We have now derived the four differential
equations of stellar
structure. We have seen that completely accurate expressions for
the three associated relations of
pressure,
opacity and
energy generation
are extremely complicated, but it is possible
to find simple, approximate forms for them.
The equations of stellar structure are too complex to find an exact
analytical solution and hence they must be solved using a computer.
It is possible, however, to verify the gradient of the main
sequence in the HR diagram and of the mass-luminosity relation without
solving the equations of stellar structure completely. In what follows,
we shall describe how this can be done. We shall then look at an example of
a simple stellar model, known as a polytrope, in which we assume a
relation between pressure and density that enables the equations of stellar
structure to be solved in a straightforward manner on a computer.
Finally, we shall look at the results of a full solution
of the equations of stellar structure derived using a
computer, describe what these detailed models
teach us about the interiors of stars and how
the results compare with observations.
©Vik Dhillon, 27th September 2010