The extensive theory for magnetohydrodynamic instability of a flux tube is briefly reviewed, together with its application to tokamaks and solar flares. In a star a single coronal loop whose footprints are anchored in the dense photosphere may become unstable to the kink instability when it is twisted too much. Magnetic arcades may also be subject to an eruptive instability when they are sheared too much. After the eruption the magnetic field closes back down by reconnection and continues to heat the plasma long after the impulsive phase. Global instability of a large part of the coronal magnetic field is also possible when the stored energy is too great.

Linsky: We do not know all of the energy released in the course of a dMe star flare. What we actually measure however is often 104 to 105 times larger than what is seen in large solar flares. I have two questions. Why do you think flares in dMe stars are so much more energetic than in the solar case? Secondly, why are solar flares so much less energetic than those in dMe stars?

A review is presented on empirical flare models of UV Cet type stars based upon optical,UV, X-ray, and radio observations. The observational constraints on the flare energetics, nature of radiation sources, and flare structures are discussed, with special attention to the geometrical dimension and the magnetic field of the flaring region. The hot-plasma model in the solar analogy is critically examined by comparing it with observations. Possible future observations are suggested to tighten the constraints on the stellar flare theories.

Complementarity of solar and stellar observations should increase our knowledge of the basic facts and mechanismsof activity. The great development of stellar activity observations has enhanced theoretical study, most of which is in the framework of dynamo theory.

Even if dynamo theory seems plausible and successful in capturing the essential processes, several uncertainties and intrinsic limits do still exist and are discussed here together with alternative or complementary suggestions.

Possible (small-scale) photospheric sources of coronal magnetic field aligned currents are discussed. Such currents are equivalent to local (small-scale) twists of the coronal magnetic field, and may cause field topologies that are (MHD or resistively) unstable, and thus contribute to the (small-scale) coronal activity.

One electro-motive force associated with photospheric magnetic fields is due to the asymmetry between ions and electrons as agents of conductivity and as agents of momentum transfer to the (dominant) neutral gas component. In the solar photosphere, where only some of the easily ionized heavier elements (Mg, Si, Fe, ...) are significantly ionized, the ratio of number density of electrons and ions to neutrals is very small, of the order of the total abundance of these elements, which is of the order 10-4, by number. Due to the larger electron than ion mobility, electric currents are mainly carried by the electron component of the plasma whereas, because of the ions greater momentum transfer to the neutrals in collisions, the friction between the charged and the neutral components of the plasma is mainly due to the ions. Thus, the Lorenz force i x B acts mainly on the electron component of the plasma, whereas the balancing gas pressure gradient and gravity terms act mainly on the neutral component.

Since the acoustic heating theory (c.f. Ulmschneider 1979) has been proven successful for the solar chromosphere, it was common practice to extend this concept to other stars. However, as it appeares from observed chromospheric and coronal emissions, the usual theoretical acoustic fluxes for red dwarf star, particularly, are too small to account for the heating of chromospheres and coronae (e.g. Blanco et al 1974; Vaiana et al, 198l) . It is therefore the intention of this paper to discuss improvements on the current model calculations for turbulent sound generation from outer convection zones.

The flare phenomenon associated with dMe stars has received much attention in recent years (Gershberg 1975). Most of the flares have been detected in both optical and radio band (Lovell 1969; Kunkel 197U; Karpen et al, 1977). But as expected (Tandon 1976) only a few display weak soft X-ray emission (Karpen et al, 1977; Haisch and Linsky 1978)- Simultaneous X-ray, optical and radio observations of YZ CMi by Karpen et al (1977) shows no X-ray emission above 3σ level accompanying minor flares. Even coincident X-ray coverage with seven radio bursts shows no enhanced X-ray emission. Recently Haisch et al (1981) detected one well resolved X-ray flare on dM5e flare star Proxima Centauri and one coincident optical and radio flare out of five optical and twelve radio flare events. However, the X-ray flare on Proxima Centauri is not accompanied by any ultraviolet, optical or radio emission. Observations on flare stars show that they are more energetic, 102 - 103 times, than the corresponding solar flares. Considering the flare activity in dwarf M-stars to be similar but more energetic to that of a large solar flare, Tandon (1961) proposed red dwarf flares to be the source of low energy galactic cosmic rays. This hypothesis has been reexplored recently by Lovell (1974).

