Because stars are large and massive compared to a rocky planet like the Earth, we expect that a balance between pressure gradients and gravity inside a star will require very high internal pressure. However, there can be very different ways in which high pressure can be achieved, as two examples from the Earth make clear. Both the atmosphere and the oceans are in hydrostatic equilibrium; air pressure thus decreases with altitude above sea level, while pressure in the ocean increases with depth.

A star can be defined as a self-gravitating ball of gas, usually spherical or spheroidal, that is powered by nuclear fusion in its interior. In this text, we will go slightly beyond the boundaries of this definition to discuss protostars and pre-main sequence stars (not yet powered by fusion), stellar remnants (no longer powered by fusion), and brown dwarfs (too small to be powered by fusion).

In 1938, Ernst Öpik pointed out that if the process that comes into play is thermonuclear fusion, then main sequence stars are powered by fusion in their cores, and red giants are stars that have exhausted their central fuel.

Thus, the Sun has existed for one-third of the total history of the universe. Some stars are older than the Sun; some are younger. In Chapter 6, our examination of main sequence models neglected the question of how stars form.

However, although stars are generally in hydrostatic equilibrium, all stars are also variable. We can distinguish broad families of variation. The most spectacular variation involves catastrophic changes such as supernova explosions. Some stellar variability arises from external influences, such as accretion of mass from a disk or a companion.

In addition, even modest rotation rates can cause significant alterations to the internal structure of stars. Finally, knowing how stars are spun up and spun down is important if we are to study a star’s complete history, from a slowly whirling gas cloud to a swiftly spinning white dwarf or a millisecond pulsar.

Since this was about 50 times the Kelvin–Helmholtz time for the Sun, a non-gravitational source of energy was obviously required to keep the Sun shining over the age of the solar system. A hint of what that energy source could be was provided by the physicist Francis Aston in 1920.

Up to this point, we have mainly been treating stars as if they exist in splendid isolation. However, stars are frequently found in binary systems, with two stars orbiting their barycenter. If the stars are sufficiently close to each other, then they will be tidally distorted, destroying the spherical symmetry of the standard equations of stellar structure.

Since all stars other than the Sun are at a distance that is large compared to their diameter, discerning their detailed structure is challenging. In this chapter, we start with the Hoyle-ish assumption that a star is a pretty simple structure: a static, isolated sphere.