Observations of molecular clouds show evidence of rotation and of fragmentation of subregions of the clouds into multiple stellar or protostellar systems. This review concentrates on the effects that rotation and pressure gradients have in a self-gravitating cloud to cause it to undergo the crucial process of fragmentation. Recent two-dimensional and three-dimensional numerical hydrodynamic calculations have made progress in determining these effects. In most cases the calculations are performed with modest spatial resolution and are limited to isothermal clouds with neglect of viscous and magnetic effects. The combined results of several calculations strongly suggest that rotating clouds that are unstable to collapse are also unstable to fragmentation.

We review the role of the interstellar magnetic field: (i) in the formation of interstellar clouds; (ii) in determining critical states for gravitational collapse; (iii) in affecting the collapse and fragmentation of interstellar clouds; and (iv) in resolving the “angular momentum problem” during star formation. Finally, we review the manner in which the field decouples from the matter via ambipolar diffusion; new time-dependent solutions are discussed.

A protostar with sufficient magnetic flux can be in quasistatic equilibrium. The structure at the time t of such an axisymmetric protostar immersed in a medium of finite pressure is determined when the mass m(ϕ, t) in each axisymmetric magnetic tube with the flux ϕ is given. A new distribution m(ϕ, t+δt) is found by calculating the amount of matter which crosses the surface of the magnetic tube ϕ in a time δt due to plasma drift (ambipolar diffusion), and then the structure at t+δt is determined. By repeating this procedure we can follow the quasistatic contraction of a protostar. Here we take into account the effect of charged grains in addition to ions upon the plasma drift.

The magnetic flux through an interstellar cloud or through a part of the cloud must decrease considerably by the drift of plasma and magnetic field in order that stars form in the cloud. Because most grains are negatively charged in dense clouds (Elmegreen 1979; Umebayashi and Nakano 1980), they retard magnetic flux leakage in addition to ions (Elmegreen 1979). We investigate this effect for different situations and obtain the following results (for details, see Nakano and Umebayashi 1980):

1. 1. For nearly spherical clouds of mass ≳ 103M⊙ sustained by magnetic force the friction of grains is efficient at nH⊙ ≳ 105 cm−3, and the magnetic flux leakage time tB is greater than a few million years at any density. Grains drift as fast as ions and electrons.

2. 2. For spherical clouds of smaller mass and disk-shaped clouds, tB becomes much smaller and the drift of grains is much slower than ions and electrons at nH ≳ 106 cm−3.

3. 3. Thus magnetic flux leakage occurs mainly in the condensations described in 2, and the abundance of heavy elements in stars deviates little from that of the parent clouds because of small grain drift.

VLBI observations have revealed that OH/H2O maser sources are the aggregations of blobes with the sizes of a few A.U., spreading over the distance of several 1017 cm. From the standpoint of masing mechanism, especially for the hydroxyl case, we will argue that the blobes correspond to proto-stars in the stage of forming an opaque core, and the aggregations correspond to proto-clusters.

Evolution and fragmentation of a gas cloud are investigated for the primordial chemical composition which is the same as the products of the Big Bang. A pure-hydrogen gas cloud collapses isothermally at 500–1000 K when a low fraction of molecular hydrogen works as a coolant, and breaks into small subcondensations with mass less than 10 M⊙ due to thermal instability associated with molecular dissociation. On the other hand a pure-hydrogen gas cloud which contains no molecular hydrogen collapses isothermally at 6000–8000 K in a thermally stable condition, and enters the region where thermal energy exceeds radiation energy when thermal equilibrium between matter and radiation is achieved in the cloud. Consideration of energetics in the subsequent stage of the cloud evolution leads to the mass range of 0.1–20 M⊙ for the stable nuclear-burning protostars of the first generation. The thermal behavior of a gas cloud in the regime of z (the ratio of heavy element abundance to solar one) less than 10−4 is essentially similar to that in the case of no heavy element, and the heavy element cooling brings about thermal instability in a wide range of parameters in the regime of z greater than 10−3. Linear perturbation analysis gives growth time of the instability much shorter than the free-fall time, and suggests the efficient excitation of density fluctuation driven by thermal instability. Thus the possibility of the initial mass function relatively enhanced in massive star at early times is denied, and the slow rate of metal enrichment in the interstellar medium is suggested.

