An analysis of the collapse and fission of the isothermal gas cloud examined by Boss and Bodenheimer (BB, 1979) has been made using SPH (Lucy 1977, Gingold and Monaghan 1977, 1978). While SPH is not as effective as finite difference methods for problems with spherical symmetry, it has the advantage in fragmentation problems that the description of the fragments is independent of their position and orientation. Furthermore, the SPH algorithm has been tested by applying it to non axisymmetric problems for which accurate solutions are known as well as spherically and axially symmetric problems.

The fission hypothesis suggests that close binary stars form due to global nonaxisymmetric instabilities in rotating, quasistatically contracting stars. We study this hypothesis by using an explicit, donor cell, finite difference 3-D hydrodynamic code with self-gravitation to follow dynamic two-armed instabilities in rapidly rotating polytropes. Typical grids are 32 × 16 × 16 in cylindrical coordinates and assume reflection symmetry about the equator plane and rotation axis. Initial conditions are obtained by applying density perturbations δρ = aρ cos 2ϕ with a = 0.10 or 0.33 to axisymmetric equilibrium models with the same angular momentum distribution but with various values of polytropic index n and of β = T/|W| where T = total rotational kinetic energy and W = total gravitational energy. We find dynamic growth of perturbations when β ≳ 0.30 for both n = ½ and 3/2. To within the limitations of our methods, this agrees well with the classical dynamic stability limit of β ≈ 0.274 for the bar modes of the Maclaurin spheroids. An unstable case with n = 3/2 and β = 0.33 is evolved for about ten initial central rotation periods. The part of the star inside corotation develops into a stable bone-shaped or dumbbell-shaped structure after about three pattern rotations. At about the same time, material outside corotation is ejected in the form of two trailing spiral arms. These arms wrap due to differential rotation, merge into a detached disk, and eventually narrow into a radially expanding ring with slight cos 2ϕ density enhancements. The ring contains 16% of the mass but more than half the angular momentum. The central bone-shaped object is an analog of the Riemann S-type ellipsoids. Fluid circulates dynamically and stably from one knob of the bone to the other. In this sense, the object is probably better described as a triaxial star than as a contact binary. Similar behavior is exhibited by an extensive n = ½ and β = 0.33 evolution. This work was supported by U.S. National Science Foundation Grant AST-7821449.

The scenario begins with two spherical masses of Roche radii, as given by Paczynski (1971), at a separation of centers, A. The mass flows from the initially more massive star a in rapid rotation to its companion b. The separation changes in accordance with the conservation of orbital angular momentum. The corresponding Roche radius of b is considered to be its radius. The luminosities of the stars are given in the approximate expressions following Schatzman (1963) for convective or radiative equilibrium. The luminosity of b determines the time for a given mass transfer with the use of the virial theorem. This time step and the virial theorem, then, determine the change of the radius of a. The angular speed of a is maintained such that the centrifugal and gravitational accelerations are equal at the equator. If the total angular momentum of the system is conserved, the angular momentum of b can be computed. Initially, b is considered to rotate in synchronism with the orbital revolution. The mass transfer stops when the centrifugal and gravitational accelerations become equal at the equator of b, or when the change in potential energy becomes zero. In the table, Sf is the ratio of final rotational and orbital angular speeds; t is the time interval in 103y; initial Ma is 3 solar masses; Mbi = 0.7 for part 1, and Ai = 32.2 solar radii for part 2.

A timetable for an evolutionary sequence of processes, which begins with the formation of the solar nebula being nearly in equilibrium and ends with the planetary formation, is presented. Basic features of the processes and grounds for the estimation of time-scales are explained for each of the processes.

Biermann (1979) has revived the earlier suggestion of Cameron and of Donn that the proto-cometary cloud and the proto-solar nebula were contiguous but distinct cloudlets, forming e.g. as fragments within the same massive interstellar cloud. As in Goldreich and Ward (1973) and Biermann and Michel (1978), the cometesimals are thought to have formed in a layer of dust that settled in the equator of a cloudlet maintained at a moderate density by a combination of thermal pressure and centrifugal force due to a high angular momentum. The solar nebula had much less angular momentum and so could contract to about the radius of Pluto's orbit before achieving centrifugo-gravitational balance. In this paper it is noted that modest variations in the initial parameters of fragments forming within the same massive magnetic cloud can yield both high and low angular momentum cloudlets (Mestel and Paris 1979). A fragment of mass M greater than a critical mass Mc, defined in terms of its magnetic flux F by GM2c~F2/π2, contracts in approximate mechanical equilibrium, at the rate determined by the magnetic transport of angular momentum, and with centrifugal force remaining comparable with gravity. Rapid flux-loss at molecular cloud densities leaves a weakly magnetic, rapidly rotating, low-density cloudlet which could be the locale of cometary formation. If M<Mc, the magnetic stresses both limit contraction and enforce corotation with the surroundings. As flux leaks out slowly, the cloudlet contracts in approximate magneto-gravitational equilibrium, with centrifugal forces becoming a steadily smaller fraction of gravity. At the molecular cloud phase, rapid flux-loss leaves now a slowly rotating cloudlet, which can therefore become the proto-solar nebula. Whether a cloudlet is super- or sub-critical in mass will depend on the details of the fragmentation process in the parent cloud, in particular on the amount of mass agglomeration down the field-lines.

