Introduction

Stellar physics provides a natural starting point for the study of astrophysics for several reasons. To begin with, this is probably the best understood area of astrophysics. Second, there is a vast amount of reliable data dealing with stellar physics. This observational input motivates accurate and sophisticated theoretical modelling as well as provides the opportunity for a detailed comparison between models and observations. Finally, stellar physics also forms the basis for the study of several other related areas, even in the domain of extragalactic astronomy and cosmology. For example, measurements of cosmic distances and the ages of different structures – which are very important in cosmology – cannot be done without accurate modelling of the stellar phenomena that are used as tools; the study of formation and evolution of galactic systems requires an understanding of star formation and stellar evolution, etc. This volume deals with different aspects of the astrophysics of stellar systems.

The evolution of stars differs significantly, depending on whether the star is isolated or is a member of a binary system. The bulk of the chapters in the book (from Chap. 3 to Chap. 6) deal with stellar evolution and stellar remnants in isolated contexts. Chapter 7 is devoted to the study of evolution of binary stars, and Chap. 10 covers the dynamics of systems like globular clusters that have a very large number of stars.

Introduction

This chapter discusses the structure of stars that are in steady state. Concepts described in Vol. I, Chaps. 5–7, will be used extensively here. The models described here will be needed in several subsequent chapters dealing with stellar evolution, compact remnants, and binary stars.

Equations of Stellar Structure

A self-gravitating body of mass M and radius R will have gravitational potential energy of U ≈ −(GM2/R). If such a body is in equilibrium with the gas pressure balancing the gravity, the virial theorem implies that it will have temperature T such that NkBT ≈ (GM2/R that is, T ≈ (GMmp/kBR). For a sufficiently large value of M/R, this temperature can be high enough to ignite nuclear reactions at the centre of the body. The nuclear energy generated near the centre will be transported by radiation and convection towards the outer regions and will eventually escape from the body. This will establish a temperature gradient inside the body such that, in steady state, the energy produced by nuclear reactions is equal to the energy radiated away from the outer surface. Such a steady-state situation can last as long as the conditions in the body allow the generation of nuclear energy inside it. Observations suggest that the stars belong to such a category of self-gravitating bodies that are essentially powered by the nuclear reactions.

Introduction

This chapter discusses the physical features of the material that exists between the stars in our galaxy. It draws heavily from Vol. I, Chaps. 6–9.

Overview

We have seen in Chap. 3 that stars form out of clouds of gas in the galaxy. This process of star formation from the protostellar cloud is never totally efficient and will certainly lead to the existence of a residual, ambient medium around the stars. We also saw that the there is transfer of material from the stars to the surrounding region; stellar winds of high-mass stars, ejection of the outer mantle in the formation of planetary nebulas, and supernova explosions are three processes that lead to such a mass transfer. These phenomena couple the stars directly with the medium around them. This medium is generically called the interstellar medium (ISM).

The physics of the ISM is extremely complex because the medium is very inhomogeneous and is made of regions with fairly diverse physical conditions. We shall first provide a general overview and a description of the ISM and then take up specific topics for discussion.

The composition of our galaxy is made of stars that provide a mass of approximately (1010−1011) M⊙ and the ISM that provides a mass of ~109M⊙. Both stars and the ISM are distributed predominantly on the disk of the galaxy, with a typical radius of 10 kpc and a thickness of 250 pc.

Introduction

This chapter deals with several observed phenomena in binary star systems and depends on the material developed in dynamics (Vol. I, Chap. 2) and Chaps. 3, 5, and 6 of this volume. The material related to accretion disks developed here will be needed in the modelling of active galactic nuclei in Vol. III.

Overview

The discussion of stellar evolution in Chaps. 2–6 concentrated on the star as a single dynamical entity, uninfluenced by its surroundings. The evolutionary phenomena change significantly and a variety of new effects come into play if the star is a member of a binary system that consists of two stars gravitationally bound to each other. We saw in Chap. 3 that star formation takes place in giant molecular clouds in the ISM. The chances that a given star is gravitationally bound to another star is fairly high under such circumstances and – in fact – well over half of all the stars in the sky are members of binary or multiple star systems. It is therefore necessary to study the effect of a close companion on the evolution of a star.

Such an effect clearly depends on how close the two stars are. When the stars are reasonably far away (compared with the sum of their radii at any stage in their evolution) they are said to form a detached binary system, and the influence of one star on another is minimum.

During the past decade or so, theoretical astrophysics has emerged as one of the most active research areas in physics. This advance has also reflected the greater interdisciplinary nature of the research that has been carried out in this area in recent years. As a result, those who are learning theoretical astrophysics with the aim of making a research career in this subject need to assimilate a considerable amount of concepts and techniques, in different areas of astrophysics, in a short period of time. Every area of theoretical astrophysics, of course, has excellent textbooks that allow the reader to master that particular area in a well-defined way. Most of these textbooks, however, are written in a traditional style that focusses on one area of astrophysics (say stellar evolution, galactic dynamics, radiative processes, cosmology, etc.) Because different authors have different perspectives regarding their subject matter, it is not very easy for a student to understand the key unifying principles behind several different astrophysical phenomena by studying a plethora of separate textbooks, as they do not link up together as a series of core books in theoretical astrophysics covering everything that a student would need.

