Introduction

I have chosen a deliberately provocative title, in order to communicate a sense of frustration I have felt for many years about how otherwise sensible people, some of whom are among the scientists I most respect and admire, espouse an approach to cosmological problems — the Anthropic Principle (AP) — that is easily seen to be unscientific. By calling it unscientific I mean something very specific, which is that it lacks a property necessary for any scientific hypothesis — that it be falsifiable. According to Popper [1—4], a theory is falsifiable if one can derive from it unambiguous predictions for practical experiments, such that — were contrary results seen — at least one premise of the theory would have been proven not to true. This introduction will outline my argument in a few paragraphs. I will then develop the points in detail in subsequent sections.

While the notion of falsifiability has been challenged and qualified by philosophers since Popper, such as Kuhn, Feyerabend and others, few philosophers of science or working scientists would be able to take seriously a fundamental theory of physics that had no possibility of being disproved by an experiment. This point is so basic to how science works that it is perhaps worthwhile taking a moment to review its rationale.

Problems with bottom-up approach

The usual approach in physics could be described as building from the bottom up. That is, one assumes some initial state for a system and then evolves it forward in time with the Hamiltonian and the Schrödinger equation. This approach is appropriate for laboratory experiments like particle scattering, where one can prepare the initial state and measure the final state. The bottom-up approach is more problematic in cosmology, however, because we do not know what the initial state of the Universe was, and we certainly cannot try out different initial states and see what kinds of universe they produce.

Different physicists react to this difficulty in different ways. Some — generally those brought up in the particle physics tradition — just ignore the problem. They feel the task of physics is to predict what happens in the laboratory, and they are convinced that string theory or M-theory can do this. All they think remains to be done is to identify a solution of M-theory, a Calabi—Yau or G2 manifold that will give the Standard Model as an effective theory in four dimensions. But they have no idea why the Universe should be 4-dimensional and have the Standard Model, with the values of the forty or so parameters that we observe. How can anyone believe that something so messy is the unique prediction of string theory?

Some sort of philosophy is inescapable

Most scientists concede that there are features of the observed Universe which appear contrived or ingeniously and felicitously arranged in their relationship to the existence of biological organisms in general and intelligent observers in particular. Often these features involve so-called fine-tuning in certain parameters, such as particle masses or coupling constants, or in the cosmic initial conditions, without which life (at least life as we know it) would be either impossible or very improbable. I term this state of affairs bio-friendliness or biophilicity. Examples of such fine-tuning have been thoroughly reviewed elsewhere [1] and in this volume, so I will not list them here.

It is normally remarked that cosmic bio-friendliness has two possible explanations (discounting sheer luck). One is that the Universe has been designed by a pre-existing creator with life in mind. The other, which is often motivated explicitly or implicitly by a reaction to supernatural explanations, is the multiverse. According to the latter explanation, what we call ‘the Universe’ is but a small component in a vastly larger assemblage of ‘universes’, or cosmic regions, among which all manner of different physical laws and conditions are somewhere instantiated. Only in those ‘Goldilocks’ regions where, by accident, the numbers come out just right will observers like ourselves arise and marvel at the ingenious arrangement of things.

Preamble

The task that I have been assigned is to set the scene for the discussions that follow: to present my view of the principal issues that had confronted us before the meeting when trying to understand the dynamics of the solar tachocline. Most of what I write here is enlarged upon, and in some cases superseded by, the chapters that follow, in which references to most of the original publications can also be found. Nevertheless, I trust that it can serve as a useful elementary introduction to the subject, setting it into its wider astronomical context.

The tachocline is interesting to astrophysicists for a variety of reasons, the most important being (i) that it couples the radiative interior of the Sun, where nearly 90% of the angular momentum resides, to the convection zone, which is being spun down by the solar wind, (ii) that it controls conditions at the lower boundary of the convection zone, and is therefore an integral component of the overall rotational dynamics of the convection, and (iii), perhaps most relevant to the interests of the greater proportion of the participants of the workshop, it is now generally recognized as being the seat of the solar dynamo. It plays some role in shaping the evolution of the Sun, and it must be taken into account when interpreting the helioseismological diagnostics of the solar structure.

