MOTIVATION

Solar activity manifests itself in many forms but perhaps most importantly through the presence of a magnetic field. The topic of this meeting is that of dynamos, in Solar and planetary contexts. In the case of the Sun the dynamo, which seems likely to be responsible for at least part of the Solar activity we observe, acts on a global scale. That is, the period of the dynamo is 22 years (a timescale distinct from those usually encountered on the Sun), sunspots appear within latitude bands and their numbers (in terms of monthly or yearly running means) increase and decrease over one cycle. There is however, a strong asymmetry of the Solar cycle in time, i.e. the growth phase is shorter (and dependent of the amount of activity) than the decay, or descending phase. In addition, the polar field of the Sun is observed to reverse around Solar maximum, again with a distinct asymmetry between hemispheres. Despite these global-scale features, the Solar magnetic field has many spatial components (Stenflo 1991) and the majority of the magnetic flux appears in small elements.

INTRODUCTION

The aim of this short paper is to attract attention to one feature in the Earth's fluid core. The feature is an internal shear layer induced by a relative rotation of the inner core. Large gradients of the velocity around this layer may be important for the geodynamo. Note, in particular, that in the geodynamo model-Z without an account of the inner core rotation one of the basic sources (the α-effect) is assumed to be concentrated near the core-mantle boundary (Braginsky 1993).

The inner core of the Earth can be considered as a hard iron ball of radius approximately 0.2R, where R is the Earth's radius. The rest of the planet is occupied by the outer liquid core and the rock mantle in the form of spherical shells of almost equal width, 0.4R. The other iron-rock planets (Mercury, Mars), except probably Venus, also have inner cores (Stevenson 1983). As the source of compositional convection (Loper & Roberts 1983) the inner core is apparently a necessary part of the planetary dynamo.

STATISTICAL PROPERTIES OF PLASMA TURBULENCE

Recent measurements have shown the existence of fine-scale density structures in Tokamak plasmas (Cripwell & Costley 1991). There is also experimental evidence that the anomalous (i.e. greater than collisional) particle and energy transport may be in some circumstances due to particle drift motion caused by microturbulence. These facts make the investigation of the turbulence in Tokamaks very important. To describe the phenomena, it is useful to know statistics of random magnetic and density fields.

In this paper we discuss the statistical properties of plasma which can be studied with the so-called refractometry technique probing plasma with a plane polarized electromagnetic laser or microwave beam (Gill & Magyar 1987; Weisen et al. 1988.

THEORETICAL EVOLUTION

In order to discuss the observations in a meaningful way, it is useful to first discuss the theory, because only then does one have a meaningful context in which to place the observations. One must note that this does not imply that the theory is well understood, because this is not necessarily the case. But this approach gives some insight as to what the key observations are, and by comparing the observations with the theory one can find the weakness in the theory which can be more thoroughly studied.

Review of the early evolution

The main sequence star transforms hydrogen into helium in the central regions of the star as its source of energy. This stage is usually referred to as hydrogen burning. As the hydrogen burns, the core gradually contracts and heats up, which produces an increase in the rate at which the hydrogen is burned. The increased burning rate closely offsets the diminished fuel supply, and the luminosity of the star does not change substantially. For the first 90% of its lifetime the star remains close to the main sequence, and may double its luminosity in this time. This is shown schematically in the H-R diagram, Fig. 1, as the motion from points A to B. The initial position on the main sequence is determined only by the mass of the star, as long as it consists mainly of hydrogen. Evolutionary tracks are shown for stars of 1.1 M⊙ and 5 M⊙. The former represent the ‘low’ mass stars and the latter represent ‘intermediate’ mass stars which will be presently more completely defined.

INTRODUCTION

Numerical computations comprise an increasingly important tool in the understanding of the Earth's dynamo, and, with the increased accessibility of supercomputers, direct, realistic simulations of the geodynamo are not far off. Any such simulation must solve the equations governing a three dimensional, rapidly rotating, dynamically consistent dynamo with Lorentz force J × B present in the dominant balance of forces. The simplest dynamo with these characteristics, first proposed by Childress & Soward (1972), uses the convective motions of rapidly rotating Benard convection to drive a dynamically consistent MHD dynamo. Computationally, the Childress–Soward dynamo has the advantage of permitting the expansion of the unknown fields in Fourier series in all directions, allowing three dimensional fast Fourier transforms (FFT's) to be used in calculating the nonlinear terms. Since no fast Legendre transform exists at the moment, the resulting programs will be faster than more realistic spherical dynamo simulations, while at the same time reflecting the important features of these models.

