It is a great pleasure and privilege to give the opening lecture at this IAU Colloquium “Inside the Stars”. It is particularly appropriate that it is held in Austria, the country of Ludwig Boltzmann whose name will appear explicitly or implicitly in every lecture.

My task is to describe the astrophysical and cosmological setting within which our discussions will take place. I emphasise that I am an outsider at this colloquium in all possible senses. My own research interests are in the areas of high energy astrophysics, extragalactic research and astrophysical cosmology. In lecturing to my students, however, I emphasise that the subject of the present colloquium is at the very heart of virtually all astrophysics and these studies are quite essential in order to make sense of galaxies and extragalactic systems. If we did not have this confidence in our ability to understand the stars, at least in principle, we would worry about the reliability of the enormous astrophysical edifice which has been built up to explain the large scale features of our Universe. I also emphasise to my students that the study of the stars is among the most exact of the astrophysical sciences — in my enthusiastic moments, I claim that, in the very best of these studies, astrophysics approaches the precision of laboratory experiment. I hope to find many examples this week to reinforce this belief.

From my perspective, what I need is a User’s Guide to Stars and Stellar Evolution, in other words, a reliable set of rules about the origin and evolution of stars in order to diagnose the physical properties of the systems I am trying to understand. I will illustrate the types of information we need by discussing three case studies in the areas of (i) high energy astrophysics, (ii) classical cosmology and (iii) astrophysical cosmology and the origin of galaxies. Necessarily, these studies will be far from complete, but I hope they will illustrate some of the issues which come up in these disciplines. In the course of the discussion, it will become apparent that I will touch upon essentially all branches of contemporary astrophysics. I will take very different approaches to the three case studies.

The sun serves as an important test case for a variety of problems related to stellar structure and evolution as well as fundamental physics. The sun also influences the terrestrial environment through its varied outputs. These two aspects of the solar interior combine to generate a surprising level of controversy for such an inherently simple star. I review three topics each of which is the subject of some degree of controversy: 1) the solar neutrino problem, 2) the status of modeling and observational efforts to understand the solar cycle of activity and 3) observational efforts to detect and identify solar g–modes.

Observations from space relevant to solar global properties (oscillations, magnetic activity, etc.) are helpful both scientifically and technically in preparing for stellar observations. This paper summarizes the results from the main previous experiments (ACRIM, SOUP, and IPHIR), and also give an initial technical report from the SXT instrument on board Yohkoh, launched in August 1991. The solar observations to date demonstrate the existence of several mechanisms for low–level variability: spots, faculae, the photospheric network, granulation, and p–mode oscillations. The observations of oscillations have been particularly helpful in setting limits on solar interior rotation. In addition to the solar processes, stars of other types may have different mechanisms of variability. These may include the analogues of coronal holes or solar flares, modes of oscillation not detected in the Sun, collisions with small bodies, duplicity, and probably mechanisms not invented yet but related in interesting ways to stellar convection and magnetism.

The microphysics of the solar standard model is revised. We discuss the contribution of composition, nuclear reaction rates, screening effect and opacity (OPAL project) to the theoretical predictions on neutrino flux and acoustic modes.

Solar models have been computed using the code CESAM constructed at Nice (Morel, 1992), and the new opacities of Livermore for different mixtures. Their global characteristics, predicted capture rates of neutrinos for the chlorine and gallium experiments and their seismological properties are given.

From models of the Sun atmosphere obtained with ATLAS 9 (Kurucz 1992) it appears that the diffusion limit of the transfer equation becomes valid only at depths larger than TR ~ 10. Even with physics as consistent as possible one restores the atmosphere with an accuracy not better than ~ 40%, but with small consequences on solar calibrated models. Despite the eigenmodes have turning points located in the atmosphere, the study of the oscillations reveals differences less than 2μHz when the atmosphere is restored with various assumptions.

Penetrative convection is expected below stellar convection sones, where it should achieve a nearly adiabatic stratification. A theoretical prediction of the penetration depth has been recently made by Zahn (1991) which includes an arbitrary parameter ζ depending on the properties of the convective motions. We use the helioseismological constraints to calibrate the value of this parameter.

Two evolutionary models of the Sun have been tested using helioseismological data. The two models use the same input micro-physics (nuclear reaction rates, opacity, equation of state) and the same numerical evolutionary code, but differ in the treatment of turbulent convection. The first model employs the standard mixing - length theory of convection, while the second one employs a new turbulent convection model which overcomes some basic inconsistencies of the standard theory of convection.

The test rests on the calculation of p-mode eigenfrequencies and on the comparison with the helioseismological data.

