Consider a cylindrical, homogeneous magnetic flux tube embedded in a field-free compressible plasma. We employ the method of successive approximations to solve the magnetohydrodynamic equations analytically for an axisymmetrical (m=0) torsional Alfvén mode. The m=0 mode inside the tube may excite surface-, stationary- or progressive waves in the field-free plasma. We conclude that, in contrast to the linear theory, the flux tube may lose energy by wave radiation to the surroundings.

Simultaneous spectroheliograms of a quiet region at solar disk centre in Hα + 0.29 Å, Hα − 0.29 Å, K + 0.18 Å and K − 0.18 Å show much similarity in the asymmetries in the two lines. The fibrils are identical geometrically. Both lines show patterns of line-of-sight motions propagating along the fibrils. Close to the network, the velocity of propagation is of the order of 12 km s−1 towards or away from the network; further away the patterns propagate away from the network at velocities of the order of 75 km s−1. The latter are interpreted as Alfvén waves, the former as due most likely to variations in longitudinal velocities along the fibrils.

Theoretical models of intense magnetic flux tubes embedded in the photospheres of late-type stars have been calculated. Magnetohydrodynamic waves generated in the convective zone are radiatively damped in the lower part of the flux tube and then dissipated. We discuss how the presence of flux tubes in stellar photospheres influences the temperature minimum and the chromospheric activity. We suggest a possible interpretation of the Wilson-Bappu effect in stars with strong chromospheric activity.

Stars with masses ≲ 1 M⊙ are observed to rotate more slowly as they age. The angular momentum loss is undoubtedly caused by the coupling of the stellar magnetic field to the escaping wind (Schatzman 1962). Chromospheric and coronal radiative losses depend upon rotation (Wilson 1966a, b; Kraft 1967; Skumanich 1972; Hall 1976; Bopp 1980; Walter and Bowyer 1981; Walter 1981; Vaiana et al. 1981). It is therefore likely that both magnetic fields (Skumanich 1972) and the mechanical energy fluxes required to drive mass loss also depend upon rotation as well. This complicated feedback between magnetic fields, winds, and rotation must control the variation of solar-type activity over much of the HR diagram, and may have very important effects on pre-main sequence evolution.

A chromospheric color-magnitude diagram has been constructed from the Vaughan-Preston survey of Ca II emission among solar neighborhood stars. The relative flux in the H and K lines declines with mass on the lower main-sequence as a consequence of the decline of the ZAMS rotational velocity with mass. The features of this C-M diagram are discussed, and some evidence for a gap in the distribution of Ca II emission with age is examined.

New data indicate that red giants are surrounded by geometrically thick chromospheres of several stellar radii extent. Such chromospheres occur among stars which apparently lack coronae. Maintenance of this extended warm region may require non-compressional wave heating of a magnetic character, and this may provide a crucial clue to the mechanism of rapid mass loss from red giant stars.

The angular momentum loss produced by stellar winds is reviewed and a simple model of angular momentum loss with multipole fields is presented in which the field is potential when the flow speed is less than the Alfvén speed, and radial when greater than the Alfvén speed. The simpler the magnetic geometry, the larger is the angular momentum loss rate. This result is used to explain the rotational discontinuity across the Vaughan-Preston gap as being due to a sudden increase in angular momentum loss when the dynamo field switches from a quadropole to a dipole geometry.

The evolution of the internal rotation of stars as a result of surface angular momentum loss is considered. In the absence of a magnetic field, differential rotation can drive instabilities which then transport angular momentum out from the interior down the angular velocity gradient. Other instabilities such as that caused by the build up of 3He can also transport angular momentum outwards. If angular momentum is transported by such weak turbulence, it also makes the star more homogeneous than standard evolutionary models and lowers the predicted value of the solar neutrino flux.

The recent results on rotational splitting of solar oscillations are considered: these suggest that the inside of the sun is spinning faster than the surface and are compatible with models in which angular momentum is transported by mild turbulence. But data is scarce — and in such circumstances the speculations of the theorist must be viewed with caution!

The strong rotational braking seen in the G5 III stage of evolution may be the key to understanding how stellar dynamos work.