In this paper, the strong field branch of the Childress–Soward dynamo is investigated using direct numerical simulations.

INFRARED ASTRONOMY AND STAR FORMATION

In a report of the current status of the observational studies of star formation published in 1982, Wynn-Williams introduced the subject by boldly stating “Protostars are the Holy Grail of infrared astronomy”, one of the most (ab)used astronomical quotations ever. At the time of the review, searches had been made at IR wavelengths towards a restricted sample of objects, guided by the theoretical expectation that protostars would undergo a phase of high IR luminosity during the main accretion phase (Larson 1969). The aim of these studies, and of those that followed, was to get an unambiguous example of Spitzer's definition (1948) of a protostar as “an isolated interstellar cloud undergoing inexorable gravitational contraction to form a single star”.

This definition appears now rather restrictive, since observations have shown that the structure of star forming regions is highly complex, rarely revealing well isolated, noninteracting interstellar clouds. In addition, observations in the near infrared at high spatial resolution have shown that many young stars are not single, but do have companions (Zinnecker & Wilking 1992). However, despite great effort, resulting from improvements in instrumentation and progress in the theoretical models, the same discouraging conclusion reached by Winn-Williams in 1982 still holds true: no conclusive identification of a genuine protostar has yet been made. Nevertheless, the motivation for continuing the search using the IR band remains still unquestionable.

In these lectures I will present an overview of the main properties of the star formation process with a special emphasis on stars of low- and intermediate-mass, for which observations are the most detailed and a consistent theoretical framework has been developed and tested.

Early measurements of the interstellar extinction curve at visual wavelengths (Stebbins et al., 1939) established a broad result which has survived unchanged, namely that the amount of the extinction on a magnitude scale has an approximately linear dependence on wavenumber, i.e. Aλ ∝ 1/λ. This result was later refined (Nandy 1964a, b, 1965) to show that in a second order of approximation Aλ could be represented in a plot against 1/λ, by two straight line segments intersecting at 1/λ ≅ 2.4 (μm−1), with the segment corresponding to blue wavelengths being somewhat shallower in slope than the segment corresponding to red wavelengths. The shape of the interstellar extinction curve over the waveband 1 < λ−1 λ 3μm−1 remained more or less invariant from star to star. Grain models were thus constrained to possess a wavelength dependence of extinction that accorded with this general result.

Another observational criterion that was available from the 1930's related to the amount of the interstellar extinction per unit path length. For instance at the visual wavelength, corresponding to 1/λ = 1.8 (μm)−1, the mean extinction of starlight in directions close to the galactic plane is about 2 mag/kpc.

A further result of relevance is the so-called Oort limit for the total mass density of interstellar material – gas and dust – which amounts to ˜ 3 × 10−24 g cm−3 (Oort, 1932, 1952). The dust grain density had certainly to be less than this value, probably considerably less, in view of the fact that the bulk of cosmic material is made up of H which cannot by itself condense into solid grains at a temperature above that of the cosmic microwave background, ˜ 2.7°K.

INTRODUCTION

The key characteristic of a fluid motion necessary for fast dynamo action is the existence of a positive Liapunov exponent. Childress (1992) calls a motion with this property a stretching flow and it is generally manifest by chaotic particle paths. For steady flows the regions of exponential stretching are often small, as they are, for example, in the case of the spatially periodic flows discussed by Dombre et al. (1986). The numerical demonstration of fast dynamos in such flows has proved difficult and Galloway & Frisch's (1984, 1986) results were inconclusive even at the largest values of the magnetic Reynolds number reached.

It is known that the action of a small-scale incompressible flow (having suitable symmetries) on a large-scale perturbation of small amplitude is ‘formally’ diffusive (Kraichnan 1976; Dubrulle & Frisch 1991). There are two essential assumptions. The first one is scale-separation: the ratio e between the typical length-scale of the basic flow and that of the perturbation is small. The second one is the absence of a large-scale AKA effect (Frisch et al 1987). If the basic flow is parity-invariant (i.e. has a center of symmetry), this condition is automatically satisfied. By ‘formally’ diffusive, we understand that, unlike the case of the eddy diffusivity for a passive scalar (Frisch 1989), the eddy viscosity tensor need not be positive definite. There are indeed examples of strongly anisotropic flows (e.g. the Kolmogorov flow), where some components of the tensor are negative, resulting in a large-scale instability (Meshalkin & Sinai 1961; Green 1974; Sivashinsky 1985; Sivashinsky & Yakhot 1985).