The combination of differential rotation and toroidal fields believed to exist in the solar tachocline should be unstable to global MHD modes, typically dominated by longitudinal wavenumber m = 1 modes for toroidal fields of peak value 30 kG and higher, and a broader range of low m values for weaker fields. For toroidal field bands, the high field instability takes the form of a ‘tipping’ of the band away from coincidence with circles of latitude. For a wide range of toroidal fields and differential rotations, and in both the overshoot and radiative parts of the tachocline, the unstable modes grow in a time short compared to a solar cycle, and are therefore of interest for the solar dynamo problem, as well as for creation of longitude-dependent magnetic patterns seen at the solar surface. The latitudinal momentum transport by Reynolds and Maxwell stresses associated with unstable modes provides a way to mix angular momentum in latitude, and help limit the thickness of the tachocline.

Introduction

The study of global MHD instabilities of differential rotation and toroidal fields that might be present in the solar tachocline began with Gilman & Fox (1997). Their original motivation was to see whether the magnetic field could destabilize the differential rotation of the tachocline, estimated to be stable to hydrodynamical disturbances by itself.

Two distinct classes of magnetic confinement models exist for the solar tachocline. The ‘slow tachocline’ models are associated with a large-scale primordial field embedded in the radiative zone. The ‘fast tachocline’ models are associated with an overlying dynamo field. I describe the results obtained in each case, their pros and cons, and compare them with existing solar observations. I conclude by discussing new lines of investigation that should be pursued, as well as some means by which these models could be unified or reconciled.

Introduction

Magnetic fields in the tachocline

Two distinct possible origins for solar magnetic fields in the tachocline region can be identified. The Ohmic decay timescale of a large-scale dipolar field embedded in the radiative interior is much larger than the estimated age of the Sun (Cowling 1945; Garaud 1999), so that a fraction of the magnetic flux initially frozen within the accreting protostellar gas is likely to persist today. In parallel, according to the standard dynamo field theory, small-scale magnetic fields are thought to be constantly generated by fluid motions within the solar interior. Optimal conditions for the generation of large-scale fields require the combination of large-scale azimuthal shear and small-scale helical motion, which are both naturally found in the region of the tachocline (Parker 1993; Ossendrijver 2003; Tobias 2005).

The discovery by Spruit of a new small-scale turbulent dynamo has significantly changed the tachocline model proposed by Gough & McIntyre (1998). The small-scale dynamo is shear driven, is characteristic of stably stratified flows, and is mediated by the kink or ‘tipping’ instability elucidated for such flows by R. J. Tayler. The dynamo works best in high latitudes and supports turbulent Maxwell stresses large enough to dominate the angular momentum transport, taking over from the pure mean meridional circulation (MMC) proposed by Gough & McIntyre (1998). What survives from the Gough & McIntyre proposal is the laminar thermomagnetic boundary layer at the tachopause, essential for the confinement of the interior field Bi by high-latitude downwelling. That downwelling is, however, itself confined within a double boundary layer at the tachopause. The thermomagnetic boundary layer sits just underneath a modified Ekman layer, in which the turbulent Maxwell stress of the small-scale dynamo diverges.

The effects of compositional stratification in the helium settling layer under the tachopause are considered. It is concluded that Gough & McIntyre's (1998) ‘polar pits’ to burn lithium are dynamically impossible and that the tachopause is not only sharp but globally horizontal. That is, the tachopause, as marked by the top of the helium settling layer, follows a single heliopotential to within a very tiny fraction of a megametre from equator to pole.

Afterthoughts

Even the most casual of readers of this book will have noticed that the subject of the solar tachocline is highly controversial, in the best traditions of our science: we are all well aware that the tachocline constitutes an important physical structure in the solar interior, but we are not at all in agreement about any of the details. While this makes for a good deal of excitement – much in evidence both at the workshop and in this book – I did early on recognize that a straightforward summary of the workshop was therefore an impossibility; and my strong belief is that it is very premature for me to act as a ‘referee’ judging the merits of the various points of view expressed by my co-authors of this volume. This does not mean of course that I will not venture an opinion when appropriate – but it does mean that, in many cases, ex cathedra declarations of what is correct, and what is incorrect, are entirely premature.