Of the formation processes of the solar system, the process of growth and sedimentation of dust particles in the primordial solar nebula is investigated for a region near the Earth's orbit. The growth equation for dust particles, which are sinking as well as in thermal motion, is solved numerically in the wide mass range between 10−12 g and 106 g.

The structure of a gaseous envelope surrounding a icy/rocky core is studied in consideration of radiative transfer. It is found that when the core grows beyond a critical core mass, the envelope cannot be in equilibrium and collapses onto the core to form a proto-giant planet. The results are as follows (for details, see Mizuno 1980).

1) The critical core mass is smaller than that estimated by Perri and Cameron (1974) and Mizuno, Nakazawa and Hayashi (1978). 2) When the grain opacity in the envelope varies from 0 to 1 cm2/g, the critical core mass changes from ~2 to ~12 Earth's masses. 3) The critical core mass is independent of the region in the solar nebula.

These are due to the existence of the radiative region in the envelope.

When the Earth had grown to the present mass through accretion of the planetesimals in the solar nebula, the Earth was surrounded by a dense primordial atmosphere which was mainly composed of hydrogen and helium (Hayashi et al. 1979). Mass of the atmosphere was about 1×1026 g. We investigate the dissipation of this atmosphere due to the irradiation of solar EUV. The effect of solar wind is neglected. We assume that the flow of the escaping gas is spherically symmetric and steady. We impose the boundary condition that the flow velocity go through a sonic point. The results show that the primordial atmosphere is dissipated within a period of 5 × 108 yrs, which is the upper limit imposed from the theory of the origin of the present terrestrial atmosphere (Hamano and Ozima 1978), as far as the solar EUV flux is more than two hundred times as large as the present one. In this case, the rare gases contained in the promordial atmosphere are also dissipated owing to the drag effect (Sekiya et al. 1980).

Most stars of our Galaxy's disk are double. The existing estimation of duplicity αα range from ~ 50-70 % (Abt, Levy, 1976, Abt, 1979) to ~ 100 % (Kraitcheva et al., 1978). About half of all stars are close binaries (CB) and hence their components fill their Roche lobes during evolution. This accounts for the constantly increasing interest to their evolution. Several review papers were published in the last years: Paczynski (1971), Tutukov et al. (1975), van den Heuvel (1976), Massevitch et al. (1976), Thomas (1977), Paczynski (1979), Webbink (1979b), Yungelson and Massevitch (1980). The subject matter of close binary evolution is very wide now, therefore, I will limit myself to the review of modern scenarios for evolution of massive (M ≳ 10 M ⊙) close binaries (MCBS) and close binaries of moderate (M ≲ 10 M⊙) mass.

The various ways in which compact objects (neutron stars and black holes) can be formed in interacting binary systems are qualitatively outlined on the basis of the three major modes of binary interaction identified by Webbink (1980). Massive interacting binary systems (M1 ≳ 10–12 M⊙) are, after the first phase of mass transfer expected to leave as remnants:

(i) compact stars in massive binary systems (mass ≳ 10 M⊙) with a wide range of orbital periods, as remnants of quasi-conservative mass transfer; these systems later evolve into massive X-ray binaries.

(ii) short-period compact star binaries (P ~ 1–2 days) in which the companion may be more massive or less massive than the compact object; these systems have high runaway velocities (≳ 100 km/sec) and start out with highly eccentric orbits, which are rapidly circularized by tidal forces; they may later evolve into low-mass X-ray binaries;

(iii) single runaway compact objects with space velocities of ~ 102 to 4.102 km/sec; these are expected to be the most numerous compact remnants.

Compact star binaries may also form from Cataclysmic binaries or wide binaries in which an O-Ne-Mg white dwarf is driven over the Chandrasekhar limit by accretion.

