The central premise of modern cosmology is that, at least on large scales, the Universe is homogeneous and isotropic. This is borne out by a variety of observations, most spectacularly the nearly identical temperature of microwave background radiation coming from different parts of the sky. Despite the belief in homogeneity on large scales, it is all too apparent that in nearby regions the Universe is highly inhomogeneous, with material clumped into stars, galaxies, and galaxy clusters. It is believed that these irregularities have grown over time, through gravitational attraction, from a distribution that was more homogeneous in the past.

It is convenient then to break up the dynamics of the Universe into two parts. The largescale behaviour of the Universe can be described by assuming a homogeneous and isotropic background. On this background, we can superimpose the short-scale irregularities. For much of the evolution of the Universe, these irregularities can be considered to be small perturbations on the evolution of the background Universe, and can be tackled using linear perturbation theory; we discuss this extensively, starting in Chapter 4. It is also possible to continue beyond the realm of linear perturbation theory, via a range of analytic and numerical techniques, which we discuss only briefly, in Chapter 11. In this chapter and the next, we concern ourselves solely with the evolution of the background, isotropic Universe. This usually is called the Robertson Walker Universe, often with Friedmann and occasionally with Lemaitre also named.

When I wrote my first book – Theory of Rotating Stars (Princeton: Princeton University Press, 1978) – I was not aware of the fact that the 1970s were a period of transition and that major unexpected developments would take place in the field of stellar rotation during the 1980s.

In the mid-1970s, we had no direct information about the internal rotation of the Sun. Little was known about the rotation of main-sequence stars of spectral type G and later, although it was already well established that the surface rotation rate of these stars decayed as the inverse square root of their age. We certainly had much more information about axial rotation in the upper-main-sequence stars, but the actual distribution of specific angular momentum within these stars was still largely unknown. On the theoretical side, important progress in the study of rotating stars had been made by direct numerical integration of the partial differential equations of stellar structure. However, because there was no clear expectation for the actual rotation law in an early-type star, the angular momentum distribution always had to be specified in an ad hoc manner. The presence of large-scale meridional currents in a stellar radiative zone was also a serious problem: All solutions presented to date had unwanted mathematical singularities at the boundaries, and the back reaction of these currents on the rotational motion had never been properly taken into account.

The magnetic field that corresponds to conspicuous features in the solar atmosphere is found to be confined to relatively small magnetic concentrations of high field strength in the photosphere. Between such concentrations, the magnetic field is very much weaker. The strong-field concentrations are found at the edges of convective cells: convective flows and magnetic field tend to exclude each other. These time-dependent patterns indicate that the magnetic structure observed in the solar atmosphere is shaped by the interplay between magnetic field, convection, and large-scale flows.

The construction of a comprehensive model for the main phenomena of solar magnetic activity from basic physical principles is beyond our reach. The complex, nonlinear interaction between turbulent convection and magnetic field calls for a numerical analysis, but to bring out the main observed features would require simulations of the entire convection zone and its boundary layers. The intricacy of convective and magnetic features indicates that extremely fine grids in space and in time would be required. Such an ambitious program is far beyond the power of present supercomputers. Hence, we must gain insight into the solar magnetic structure and activity first by studying the observational features, and subsequently by trying to interpret and model these with the theoretical and numerical means at hand.

Our approach is to map the domain of solar magnetic activity by a mosaic of models. Some of these models are well contained; others are based on ad hoc assumptions.

Historical development

The study of stellar rotation began at the turn of the seventeenth century, when sunspots were observed for the first time through a refracting telescope. Measurements of the westward motion of these spots across the solar disk were originally made by Johannes Fabricius, Galileo Galilei, Thomas Harriot, and Christopher Scheiner. The first public announcement of an observation came from Fabricius (1587–c. 1617), a 24-year old native of East Friesland, Germany. His pamphlet, De maculis in Sole observatis et apparente earum cum Sole conversione, bore the date of dedication June 13, 1611 and appeared in the Narratio in the fall of that year. Fabricius perceived that the changes in the motions of the spots across the solar disk might be the result of foreshortening, with the spots being situated on the surface of the rotating Sun. Unfortunately, from fear of adverse criticism, Fabricius expressed himself very timidly. His views opposed those of Scheiner, who suggested that the sunspots might be small planets revolving around an immaculate, nonrotating Sun. Galileo made public his own observations in Istoria e Dimostrazioni intorno alle Macchie Solari e loro Accidenti. In these three letters, written in 1612 and published in the following year, he presented a powerful case that sunspots must be dark markings on the surface of a rotating Sun. Foreshortening, he argued, caused these spots to appear to broaden and accelerate as they moved from the eastern side toward the disk center.

