412 CHAPTER 7. ASTROPHYSICS AND COSMOLOGY
supplemented with the boundary conditions:
(7.1.86)
∂T
∂r= 0 , Pr= 0 ,∂Pθ
∂r=
∂Pφ
∂r=0 atr=r 0.The model (7.1.85)-(7.1.86), we just derived describes interior dynamics of the Universe,
galaxies and stars.
7.2 Stars
7.2.1 Basic knowledge
The large scale structure of the Universe consists of mainlythe following levers:
stars, stellar clusters, galaxies, clusters of galaxies.Star is the most elementary constituent of the Universe, andwe now explore some of their
basic properties.
1.Mass m. The mass of the Sun ism⊙= 2 × 1030 kg, and the range of the masses of the
main-sequence stars is about
0. 1 m⊙∼ 40 m⊙.
A few extreme stars have massesm≃ 60 m⊙, and the least massive stars have masses around
m≃ 0. 07 m⊙.
2.Radius R.The radius of the Sun isR⊙= 7 × 105 km, and the radii of the main-sequence
stars are
0. 3 R⊙∼ 25 R⊙.
A neutron star has radiusR≃10km, and a red giant star hasR= 103 R⊙.
3.Surface temperature T.The surface temperature of the Sun isT⊙= 5800 ◦K, and the
range of surface temperatures of stars in general is
2600 ◦K∼ 35000 ◦K.4.Luminosity L.The Sun’s luminosity isL⊙= 1 ( 4 × 1033 erg/s),and the luminosities of
the main-sequence stars have ranges in
8 × 10 −^3 L⊙∼ 3. 2 × 105 L⊙.5.Parameter relation. Based on the radiation theory of black bodies, the above three
parametersR,T,Lenjoy
(7.2.1) L= 4 π σR^2 T^4 ,
whereσis the Stefan-Boltzmann constant:
σ= 5. 7 × 10 −^5 erg/cm^2 ·s·k
4
.