Introduction

This chapter deals with the physics of the Sun and the constituents of the solar system. It draws heavily on the material developed in Chaps. 2 and 3 and on Vol. I, Chaps. 2, 8, and 9.

The Standard Solar Model

Given the mass of the Sun, its initial composition, and its current age, we should be able to develop a model for the Sun by using the equations described in Chaps. 2 and 3. Such an evolutionary calculation will predict all other structural properties of the Sun at the present time, which may then be compared with observations. Among the input variables, the mass of the Sun, M⊙ = (1.9891 ± 0.0004) × 1033 gm, is known quite accurately. The age of the Sun has to be estimated indirectly and is expected to be approximately (4.5 ± 0.1) × 109 yr. The initial composition of the Sun is not well known but the ratio Z/X = 0.02739–0.02765 is thought to be well determined. Because X + Y + Z = 1 and Z/X are given, the initial composition can be parameterised by a single variable, say, the value of helium fraction Y. By varying the value of Y, we can construct a class of solar models and choose the one that fits best with the observations. In reality, there arises (at least) one more parameter in modelling the solar structure because of theoretical uncertainty in the description of convection.

Introduction

This chapter deals with several time-dependent stellar phenomena and – in particular – with the time evolution of stellar structures. It uses the results of the last chapter extensively and also draws on the material covered in Chaps. 5, 8, 10, and 12 of Vol. I.

In the last chapter we discussed the time-independent equilibrium configuration for stars, which were treated as self-gravitating bodies with ongoing nuclear reactions in the core. These stars have characteristic masses in the range (0.1–60) M⊙ and central temperatures that are higher than ~107 K. Because nuclear reactions can fuel an object for only a finite period of time, of the order of tnuc ≈ 1010(M/M⊙)−2.5 yr [see Eq. (2.31) of Chap. 2], it is clear that any particular star must have formed at some finite time in the past. Similarly, the nuclear reactions will be able to provide a steady state for the star for only a finite period into the future. The structure of the star must evolve over time scales comparable with the nuclear-reaction time scale.

In studying such evolution, there are three phases that are best addressed individually. To begin with, we have to understand how the stars of different masses form out of gas in the interstellar medium (ISM). Second, we should follow the structural changes in the star as the nuclear reactions that power the star evolve in time.

Introduction

This chapter deals with three possible stellar remnants: white dwarfs, neutron stars, and black holes. It relies heavily on the previous two chapters as well as on Chaps. 3, 5, and 9–12 of Vol. I. The material covered here will be needed in Chap. 6 (pulsars), Chap. 7 (binary stars), and in the study of active galactic nuclei in Vol. III.

Another closely related class of remnants, called pulsars, are known to be rotating neutron stars and will be discussed separately in Chap. 6. An entirely new class of physical phenomena arises when a compact object forms a constituent of a binary system. The role of stellar remnants in binary systems will be studied separately in Chap. 7.

Structure of White Dwarfs

It was seen in Chap. 3 that the end point of stellar evolution can lead to self-gravitating objects supported by degeneracy pressure. Such astrophysical objects are usually termed compact because, as we shall see, their sizes are significantly smaller than main-sequence stars of similar mass.

Introduction

The points of light in the night-time sky that we call stars can be divided into two categories. There are the truly single stars, like the Sun, which may happen to have a retinue of planets in orbit about them, with planetary masses that are found, at least in our Solar System, to total less than one-thousandth of the mass of the parent star. There are also pairs of stars, with the two components moving in bound orbits about their common centre of mass, which we call binary systems of stars, or just binary stars. Extensive observational programmes (Abt 1983) have demonstrated that single stars are about as common as binary stars, or, to put it another way, there are about 50% more individual stars in the sky than there are observable points of light. This means that the components of these binary stars are so close together that we cannot visually resolve them spatially into two separate stars. Appropriately, they are referred to as close binary stars, as distinguished from the more obvious visual binary stars, for which the observer can clearly resolve the two components and measure their apparent motions on the sky around the centre of mass of the binary system. Indeed, we have discovered a substantial number of visual binaries whose components are themselves close binaries, so that some apparently double, or even triple, stars have been found to be quadruple or sextuple systems.

Introduction

Imaging, or mapping, is a natural part of our studies of binary stars, because of two factors: Stars spin on their rotation axes, usually in synchronism, and they orbit the centre of mass of the system, together with any other structures that belong to the binary. In effect, an observer ‘walks around’ the binary once per orbital period and is able to view the system from all of the orbital phase angles that are recorded via photometric, spectroscopic, and polarimetric means. In addition, because of the modem developments in astronomy, an observer has a more nearly bolometric view, and the radiation emitted from gases at very different temperatures, even within one binary system, can now be studied properly. Unfortunately, no close-binary system with interesting interactions between its components can yet be spatially resolved directly from Earth, because of the large distances to all the stars, so an observer sees only an integrated total amount of radiation at each observed wavelength from all the contributors in the binary – our points of light in the night-time sky again. But, as we have seen, the mutual eclipses of the components in suitably oriented binaries offer us a natural scanning mechanism that reveals the presence of those separate components, which can then be studied via all our observational tools. The Doppler effect, acting through the absorption/emission lines, provides velocities and hence inferred locations for the various contributors as well, and the polarization of the radiation reveals the distributions of scatterers and of magnetic fields.