# Red Giants and Supergiants

Two stars at the same spectral type, say type G, can have quite different brightnesses. One could be a main sequence star with M = +5 and the other a giant star with M = –2.5. By the definition of spectral type, both stars have the same surface temperature T, yet their luminosities L differ by 7.5 magnitudes or a factor of 1000 in luminosity. Stefan‐Boltzman's law allows the luminosity of each star to be expressed in terms of its surface temperature and surface area. For example, L = σT 44πR 2, where R is the radius of the star. Relating the luminosity of the first star to the second,

A ratio of 1000 in luminosity means the more luminous star must be √1000 = 31 times larger than the main sequence star. As the Sun has a radius of 700,000 km, the radius of the more luminous star is 22 million km. If such a star were placed in the center of the solar system, its surface would be one‐third of the distance out to the planet Mercury. As seen from Earth, it would appear 15° in diameter. It is because of the size of these objects that they are termed giant stars. As most stars of this type are cooler and redder, the term red giant is often used.

A similar comparison with an even brighter G star at M = –7.5 produces a size that is 310 times that of the Sun, or a radius of 220 million km, placing the photosphere at the orbit of Mars if this star were to replace the Sun in the solar system. These immense stars are accordingly termed supergiants.

The classification as a giant or supergiant star, however, is as much dependent upon the grouping of stars in the HR diagram as upon radial size. There are giant stars that are actually larger than some supergiant stars.