Mathematical Principles of Theoretical Physics

7.2. STARS 413

For the main-sequence stars, we have the following the relation

(7.2.2) L/L⊙= (m/m⊙)α,

whereαtakes different values as

α=







1. 8 form< 0. 3 m⊙,

4 for 0. 3 m⊙<m< 3 m⊙,

2. 8 for 3m⊙<m.

6.Main-sequence stars. In (7.2.1) we see that the luminosityLdepends onTandR.
However, the radiusRis also related with the temperatureT. In 1910, two astronomers
E. Hertzsprung and H. R. Russell independently obtained thestatistical law betweenLand
T. They discovered that for most stars, called the main-sequence stars, their luminosity and
temperature possess certain relation. This relation is illustrated by a diagram, called theHR
diagram, which is shown in Figure7.1.

24000 12000 6000 3000

1

white dwarfs

10 −^2

102

104

red giants

Luminosity

L

(L

⊙

)

surface temperature T(K)

main sequence

Figure 7.1: TheHRdiagram in which the luminosityLand the surface temperatureTof stars
are plotted.

Each star is plotted as a point in theHRdiagram in Figure7.1. The stars in the band are the
main-sequence stars. The red giants are in the right-top region, and have lower temperatures
and higher brightness, and the white dwarfs are in the left-bottom region, and have higher
temperatures and low brightness.
The main-sequence stars are young and middle aged stars, thered giants are old aged,
and the white dwarfs are dead stars.

7.Variable stars.Most stars shine with almost constant brightness, but a small number of
stars, called variable stars, change periodically their brightness. Since the luminosity of a star
depends on its radius (see (7.2.1)), variable stars are rhythmically expanding and contracting,
pulsating in size and brightness.