Introduction

Consider a single star that rotates about a fixed direction in space, with some assigned angular velocity. As we know, the star then assumes the shape of an oblate figure. However, we are at once faced with the following questions. What is the geometrical shape of the free boundary? What is the form of the surfaces upon which the physical variables (such as pressure, density, …) remain a constant? To sum up, what is the actual stratification of a rotating star, and how does it depend on the angular velocity distribution? For rotating stars, we have no a priori knowledge of this stratification, which is itself an unknown that must be derived from the basic equations of the problem. This is in sharp contrast to the case of a nonrotating star, for which a spherical stratification can be assumed ab initio.

In principle, by making use of the equations derived in Section 2.2, one should be able to calculate at every instant the angular momentum distribution and the stratification in a rotating star. Obviously, this is an impossible task at the present level of knowledge of the subject, even were the initial conditions known. Until very recently, the standard procedure was to calculate in an approximate manner an equilibrium structure that corresponds to some prescribed rotation law, ruling out those configurations that are dynamically or thermally unstable with respect to axisymmetric disturbances (see Sections 3.4.2 and 3.5).

Introduction

In Section 3.3.1 we noted that the conditions of mechanical and radiative equilibrium are, in general, incompatible in a rotating barotrope. This paradox can be solved in two different ways: Either one makes allowance for a slight departure from barotropy and chooses the angular velocity Ω = Ω(ϖ, z) so that strict radiative equilibrium prevails at every point or one makes allowance for large-scale motions in meridian planes passing through the rotation axis. The first alternative is mainly of academic interest because there is no reason to expect rotating stars to select zero-circulation configurations. Moreover, these baroclinic models are thermally unstable with respect to axisymmetric motions, as well as dynamically unstable with respect to nonaxisymmetric motions (see Sections 3.4 and 3.5). Hence, the slightest disturbance will generate three-dimensional motions and, as a result, a large-scale meridional circulation will commence. The second alternative was independently suggested by Vogt (1925) and Eddington (1925), who pointed out that the breakdown of strict radiative equilibrium in a barotrope tends to set up slight rises in temperature and pressure over some areas of any given level surface and slight falls over other areas. The ensuing pressure gradient between the poles and the equator thereby causes a flow of matter. In fact, it is the small departures from spherical symmetry in a rotating star that lead to unequal heating along the polar and equatorial radii, which in turn causes large-scale currents in meridian planes.

Introduction

Star formation (SF) is a local phenomenon which must find its explanation in the stability and fragmentation of dense molecular clouds. Studies in our own Galaxy have focussed on the structure of dense proto-stellar cores and the chemical and thermal balance of star-forming regions. These studies lend indirect support to a Schmidt (1959) law, but emphasize the need to include explicitly the structure of the multi-phase ISM to model accurately the most important heating and cooling processes. A large unknown in these investigations is the role of feedback. Supernova explosions and stellar radiation associated with the process of SF influence the global physical structure of the interstellar gas which supports this process.

Introduction

The nature of the X-ray emission of early-type, prominent-bulge spirals has been the subject of an on-going controversy, which has sought to establish if and how much of this emission can be ascribed to thermal emission of an optically thin hot gaseous medium. This is an important issue, because if it can be established that the X-ray emission is dominated by gravity-bound gaseous halos, the X-ray data may be used to measure the mass of these galaxies (see review in Fabbiano 1989).

In what follows, I give a summary of the work on this subject, and point out future opportunities.