We are all familiar with the leisurely spin-down seen in cool main-sequence stars like our Sun. The time scales here are ∼ 109 years and the accepted cause is the loss of high angular momentum mass in the form of stellar winds interacting with the stellar magnetic field. The magnetic field is believed to result from the interaction of envelope convection with the rotation of the star through a dynamo mechanism. Our understanding of how a dynamo actually operates, how that operation depends on the driving forces of rotation and convection, what kind of stochastic and secular time variations are to be expected, remains fragmentary even though many inventive minds have contributed. One reason for slow progress is simply that the Sun is almost the only example of a stellar dynamo we have had. But nature has given us another, much more powerful dynamo in the G5 giants, it just took us a little longer to discover it.

A theory of the white light transient phenomena in the solar corona is given, based on recent analytic treatments of magnetohydrodynamics.

In the vicinity of the Sun — especially above coronal holes — the magnetic field lines show strong non-radial divergence and considerable curvature (see e.g. Kopp and Holzer, 1976; Munro and Jackson, 1977; Ripken, 1977). In the following we study the influence of these characteristics on the expansion velocity of the solar wind.

A contracting, typical, isothermal interstellar cloud or fragment, magnetically linked to the surrounding medium, loses angular momentum so efficiently that it remains in nearly synchronous galactocentric orbit as long as the field is frozen in the matter. At a high enough density ndec, the field decouples from the matter due to ambipolar diffusion. Thereafter angular momentum is essentially conserved and, consequently, there is a one-to-one correspondence between ndec and the angular momenta of binary and single stars that can ultimately form. Although the calculated rotational velocities (typically, 100 km/sec) are not yet refined enough to account for peculiarities among different spectral classes which may be due to phenomena following protostar formation, they are encouragingly consistent with observations.

We propose that the onset of rapid mass loss among cool giants, and the absence of hot coronal material from their atmospheres, is associated with a transition in the large-scale magnetic topology of the atmosphere from closed to open. According to this view, field loops in the atmospheres of giants of spectral class K and later cannot find equilibrium, but are in a state of dynamical evolution throughout their lifetime in the atmosphere.

Recent observations of rotation rates in G and K giants show a sudden drop in the rotation rate at spectral type G5. The observed behavior requires a strong external brake, such as applied by a magnetized stellar wind. Since spectral type G5 coincides with the onset of deep envelope convection in giants, a dynamo mechanism is suggested as the controlling factor. Stellar evolution models have been used to estimate the time scale for the rotational braking, the angular momentum loss rate, and the required magnetic field strengths.

Recent observational and theoretical findings have clarified the physical mechanisms which underlie magnetic activity production in stars, and point the way naturally to a number of new or more crisply defined questions, whose answers can lead to major progress in the near future. Concerning observational programs, a guiding principle has been evident throughout this symposium: We should rely heavily on the Sun for understanding the detailed physics of magnetic activity and its generation, while at the same time we study analogous stellar phenomena for comparison with the Sun, and for new insights and extension to different regions. I list below some broad observational areas in which conditions seem ripe for important progress in understanding solar and stellar magnetic activity, leaving to other summarizers the discussion of particular observational programs.

Vigorous pursuit of the investigation of magnetic activity in stars with convective envelopes requires a diversity of observational studies and a variety of instrumentation. I leave out purely solar studies of magnetic structure and activity; it goes without saying that any well designed solar investigation contributes to better understanding of general astrophysical problems. Hence I restrict myself to observational programs pointed at stars (sections 1, 2, 3) and to solar studies necessary to interpret stellar data (section 4).

The presentations given at this Symposium have made clear that we are witnessing an exciting period in the study of solar activity, and in the ancillary study of magnetic field dynamics in solar-type stars: the new space observations obtained within the past four years, together with the renaissance in ground-based observations, have occasioned a burgeoning in our phenomenological understanding of stellar activity in its manifold facets, and have encouraged a substantially greater interest in the problem of magnetically-coupled activity in stars by the theoreticians. This excitement must not distract us from the realization that in this branch of our science, much of the impetus towards new research has come, and very likely will continue to come, from observations; with this fact in mind, I would like to address the possible evolution of our experimental science in response to the new observational and theoretical results.

The purpose of theoretical work is twofold: we want to understand physical mechanisms — and we want to predict numbers which can be compared with observations. In the field of solar and stellar magnetism much of the work still belongs to the first category.

Observational and theoretical studies of solar and stellar magnetic fields are reviewed. The discussion draws together several themes that emerged during IAU Symposium 102 on “Solar and Stellar Magnetic Fields: Origins and Coronal Effects,” and identifies a number of areas in which research over the next few years is likely to be fruitful.