The r-Modes of the Maclaurin Spheroids

Preprint
Publisher Website
Google Scholar
  • 19 July 1998
Abstract
Analytical solutions are presented for the r-modes of rigidly rotating uniform density stars-the Maclaurin spheroids-with arbitrary values of the angular velocity. Our analysis is based on the work of Bryan; however, we derive the solutions using slightly different coordinates that give purely real representations of the r-modes. We find a much larger class of r-modes than have previously been studied. In particular, for each l and m we find l-m (or l-1 for the m=0 case) distinct r-modes. Many of these previously unstudied r-modes (about 30% of those examined) are subject to a secular instability driven by gravitational radiation. The eigenfunctions of the `classical' r-modes, the l=m+1 case here, are found to have particularly simple analytical representations. These r-modes provide an interesting mathematical example of solutions to a hyperbolic eigenvalue problem.

This publication has 0 references indexed in Scilit: