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**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.

**Program
listing for Wednesday**