| 46 | 46 | There are only three analytic solutions: n=0. n=1 and n=5. The n=0 case corresponds to an incompressible fluid, i.e when [[latex($\rho=\rho_{c}=const.$)]]. Thus the density is constant through out the star, but the pressure still goes to zero at the surface. This case is considered a crude approximation to the interior of our earth. The n=5 corresponds to the radius of this star being infinite. It can be shown that all indices greater than or equal to five will have infinite radii. The two cases that correspond to real stars are the n=1.5 and n=3 case, whose solutions are found numerically. The n=1.5 case is useful for approximating fully convective stars, and the n=3 case useful for approximation main sequence and relativistic degenerate cores of white dwarfs (though for the white dwarf case there is some special additions that need to made concerning K). |