When the eddy viscosity tensor is isotropic, the equation for the perturbation reduces to an ordinary diffusion equation, with diffusion coefficient uE.

THE INFRARED WAVEBAND

The infrared region of the electromagnetic spectrum spans a large range in wavelengths compared to that of normal visible light and it has not been easy to develop technologies which allow astronomers to study the infrared waveband. However, in the last 8 – 10 years there has been a tremendous growth in the field of infrared astronomy. This growth has been stimulated in part by the construction of infrared telescopes and by successful space missions, but the most important event has been the development of very sensitive imaging devices called infrared arrays. Before describing these detectors and their uses in instrumentation, it is useful to begin with a brief historical review of infrared astronomy and an explanation of the terminology of the subject.

Historical review: from Herschel to IRAS

Infrared astronomy had an early beginning when, in 1800, Sir William Herschel noted that a thermometer placed just beyond the red end of the optical spectrum of the Sun registered an increase in temperature due to the presence of invisible radiation which he called calorific rays. He even demonstrated that these rays were reflected and refracted like ordinary light. This discovery came 65 years before James Clerk Maxwell's theory on the existence of an entire spectrum of electromagnetic radiation.

Despite that early start, and some additional development of infrared detectors by Edison, and later by Golay, no major breakthroughs in infrared astronomy occurred until the 1950s — the era of the transistor — when simple, photoelectric detectors made from semiconductor crystals became possible.

INTRODUCTION

An essential aspect of virtually all astrophysical magnetic dynamos is the role played by turbulent magnetic field diffusion. From the analytical perspective, discussions of turbulent diffusion have until recently been generally couched in the language of mean field theory, and in particular, within a kinematic context (cf. Moffatt 1978; Krause & Rädler 1980). Indeed, the great theoretical elegance of mean field electrodynamics, together with its attractive intuitiveness, have led to a situation where basic constructs of this theory, such as turbulent diffusion and the ‘α-effect’, have carried over into domains, such as numerical simulations, where their meaningfulness is not a priori obvious (cf. Glatzmaier 1985). In a recent series of papers, we have examined precisely the question of how such notions can be carried over into the nonlinear domain, and further have asked under what circumstances nonlinear effects are likely to matter (Vainshtein & Rosner 1991; Cattaneo & Vainshtein 1991; Vainshtein & Cattaneo 1992; Tao, Cattaneo & Vainshtein 1993).

INTRODUCTION

The theory of linear, kinematic, mean field dynamos has been studied extensively since the pioneering paper by Parker (1955). In such dynamos, the mean magnetic field grows despite the action of resistivity through the combined action of small-scale, helical motions (α effect) and large-scale shear flows (ω effect). If the background state is time independent, the mean field evolves exponentially in time, and saturation of the field amplitude must occur through effects not included in the model.

Astrophysical systems typically have very low resistivities and correspondingly high magnetic Reynolds numbers Rm (of order 108–1010 in the Solar convection zone and 1018–1020 in the galactic disk). This raises a problem for dynamo theory: if the resistivity is assumed to be molecular, the fastest growing wavelengths are extremely short and it is difficult to see how large scale fields could be generated. Moreover, the resistivity plays a central role in the calculation of the a effect (e.g., Moffatt 1978). Most workers therefore assume that turbulent resistivity is present.

INTRODUCTION

The influence of varying conductivity on the dynamo process has been investigated for example for galaxies (Donner & Brandenburg 1990) and accretion disks (Stepinski & Levy 1991) and found to be negligible there. Jeanloz's (1990) interpretation of the D′′ layer as a laterally inhomogeneous distribution of conducting and insulating alloys, resulting from chemical reactions at the core-mantle boundary and the percolation of iron into the mantle, has motivated us to consider the possibility of a dynamo induced by varying conductivity on the Earth's dynamo. Two questions arise in this context. Firstly, one may ask how a lower mantle with laterally varying conductivity will affect the extrapolation of magnetic fields from the Earth surface to the core. Poirier & le Mouel (1992) have investigated this question in detail and found the effect to be negligible. Jeanloz's (1990) view of pinned fieldlines is too dramatic.