Project for ASTR7741

Fall Semester, 2007

Radial Oscillations of n = 0 and n = 1 Polytropes

Part I: Derive the Mathematical Form of the Relevant Eigenvalue Problem

By far the best reference on this topic is chapter 38 of the following textbook:

Starting from equations (2.22) and (2.23) of Padmanabhan (Vol. II), that is,

along with the polytropic equation of state, that is, derive BOTH forms of the "oscillation" equation that are presented as eqs. (38.8) and (38.34) of KW. Show that the eigenfrequencies (w0 and w1) -- along with the corresponding eigenfunctions x0 and x1 -- given by eqs. (38.27) and (38.28) of KW are solutions to the stated eigenvalue problem in the case of a uniform-density sphere.

Part II: Pulsation Modes for n=0 and n=1 Polytropic Spheres

Solve the relevant eigenvalue problem for two other cases:

In both cases, plot your resulting eigenfunction in a manner that can be easily compared to Figs. 38.1 and 38.2 of KW.