Traditionally, solar and stellar physics have been two separate branches of astronomy, which independently of each other have developed their own scientific goals and methods. During the last decade, however, we have witnessed a gradual convergence of these two areas: The solar physicists realize more and more that the sun has to be seen as a special case in a large family of stars of various properties. A more complete understanding of the sun can only be achieved by considering it in this broader context. The stellar physicists on the other hand have become aware that the detailed knowledge of the physical processes that the solar physicists have reached has a more general significance and can be applied to a variety of other astrophysical objects. Observational techniques developed in solar work can frequently be adapted for other stars as well. This unified approach to solar and stellar physics is often called the “solar-stellar connection”.

The “Robinson” method for measuring magnetic fields on solar- and late-type stars is reviewed. The results of such measurements for a sample of 29 G and K main-sequence stars are presented. The area covering-factors of magnetic regions are greater in the K dwarfs than in the G dwarfs, but no spectral-type dependence is found for the field strengths, contrary to expectations of some flux-tube models. The dependence of Ca II H and K emission on magnetic fields and Teff is consistent with theoretical expectations for “slow-mode” mhd wave-generation rates, but inconsistent with those of other mhd modes. Coronal soft X-ray fluxes correlate well with the magnetic fields, and it is argued that Alfvén waves are the likely energy-transport mechanism. Surface magnetic fluxes vary with rotation as , depending on spectral type.

To investigate periodic variations of the magnetic field of the Sun as a star (SMMF; see Severny, 1969) we have used the mean field measurements made in Crimea, Mt. Wilson, and Stanford observatories; in total N = 5783 daily values were available for the time interval 1968–1981. In essence, these data offer a unique possibility to study the Sun as a variable magnetic star (Scherrer et al., 1977).

We discuss our program to detect and measure magnetic flux on the surfaces of late-type stars. We adopt a novel technique to deconvolve magnetically insensitive lines from similar, magnetically sensitive lines to infer the degree of Zeeman splitting in the latter lines. These measurements yield values for the magnetic field strength and filling factor (flux). To illustrate our approach we present multiple observations of the RS CVn star λ And. At the epoch of observation 26 April 1981 we find a field strength of 1290 ± 50 gauss covering 48 ± 2 percent of this star's surface. Observations at other epochs clearly demonstrate magnetic flux variability on λ And.

Although magnetic fields are presumed to be of substantial importance in the physics of stellar chromospheres (e.g., Vaiana et al. 1981), firm detections of magnetic fields in stars later than type A are rare, if not entirely absent. For example, Boesgaard (1974) made careful photographic measurements of longitudinal fields in a number of dwarf stars, and obtained 5 σ or greater detection of fields at the level of 100 G in the G8 V stars in ξ Boo A and in the KO V star 70 Oph A. Robinson et al. (1980) studied ξ Boo A by means of an analysis of the widths of magnetically sensitive lines, and obtained a mean field magnitude of 2600 G. However, Marcy (1981) used the same technique and found no significant field in this star. Brown and Landstreet (1981) looked for longitudinal fields in a variety of late type stars with an adaptation of a Griffin-type radial velocity spectrometer, which yielded standard errors near 10 G. They found no fields in any of the stars which they surveyed, including ξ Boo A, 70 Oph A, and a number of RS CVn stars and other stars with strong Ca II K and He I 10830 A emission.

In this review I discuss from a theoretical point of view the magnetic fields seen at the solar (stellar) surface. Since magnetic field lines have no ends, and the photospheric fields are mostly vertical, the discussion necessarily includes some of the properties of the fields above and below the photosphere. A more general discussion of the theory of solar magnetic fields can be found in Priest (1982).

The highly inhomogeneous nature of the solar atmosphere leads us to suggest that solitons may occur in magnetic structures such as coronal loops or photospheric flux tubes. The theory is outlined for the simple case of a magnetic slab in a field-free atmosphere and shown to lead to the Benjamin-Ono equation.

