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.

INTRODUCTION

Very naturally, many of the investigations into astrophysical dynamo theory have been directed to explaining the Solar cycle: after all, this is the system for which the most detailed information, both spatial and temporal, is available. The large scale Solar magnetic field appears to be approximately axisymmetric and so it is appropriate to study strictly axisymmetric dynamos. More recently, evidence has accumulated that magnetic fields with a significant nonaxisymmetric component may be present in late type ‘active giant’ stars (see, e.g., the discussion in Moss et al. 1991a, and references therein), and also in one or two spiral galaxies, notably M81 (e.g. Krause et al. 1989; Sokoloff et al. 1992). Thus the conditions under which nonaxisymmetric fields can be excited in astrophysical systems are of current interest. Radler et al. (1990) and Moss et al. (1991a) have recently investigated nonlinear spherical mean field dynamo models in which stable nonaxisymmetric fields may be excited with suitably chosen distributions of alpha effect and differential rotation; see also Stix (1971). Rüdiger & Elstner (1992) considered models where the introduction of an anisotropy in the alpha tensor may have a similar effect; see also Rüdiger (1980).

INTRODUCTION

It is widely appreciated that magnetic fields can play an important role in accretion disk dynamics. Shakura & Sunyaev (1973), in their well known paper, pointed to magnetic fields as the source of a viscous couple necessary for the accretion to take place. Disk magnetic fields have also been invoked to explain spectra of compact X-ray sources, as a source of coronal heating, and as a source of wind production. In the context of the Solar nebula, which is widely assumed to represent a typical protoplanetary disk, the existence of a magnetic field is inferred from the residual magnetization of primitive meteorites, which are assumed to owe their magnetization to nebular magnetic fields. However, in a typical accretion disk, the timescale for ohmic dissipation is much smaller than the typical radial infall time, thus it is difficult to see how any magnetic field contained in the gas that falls onto the disk can persist long enough to be dynamically or otherwise important, unless it is regenerated by a dynamo cycle.

INTRODUCTION

Rotating fluid dynamics is of primary importance in the understanding of the origin of planetary magnetic fields which are generated by dynamo processes in the rotating fluid interiors of planets. There are two important but traditionally separate branches in the subject of rotating fluid dynamics: inertial oscillation and convection. Both have been extensively investigated. Inertial oscillation in rotating systems is governed by the Poincare equation; it was also shown by Malkus (1967) that the problem of hydromagnetic inertial oscillation can be changed to the Poincaré problem with a special form of the basic field. A classic introduction and most of the earlier research results concerning this problem can be found in Greenspan's monograph (1969). The important application to the dynamics of the Earth's fluid core was discussed by Aldridge & Lumb (1987).