We present new spectroscopic and photometric observations and discuss a small but important group of rapidly rotating G - K giants (FK Com=HD 117555, UZ Lib=BD−8°3999, HD 199178 possibly others) which are photometrically variable, show slightly redshifted and variable Ca II H and K emission and variable Hα emission, show rotationally broadened spectral lines (50–100 km/s), and yet show no large radial velocity variations. Possible explanations of the properties of these stars are discussed and coalescence of a W UMa binary system seems to be the most probable evolutionary state.

The most extreme of the group, FK Com is discussed in detail. Its type, G2IIIa (Keenan, priv.comm.) implying MV=−1 (the IR indices are consistent with a giant) suggests a reduction of log g (relative to Sun) −1.5 to −2.5; this can be only marginally reconciled with the dimensions of about 5 Ro resulting from the photometric period 2.4 d. and Vrot sin i about 100 km/s. The photometric variability (0.05 in I, 0.07 in R) is most probably due to spots asymmetrically distributed in longitude. The brightness minima observed by Chugainov in 1966 and 1974 and the new minimum observed in 1979 (JD 2443949.025) can be phased with one period 2.3995±0.0002 d. The erratic behavior of rotationally broadened spectral lines precludes obtaining a radial velocity orbit but an upper limit of 25 km/s for any periodic variations implies that the secondary must be a very low mass object. The strong Hα emission is variable in relative intensity of its double peaks but has a constant full width in excess of 20 A. The full half width at base implies rotational velocities of the order of 570 km/s; the half separation of peaks implies 300 km/s. Existence of an excretion disc of the type suggested by Webbink is possible.

When mass is transferred between the two components in a close binary system, the matter falling towards the secondary star can gain a considerable amount of angular momentum. Eventually a ring or disk around this star is formed. The star can increase its angular momentum by accreting part (or the whole) of this matter. We have examined the ensuing changes in rotational velocity of the mass-accreting star. A simplified calculation (assuming accretion from a ring, rigid rotation of the star, and taking the stellar radius as well as its radius of gyration constant) shows that the star reaches its break-up velocity after increasing its original mass by only a few percent.

Some fundamental problems connected with the evolution of W UMa stars are considered. While no generally accepted theory for the evolution of these systems exists, different scenarios lead to single stars on a nuclear or thermal time scale, or even to dwarf novae. The cycling and contact discontinuity models for zero age systems have gained much attention during the last few years. The contact discontinuity hypothesis has been heavily criticized on physical grounds, and the cycling at small mass ratios will probably be too violent leading to overcontact. On the other hand, there is increasing evidence of strong magnetic activity in short period solar type binaries, including W UMa stars (spots, flares, strong chromospheres and coronae etc.). This points to enhanced dynamo action inside rapidly rotating components of solar type close binaries. Extrapolating from single stars one finds that this may efficiently brake the orbital rotation. With an angular momentum loss rate of about 1043 g cm2 s−1 per year corresponding to the thermal time scale of the secondary the scenario, where the angular momentum loss controls the zero age contact evolution, seems at least possible. This scenario needs an (hypothetical) equilibrium process between the degree of contact and magnetic activity, damping the angular momentum loss if the contact becomes too thick, so that marginal contact will be preserved. If the angular momentum loss time scale is longer (comparable to the nuclear time scale of the primary), the system is likely to evolve towards more extreme mass ratios and with less violent cycling. (The complete paper will be published elsewhere.)

The general evolutionary pattern of massive O type close binaries evolving according to a case B mode of mass transfer, including mass loss by stellar wind prior to Roche lobe overflow (RLOF) at rates appropriate for O type stars, only marginally depends on the choice of the initial chemical composition whether the galactic or the MC abundances are used (the difference never exceeds 10%). The theoretical results are compared to the observations, O type binaries describing the evolutionary phase prior to RLOF, WR type binaries describing the helium burning phase after RLOF. The large mass loss by stellar wind in WR stars considerably affects the evolution during the latter phase. The comparison yields the following conclusions:

a) from the ZAMS up to the WR stage, 50%-60% of the initial primary mass is leaving the system corresponding to at least 70%–80% of the total mass lost by the primary due to stellar wind and RLOF;

b) during the WR phase the star is losing approximately half of its mass;

c) the average mass ratio for binaries prior to the supernova explosion equals 3, i.e. the exploding star is 3 times less massive than its companion.

