Introduction

The Small Cloud is an irregular dwarf of DDO type Ir IV–V that has a low mean metallicity and a high mass fraction remaining in gaseous form. These characteristics suggest that the SMC is, from an evolutionary point of view, a more primitive and less evolved galaxy than the Large Cloud. The metallicity difference between the Galaxy and the LMC was discovered by Arp (1962), who wrote: “Taken together with the marked differences in the evolved giant branches and [C]epheid gaps in the SMC and [G]alactic clusters, there exists the inescapable implication that the chemical composition of the SMC stars is different from the chemical composition of the solar neighborhood.”

The fact that the SMC contains only a single true globular cluster may indicate that star formation started off later, or more gradually, than it did in the Large Cloud.

At the present time the SMC is forming stars less actively than is the LMC. Prima facie evidence for this is that the Small Cloud contains much smaller, and less spectacular, H II regions than does the Large Cloud. Furthermore, the LMC presently contains 110 massive Wolf–Rayet stars, whereas there are only 9 WR stars in the Small Cloud. Finally, CCD observations by Bothun & Thompson (1988) show that the SMC is redder than the LMC. They find B – V = 0.52±0.03 for the Large Cloud, versus B – V =0.61±0.03 for the integrated color of the Small Cloud.

Introduction

The compact E2 galaxy M32 is the closest companion to the Andromeda galaxy. The projected separation of these two objects on the sky is only 24′ (5.3 kpc). It was first suggested by Schwarzschild (1954) that the tides induced by M32 were responsible for the distortion of the spiral structure of M31 and the warping of its disk. Later Faber (1973) noted that CN and Mg absorption in M32 was stronger than might have been expected from its luminosity (i.e., it has the metallicity usually seen in significantly more luminous objects). She therefore proposed that M32 was initially a much more luminous galaxy had suffered severe tidal truncation by M31. The very compact object NGC 4486B, which is a companion to M87, appears to be another example of a similar type of galaxy that has suffered tidal truncation. The absence of globular clusters in M32 probably also results from its outer swarm of globulars being stripped off by tidal forces. [The innermost M32 globulars might have been sucked into its massive semi-stellar nucleus by tidal friction (Tremaine, Ostriker & Spitzer 1975).] It would be interesting (M. Mateo 1999, private communication) to study the distribution of globular clusters in NGC 4486B, which, like M32, is thought to have suffered severe tidal truncation.

Kormendy (1985) and Ziegler & Bender (1998) have pointed out that M32 is quite a unique object and that there are very few other ellipticals like it. Compared to other dwarf galaxies having similar values of MV, its central surface brightness is four orders of magnitude higher, and its core radiusrc is three orders of magnitude smaller.

In this book, the term solar dynamo refers to the complex of mechanisms that cause the magnetic phenomena in the solar atmosphere. Usually, however, that complex is broken down into three components: (1) the generation of strong, large-scale fields of periodically reversing polarity, (2) the rise of these fields to the photosphere, and (3) the processing in, spreading across, and removal from the photosphere of magnetic flux. Components (2) and (3) are discussed in Chapters 4–6; in this chapter, we concentrate on aspect (1). Even on this limited topic, there is a stream of papers, but, as Rüdiger (1994) remarked, “it is much easier to find an excellent… review about the solar dynamo… than a working model of it.”

In dynamo theory, the mean, large-scale solar magnetic field is usually taken to be the axially symmetric component of the magnetic field that can be written, without loss of generality, as the sum of a toroidal (i.e., azimuthal) component Bφ ≡ (0, Bφ, 0) and a poloidal component, which is restricted to meridional planes: Bp ≡ (Br, 0, Bθ′), where θ′ is the colatitude. The poloidal component is usually pictured as if a dipole field aligned with the rotation axis were its major component, which is a severe restriction.

All solar-cycle dynamo models rely on the differential rotation v0(r, θ′) to pull out the magnetic field into the toroidal direction, as sketched in Fig. 6.10a; about this mechanism there is no controversy.

Introduction

On the main sequence, it has long been known that large mean rotational velocities are common among the early-type stars and that these velocities decline steeply in the F-star region, from 150 km s−1 to less than 10 km s−1 in the cooler stars (see Figure 1.6). As was shown in Section 6.3.2, the observed projected velocities indicate that the mean value of the total angular momentum 〈J〉 closely follows the simple power law 〈J〉 α M2 for stars earlier than spectral type F0, which corresponds to about 1.5M⊙ (see Figure 6.7). The difficulty is not to account for such a relation, which probably reflects the initial distribution of angular momentum, but to explain why it does not apply throughout the main sequence. It has been suggested that the break in the mean rotational velocities beginning at about spectral type F0 might be due to the systematic occurrence of planets around the low-mass stars (M ≲ 1.5M⊙), with most of the initial angular momentum being then transferred to the planets. Although this explanation has retained its attractiveness well into the 1960s, there is now ample evidence that it is not the most likely cause of the remarkable decline of rotation in the F-star region along the main sequence. Indeed, following Schatzman's (1962) original suggestion, there is now widespread agreement that this break in the rotation curve can be attributed to angular momentum loss through magnetized winds and/or sporadic mass ejections from stars with deep surface convection zones.

