The interstellar medium

Although to all intents and purposes a single or binary star may be regarded as evolving isolated in empty space, not only is it a member of a very large system of stars – a galaxy – but it is also immersed in a medium of gas and dust, the interstellar medium. This background material (mostly gas) amounts, in our Galaxy, to a few percent of the galactic mass, some 109 M ⊙, concentrated in a very thin disc, less than 103 light-years in thickness (we recall that 1 ly ≃ 9.5 × 1015 m), and ∼105 light-years in diameter, near the galactic midplane. Its average density is extremely small, about one particle per cubic centimetre, corresponding to a mass density of 10−21 k gm−3 (10−24 g cm−3); in an ordinary laboratory it would be considered a perfect ‘vacuum’. The predominant component of galactic gas – of which stars are formed – is hydrogen, amounting to about 70% of the mass, either in molecular form (H2), or as neutral (atomic) gas (HI) or else as ionized gas (HII), depending on the prevailing temperature and density. Most of the remaining mass is made up of helium. The interstellar material is not uniformly dispersed, but resides in clouds of gas and dust, also known as nebulae. We have already encountered special kinds of such nebulae: planetary nebulae, supernova remnants and nova shells.

What is a binary star?

As it turns out, the majority of stars are members of binary systems, or even multiple systems. The term binary in the stellar context was coined in 1802 by William Herschel only a few years after he introduced the term planetary nebula, as mentioned in Section 9.7. The first telescopic discovery of a double star, Mizar, is attributed to Giambattista Riccioli in 1650, just 41 years after Galileo's first telescope. Other stellar pairs were found by the mid-eighteenth century, but little effort was devoted at the time to their study.

A binary system consists of two stars revolving around their common centre of mass, as shown in Figure 11.1, and is defined by three parameters: the masses of its member stars and the distance d between their centres. The distance is not necessarily constant in time; it may vary periodically or change secularly. The masses, too, may change in the course of time. So perhaps a better characterization should be: initial masses and separation, and current age. Each parameter spans a wide range of values and their combinations are innumerable. In most cases, however, the members are so far apart that their individual structures and evolutionary courses are barely affected; they are thus no different from single stars, except that their dynamics as point masses is more complicated.

Binary stars are born together as a bound system; in principle, a star may capture another, in the presence of a third body, into a bound (negative energy) state, but the chances for that to happen are small even in a dense star cluster.

Having answered the two basic questions posed at the the end of Chapter 2, our present task is to combine the knowledge acquired so far into a general picture of the evolution of stars. We recall that the timescale of stellar evolution is set by the (slow) rate of consumption of the nuclear fuel. Now, the rate of nuclear burning increases with density and rises steeply with temperature, and the structure equations of a star show that both the temperature and the density decrease from the centre outward. We may therefore conclude that the evolution of a star will be led by the the central region (the core), with the outer parts lagging behind it. Changes in composition first occur in the core, and as the core is gradually depleted of each nuclear fuel, the evolution of the star progresses.

Thus insight may be gained into the evolutionary course of a star by considering the changes that occur at its centre. To obtain a simplified picture of stellar evolution, we shall characterize a star by its central conditions and follow the change of these conditions with time. We have seen that besides the composition, the temperature and density are the only properties required in order to determine any other physical quantity. If we denote the central temperature by Tc and the central density by ρc , the state of a star is defined at any given time t by a pair of values: Tc (t) and ρc (t). Consider now a diagram whose axes are temperature and density.

It is now a decade since the publication of the first edition of this book. Despite the large number of research papers devoted to the subject during this period of time, the basic principles and their applications that are addressed in the book remain valid and hence the original text has been mostly left unchanged. And yet a major development did occur soon after the book first appeared in print: the ‘solar neutrino problem’ that had puzzled physicists and astrophysicists for almost four decades finally found its solution, which indeed necessitated new physics. However, the new physics belongs to the theory of elementary particles, which must now account for neutrino masses, rather than to the theory of stars. Also worth mentioning is a major recent discovery that finally provides support to the theory proposed about four decades ago regarding the end of very massive stars in powerful supernova explosions triggered by pair-production instability: SN2006gy, the first observed candidate for such a mechanism. Thus the section on solar neutrinos is now complete and that on supernovae expanded.

Stellar evolution calculations have made great progress in recent years, following the rapid development of computational means: increasingly faster CPUs and greater memory volumes. Nevertheless, I have made use of new results only when they provide better illustration for points raised in text. For the most part, old results are still valid and this long-term validity is worth emphasizing; the theory of stellar structure and evolution, with all its complexity, is a well-established physical theory.

In the previous chapter we have dealt with models of the stellar structure under conditions of thermal and hydrostatic equilibrium. But in order to accomplish our first task toward understanding the process of stellar evolution – the investigation of equilibrium configurations – we must test the equilibrium configurations for stability. The difference between stable and unstable equilibrium is illustrated in Figure 6.1 by two balls: one on top of a dome and the other at the bottom of a bowl. Obviously, the former is in an unstable equilibrium state, while the latter is in a stable one. The way to prove (or test) this statement is also obvious and it is generally applicable; it involves a small perturbation of the equilibrium state. Imagine the ball to be slightly perturbed from its position, resulting in a slight imbalance of the forces acting on it. In the first case, this would cause the ball to slide down, running away from its original position. In the second case, on the other hand, the perturbation will lead to small oscillations around the equilibrium position, which friction will eventually dampen, the ball thus returning to its original point. The small imbalance led to the restoration of equilibrium by opposing the tendency of the perturbation. Thus a stable equilibrium may be maintained indefinitely, while an unstable one must end in a runaway, for random small perturbations are always to be expected in realistic physical systems.

