## The Hertzsprung Russell Diagram

Around 1910, Ejnar Hertzsprung and Henry Norris Russell studied the relation between the absolute magnitudes and the spectral types of stars. The diagram showing these two variables is now known as the Hertzsprung-Russell diagram or simply the HR diagram (Fig. 8.8). It has turned out to be an important aid in studies of stellar evolution.

In view of the fact that stellar radii, luminosities and surface temperatures vary widely, one might have expected the stars to be uniformly distributed in the HR diagram. However, it is found that most stars are located along a roughly diagonal curve called the main sequence. The Sun is situated about the middle of the main sequence.

Spectral class

Spectral class

100,000

0.0001

0.01

Effective temperature

3,000 K

100,000

0.01

0.0001

Effective temperature

3,000 K

Fig. 8.8. The HertzsprungRussell diagram. The horizontal coordinate can be either the colour index B — V, obtained directly from observations, or the spectral class. In theoretical studies the effective temperature Te is commonly used. These correspond to each other but the dependence varies somewhat with luminosity. The vertical axis gives the absolute magnitude. In a (lg(L/Le), lg Te) plot the curves of constant radius are straight lines. The densest areas are the main sequence and the horizontal, red giant and asymptotic branches consisting of giant stars. The supergiants are scattered above the giants. To the lower left are some white dwarfs about 10 magnitudes below the main sequence. The apparently brightest stars (m < 4) are marked with crosses and the nearest stars (r < 50 ly) with dots. The data are from the Hipparcos catalogue

The HR diagram also shows that the yellow and red stars (spectral types G-K-M) are clustered into two clearly separate groups: the main sequence of dwarf stars and the giants. The giant stars fall into several distinct groups. The horizontal branch is an almost horizontal sequence, about absolute visual magnitude zero. The red giant branch rises almost vertically from the main sequence at spectral types K and M in the HR diagram. Finally, the asymptotic branch rises from the horizontal branch and approaches the bright end of the red giant branch. These various branches represent different phases of stellar evolution (c.f. Sects. 11.3 and 11.4): dense areas correspond to evolutionary stages in which stars stay a long time.

A typical horizontal branch giant is about a hundred times brighter than the Sun. Since giants and dwarfs of the same spectral class have nearly the same surface temperature, the difference in luminosity must be due to a difference in radius according to (5.21). For example Arcturus, which is one of the brightest stars in the sky, has a radius about thirty times that of the Sun.

The brightest red giants are the supergiants with magnitudes up to MV = -7. One example is Betelgeuze. in Orion, with a radius of 400 solar radii and 20,000 times more luminous than the Sun.

About 10 magnitudes below the main sequence are the white dwarfs. They are quite numerous in space, but faint and difficult to find. The best-known example is Sirius B, the companion of Sirius.

There are some stars in the HR diagram which are located below the giant branch, but still clearly above the main sequence. These are known as sub-giants. Similarly, there are stars below the main sequence, but brighter than the white dwarfs, known as subdwarfs.

When interpreting the HR diagram, one has to take into account selection effects: absolutely bright stars are more likely to be included in the sample, since they can be discovered at greater distances. If only stars within a certain distance from the Sun are included, the distribution of stars in the HR diagram looks quite different. This can be seen in Fig. 8.8: there are no giant or bright main sequence stars among these.

The HR diagrams of star clusters are particularly important for the theory of stellar evolution. They will be discussed in Chap. 16.

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