Session 59 - Pulsating/Variable Stars.
Display session, Wednesday, June 12
Great Hall,

## [59.04] On the Numerical Solution of High-Order Gravity Modes in Rapidly Rotating Stars

M. J. Clement (University of Toronto)

The slowly pulsating B stars and the line-profile variables on the upper main sequence are now believed to involve nonradial gravity modes of high radial order (n\! >\! 15) and be driven by the ionization zones of mainly iron group metals. This paper is a progress report on efforts to compute numerically the eigenfunctions of these particular modes, including the effects of rapid rotation. This computational problem is very challenging for several reasons: (i) high radial orders require very small integration stepsizes to achieve acceptable numerical accuracy and stability, (ii) for a given azimuthal symmetry m, rotation couples or mixes components of different latitudinal symmetry \ell, each having quite different radial orders, and (iii) in the long-period limit (high n), the g-mode spectrum is so rich'' (due in part to rotational mixing) that convergence is possible only if the trial eigenfrequency and the trial eigenfunction boundary values are very close to being the correct ones. Moreover, Murphy's Laws apply here in that the modes of greatest observational interest -- the sectorial or \ell\! =\! m ones -- are the most difficult to compute because for a given radial order they have the longest periods and, therefore, lie in the richest part of mode-space. Nevertheless, I have been successful so far in computing sectorial modes up to radial order n\!\sim\! 10 and tesseral ones (\ell\! >\! m) up to n\!\sim\! 20. Some examples will be presented.