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.

Making the Main Sequence

Working independently, two astronomers, Ejnar Hertsprung (1873–1967) of Denmark and Henry Norris Russell (1877–1957) of the United States studied the relationship between the luminosity of stars and their surface temperatures. Their work (Hertsprung began about 1911) was built on the classification scheme of another woman from the Harvard College Observatory, Antonia Maury. She first classified stars both by the lines observed and the width or shape of the lines. Her scheme was an important step toward realizing that stars of the same temperature could have different luminosity. Plotting the relationship between temperature and luminosity graphically (in what is now known as a Hertzsprung-Russell diagram or H-R diagram), these two men discovered that most stars fall into a well-defined region of the graph. That is, the hotter stars tend to be the most luminous, while the cooler stars are the least luminous.
The region of the temperature luminosity plot where most stars reside is called the main sequence. Most stars are there, because as we will discover, that is where they spend the majority of their lives. Stars that are not on the main sequence are called giants or dwarfs, and we will see how stars leave the main sequence and end up in the far corners of the temperature-luminosity plot.

Sorting the Stars by Size

The radius of a star can be determined from the luminosity of the star (which can be determined if the distance is known) and its surface temperature (from its spectral type). It turns out that stars fall into several distinct classes. In sorting the stars by size, astronomers use a vocabulary that sounds as if it came from a fairytale:

• A giant is a star whose radius is between 10 and 100 times that of the sun.
• A supergiant is a star whose radius is more than 100 times that of the sun. Stars of up to 1,000 solar radii are known.
• A dwarf star has a radius similar to or smaller than the sun.

How Hot Is Hot?

Stars are too distant to stick a thermometer under their tongue. We can’t even do that with our own star, the sun. But you can get a pretty good feel for a star’s temperature simply by looking at its color.
The temperature of a distant object is generally measured by evaluating its apparent brightness at several frequencies in terms of a blackbody curve. The wavelength of the peak intensity of the radiation emitted by the object can be used to measure the object’s temperature. For example, a hot star (with a surface temperature of about 20,000 K) will peak near the ultraviolet end of the spectrum and will produce a blue visible light. At about 7,000 K, a star will look yellowish-white. A star with a surface temperature of about 6,000 K—such as our sun—appears yellow. At temperatures as low as 4,000 K, orange predominates, and at 3,000 K, red.
So simply looking at a star’s color can tell you about its relative temperature. A star that looks blue or white has a much higher surface temperature than a star that looks red or yellow.

Creating a Star Scale of Magnitude

So astronomers have learned to be very careful when classifying stars according to apparent brightness. Classifying stars according to their magnitude seemed a good idea to Hipparchus (in the second century B.C.E.) when he came up with a 6-degree scale, ranging from 1, the brightest stars, to 6, those just barely visible. Unfortunately, this somewhat cumbersome and awkward system (higher magnitudes are fainter, and the brightest objects have negative magnitudes) has persisted to this day.
Hipparchus’ scale has been expanded and refined over the years. The intervals between magnitudes have been regularized, so that a difference of 1 in magnitude corresponds to a difference of about 2.5 in brightness. Thus, a magnitude 1 star is 2.5 ×2.5 ×2.5 ×2.5 ×2.5=100 times brighter than a magnitude 6 star. Because we are no longer limited to viewing the sky with our eyes, and larger apertures collect more light, magnitudes greater than (that is, fainter than) 6 appear on the scale. Objects brighter than the brightest stars may also be included, their magnitudes expressed as negative numbers. Thus the full moon has a magnitude of –12.5 and the sun, –26.8. In order to make more useful comparisons between stars at varying distances, astronomers differentiate between apparent magnitude and absolute magnitude, defining the latter, by convention, as an object’s apparent magnitude when it is at a distance of 10 parsecs from the observer. This convention cancels out distance as a factor in brightness and is therefore an intrinsic property of the star.

Luminosity Versus Apparent Brightness

Ask an astronomer this question, and she will respond that the flashlight, a few feet from your eyes, is apparently brighter than the distant headlights, but that the headlights are more luminous. Luminosity is the total energy radiated by a star each second. Luminosity is a quality intrinsic to the star; brightness may or may not be intrinsic. Absolute brightness is another name for luminosity, but apparent brightness is the fraction of energy emitted by a star that eventually strikes some surface or detection device (including our eyes). Apparent brightness varies with distance. The farther away an object is, the lower its apparent brightness.
Simply put, a very luminous star that is very far away from the earth can appear much fainter than a less luminous star that is much closer to the earth. Thus, although the Sun is the brightest star in the sky, it is not by any means the most luminous.