For these reasons, I thought it would be more appropriate for me to step back from the fray, and to discuss some of the larger issues related to the tachocline, most especially those that I believe will play a key role in further developments of this subject; and to explain, whenever appropriate, why exactly it is that a definitive result remains to be obtained.

The tachocline is believed to play a crucial role in the dynamo that maintains magnetic activity in the Sun. We first review the observational properties of the 11-year activity cycle and the 22-year magnetic cycle, as well as of the recurrent grand minima, with a characteristic 200-year timescale, that are revealed by proxy records. Then we discuss dynamo mechanisms, including differential rotation (the ω-effect), the net effect of gyrotropic motions (the α-effect) and flux transport by both large-scale motions (e.g. meridional flows) and small-scale processes (e.g. turbulent transport). Next we consider the location of the solar dynamo, comparing models with dynamo action distributed throughout the convection zone, located near the surface or (most likely) concentrated near the interface between the convective and radiative zones. Local pockets of strong field can then escape from the vicinity of the tachocline and emerge through the photosphere as active regions. The nonlinear back-reaction of the magnetic field affects transport coefficients (both α and the turbulent diffusivity β) and also drives the zonal flows that are observed. Furthermore, it provides a mechanism for the modulation associated with grand minima. We conclude with our picture of the relationship between convection, differential rotation and the dynamo in the tachocline.

Observations

The Sun exhibits cyclic magnetic activity, as do other slowly rotating stars with deep convective envelopes. This activity is manifested in the sunspot cycle, which has an average period of 11 years, as shown in Figure 13.1.

Helioseismic inversions suggest that the tachocline straddles the base of the convection zone, incorporating the overshoot region and extending into the stably stratified radiative interior. Thus, the upper tachocline is dominated by penetrative convection while the lower tachocline is a stably stratified shear flow under the influence of rotation and magnetism. We review the nature of the turbulence that is likely to exist in these two disparate regions, focusing on the interaction between turbulence and differential rotation. It is argued that turbulent angular momentum transport is likely to be poleward throughout the tachocline, tending to suppress the latitudinal differential rotation maintained by turbulent stresses in the overlying convective envelope. Meanwhile, vertical angular momentum transport in the lower tachocline may be anti-diffusive, tending to amplify the vertical shear. The turbulent alignment of convective plumes may also drive an equatorward meridional circulation in the upper tachocline where it overlaps with the overshoot region.

Introduction

The solar tachocline lies near the base of the solar convection zone. This is a well-known result of course, but it is essential to establish precisely what near means in this context. Helioseismic structure inversions reveal a stiff transition between the nearly adiabatic stratification of the convection zone and the strongly subadiabatic stratification of the radiative interior, mediated by only a narrow region of convective overshoot. As others have argued in this volume, tachocline dynamics is very sensitive to where the rotational shear occurs relative to this structural transition.

Solar activity takes place in narrow bands of latitude that move like solitary waves from mid-latitudes toward the solar equator. This behaviour points to the existence of a thin layer in the Sun that may serve as a waveguide. With its grand minima, the cycle is intermittent in a way that does not occur in the simplest chaos models. To be useful as a primitive model of the cycle, a differential equation should be of high enough order to display such strong intermittency. These and other features of solar fluid dynamics led to the adumbration of an intermediate shear layer between the convection zone and the radiative core. This layer, like the weather layers in planetary atmospheres, produces coherent structures – sunspots and perhaps vortices. Similar layers may play a role in stellar activity in cool stars other than the Sun and perhaps even in hot stars if their atmospheres are turbulent.

The maculate Sun

Rotation and turbulence in stars are significant for an understanding of stellar evolution and for the fluid dynamics of accretion discs. We can watch these processes most closely in our own Solar System. Observations of the Sun, the giant planets and the earth reveal coherent structures whose study has been one of the most exciting adventures in the mathematical science of the twentieth century. (At a meeting in the Newton Institute, we ought to recall this.)