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.

Introduction

If binary stars simply executed their orbits according to Newtonian theory for point masses, then interest in their properties would have waned long ago, save for the need to improve determinations of stellar masses. The universe is rather more exciting, however, and at least the close binary stars (as defined in Chapter 1) display all manner of perturbations and interactions that guarantee that they will continue to provide an abundance of astrophysical phenomena that will require explanation. In this chapter we consider a sequence of progressively greater departures from the point-mass, spherical-star model that we used in Chapters 2 and 3.

We consider, firstly, a theory of mild perturbations, or deviations from the idealized spherical shape for a star, which theory can fully explain the observed phenomena of apsidal motion, the circularization of orbits, and the synchronization of stellar axial-rotation periods and orbital periods. The stars in such binary systems become tidally locked, such that two stellar hemispheres face each other, and two are permanently averted. The logical extension of these perturbations is to the Roche model for binary stars that is applicable to tidally locked systems in circular orbits. Here the stars can be virtually spherical in shape when their radii (R) are small relative to their separation (a)(R/a < 0.10), and they appear no different from those in the earlier point-mass theory. But the Roche model also permits stars to become seriously distorted from spherical shape, with R/a > 0.20, far beyond the limitations of the earlier perturbation theory.

Introduction

For many observational astronomers who study the properties of binary stars, the ultimate goal of their work is to make direct determinations of the masses, radii, shapes, temperatures, and luminosities of the component stars, often referred to as the astrophysical parameters. The term absolute dimensions has been used to indicate that analyses of the radial-velocity curves and light curves for binaries really do provide descriptions of the stars in SI units, regardless of the distances of the binaries from us. As noted in Chapter 1, because the luminosities of the stars in binaries are determined directly, they act, potentially, as excellent standard candles for distance determinations amongst nearby galaxies. Much effort has been devoted to finding ways of ensuring that such data are free from systematic errors and have the smallest possible random errors, so that direct comparisons can be made between these empirical results and the predictions from stellar-structure and stellar-evolution theories applied to binary stars. The main theme underlying Chapters 3–5 in this text has been to demonstrate the ways in which systematic errors can be overcome, and random errors minimized, by making use of spectroscopy and photometry at the best spectral and temporal resolution consistent with the observational task at hand. This chapter will summarize the progress that has been achieved in these directions amongst the different subclasses of binary stars.

The subject of binary stars is always discussed in introductory texts in astronomy and astrophysics. The usual prescription involves the distinctions between visual (or resolved) binaries and the spectroscopic and eclipsing binaries, as well as schematic examples of resolved orbits, radial-velocity curves, and light curves. Examples of interacting binaries are discussed, and there are artists' impressions of Roche-lobe-filling stars sending gas streams across to impact an accretion disc surrounding a black hole, with jets of ejected matter from the inner regions of a thick accretion disc interacting with the local interstellar medium. A brief discussion usually emphasizes the importance of binaries for the determination of stellar masses and other parameters and their central role in explaining the properties and evolutionary states of many unusual stellar objects, such as novae, symbiotic stars, and x-ray binaries.

I have assumed that the reader of this text has already benefited from an introductory course in astronomy, including a careful reading of one of the many excellent introductory texts currently available. The basic ideas of astrophysics, including stellar evolution and the essential ideas about binary stars, should be well understood. I have assumed also that the reader has studied physics and mathematics to a similar level. Beyond these assumptions, I have tried to write a text that will be readily understood by an intermediate-to-advanced-Ievel undergraduate in astrophysics who is interested in the more practical, observational, and data-analysis aspects of studies of close binary stars.