The comparison shows an overall improvement of the eigenfrequencies calculated with the new model with respect to those calculated with the standard model, although it appears that both models still suffer from inaccuracies especially in the treatment of the surface layers.

We have modeled the ‘steady’ part of sun’s internal poloidal magnetic field in the form of a central dipole and a central hexapole with strengths (0.6±0.1) and embedded in an asymptotically uniform field Bo. A small deviation from isorotation seems to indicate:(i) a slow build-up of toroidal field near the base of the convection zone and (ii) presence of torsional MHD perturbations in the outer radiative core, with latitudinal structure and time scales which may be similar to those of solar activity.

Given the chemical composition (essentially the hydrogen abundance), mass and the physics of the interior, the structure of a star is uniquely determined. The usual method for the determination of the hydrogen-abundance profile of the present Sun is via evolutionary calculations. But the existing uncertainties in the physics and evolutionary history suggest considering a more extended set of possible solar models. Here, we examine models with solar values of radius, luminosity and mass, but with arbitrary profiles of the hydrogen abundance in the core. Of course, the profiles X(m/M) must satisfy some (rather weak) restrictions, so that the solar values (determined by fitting) can be attained.

We present results of investigations of different inversion methods for inferring from helioseismic observations the rotation rate in the solar interior as a function of radius and latitude, using a mode set similar to that which is expected from the GONG network.

The rotation of a star perturbs the frequency wnlm of a normal mode by

where n, l and m are the mode ‘quantum’ numbers, θ the colatitude, Ω the rotation rate and Knlm a known function. Until now the observations have not been in terms of individual Δwnlm ’s; rather, coefficients ai(n,l) of a parametrization of the m-dependence of Δwnlm have been given. By representing the latitudinal dependence of the rotation rate in terms of an expansion in cos θ, an inversion of the ai, can be carried out as a series of 1-dimensional inversions. Such inversions have been dubbed “1.5-dimensional”. Our present implementation of a 1.5D procedure follows Schou et al. (1992), and uses a1, a3 and a5.

I analyze here the recent solar seismology data relevant to the core regarding the energetics. The result is that the magnetic torsional oscillations are hardly able to support the observed rate of change of the solar core rotation. Interpreting the solar neutrino data as directly coming from the core and showing the activity cycle of the core, the energetics of the core can be balanced. I show here a simple model for the global and local activity-related changes of the solar core. The parameters of this model are consistent with the values derived by the Convective Flare Theory. This model is able to interpret the anticorrelation of the sunspot number with the neutrino flux, the related changes in the rotation of the core and the first which interprets the observed activity-related element abundance anomalies with a model for the solar core.

The generation mechanism of the toroidal magnetic field by the angular velocity radial gradient acting on the relict poloidal magnetic field on the boundary between the con-vective and radiative zones is proposed. The magnetic induction magnitude of the toroidal field reaches about 2×10σ G, the limiting effect of the magnetic buoyancy being taking into account. This value conforms to the estimation of toroidal field obtained from helioseismological data.

The expected giant convection pattern has been studied by using its probable twisting influence on the emerging magnetic fields. The studies carried out on extended computations and material have confirmed the previously found evidence for a pattern with longitudinal wavenumber 1=11 in the year 1977.

The historical record of daily sunspot areas (1874 - 1989) has been analysed, looking for the short (155 days) and intermediate (323 and 540 days) term periodicities. Also the North - South asymmetry during those years has been studied.

Systematic daily observations of solar radio emission were started at the Fort Skała Observatory on 1st October 1957. The observations were made at the frequency of 810 MHz first with a 5m radio telescope - and since 1964 with a 7m one; at present they comprise already almost 70 thousand hours of observations (Michalec 1991). During that period there were two longer interruptions in the observations: from 23 September 1963 to 2 February 1964 - due to transferring the radio telescope’s antenna from the top of the Fort to a new site, and from 6 November 1973 to 11 March 1974 - connected with the reconstruction of the receiver. Other, fortunately short, interruptions in the course of observations had no influence on the homogeneity of the series.

Recently several interesting results concerning the time dependence of solar p-mode frequencies have appeared. In particular it has been shown that the mode frequencies change with solar activity (Libbrecht and Woodard 1991).

We present preliminary results from an analysis of two ≈ 3 month observation runs with the Fourier Tachometer (which was operated by HAO and NSO) from 1987 and 1989. The analysis was done with two different methods in order to test for systematic errors. We show that the mode frequencies change in a manner similar to that reported by Libbrecht and Woodard. We also present results for the frequency splittings caused by the solar rotation.