The physics of fusion in stars
Most stars derive their luminosity from the conversion of hydrogen to helium. The rest
mass of one 4 He atom is about 0.71% less than the combined rest masses of four hydrogen
atoms (note that the electrons are included in t

Stellar timescales
One way to come to grips with the physics of stars is to look at the timescales on which they change,
or on which important internal processes come to equilibrium.
Dynamical timescale
Suppose the internal pressure of the sun were sudden

IONIZATION, SAHA EQUATION
Let the energies of two states, A and B , be EA and EB , and their statistical weights gA and gB ,
respectively. In LTE (Local Thermodynamic Equilibrium) the number of particles in the two states,
NA and NB , satises Boltzman equ

GENERAL THERMODYNAMIC CONSIDERATIONS
The rst law of thermodynamics may be written as a heat balance within one gram of matter
dQ = T dS = du + P dV,
(gt.1a)
where dQ is the heat input or the heat loss, T is temperature, S is entropy per gram, u is interna

HAYASHI LIMIT
Let us consider a simple model atmosphere of a star. The equation of hydrostatic equilibrium
and the denition of optical depth are
d
= ,
dr
dP
= g,
dr
(s2.24)
and may be combined to write
dP
g
=.
d
(s2.25)
Assuming = const we may integrate t

EQUATION OF STATE
Consider elementary cell in a phase space with a volume
x y z px py pz = h3 ,
(st.1)
where h = 6.63 1027 erg s is the Planck constant, x y z is volume in ordinary space measured
in cm 3 , and px py pz is volume in momentum space measured

STARS IN HYDROSTATIC EQUILIBRIUM
Gravitational energy and hydrostatic equilibrium
We shall consider stars in a hydrostatic equilibrium, but not necessarily in a thermal equilibrium.
Let us dene some terms:
[ erg cm 3 ],
U = kinetic, or in general internal

Astronomical terms and constants
Units of length
1 AU 1.5 1013 cm = one astronomical unit, i.e. the earthsun distance.
1 pc = 2.06 105 AU = 3.1 1018 cm = one parsec, i.e. a distance to a star with a parallax equal to
one second of arc. A parallax is an an

POLYTROPES
Polytropes are self-gravitating gaseous spheres that were, and still are, very useful as crude
approximation to more realistic stellar models. Properties of polytropes are thoroughly described
in a classical, and very old, textbook: An Introduc

EQUATIONS OF STELLAR STRUCTURE
General Equations
We shall consider a spherically symmetric, self-gravitating star. All the physical quantities will
depend on two independent variables: radius and time, (r, t). First, we shall derive all the equations
of s