414 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY
8.Red giants.Stars are held together by gravity. The gravitational forcepulling inward
is opposed by a force pushing outward, consisting mainly thethermal pressure in the interior.
Stars maintain their balance of pressure and gravity by the heat energy produced by burning
hydrogen.
Stars less massive than the Sun evolve more slowly and stay onthe main-sequence longer
than 10^10 years. But more massive stars evolve more quickly, and end their life becoming
white dwarfs and neutron stars (or possibly black holes) as their final fate determined by their
masses.
After a more massive star consumes its central supply of hydrogen, it leaves the main
sequence and enters into the group of red giants in theHRdiagram.
When the central nuclear reaction has ceased to generate heat, the interior pressure re-
duces and the star begins to contract, leading to the releaseof gravitational energy. Hence,
this contraction causes the temperature to rise. Thus, the hydrogen outside the core begins to
burn. The burning shell causes the star to expend. Thus, the star is luminous, large and cool,
and becomes a red giant.
9.White dwarfs.For a star with mass in the range(7.2.3) 1 m⊙≤m< 5 m⊙,
when it is in the red-giant phase, its expanding shell is thrown off into space, and the naked
core is all that remains. Contraction ceases, nuclear burning ends, and the core cools down as
a white dwarf. A white dwarf has a size approximatively equalto that of the earth, with mass
m≤ 1. 44 M⊙.
10.Neutron stars and pulsars.A star with mass(7.2.4) 5 m⊙<m,
will eventually evolve to a neutron star. A neutron star has aradius of about 10km with mass
m> 3 m⊙, and has a high density of nearly 10^9 ton/cm^3. The neutron star has a magnetic field
of 10^12 gauss that is 10^12 times stronger than the earth’s magnetic field.
The pulsar is a special neutron star, which emits a pulse-like energy message.
11.Supernovae.When a large massive red giant(m> 5 m⊙)exhausts its nuclear fuels, it
begins to collapse. This contraction will lead to explosion, and the explosive star is called a
supernova. A neutron star is born after a huge explosion of a supernova.
7.2.2 Main driving force for stellar dynamics
Stars can be regarded as fluid balls. To investigate the stellar interior dynamic behavior, we
need to use the fluid spherical models coupling the heat conductivity equation. There are
two types of starts: stable and unstable. The sizes of stablestars do not change. The main-
sequence stars, white dwarfs and neutron stars are stable stars. The radii of unstable stars may
change; variable stars and expanding red giants are unstable stars. The dynamic equations
governing the two types of stars are different, and will be addressed hereafter separately.
We note that the fluid dynamic equations (7.1.78) represent the Newton’s second law, and
their left-hand sides are the acceleration and their right-hand sides are the total force. The