Brief reviews of the classical ‘angular momentum problem’ and the statistics of upper-main-sequence binaries are presented as background for the suggestion that the close, early-type, binaries are produced by fission of rapidly rotating protostars.

Next, theoretical sequences of contracting, rotating stars are described. Recent work demonstrates that the zero-viscosity, polytropic sequences, have essentially the same properties as the McLaurin sequence. Thus, fission is possible for centrally condensed stars. Observations of close early-type binaries are compared with theoretical predictions for the minimum angular momentum in binary systems of given total mass; the agreement is excellent.

Finally, the existing theoretical objections to the fission hypothesis for the origin of binary stars are reviewed, and it is concluded that, although fission remains unproven, there are now no strong theoretical arguments against the process, and there is considerable observational support for its existence.

An extension of the method devised by Monaghan and Roxburgh (1965) for rapidly rotating polytropes is used to study the structure of the primary component of a synchronous close binary system. Results are presented for polytropes of index 1.5, 2.0, 3.0, 4.0 and 4.9. We conclude that the extended Monaghan and Roxburgh method can be applied to real stars which are perturbed by both tidal and rotational forces.

A method for testing the possible correlation between axial rotations of pairs of stars is developed. The test is applied to a sample of visual binaries. It is concluded that some kind of coupling between the spins of components of visual binaries does in fact exist.

Newly determined rotational velocities of the main-sequence components of 14 Algol-type semi-detached systems and of 2 detached systems are presented. Combination of these data with the existing data on the rotation of the components of semi-detached systems shows that (i) in systems with primaries of spectral type B8 or later and with P<5 days, deviations from synchronism between rotation and revolution are small in 14 out of 15 cases. The average rotational velocity of the primaries in such systems is 75 km/sec, viz. only 40% of the average rotational velocity of single main-sequence stars in the same spectral region: (ii) primaries of spectral type earlier than B8 in systems with short as well as long periods tend to rotate more than twice as fast as one would expect from synchronism. A tentative explanation for these results is presented.

Calculations show that a significant variation in the minima of eclipsing binaries should arise for systems where axial precession exists. Several different angular velocity distributions are assumed in order to estimate the expected photometric variation as a function of the model parameters. It is found that the solid body rotation approximation is a reasonable representation unless interiors rotate more rapidly than present models predict.

The characteristics of rotational velocities in fifteen open clusters and associations are summarized. The differences in mean rotational velocities observed between individual groups are found to be due primarily to three mechanisms: evolutionary expansion, tidal coupling of rotational and orbital motion in binaries, and magnetic braking in Ap stars.

Calibration of four-color and Hβ photometry, in terms of intrinsic color and absolute magnitude, for the B-, A- and F-type stars is about finished, though still subject to small changes. The data for the bright stars in the northern and southern hemispheres and for a number of the brighter open clusters were used in obtaining these calibrations. Some of the data have been published; much more of it will be going to press shortly. The calibration is interesting not only for itself and its applications, but because deviations from it may be due in part to rotational velocity effects.

For stars in the main-sequence band, the distributions of ‘line-widths’ Ksin; are rediscussed, with the inclusion of recent measurements by Walker and Hodge for B stars, and by Preston for Ap stars. The Ap stars are counted with normal stars of the same color-class. Over the whole range from B2 to A2, the observed incidence of sharp-line stars far exceeds the incidence predicted on the hypothesis that the true rotational velocities have a Maxwellian distribution. The ‘extra’ slow rotators are probably close binary remnants, in the sense of Van den Heuvel. However, it remains unclear how to distinguish individual members of this group of stars.

Based upon the statistics of V sini among A-type stars it is shown that (1) no relationship exists between rotational velocity and UBV colours, (2) there might be an influence of rotation upon spectral classification, and (3) spectroscopic binaries are associated with low rotational velocity.

This paper develops a new statistical approach to the study of the axial rotational velocities of the stars, by considering the break-up limit or any upper limit for the equatorial rotational velocities. The main conclusions are as follows: (1) For random orientation of the axis of rotation, the frequency function of the inclination α to the line of sight is not sina, as assumed until now. (2) For stars with the same break-up velocity vb, the distribution of α is given by :

where f(y) is the distribution of the apparent velocities y = v sin α, v being the true rotational velocity. New integral equations governing the frequency function of α, y and v have been derived and the correct procedure to treat observations has been discussed; a simple method is also suggested to get an approximate trend of the distribution of the true velocities directly from the observed histogram. The method of analysis proposed in this paper has been applied to a re-discussion of the rotational behaviour of a group of Be stars.

The upper limits of flare star rotational velocities are evaluated from the photometric features of the stars and on the basis of the widths of the Ha emission line in the quiet chromospheres. The rotational velocity of UV Cet does not exceed 22 km/sec, YZ CMi: 37 km/sec, the value v sini of AD Leo does not exceed 52 km/sec, and that of EV Lac: 25 km/sec.