We give a short summary of some results of a numerical study of magnetic field concentrations in the solar photosphere and upper convection zone. We have developed a 2D time dependent code for the full MHD equations (momentum equation, equation of continuity, induction equation for infinite conductivity and energy equation) in slab geometry for a compressible medium. A Finite-Element-technique is used. Convective energy transport is described by the mixing-length formalism while the diffusion approximation is employed for radiation. We parametrize the inhibition of convective heat flow by the magnetic field and calculate the material functions (opacity, adiabatic temperature gradient, specific heat) self-consistently. Here we present a nearly static flux tube model with a magnetic flux of ∼ 1018 mx, a depth of 1000 km and a photospheric diameter of ∼ 300 km as the result of a dynamical calculation. The influx of heat within the flux tube at the bottom of the layer is reduced to 0.2 of the normal value. The mass distribution is a linear function of the flux function A: dm(A)/dA = const. Fig. 1 shows the model: Isodensities (a), fieldlines (b), isotherms (c) and lines of constant continuum optical depth (d) are given. The “Wilson depression” (height difference between τ = 1 within and outside the tube) is ∼ 150 km and the maximum horizontal temperature deficit is ∼ 3000 K. Field strengths as function of x for three different depths and as function of depth along the symmetry axis are shown in (e) and (f), respectively. Note the sharp edge of the tube.

The time-dependent collapse of a slender flux tube extending vertically in the convection zone of the Sun is modelled. Starting from an initial state in which the flux tube is in hydrostatic equilibrium, the non-linear MHD equations are used to examine its temporal evolution. A detailed study of the flow variables and magnetic field within the tube is presented. It is seen that asymptotically in time a unique state of dynamic equilibrium is established, irrespective of the value of βo (the ratio of the thermal to magnetic pressure at the initial epoch).

The interaction of photospheric granular convection with a small scale magnetic field has been simulated numerically in a three-dimensional model, with an extension of techniques recently used to simulate field-free granulation. The evolution of an initially homogeneous magnetic field was followed numerically, both in a kinematic (weak-field limit) description, and in a dynamic description, where the back-reaction of the field on the motion through the Lorentz force is taken into account. The simulations illustrate the strong tendency for the field to be swept up and concentrated in the inter-granular lanes because of the topology of the granular flow. The convectively unstable stratification allows field concentration up to a kilogauss field because the temperature reduction in the magnetic plasma.

This paper discusses attempts to derive information on magnetic structure in late-type stars, only from emission fluxes in the cores of the Ca II H and K lines, in UV emission lines and in soft X-rays — and from relations between these emission fluxes. However simpleminded and indirect this approach may seem, it brings out stimulating results. Studies of this kind are guided by solar research, so let us look first at the solar data.

Several parameters of the solar rotation show variations which appear to relate to the phase of the solar activity cycle. The latitude gradient of the differential rotation, as seen in the coefficients of the sin2 and sin4 terms in the latitude expansion, shows marked variations with the cycle. One of these variations may be described as a one-cycle-per-hemisphere torsional oscillation with a period of 11 years, where the high latitudes rotate faster at solar activity maximum and slower at minimum, and the low latitudes rotate faster at solar activity minimum and slower at maximum. Another variation is a periodic oscillation of the fractional difference in the low-latitude rotation between north and south hemispheres. The possibility of a variation in the absolute rotational velocity of the sun in phase with the solar cycle remains an open question. The two-cycle-per-hemisphere torsional waves in the solar rotation also represent an aspect of the rotation which varies with the cycle. We show that the amplitude of the fast flowing zone rises a year before the rise to activity maximum. The fast zone seems to be physically the more significant of the two zones.

The present review will focus upon the incidence, form, and characteristic timescale of long-term chromospheric variations that, from the work of O.C. Wilson and his successors, can be descerned in records of CaII H and K emission now extending over 16 years, and the relation, if any, between properties of activity cycles and stellar mass, age, and rate of rotation, in the light of current evidence.

