Chapter 12: Properties of Stars

We see each star at a moment in its life, like a snapshot. We have information that can tell us the mass, size, and luminosity of a star. We know that main sequence stars get their energy by the fusion of hydrogen into helium. Now we are ready to see if we can use this information to deduce how stars live their lives. It turns out that the key quantity that controls the evolution of a star is its mass. Once the mass of a star is measured or estimated, the entire life story of the star is known.

Stars must evolve because they are gradually using up their fuel supply. In 1926, astrophysicists Henry Norris Russell and Heinrich Vogt showed that the structure of an ordinary (main sequence) star is determined uniquely by its mass and chemical composition. So a certain mass of material with fixed composition — for example, one solar mass consisting of ¾ hydrogen and ¼ helium — can reach only one stable configuration. The temperature and luminosity of such would place it on the H-R diagram at the position occupied by the Sun. But if the composition were altered to ½ hydrogen and ½ helium, the rate of nuclear fusion would be different, and so the configuration of the star and its location on the H-R diagram would be different. Using this principle, plus the physics of nuclear reactions, we can make models of stars. Astronomers have calculated the pressures, temperatures, and other characteristics of the interiors, surfaces, and atmospheres of stars. Even though we have never directly explored another star, we know quite accurately what they look like and how they are put together.

The theorem derived by Russell and Vogt explains the cause of stellar evolution from one form to another: as a star converts hydrogen into helium, it changes its composition and then must reach a new equilibrium structure. All nuclear reactions cause changes in composition and all changes in composition cause evolution to a new structure. We can bring this discussion down to Earth by using the example of our own Sun. As it consumes its nuclear fuel, application of the Russell-Vogt theorem shows that it reconfigures itself to grow slightly larger and shine slightly brighter. The Sun has brightened by about 60% since it formed about 4.6 billion years ago. It is expected to brighten by another factor of two by the time it is finished life as a main sequence star 5 billion years from now. This will raise the Earth's temperature by about 20°C. While the Sun brightens, the polar caps will melt, the oceans will slowly evaporate, and the atmosphere will leak away into space! This is bad news for the Earth, but still mild evolution for the Sun; the real drama will occur when it runs out of hydrogen.

Stars evolve at different rates. The more massive a star, the higher its interior temperatures and the faster it will consume its nuclear fuel. A sun-like star of 1 solar mass stays on the main sequence for about 9 billion years (9 x 10⁹ years), but a star of 10 solar masses stays there only about 20 million years (2 x 10⁷ years). The entire history of a star of 1 solar mass (from protostar to white dwarf) takes about 11 billion years, whereas a 10 solar mass star lasts only about 24 million years. In spite of the differences in total time, the largest fraction of any star's life is still spent on or near the main sequence.

Since a star's hydrogen-burning lifetime depends mostly on its mass and luminosity, a simple formula gives the time the star will spend on the main sequence — which is most of the star's lifetime. The hydrogen-burning lifetime equals M/L times 9 billion years, where M and L are the mass and luminosity of the star in solar units. Main sequence stars span a large range in mass — a factor of 1000 — but an even larger range in luminosity — a factor of 10 billion!

Consider the analogy of the "main sequence" of car properties. Imagine that a mid-size sedan is a Sun-like star, with a fuel tank of average size and an engine of average fuel economy. Compared to this, a luxury car has a bigger fuel tank but far worse fuel economy, so it will not go as far on a tank of gas (analogous to a driving "lifetime"). A compact car, on the other hand, will have a smaller fuel tank but far better fuel economy, so it will go farther on a tank of gas. In these terms, low-mass main sequence stars are misers, eking out their meager fuel supply for a very long time. Massive main sequence stars are extravagant, burning through their large fuel supply in a brief blaze of glory.

The most massive stars stay on the main sequence for only the twinkling of a cosmic eye. They consume their nuclear fuel at a ferocious rate. Some of them evolve into the supergiant region of the H-R diagram, and some less massive ones become ordinary giants. All of them quickly evolve to unstable configurations; many may explode, and all disappear from visual prominence.

Astronomers have techniques for measuring the evolution of populations of stars, but how do they measure the age of a single star? The ages of individual stars are difficult to determine. The Sun's age was measured at 4.6 billion years by dating planetary matter that is unavailable in the case of other stars. Certain indicators, such as the amount of "unburned" light elements (lithium, for example) in a star's atmosphere, can also be used to estimate a star's age. On the other hand, astronomers can use an H-R diagram and our model of the structure of a main sequence star to date populations of stars.

Consider a group of stars that formed at the same time. After about 10 million years, stars larger than 20 solar masses will have disappeared from the main sequence. Astronomers call the place on the H-R diagram where stars are just exhausting their nuclear fuel the main sequence "turn-off." That is, the H-R diagram of the group will contain no main-sequence O stars. After about 100 million years, stars more massive than 4 solar masses will have evolved off the main sequence, and the H-R diagram will contain scarcely any main sequence B-type stars. The older the cluster, the more of the main sequence stars will be gone. The missing stars will have been transformed into giants, white dwarfs, or even fainter terminal objects. Thus we reach an important conclusion: the H-R diagram can serve as a tool for dating groups of stars that formed together. This principle is extremely useful to astronomers as they probe the ages of stars in our galaxy, and in other galaxies.