Negative preflares (NPFs) of UV Cet stars, which were first observed by Italian astronomers |1|, are a highly unusual type of preflare activity without direct analogy in solar flares. The rarity of these events in the visual region leads to difficulties in statistical investigations. At present one can consider as reliably established only that the mean NPF-amplitudes increase and the probability of their appearance decreases with a shift toward blue |2|. According to |3| NPFs are observed mainly before flares of smaller amplitudes. Beginning in 1974 at the Crimea and the Astronomical Institute of Tashkent a series of works on the theory and observation of NPFs was carried out. A short review of these is given below.

The impulsive hard X-ray, EUV and microwave radio bursts always start at or after the onset of a soft X-ray increase - the main phase of a solar flare - before the Hα flare maximum. This hard phase of a solar flare lasts ~ 100 s and consists of several elementary bursts of 10 s duration. In this time electrons are accelerated up to energy 20-100 keV, then they are injected vertically downwards into denser chromospheric layers. The electron heating as well as the thermal conductivity heating leads to the appearance of the secondary process, in particular, to gasdynamical motions (Kostyuk and Pikel'ner, 1940.

The Einstein Observatory survey of stellar coronae (Vaiana et al. 1981) and, specifically, the results on cool, low luminosity stars has suggested a correlation between stellar X-ray luminosity and stellar rotational velocity (Pallavicini et al. 1982, Walter 1981, Vaiana et al. 1981). In addition the Skylab observations of the solar corona have demonstrated a tight correlation between photospheric surface magnetic structures, which emerge from the interior in the form of “loops” above the photosphere by, viz., buoyancy instabilities, (Parker 1979; see also Acheson 1979, Schmitt & Rosner 1982, and references therein), and coronal X-ray emission (Golub et al. 1980). It therefore becomes important to ask how a coronal state (i.e. low density and high temperature plasma) of a stellar atmosphere is formed , presumably from a pure radiative equilibrium configuration.

A magnetodynamic model is proposed to interpret the observed inflow-outflow-X-ray emitting region complex in the atmospheres of T Tau stars.

Coronae and flares of RS CVn systems are interpreted as due to gradual and sudden releases of magnetic free energy which is built up throught the interaction of magnetic fields of stars in these close binary systems.

This is a merely exploratory search for estimating the importance of those stellar parameters which we believe to be relevant to the X-ray emission from stars possessing outer convective envelopes.

Belvedere et al.(1981,1982) have shown that a mechanism which converts magnetic into thermal energy is plausible for explaining the X-ray emission level in late type main sequence and giant stars. One of the main conclusions of their work is that the average surface X-ray flux Fx depends on the square of the average surface magnetic field strength B. The surface magnetic activity,in stars possessing outer convective envelopes, is likely due to the interaction of rotation with convection which produces both differential rotation (Belvedere et al. 1980a) and dynamo action by the α-effect (Belvedere et al. 1980b).Therefore we would expect that the level of magnetic field intensity depends on star's rotation Ω and the depth of the convection zone(c.z.) D,because both parameters are very important in determining the strength of the interaction.

It is difficult to provide a comprehensive theoretical explanation for the activity of red dwarf stars. Among particular problems that are ripe for further investigation are: the production of steady, cyclic or irregular patterns of activity by nonlinear dynamo action in stars; the effect of magnetic buoyancy in producing photospheric magnetic fields; the formation of isolated flux tubes and their interaction with convection. These topics are discussed and some future lines of research are suggested.

Goldberg: Well you did not cover more than half of my planned talk! (laughter). Let me comment on interferometric techniques, in particular speckle imaging which you mentioned. Doing speckle imaging with the largest telescopes now available will not give you better than the theoretical resolving power of the telescope. With a 4m telescope that is about 30 marc sec in the visible. That happens to be the radius of the supergiant Betelguese. So you are not going to achieve much with speckle imaging on these stars. One technique which has not been adequately exploited is that of lunar occultation which can give much better angular resolution than speckle, of the order of 2-3 marc sec. By using suitably chosen filters it may be possible to see structure on the disks of stars.

I have rarely had the pleasure of attending a conference in which the sheer volume of information has been so impressive and the contributions have been so diversified. Ordinarily, an I.A.U. colloquium is quite specialized, but this one might easily have been sponsored by half a dozen commissions and several international scientific unions. Astronomers from many sub-disciplines, atomic physicists, plasma physicists, aerodynamicists and applied mathematicians have come together to unite solar and stellar physics and to learn one another's scientific language. In principle, my task is to summarize more than 100 papers, which is clearly impossible even if I had had two evenings to prepare instead of one. The best I can do is to mention a few of the papers which seem to me to have conveyed the flavor of the conference and to ask the forgiveness of the remaining authors.