As a star consists of a mixture of ions, electrons and photons, the physics of stellar interiors must deal with (a) the properties of gaseous systems, (b) radiation and (c) the interaction between gas and radiation. The latter may take many different forms: absorption, resulting in excitation or ionization; emission, resulting in de-excitation or recombination; and scattering. In order not to stray too far from our main theme, we shall only consider processes and properties that are simple enough to understand without requiring an extended physical background, and yet sufficient for providing some insight into the general behaviour of stars. The full-scale processes are incorporated in calculations of stellar structure and evolution, performed on powerful computers by means of extended numerical codes that include enormous amounts of information. These, however, should be regarded as computational laboratories, meant to reproduce, or simulate, rather than explain, the behaviour of stars. Our purpose is to outline the basic principles of stellar evolution and we are therefore entitled to some simplification. Eddington defends this right quite forcefully:

Observational evidence of mass loss

It is an acknowledged fact that stars lose mass. In addition to the outflow of photons, there usually is an outflow of material particles. But unlike the flow of radiation, which is supplied by energy generation in the interior, the flow of mass is not replenished. As a result, the stellar mass decreases at a rate that is usually measured in solar masses per year and denoted by Ṁ, where the negative sign is omitted. Shedding of mass may take two forms: a sudden ejection of a mass shell, usually following an explosion, or a continuous flow, usually referred to as a wind. We shall deal with explosive mass ejection in Chapter 10, and devote the present discussion to stellar winds.

Indirect evidence for mass loss was brought in the previous chapter and theoretical indication for its probable occurrence was mentioned in Chapter 5. There is, however, direct observational evidence for continuous rapid expansion of the outer layers of stars beyond the stellar photosphere that marks the outer edge, and into the interstellar medium. The most common is exhibited by a characteristic shape of spectral lines, known as P-Cygni lines, named after the star P Cygni – one of the brightest in our Galaxy, discovered in 1600 as a new star (see upcoming Chapters 10 and 11) – where they are prominent. A P-Cygni line profile consists of a blue-shifted absorption component and a red-shifted emission component.

What is a star?

A star can be defined as a body that satisfies two conditions: (a) it is bound by self-gravity; (b) it radiates energy supplied by an internal source. From the first condition it follows that the shape of such a body must be spherical, for gravity is a spherically symmetric force field. Or, it might be spheroidal, if axisymmetric forces are also present. The source of radiation is usually nuclear energy released by fusion reactions that take place in stellar interiors, and sometimes gravitational potential energy released in contraction or collapse. By this definition, a planet, for example, is not a star, in spite of its stellar appearance, because it shines (mostly) by reflection of solar radiation. Nor can a comet be considered a star, although in early Chinese and Japanese records comets belonged with the ‘guest stars’ – those stars that appeared suddenly in the sky where none had previously been observed. Comets, like planets, shine by reflection of solar radiation and, moreover, their masses are too small for self-gravity to be of importance.

A direct implication of the definition is that stars must evolve: as they release energy produced internally, changes necessarily occur in their structure or composition, or both. This is precisely the meaning of evolution. From the above definition we may also infer that the death of a star can occur in two ways: violation of the first condition – self-gravity – meaning breakup of the star and scattering of its material into interstellar space, or violation of the second condition – internally supplied radiation of energy – that could result from exhaustion of the nuclear fuel.

For over ten years I have been teaching an introductory course in astrophysics for undergraduate students in their second or third year of physics or planetary sciences studies. In each of these classes, I have witnessed the growing interest and enthusiasm building up from the beginning of the course toward its end.

It is not surprising that astrophysics is considered interesting; the field is continually gaining in popularity and acclaim due to the development of very sophisticated telescopes and to the frequent space missions, which seem to bring the universe closer and make it more accessible. But students of physics have an additional reason of their own for this interest. The first years of undergraduate studies create the impression that physics is made up of several distinct disciplines, which appear to have little in common: mechanics, electromagnetism, thermodynamics and atomic physics, each dealing with a separate class of phenomena.

Astrophysics – in its narrowest sense, as the physics of stars – presents a unique opportunity for teachers to demonstrate and for students to discover that complex structures and processes do occur in Nature, for the understanding of which all the different branches of physics must be invoked and combined. Therefore, a course devoted to the physics of stars should perhaps be compulsory, rather than elective, during the second or third year of physics undergraduate studies. The present book may serve as a guide or textbook for such a course.

Stars of the types considered in this chapter differ from those discussed so far, inasmuch as, for various reasons, they do not (or cannot) appear on the H–R diagram. As before, we shall rely on stellar evolution calculations to describe them. Whenever possible, we shall confront the results and predictions of the theory with observations, either directly or based on statistical considerations. We shall find that, as we approach the frontiers of modern astrophysics, theory and observation go more closely hand in hand.

What is a supernova?

We should start by making acquaintance with the astronomical concept of a supernova, as we did with main-sequence stars, red giants and white dwarfs in Chapter 1. Stars undergoing a tremendous explosion (sudden brightening), during which their luminosity becomes comparable to that of an entire galaxy (some 1011 stars!), are called supernovae. Historically, nova was the name used for an apparently new star; eventually it turned out to be a misnomer, novae being (faint) stars that brighten suddenly by many orders of magnitude. So are supernovae, but on a much larger scale. Not until the 1930s were supernovae recognized as a separate class of objects within novae in general. They were so called by Fritz Zwicky, after Edwin Hubble had estimated the distance to the Andromeda galaxy (with the aid of Cepheids) and had thus been able to appreciate the unequalled luminosity of the nova discovered in that galaxy in 1885, amounting to about one sixth of the luminosity of the galaxy itself.