Deutsch’s period vs. line-width relation for the periodic Ap stars is re-examined from the point of view of the rigid rotator with the aid of recently determined values of v sin i for these objects. The agreement between computed rotational velocities and observed values of v sin i is satisfactory if the radii of the Ap stars are twice those of zero-age main sequence stars of the same color. The computed rotational velocities also agree with the mean rotational velocities of all Ap stars if suitable allowances are made for observational limitations. However, a difficulty arises in connection with the number of ‘long-period’ stars that have been discovered. Their small computed rotational velocities and their frequency are such that they cannot be regarded as part of any rotational distribution function that describes normal stars or even most Ap stars. It is concluded that if the periods of these objects are rotational periods, then a powerful rotational deceleration mechanism must be operative in at least some Ap stars, primarily those of the SrCrEu group.

All observations of magnetic stars necessarily yield information only about their surface features. We are ignorant of the nature of the fields in the interiors of such stars, and equally we cannot be sure of the non-existence of interior fields in stars which are superficially non-magnetic. In fact, if we assume the truth of the ‘fossil’ theory – that the magnetic flux of an Ap star is a relic of the flux initially present in the gas cloud from which the star condensed – then it is surprising that magnetic stars are not observed to be much more common, since magnetic fields appear to be ubiquitous in interstellar gas clouds. For those stars with strong surface convection zones, we might expect that a fossil field of low energy would be expelled by the turbulence and would possibly be trapped in the interior. However, the majority of early-type stars with radiative envelopes also do not exhibit any observable magnetic field.

This work investigates the dynamical evolution of a rotating magnetic star which drives a stellar wind. The basic magnetic field of the star is supposed symmetric about an axis, which is inclined at an angle X to the rotation axis k (Figure 1). We adopt the familiar equations of an inviscid perfectly conducting gas. In a steady state, the velocity as seen in a frame rotating with the star is taken as

When I prepared the discussion in the subsequent sections I did not realize just how subject to question were certain basic ideas relating to the interpretation of the Be phenomenon. In view of the points already raised in the course of this Colloquium, I should like to preface my prepared remarks with certain additional ones.

There appears to be little question that the Be phenomenon has important things to tell us of stellar rotation. It appears almost equally clear that too superficial an approach could well lead to invalid conclusions at any one of a number of points. Some caution therefore, appears advisable. Nevertheless, there appear to be a number of reasons for believing that a relatively simple rotational interpretation of the phenomenon rests on much more solid ground than does any other yet put forward.

A period of 0.7 days has been found in the peak separation and VIR ratio of the double emission profiles of Hγ and Hβ in this star. The phenomenon is believed to arise from short lived condensations near the base of an equatorially extended atmosphere, and the period to be that of rotation of the star. The deduced stellar diameter is 7 R⊙. Further considerations on the emission line profiles lead to a model of an equatorial ring extending 1-2 stellar radii with angular velocity decreasing outwards, and viewed at an axial inclination of some 60°.

The author’s 1964 article in Nature on the sun’s rotation is rediscussed in the light of new data. This article suggested that the sun might be oblate because of a gravitational quadrupole moment induced by a core rotating with a period < 2 days. Angular momentum lost from the core by molecular diffusion was assumed to be transferred to the solar wind which kept the sun’s surface rotating slowly. The estimated solar wind torque was found to be in good agreement with the torque calculated from a solution of the diffusion equation.

The interaction of rotation and turbulent convection gives rise to a latitude dependent turbulent energy transport. Energy conservation demands a slow meridional circulation in the solar outer convective zone. The transport of angular momentum by this circulation is balanced in a steady state by the turbulent viscous transport across an angular velocity gradient. Models are constructed which give equatorial acceleration as observed on the sun.

The problem of determining the spectroscopic rotation of the sun is not one of instrumental sensitivity, which can be about 10 m/sec, but rather of abstracting the rotational component from the hierarchy of long-lived surface currents. Required are continued daily observations over long periods of time and this task is not presently feasible at most observatories. Past observations have indicated a height gradient of rotational angular velocities. We have determined the photosphere and chromosphere angular velocity gradient from observations across the disk of C 5380 Å(h≃ -250 km), CN 3882 Â (h ≃ 0 km), Ca+K3(h≃+ 5000 km), together with other Fraunhofer lines of intermediate origin while K-line spectra of prominences are used to sense the chromosphere-corona interface.

As the simplest model to simulate the solar spin down procedure from the hydrodynamical viewpoint, a spin down problem with a simple geometrical configuration within the frame work of the Boussinesq approximation is investigated. A new proposal of the origin of the solar differential rotation is made on the basis of the calculated asymptotic distribution of the angular velocity. A comment on the present day solar spin down controversy is also made.