Radio maps of extragalactic radio sources made with the Westerbork, Cambridge and V.L.A. synthesis telescopes have revealed collimated jets extending from the cores to the radio lobes (see Miley 1980 for a review). These observations have provided outstanding support for ‘beam models’ of extragalactic radio sources (Scheuer 1974, Blandford and Rees 1974). Two crucial pieces of information to emerge from high resolution observations are the behaviours of jet full width half maximum (FWHM) and surface brightness with angular distance from the core. Such data have for instance been provided by Formalont et al. (1980) and Bridle et al. (1981) for the jets in 3C-31 and by Willis et al. (1981) and Bridle (1981) for the jets in NGC 315. An important point is that the relationship between jet surface brightness and FWHM is not in general as predicted by simple magnetohydrodynamic models (Bridle 1981).

The distribution of mass in a spiral galaxy is usually inferred from its rotation curve. The curve is most conveniently measured using part of its extreme population I such as HI or HII. This has a low velocity dispersion so that the observed tangential motion is in the absence of non-circular motions (van der Kruit and Allen 1978; Bosma 1981a, b) close to the circular velocity required to balance the gravitational force. The main difficulty is that for a detailed interpretation of the rotation curve one has to make assumptions on some general properties of the mass distribution, even though it is true that one can estimate the total mass within the last measured point to an accuracy of about a factor two. That of axial symmetry is only the simplest of assumptions. On the basis of the light distribution with a usually prominent disk component one often assumes that the mass distribution is also basically highly flattened.

The study of radio galaxies situated within clusters of galaxies has become a broad field, with hundreds of papers published in the last few years. This review will therefore be restricted mainly to consideration of the interactions between the extended components of radio sources in clusters and the diffuse gas (intracluster medium, ICM) which occurs in clusters. In particular, attention will be focused on what we can learn about the ICM from this interaction, in conjunction with other data such as X-ray observations. In the case of quasars in clusters of galaxies the emphasis is rather different, so discussion of this topic is deferred to section 6.

Two recent observational surveys of the Ca II resonance lines (Zarro and Rodgers 1983; Linsky et al. 1979) illustrate the great diversity of line profile shapes found in the spectra of cool stars. This diversity reflects a corresponding wide range in the underlying chromospheric properties of the stars. There are, however, three well-marked systematic trends in the shapes of Ca II line profiles which presumably reflect systematic trends in chromospheric properties. One of these, the Wilson-Bappu effect (Wilson and Bappu 1957), describes the strong correlation betweeen the width of the emission core (see Figure 1) and the absolute visual magnitude of the star. Despite much work, it is still not clear whether this is due primarily to systematic changes of velocity fields (e.g. Hoyle and Wilson 1958) or optical depths (e.g. Jefferies and Thomas 1959) in stellar chromospheres.

It is generally agreed that early-type stars, and hence their HII regions, appear to develop preferentially in dense concentrations within molecular clouds. These parent molecular clouds owe their existence in two ways to the dust grains in the interstellar gas, a component which comprises about 1% by mass. First, dust grains provide stable surfaces upon which hydrogen atoms can come together to form molecules. Then, once formed, the molecules are protected in cloud interiors by dust absorption of the dissociating ultraviolet radiation which pervades the low-density interstellar medium.

There are two major difficulties associated with theoretical studies of star formation. The first of these is that the dominant physical process or processes leading to star formation have not been identified. The second is that realistic calculations at an appropriate level of accuracy have been impossible to carry out. The result has been that only minor advances have been made on the early work of Jeans (1929) and Hoyle (1953). Much greater progress can be expected in the next few years both because observations of infra-red sources have given us much more information about the site of star formation, and because access to the current generation of very fast computers is becoming more common.

Some years ago the full non-linear equations, within the one mode approximation, describing finite amplitude convection in a compressive medium with polytropic structure were derived (Van der Borght 1977). It is the purpose of the present paper to report on the numerical integrations of these equations and to show how these can be used to construct a convective model of granulation. In this way one may gain some insight into the structure of the outer layers of the Sun.