A Brief History of X-ray Studies of Early-type Spirals

With the clear exception of M31, most of the bulges of early-type spirals could not be studied in detail with X-ray observatories, starting with the Einstein Observatory, in the early ʾ80s, and including all the facilities in orbit and operational at this time.

Introduction

HST UV images of nearby galaxies presented by Maoz et al. (1996) and Barth et al. (1998), as well as analogous space-borne optical images of early-type galaxies discussed by Lauer et al. (1995) and Carollo et al. (1997) have shown that about 15% of imaged galaxies show evidence of unresolved central spikes.

In the following we discuss two ‘prototype’ galactic spheroids, NGC 2681 and NGC 4552, that we properly monitored with HST–which host UV-bright, unresolved spikes at their center. While the early-spiral (Sa) galaxy NGC 2681 shows a nonvariable unresolved cusp, the UV spike which became visible at the center of the Virgo Elliptical NGC 4552 is a UV flare caught in mid-action, presumably related to a transient accretion event onto a central supermassive black hole (Renzini et al. 1995; Cappellari et al. 1998).

Introduction

NGC 4698 is classified Sa by Sandage & Tammann (1981) and Sab(s) by de Vaucouleurs et al. (1991; RC3). Sandage & Bedke (1994; CAG) present NGC 4698 as an example of the early-to-intermediate Sa type since it is characterized by a large central bulge and tightly wound spiral arms. In addition to a remarkable geometrical decoupling between the bulge and the disk (whose apparent major axes appear oriented in an orthogonal way upon simple visual inspection of galaxy plates; see Panels 78, 79 and 87 in CAG), a spectrum taken along the minor axis of the disk shows the presence of a stellar velocity gradient which could be ascribed to the bulge.

The innermost, denser regions of galaxies, i.e., the ‘bulges’, are a fundamental component of galaxies whose properties define the entire Hubble sequence. Understanding the origin of bulges is thus a required step toward understanding how such a sequence has come to place, i.e., toward deciphering how stars and galaxies condensed from the diffuse material in space into the structure that we observe today. Several decades of exploration of the Milky Way and Local Group bulges, and of nearby bulges external to the Local Group, have slowly built the orthodox view that bulges as a family should be reasonably old isotropic rotators with near-solar mean chemical abundances (although with a very wide abundance distribution function), i.e., nothing more than low-luminosity ellipticals. However, some major breakthroughs in the last few years concerning bulges in the local and early universe suggest that the time is ripe to perhaps reconsider this orthodoxy. The new picture that emerges from the most recent Hubble Space Telescope (HST) and 10m-class ground-based telescopes studies challenges the canonical beliefs about what bulges really are, how and when they form, and about the physical mechanisms that are important in determining their fundamental properties. Basic, and yet fundamental questions still need an answer: (i) Are bulges a one-parameter or a multi-parameter family? What are the average properties of bulges in terms of stellar populations and dynamics? What are the deviations from these averages?

Introduction

An important tool for galaxy research is the study of the surface brightness (SB) distribution. For spiral galaxies the determination of the scale length of the exponential disk has a long traditition (e.g. Courteau 1996). However, the errors in these results are still rather large (Knapen & van der Kruit 1991).

For a better understanding of spiral galaxies it is necessary to study the structure of both disk and bulge as well. In order to separate non-axisymmetric structures as bars or triaxial bulges from the axisymmetric disk, two-dimensional fits are advantageous (e.g. de Jong 1996). In the following I present a generalization of a nonlinear direct fit method to the two-dimensional SB distribution of near-infrared (NIR) images of spiral galaxies.

NIR Data

The aim of this project is the study of the distribution of the mass-carrying evolved stars in spiral galaxies of different Hubble types. For this purpose, NIR observations are advantageous since they have much less perturbations due to dust or especially bright young stars.

The observations were performed during several runs at the 2.2m telescope of the German-Spanish observatory on Calar Alto, Spain. The detector was the MAGIC-NIR-camera with a NICMOS chip of (0.67″) 256×256 pixels, for a total field of view of ≈ 3′ × 3′.