The WR binary systems, consisting of a WR star and an O or B star companion, are supposed to be the progenitors of the massive X-ray binaries. The missing link is generally accepted to be the SN explosion of the WR star which leaves a pulsar remnant. As most pulsars originate from single stars, observations of their proper motions indicate that they receive at their birth a “kick” velocity of about 100 km s−1. We assume this velocity to be due to the asymmetry of the SN explosion. This asymmetry, together with the loss of the SN shell and its impact on the OB star, may cause to disrupt the remaining system.

For the ten best known WR binaries we evaluated the survival probability P after an instantaneous SN explosion, leaving a 1.5 M⊙ collapsar with a random orientated kick velocity of 75 kms−1 (case a) and 150 kms−1 (case b) respectively. The influence of the impact is found to be marginal. The run-away velocity of the remaining system and of the disrupted OB star are comparable and of the same order of magnitude, but smaller than the initial orbital velocity of the OB companion; which decreases for increasing values of the initial orbital period. They are found to be independent of the kick velocity.

Evolutionary changes of masses and periods under the influence of gravitational radiation (GR) are computed for binaries with main-sequence or degenerate hydrogen-helium (H), helium (He) and carbon (C) secondaries. Tracks in the P-M2 and P-M2 planes are determined. The orbital period of systems P with a non-degenerate dwarf filling its Roche lobe decreases until the time-scale of GR (~ 109−1010yrs) becomes shorter than the thermal time-scale τKH of the mass losing component M2. When M2 becomes ~ 0.1 M⊙, P begins to increase. This could account for the existence of the minimal P ≈ 1.3h and for the accumulation of observed cataclysmic binaries (CB) below P ≤ 2h. The GR can be the driving force for evolution of cataclysmic binaries: TT Ari, OY Car, Z Cha, and WZ Sge as their P, M2 and indicate. The rate of mass exchange driven by GR is ~ 10−9−10−10 M⊙/yrs. It is enough to feed the X-ray bursters and related objects.

The existence of blue stragglers in old open clusters with apparent mass more than twice the mass of the turnoff argues against simple binary mass transfer as the mechanism of their origin. The excess of blue stragglers to the red of the termination of the core hydrogen burning main sequence suggests that blue stragglers are not evolving normally. Stellar evolution models invoking mixing in an extended core region can account for the distribution of blue stragglers in the H-R diagram. Such models live longer, brightening and evolving further to the red before core hydrogen exhaustion than do normal stars. The distribution of blue stragglers in NGC 7789 is consistent with a range of mixed core mass fraction ~30–90 per cent and a narrow range in mass ~1.7–2.1 M⊙. Such evolution will result in a class of helium rich stars which have lived longer than normal and whose total mass exceeds the Chandrasekhar limit.

Shell flashes take place both in deep interior of red giant stars and near surface of accreting white dwarfs. Theories of shell flashes have been thus far presented piece by piece in different papers. It is the purpose of the present review to construct and generalize them in order to reach better understanding. A non-linear yet almost analytical theory is presented which treats the development of the shell flash in finite amplitude. Recurrence of the shell flashes is also shown to be well understood as a non-linear oscillation in dissipative system which tends to be its limit cycle. As a result strength of the peak energy-generation and recurrence time of the shell flashes are related with mass of the accreting white dwarfs, accretion rate, etc.

The observed properties of X-ray burst sources have recently been reviewed by Lewin and Clark (1980) and Lewin and Joss (1980). About thirty-five such sources are presently known, and they have a spatial distribution reminiscent of stellar Population II (see Figure 1). The salient features of these sources include burst rise times of ≲ls, decay time scales of ~3–100 s, peak luminosities of ~1039 ergs per burst, spectra that can generally be well fitted by blackbody emission from a surface with a constant effective radius of ~10 km and a peak temperature of ~3 × 107 K, and “tails” of softer X-ray emission that may persist for several minutes after the burst maximum. Profiles of bursts from some typical burst sources are shown in Figure 2. The intervals between bursts from a given source may be regular or erratic and are typically in the range of ~104−105 s; many sources undergo burst-inactive phases that can last for weeks or months. Most burst sources are also sources of persistent X-ray emission, and the ratio of average persistent luminosity to time-averaged burst luminosity is typically ~102 during burst-active phases. (The properties of the “Rapid Burster,” MXB1730-335, are different from those of all other known burst sources and will be discussed separately in §VI below.) There are few correlations among the burst flux, burst intervals, and persistent X-ray flux from any given source, and the detailed burst shapes vary from one source to another and often vary with time in a given source.

Thermal stabilities of hydrogen and helium shell-burnings on accreting neutron stars are studied semi-analytically, the progress of nuclear reactions during the flash is followed numerically, and the mechanism which makes different modes of Type-I X-ray bursts is discussed.