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Figure 1.14 Color-magnitude diagram for 1094 stars in the solar neighborhood.

1.3.2 Main Sequence

The single most powerful conceptual tool in stellar astronomy is the Hertzsprung-Russell (HR) diagram. This is a plot of luminosity versus surface temperature (or their equivalents) for a single star or stellar group. A plot of MV versus (B — V)Q is also known as a color-magnitude diagram, while the L*-Teff plane is often called a theoretical HR diagram. Figure 1.14 is a color-magnitude diagram for relatively nearby stars. The vast majority, including the Sun itself, lie along a band known as the main sequence. The Sun's location is shown by the large open circle at MV = +4.82 and (B — V)◦ = +0.65. Astronomers frequently refer to main-sequence stars as dwarfs, to distinguish them from the sparser group to the upper right, the giants. Also apparent is a group to the lower left, the white dwarfs.

Figure 1.15 shows the main sequence in the theoretical HR diagram. The existence of this locus, in either set of coordinates, reflects the basic physics of stellar structure. A star is a self-gravitating ball of gas, supported against collapse by its internal thermal pressure. Throughout its life, the star continually radiates energy from its surface at the rate L*. In a main-sequence object, this energy is resupplied by the fusion of hydrogen into helium at the center. The quantity L* thus equals, in this case, Lint, the luminosity crossing any interior

Stellar Birthline
Figure 1.15 Evolutionary track of a 1 Mq star in the theoretical HR diagram. The grey solid line represents the zero-age main sequence (ZAMS), while the dashed curve is the birthline.

spherical shell (see Figure 1.16). A main-sequence star is therefore in both hydrostatic and thermal equilibrium.

In a star of given mass M* and radius R*, the condition of hydrostatic equilibrium necessitates a certain interior run of temperature and density, where both quantities decrease outward. The radiative energy flux across any shell depends on the local temperature gradient, so that Lint is also specified for this object. If we now imagine squeezing the star to smaller R*, its interior density rises. So must the temperature, in order to counteract the greater self-gravity. The luminosity crossing interior shells will also increase in response to the steeper temperature gradient. On the other hand, the star's nuclear reaction rate, which reflects both the frequency and energy of proton collisions, has its own functional dependence on the central density and temperature. Thus, for each M*, we cannot really vary R* at will; there is only one value for which the interior luminosity can be sustained by reactions at the center. But the stellar radius connects L* and Teff through the equation

where aB is the Stefan-Boltzmann constant. This blackbody relation, which we derive in Chapter 2, actually defines Teff. In summary, a main-sequence star of fixed mass has a unique L* and Teff. The curve in the HR diagram is simply the functional relationship L*(Teff) obtained by letting the stellar mass range freely.

Main-Sequence Star fv/\y

Main-Sequence Star fv/\y

Jint

Figure 1.16 Energy transport in a main-sequence star. The interior luminosity Lint is generated in the nuclear-burning region near the center and is equal to the surface value L .

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