The Life Expectancy of a Star

A star dies when it consumes its nuclear fuel, its mass. We might be tempted to conclude that the greater the supply of fuel (the more massive the star), the longer it will live; however, a star’s life span is also determined by how rapidly it burns its fuel. The more luminous a star, the more rapid the rate of consumption. Thus stellar lifetime is directly proportional to stellar mass and inversely proportional to stellar luminosity (how fast it burns). An analogy: A car with a large fuel tank (say a new Ford Excursion that gets 4–8 mpg) may have a much smaller range than a car with a small fuel tank (a Saturn which might get 30–40 mpg). The key? The Saturn gets much better mileage, and thus can go farther with the limited fuel it has.
Thus, while O- and B-type giants are 10 to 20 times more massive than the our G-type sun, their luminosity is thousands of times greater. Therefore, these most massive stars live much briefer lives (a few million years) than those with less fuel but more modest appetites for it.
A B-type star such as Rigel, 10 times more massive than the sun and 44,000 times more luminous, will live 20 106 years, or 20 million years. For comparison, 65 million years ago, dinosaurs roamed the earth! The G-type sun may be expected to burn for 10,000 106 years (ten billion years). Our red dwarf neighbor, Proxima Centauri, an M-type star that is 1⁄10 the mass of the sun (and 1⁄100 that of Rigel), is only 0.00006 times as luminous as the sun, so will consume its modest mass at a much slower rate and may be expected to live more than the current age of the universe. In the next two chapters we will see how stars go through their lives, and how they grow old and die.

Understanding Stellar Mass

The overall orderliness of the main sequence suggests that the properties of stars are not random. In fact, a star’s exact position on the main sequence and its evolution are functions of only two properties: composition and mass.
Composition can be evaluated if we have a spectrum of the star, its fingerprint. But how can we determine the mass of a star?
Fortunately, most stars don’t travel solo, but in pairs known as binaries. (Our sun is an exception to this rule.) Binary stars orbit one another.
Some binaries are clearly visible from the earth and are called visual binaries, while others are so distant that, even with powerful telescopes, they cannot be resolved into two distinct visual objects. Nevertheless, these can be observed by noting the Doppler shifts in their spectral lines as they orbit one another. These binary systems are called spectroscopic binaries. Rarely, we are positioned so that the orbit of one star in the binary system periodically brings it in front of its partner. From these eclipsing binaries we can monitor the variations of light emitted from the system, thereby gathering information about orbital motion, mass, and even stellar radii.
However we observe the orbital behavior of binaries, the key pieces of information sought are orbital period (how long it takes one star to orbit the other) and the size of the orbit. Once these are known, Kepler’s third law can be used to calculate the combined mass of the binary system.
Why is mass so important? Mass determines the fate of the star. It sets the star’s place along the main sequence and it also dictates its life span.