One of the most difficult tasks facing theoretical astrophysics today is to find a satisfactory model for the convective transport of energy in regions where the temperature gradient is superadiabatic. A number of such models have been proposed, such as the mixing-length theory and its extensions (Vitense 1953, Böhm-Vitense 1958, Spiegel 1963, Travis and Matsushima 1973 a, b, Parson 1969), to take into account the combined effects of convection and turbulence but it is generally agreed that, to-date, no satisfactory theory has been put forward.

Theoretical investigations of non-linear convective motions quite often assume that either the Boussinesq or the anelastic approximations can be used.

The relevance of the results for the total heat energy transported across a fluid layer by convective motions, obtained from the time integrations of the set of non-linear partial differential equations for hydromagnetic convection, has already been designated in a previous contribution (Lopez and Murphy 1982). Some differences in the form of the boundary conditions adopted for the magnetic field disturbance, H, have been noted in other publications where the interaction of convection and a magnetic field has also been considered. The solutions of the time-dependent equations, referenced above, illustrate that the magnetic boundary conditions have a determining role in the resultant convective state for some ranges of values in parameter space.

The temporal behaviour of Rayleigh-Benard convection has attracted considerable attention in recent years, both from an experimental and theoretical point of view. Experiments (eg. Gollub and Benson 1980) have demonstrated a complicated array of non-linear behaviour, as well as the need for a model which will at least qualitatively describe what is observed.

For a spherically symmetrical distribution of gaseous matter in gravitational equilibrium the total pressure, density and other physical variables are all functions of the radial distance measured from the centre.

If computer speed and storage keeps increasing at the present rate a three dimensional numerical code modelling the exact equations governing general relativistic collapse will soon be possible; however, at present it is necessary to use simplifying approximations. Provided the general relativistic effects are limited to a ‘small’ perturbation, the post-Newtonian equations of Chandrasekhar (1965) should be adequate. These equations take the form of the Newtonian equations for a self gravitating fluid with extra terms to incorporate the 1/c2 contributions, where c is the speed of light. The numerical solution of these equations can be achieved using any method appropriate for three dimensional Newtonian hydrodynamics.

In recent years, a large amount of work has been directed towards understanding the process of star formation. However, despite these efforts, there still remain areas largely unexplored, where theories are only justified by approximate qualitative arguments rather than fully three dimensional calculations.

A standard procedure for the simulation of galaxies is to replace the ∼ 1011 stars by ∼ 104 particles. These particles are assumed to have equal mass and their distribution in space produces a mass density ϱ which mimics the average mass density of the stars. From the mass density of the particles the gravitational forces between the particles can be computed. In the literature two methods have been used to compute these forces.

Ten years ago I put forward the suggestion that the Sun may possess a small burnt-out helium-rich core covering some 2-3% of its mass (Prentice 1973a,b). The purpose of this chemically inhomogeneous solar model was to account for the anomalously low flux of neutrinos being emitted by the Sun, as observed by Davis et al. (1971).

The Ca II K line serves as an important tool in determining the physics of the photosphere-chromosphere region of the solar atmosphere (Cram 1983). To date detailed analyses have centred on the study of line intensity profiles.

It has been suggested (Holman et al 1980; Melrose and Dulk 1982a) that solar microwave spike bursts are due to electron cyclotron maser action. These bursts have been observed in the range 1-3 Ghz, and occur in conjunction with flare-associated impulsive microwave and hard X-ray bursts. The bursts have rise times of a millisecond or less (e.g. Slottje 1978).

Individual pulses from a given pulsar can differ greatly in both shape and intensity, and are often made up of narrower ‘subpulses’, i.e. local emission peaks one tenth the width of the mean pulse. Properties such as shape, polarization and position of subpulses presumably reflect details of the emission processes and of the regions that produce the radiation.

A common form of wave propagation in the highly structured magnetic fields and density profiles of the solar atmosphere should be magnetohydrodynamic surface waves, i.e. waves with magnetic and velocity fields concentrated at an interface of two regions of plasma of differing properties. For example, local concentrations of equilibrium magnetic fields forming flux tubes will support these waves on their surfaces, in addition to the more commonly considered ‘body waves’ that are supported by an isolated flux tube, waves with an oscillatory radial dependence inside the tube. Mhd surface waves have recently been identified in a laboratory plasma at Sydney University (Collins, Cramer and Donnelly 1983).