gas enters a spiral arm, and that they break up into small molecular or atomic clouds as the gas leaves the arm.

The CO Galactic Plane Survey consists of 40,572 spectral line observations in the region between 1 = 8° to 90° and b = −1°.05 to +1°.05 spaced every 3 arc minutes, carried out with the FCRAO 14-m antenna. The velocity coverage from −100 to +200 km/s includes emission from all galactic radii. This high resolution survey was designed to observe and identify essentially all molecular clouds or cloud components larger than 10 parsecs in the inner galaxy. There are two populations of molecular clouds which separate according to temperature. The warm clouds are closely associated with H II regions, exhibit a non-axisymmetric galactic distribution and are a spiral arm population. The cold clouds are a disk population, are not confined to any patterns in longitude-velocity space and must be widespread in the galaxy both in and out of spiral arms. The correlation between far infrared luminosities from IRAS, and molecular masses from CO is utilized to determine a luminosity to mass ratio for the clouds. A face-on picture of the galaxy locating the warm population is presented, showing ring like or spiral arm features at R ∼ 5, 7.5 and 9 kpc. The cloud size and mass spectrum will be discussed and evidence presented showing the presence of clusters of giant molecular clouds with masses of 106 to 107 M⊙. The two populations of clouds probably have different star forming luminosity functions. The implication of the two populations for star formation mechanisms will be discussed.

The Magellanic Clouds, by their proximity, offer a unique opportunity to study the detailed processes of star formation in a galactic context. This Review examines the dynamic and self-limiting feedback between star formation and the interstellar medium (ISM) in these galaxies. Energetic processes associated with star formation are responsible for pressurising the ISM, for maintaining the multi-phase structure of this medium and for ejecting copious quantities of both hot and cool gas to large heights above the galactic mid-plane. This circulation process determines the control of the star-formation rate.