It is now firmly established that lower main sequence (LMS) stars show a qualitative correlation between rotation rate and chromospheric and coronal emission. By analogy with the Sun, the emission is believed to be intimately associated with surface magnetic fields. This association is especially close on the Sun for the Ca II H and K lines, for which the spatial correlation between chromospheric emission and photospheric fields is essentially one-to-one down to scales at least as fine as a few arcseconds and for which the emission flux from an area on the Sun is approximately proportional to the total magnetic flux passing through the same area in the underlying photosphere (Leighton 1959; Skumanich, Smythe, and Frazier 1975; Frazier 1971). The extension of the association to other LMS stars, while based on appeal to analogy, has been strengthened by recent detections of strong magnetic fields covering large fraction of the surface area of chromospherically active stars (see review by Marcy in this symposium).

Fourier Transform Spectrometer observations of Fraunhofer line displacement and asymmetry suggest that granular convection is inhibited in regions of magnetic activity. We discuss the observations and a method for removing the effects of solar rotation. In integrated sunlight (“the sun-as-a-star”) records of line asymmetries indicate that a significant reduction in the amplitude of the sun's convective signature took place between 1980 and 1982. To the extent that full disk line asymmetry arises strictly from convective motions, the results constitute strong evidence that magnetic activity influences (inhibits) convective motion on a global scale.

A preliminary analysis of spectral lines by Fourier transformation was used to determine upper limits of differential rotation for 11 F-type stars, mainly from the main-sequence. No evidence for a much steeper differential rotation on these stars than on the Sun could be found.

The difficulties of measuring magnetic fields in late-type stars other than the sun are well known, as one is reminded by other contributions to these Proceedings. This Symposium nevertheless comes at a very opportune time, as we are now at the point where we can begin to explore the relationship of stellar magnetism to flare activity and quiescent cool star chromospheres, transition regions (TRs), and coronae.

An overview of recent Einstein Observatory observations and theoretical modeling of stellar x-ray emission is presented, with particular emphasis upon the role such studies can play furthering our understanding of stellar magnetic activity. We argue that solar observations can be used to show that coronal emission is morphologically related to surface magnetic field activity; to establish a quantitative link between the observed soft x-ray flux and the mean surface (photospheric) magnetic flux; and, in sum, to demonstrate that soft x-ray emission is a sensitive diagnostic for the presence of surface magnetic fields, uncomplicated by radiative transfer effects and the resulting coupling to the underlying atmosphere (which may introduce unwanted correlations with spectral type and luminosity class). Recent analyses of stellar x-ray observations from the Einstein Observatory have focused on the interpretation of stellar coronal emission and possibly-related surface magnetic activity within the framework of our understanding of solar activity; including “loop” models of stellar coronae, observations of coronal emission variability on a wide range of time scales (which provide information on the morphology of the emitting plasma), and observations and modeling of low-resolution spectroscopic x-ray observations (which test the applicability of solar modeling). These recent results, which I review, all reenforce the argument that stellar coronal emission constitutes an excellent probe for studying stellar magnetic activity over a wide dynamic range, one which may prove to be uniquely suited to studying such activity in distant (and hence faint) sources.

I present preliminary results from an observational investigation of very late M dwarf stars utilizing the Multiple Mirror Telescope facility. I find that dwarf stars later than spectral type M5 do not necessarily exhibit Hα line emission, contrary to the assertion by Joy and Abt (1974). The preliminary results I discuss herein tentatively suggest, but do not prove, that the generation of significant magnetic fields and magnetic flux is severely inhibited in fully convective stars.

I discuss EINSTEIN X-ray observations of late-type (G and K) stars. For the RS CVn systems and the evolved G stars, there is a linear relation between X-ray surface flux and stellar angular velocity. The situation is more complex among the G-K dwarfs: rapid rotators, with rotational periods less than ∼10d, also show a linear relation between X-ray surface flux and angular velocity, but the slow rotators fall some two orders of magnitude below that relation.