Introduction

. it is reasonable to hope that in a not too distant future we shall be competent to understand so simple a thing as a star.

The Internal Constitution of the Stars, by Arthur S. Eddington [86]

Stars are the 'integers' of our universe. There are about stars in the Milky Way alone, and countless other star-filled galaxies fill our universe. Apart from dark matter, whose nature is currently unknown, stars are the dominant component of the mass of any galaxy. They also emit their light at wavelengths that can be detected by the human eye, so historically they have been accessible to us. Long before radio telescopes, long before space-based infra-red (IR), ultra-violet (UV), X-ray or -ray telescopes, and long before Galileo turned his optical telescope on the Milky Way, we could identify these integers as pin-points of light in the sky. Stars are the first point of connection between human beings and the larger universe within which we live.

From the earliest times, we have tried to comprehend and explain the stellar firmament. Mythologies arose, from arctic Inuit tales of a brother and sister whose disagreement sent them apart from each other to become the Sun and Moon, to Greek stories of heroes and gods, to Mayans who saw the Milky Way as a road for the souls of the underworld - each civilization has attempted to make sense of the heavens. The same Sun and the same Moon shine down on all of us. If we are at the same latitude on Earth, we see the same stars as well, providing a commonality of experience and a continuity in our search to understand these twinkling messengers.

In our modern age, this search has evolved and developed into a scientific framework, one of observation, measurement and analysis. But putting it all together still requires a kind of story-telling. The story must be consistent, fit the facts, and be numerically accurate. It must make sense and not contradict what we know from other established knowledge. Ultimately, though, the final scientific step requires a synthesis of this knowledge, leading to a story that makes sense. Stars have provided rich fodder for such a process.

The Danish astronomer Tycho Brahe (1546-1601) pre-dates the telescope, but using as precise instruments as possible at the time, he made careful observations of stellar and planetary positions. One could argue that astronomy, as a science that involves accurate positional measurements, dates from that time. Shortly thereafter, Johannes Kepler (1571-1630) used the planetary measurements of Brahe to derive his three laws of planetary motion. Kepler's Laws endure to this day, but it wasn't until Isaac Newton (1642-1727) that Kepler's laws could be derived from the Universal Law of Gravitation, and it wasn't until Albert Einstein (1879-1955) that Newton's laws were put into the context of the General Theory of Relativity.

But what about astrophysics? When did astronomy morph into astrophysics?

This transition started with stars ('of the stars' is astron, in Greek ). As the atomic nucleus was being explored about 100 years ago, so was the stellar core. It is worth pausing to think about this. Our modern view of the universe as an expanding space filled with the tiny perturbations of gravitational waves, the existence of black holes, powerful jets emerging from active galactic nuclei, pulsars that rotate with a higher accuracy than man-made clocks, exploding massive stars - all of that knowledge has arisen in only 100 years, just a tiny dot on the human evolutionary roadway. It started with the physics of stars, with an attempt to understand what actually powers the stars, and the implications of that power.

Figure I.1 Two early astrophysicists. Left: The eminent Sir Arthur Stanley Eddington (b. 1882 Kendal, d. 1944 Cambridge). Credit: The Library of Congress / Wikimedia commons / Public domain. Right: Eddington's biographer and student, Dr Alice Vibert Douglas (b. Montreal 1894, d. Kingston 1988). Credit: Notman & Son Photographers. Queen's University Archives, Kingston.

There were a number of players in this process of discovery, but one individual does stand out as, arguably, the first astrophysicist: Sir Arthur S. Eddington (1882-1944), shown in Fig. I.1 (Left). Famous for his solar eclipse expedition of 1919, which supported Einstein's General Theory of Relativity, Eddington both advanced and popularized the physics of stars. Eddington's engaging and foundational book, The Internal Constitution of the Stars (1926) [86], set out the principles of physics as applied to stars, much of which stands the test of time.

Eddington's students included Subrahmanyan Chandrasekhar, Leslie Comrie, Cecilia Payne-Gaposchkin, Hermann Bondi, Georges Lemaître and Alice Vibert Douglas, each of whom nudged, pushed or hurled the new field of astrophysics forward. Dr Alice Vibert Douglas (Fig. I.1 Right) also became Eddington's biographer [309]. Each has an asteroid named after them: (2761) Eddington and (3269) Vibert Douglas. The early development of stellar astrophysics firmly establishes this field as a mature discipline, yet one in which much active, dynamic and engaging research is being carried out today. This text is designed to explore both well-established nuts and bolts as well as modern puzzles of the field.

I.1 THE SIMPLE PHYSICAL STAR

In this text, we consider a 'star' to be a self-gravitating object that is undergoing sustained nuclear fusion (referred to as 'burning') of non-isotopic hydrogen in the stellar interior. This may be a mouthful, but there are reasons for being so specific.

Many objects are closely related, but we do not call them stars. For example, gaseous planets like Jupiter may be formed by processes similar to stars. However, we do not consider them to be stars because they cannot sustain interior hydrogen fusion reactions.1 Objects like white dwarfs, pulsars and black holes are stellar remnants. They are not stars for the same reason. A nova is the brightening of a white dwarf star because of nuclear reactions at the surface when mass falls onto it, but this does not make a nova a star by our requirement of interior nuclear reactions. The burning of deuterium, which is an isotope of hydrogen (one proton and one neutron in its nucleus), occurs at a lower temperature than normal hydrogen burning. Therefore, deuterium reactions can occur in the late stages of stellar formation and can also occur in substellar objects whose masses are higher than 13 times the mass of Jupiter. These are also excluded from our pantheon of bona fide stars because deuterium is an isotope of hydrogen.

On the other hand, a red giant, depending on its evolutionary stage, may be undergoing hydrogen burning in an interior shell and not its core. Such an object, by our definition, is indeed a star. The stars, then, include all objects that are on the main sequence (see Fig. I.2 in Sect. I.4) which, by definition, represent those that are burning hydrogen into helium in their cores (Sect. 5.4) as well as all objects that have evolved off of the main squence prior to ejecting most of their mass (Sect. 8.2).

You can see that we have sought a physical definition of a star, but historically, such understanding was not necessarily known. For example, a white dwarf just looks like a faint star in the sky, so it is common to see 'white dwarf star' in the literature. Similarly, 'neutron star' is commonly used. The word 'nova' has been simplified from stella nova, meaning 'new star'. Again, such terminology predates the physics.

How could our self-gravitating star be 'simple', as the title to this section suggests? In fact, if we include stars of different masses as well as stellar remnants, just about every subfield of physics is represented: molecular, atomic and nuclear physics; particle physics; mechanics, magneto-hydrodynamics, electromagnetic theory and thermodynamics; quantum mechanics; radiative processes in physics; and special and general relativity. Indeed, it is difficult to find any area of physics that is not represented. Even condensed-matter physics shows up in the study of neutron stars (e.g. see [250]). And the new field of gravitational wave physics had its observational foundations from studies of neutron stars and black holes in binary systems [e.g. [154]]. Clearly, not every one of these areas of physics is required in any single object, but the properties of the range of stars and stellar remnants encompass them all. This hardly seems simple.

The simplicity, then, must arise from the dominant force that is at work. This force is gravity, with its well-known behaviour associated with the minimum energy geometry of the sphere. Our conclusion is that isolated stars are spherical. This is not to say that other forces can be completely ignored; regions in which nuclear energy generation is occurring, regions in which stars are convective, stellar atmospheres, or active surface regions are examples of where gravity must be tempered with other forces that are important on smaller scales. However, stars are large, and big things feel the force of gravity as the...