Project for ASTR7741
Fall Semester, 2003
Xiaomeng Peng
Xiaomeng Peng
The procedures that you should follow to construct equilibrium models of rotating polytropes are described fully in my on-line textbook. Specifically, go to the following web page,
and scroll down to the "Summary" section that includes equations III.F.13, III.F.14, and III.F.15. This summary, on through the end of this web page, sets the stage for the more technical description given on the following two pages: The most difficult part of these procedures is the solution of the two- dimensional Poisson equation. I can hand you a Fortran subroutine that provides this solution, if you like; or you can try to see if Mathematica has an appropriate solver. If you develop your own solver, the first thing you should attempt is a solution for the gravitational potential of a uniform-density spheroid. This solution is known analytically.
Part II: Equilibrium, Polytropic Binary Stars
The procedures needed to build polytropic binaries is not technically more difficult than the procedures needed to build rotating, single stars. But it is more computationally demanding. I'm not sure that you have time during this semester course to complete this part of the project. But, let's talk about it.