The evolution of massive clouds is discussed with emphasis on inhomogeneous and heterogeneous nature of the system. We start from the two-phase model of interstellar medium and choose initial conditions of the clouds as being in the vicinity of critical state for gravitational instability. The equilibrium and stability problem for clouds is formulated in terms of polytropic models. Combining this with the thermal and chemical balance problem, we find that, even before the commencement of gravitational collapse, the fragmentation due to thermal instability can occur. The system begins to contract at a rate much slower than free fall, and thereafter, its evolution is governed mainly by collisions between fragments. The collision dynamics of the N-fragment system should be examined carefully by numerical experiments. The general trend to be expected is that the system tends to develop into a core-halo structure, accompanying by sporadic local events of star formation. The core or a clustering of massive fragments near the center could grow up into a favourable formation site of star clusters.

A new type of non-linear, chain reacting instability is presented that a sequential condensation occurs in a thermally unstable interstellar CO cloud, triggered by a local density perturbation. Non-linear growth of the instability was followed numerically with a one-dimensional and slab symmetric hydrodynamical code. The result shows that a local, small density enhancement onto initial density of n0=510 cm−3 around x=0 (x: spatial coordinate) grows to a maximum density of nmax=1300 cm−3 in a time scale of 0.6×106y, and at the same time the gas in neighbouring region at x=0.1–0.2 pc shifts into a low-density phase of nmin=200 cm−3. Since we assume a constant heating per particle by photons and cosmic rays, the gas in low density region is relatively more heated so that the pressure therein becomes higher than the background pressure. Then the low density gas pushes its neighbouring gas foward increasing x to lead to a second density enhancement at x=0.2 pc. In this way many further condensations are produced in a sequential manner. The spacings and sizes of condensations are uniquely determined by the characteristic parameters, the growth time of instability and the sound velocity of the background gas alone. The present calculation gives the spacing, 0.24 pc, and the mass of each fragment, 0.2M⊙. This mechanism could be related to sequential formation of less-massive stars in interstellar CO clouds, if the condensations evolve further into star formation sites.

Assuming that the interstellar medium (ISM) is composed of the hot ionized medium (HIM), the warm ionized medium (WIM) and the cold neutral medium (CNM), we examine the interchange processes among them by supernova remnants. These are the evaporation of CNM, the shock heating of WIM and the cold shell formation at the shock front. Calculating the time variation of each component, the timescale and evolutionary characteristics till attaining a steady state are deduced. Generally speaking, the final steady state is classified to two types.

The speed and storage capacity of present-day computers have stimulated the development of numerical techniques allowing the investigation of three-dimensional gas dynamical problems of astronomical interest. Of the problems that can be attacked with these techniques, that of the formation of binaries has historically attracted the greatest interest. Several investigators have therefore tackled this problem, and their efforts will be discussed here insofar as they relate to the formation of close binaries. Earlier work, including the classical investigations of Kelvin, Poincaré, Jeans, and Cartan, have been reviewed by Chandrasekhar (1969) and Tassoul (1978).

The problems of the stellar evolution to the main sequence are reviewed, taking into account the effects of mass loss, rotation and binarity. Properties of T Tauri stars are discussed which are connected with the recent observations of these stars in ultraviolet and X-ray regions. FU Ori phenomen is considered briefly.

The Orion Nebula is a recent star formation place on a sequence of star formation in the Orion Association Ia to Id and further to the Orion Molecular cloud as shown by Kutner, Tucker, Chin, and Thaddeus (1977). From the photoelectric observations, Penston (1973, 1975) obtained the age of the Nebula younger than 3×106 years.

Monitor observations of the SiO v=1, J=2−1 transition were made toward the Kleinman-Low infrared nebula. Observations were made from September 1976 to February 1980 with the 6 m mm-wave telescope of the Tokyo Astronomical Observatory. Data were taken with an acousto-optical spectrometer with a frequency resolution of about 50 kHz(Δv=0.17 km s−1).

During last three decades an observational approach was being applied at the Byurakan Astrophysical Observatory to the problems of the evolution of astronomical bodies and systems. In contradiction to the views developed by many theoreticians who postulate as an initial state of each body or system a gaseous nebula of some kind and suppose that the processes of condensation are dominant in the Universe this approach makes use of the observed predominance of expansions, ejections and explosions.

In simulations of the collapse of gas clouds it is usual to start from a uniform sphere the evolution of which is determined by the two energy ratios = Thermal/Gravitational and = Rotational/Gravitational. In numerical calculations the two parameters are unfortunately supplemented by a number of unknown factors related to the exact numerical treatment of the collapse. It is therefore crucial to compare the results of several different methods before any judgement is made concerning the correct evolutionary track of the cloud.

The influence of angular momentum transport by turbulent friction on the structure of a rotating protostar has been investigated. Turbulence is characterized by a simple viscosity parameter η = ξ·cs·1, where cs denotes the local speed of sound, 1 the typical length scale of the largest eddies (thickness of the nebula) and ξ the “efficiency” parameter (= 1/10 in our model).