In this final chapter we present a synopsis of the observational constraints on dynamo processes in stars with convective envelopes that complements our review of studies of the solar dynamo in Chapter 7. We do not try to summarize the rapidly growing literature on mathematical and numerical models of stellar dynamos, but rather we attempt to capture the observational constraints on dynamos in a set of propositions, following Schrijver (1996). You will encounter some speculative links that attempt to bring together different facets of empirical knowledge, but we shall always distinguish conclusions from hypotheses.

Throughout this book, we use the term dynamo in a comprehensive sense, implying the ensemble of processes leading to the existence of a magnetic field in stellar photospheres, which evolves on times scales that are very short compared to any of the time scales for stellar evolution or for large-scale resistive dissipation of magnetic fields. Such a dynamo involves the conversion of kinetic energy in convective flows into magnetic energy.

Solar magnetic activity is epitomized by the existence of small-scale (compared to the stellar surface area), long-lived (compared to the time scale of the convective motions in the photosphere), highly structured magnetic fields in the photosphere, associated with nonthermally heated regions in the outer atmosphere, in which the temperatures significantly exceed that of the photosphere. Other cool stars exhibit similar phenomena, which are collectively referred to as stellar magnetic activity.

Outer-atmospheric imaging

The nearest cool star confronted us with the reality that cool stars have extremely inhomogeneous outer atmospheres. This was first confirmed for stars other than the Sun by the modulation of broadband signals, caused by starspots, and later by the discovery of the quasi-periodic variation in the Ca II H+K signal of some cool stars by Vaughan et al. (1981) caused by the rotation of an inhomogeneously covered stellar surface. Insight in stellar dynamos requires observational data on the properties of stellar active regions and their emergence patterns. For instance, we would like to know the sizes of stellar active regions and their lifetimes, the details of the structure of starspots, the emission scale height at different temperatures, and so on. In fact, we would like to know the entire three-dimensional geometrical structure of the outer atmospheres of cool stars. For that knowledge to be obtained, stellar surfaces should somehow be imaged by sounding the atmosphere from the photosphere on out. We would like to learn all this not merely for stars with activity levels similar to that of the Sun, but also for other stars, from the extremely active, tidally interacting binary systems for which much of the surface seems to be covered by areas as bright as solar active regions with a small fraction being even brighter, down to the very slowly rotating giant stars whose average coronal brightness is well below that of a solar coronal hole.

The Sun serves as the source of inspiration and the touchstone in the study of stellar magnetic activity. The terminology developed in observational solar physics is also used in stellar studies of magnetic activity. Consequently, this first chapter provides a brief illustrated glossary of nonmagnetic and magnetic features, as they are visible on the Sun in various parts of the electromagnetic spectrum. For more illustrations and detailed descriptions, we refer to Bruzek and Durrant (1977), Foukal (1990), Golub and Pasachoff (1997), and Zirin (1988).

The photosphere is the deepest layer in the solar atmosphere that is visible in “white light” and in continuum windows in the visible spectrum. Conspicuous features of the photosphere are the limb darkening (Fig. 1.1a) and the granulation (Fig. 2.12), a time-dependent pattern of bright granules surrounded by darker intergranular lanes. These nonmagnetic phenomena are discussed in Sections 2.3.1 and 2.5.

The magnetic structure that stands out in the photosphere comprises dark sunspots and bright faculae (Figs. 1.1a and 1.2b). A large sunspot consists of a particularly dark umbra, which is (maybe only partly) surrounded by a less dark penumbra. Small sunspots without a penumbral structure are called pores. Photospheric faculae are visible in white light as brighter specks close to the limb.

The chromosphere is the intricately structured layer on top of the photosphere; it is transparent in the optical continuum spectrum, but it is optically thick in strong spectral lines.

Introduction

As we may infer from the observations, most stars remain in a state of mechanical equilibrium, with the pressure-gradient force balancing their own gravitation corrected for the centrifugal force of axial rotation. Accordingly, theoretical work has tended to focus on the figures of equilibrium of a rotating star, assuming the motion to be wholly one of pure rotation. However, detailed study of the Sun has demonstrated the existence of large-scale motions in its convective envelope, both around the rotation axis and in meridian planes passing through the axis. Theoretical work has shown that largescale meridional currents also exist in the radiative regions of a rotating star. Moreover, as new results become available, it is becoming increasingly apparent that these regions contain a wide spectrum of turbulent motions embedded in the large-scale flow. All these problems are the domain of astrophysical fluid dynamics – a field that has developed quite slowly until recently.

Over the course of the past fifty years, however, meteorologists and oceanographers have made important advances in our knowledge of the behavior of rotating fluids. I thus find it appropriate to review some dynamical concepts that are applicable to both the Earth's atmosphere and the oceans. As we shall see, all of them play a key role in providing useful ideas for quantitative analysis of large-scale motions in a rotating star.