Astronomy

The fundamental tool for presentation of the diversity of stellar types and for understanding the interrelations between the different kinds of stars is the Hertzsprung‐Russell Diagram (abbreviated HR diagram or HRD), a plot of stellar luminosity or absolute magnitude versus spectral type, stellar surface temperature, or stellar color. The various forms of the HR diagram come from the different manner in which stars may be studied. Theoreticians prefer to graph directly the numerical quantities that come from calculations, for example, luminosity versus surface temperature (see Figure ). On the other hand, observational astronomers prefer to use those quantities that are observed, for example, absolute magnitude versus color (a photometrist's color‐magnitude diagram is essentially the same as an HR diagram) or absolute magnitude versus spectral type (see Figure 1).

Figure 1

Hertzsprung‐Russell Diagrams. Top: The general labeling of stars into four groups is shown. Bottom: Nearby stars and some of the brighter stars in the sky have been added, with the positions of a few well‐known stars marked.

The only stars for which absolute magnitude can be directly obtained are the nearby stars for which parallaxes may be measured and hence distances determined; given a distance, an apparent magnitude can be converted to an absolute magnitude. Inspection of a tabulation of stars out to 5 parsecs (16 ly, the distance to which astronomers have a reasonably complete sample of existing stars; at larger distances, there is an increasingly higher probability that the faintest stars have been missed) shows there to be 4 A stars, 2 F, 4 G, 9 K, and 38 M stars. Even these few stars are sufficient to show three general aspects of stars. First, the typical star is much fainter and cooler than the Sun. Second, the fainter the star, the more stars there are. And last, there is a general trend in the sense that the cooler the star, the fainter it is. This track of stars that runs from high luminosity, hot stars to low luminosity, cool stars is known as the Main Sequence. A few stars also are found in a clump to the bottom left of the HR diagram, at relatively high surface temperatures, but low luminosities. These stars have been termed white dwarfs, and the differentiation of their observational properties from the main sequence stars shows that they must be a very different type of star internally.

The sample of nearby stars contains no highly luminous stars. A survey of greater distances requires the Hipparcos satellite or the application of alternative distance determination techniques, such as those involving star clusters. A cluster of stars may have fainter and brighter stars all at the same distance. Those fainter stars that show a trend from high luminosity, hotter surfaces to low luminosity, cooler surfaces are similar to the main sequence stars in our solar neighborhood. At a given spectral type, those stars must have the same absolute magnitude as the nearby stars, and these absolute magnitudes may be compared with the measured apparent magnitudes to obtain the distance to the cluster. With a known distance, the apparent magnitudes of the brightest stars may also be converted to absolute magnitudes, making it possible to plot these stars in an HR diagram. By use of main sequence fitting applied to star clusters (as well as other, more sophisticated techniques), the upper (brighter) portion of the HR diagram may be filled in. Such a technique enhances the importance of the HR diagram — it is not only a means to display (some of) the properties of stars, but it becomes a tool by which information about other stars may be derived. (See Figure 2.)

Figure 2

Schematic diagram for computed models of main sequence stars, showing luminosities in units of the Sun's luminosity and surface temperature in Kelvins. Adjacent to each model star is its mass in units of the mass of the Sun.

When a large number of stars are plotted in the HR diagram, it becomes clear that the main sequence stars are represented across the full range of spectral types as well as across the full range of absolute magnitudes. The hottest main sequence stars have absolute magnitudes M ≈ –10 and the coolest M ≈ +20, and alternatively, luminosities that go from 10 ⁶ to 10 ^–6 solar luminosities. The Sun is at the middle point of this luminosity range and, in that sense, could be considered an average star.

In addition to the main sequence stars and the white dwarfs, two other distinct groupings of stars may be noted. The first is a concentration of stars with moderately high luminosities (M ≈ –2 to –4 or so) and relatively cooler spectral types (to the right) of the main sequence. These stars are called giants or red giants. The second is a distribution of stars at high luminosities (M < –5), thinly scattered across the top of the HR diagram, representing the full range of spectral types from O to M. These stars are called supergiants.

Consideration of the luminosities of the apparent brightest stars in the sky shows they appear bright because they are intrinsically bright. Of these stars, there are only five with M < –5 (for example, with luminosity L > 10 ⁴ solar luminosities). These are the most luminous stars within a distance of 430 pc, the greatest distance to any of these five (the bright summer sky star Deneb). The volume of space centered on the Sun enclosed by a sphere of this radius is 4π(430 pc) ³/3 = 330,000,000 cubic parsecs, yielding an average stellar density of 5 stars / 330,000,000 pc ³ = 1.5 × 10 ^–8 stars/pc ³. In contrast, there are 38 cool, low luminosity M stars within 5 parsecs of the Sun, in a volume of space 4π(5 pc) ³/3 = 520 cubic parsecs, for an average density of 34 stars / 520 pc ³ = 0.065 stars/pc ³. The ratio of cool main sequence M stars to all classes of highly luminous stars is a factor of 4.4 million. Highly luminous stars are rare, whereas the cool, faint stars are quite common. In this sense, the Sun is actually one of the brighter stars in the Galaxy.