(W is scalar for displacement, T is scalar for traction) Note that matrix does not depend on m.

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Presentation transcript:

(W is scalar for displacement, T is scalar for traction) Note that matrix does not depend on m

Algorithm for toroidal modes Choose harmonic degree and frequency Compute starting solution for (W,T) Integrate equations to top of solid region Is T(surface)=0? No: go change frequency and start again. Yes: we have a mode solution

T(surface) for harmonic degree 1

Radial and Spheroidal modes

Spheroidal modes

Minors To simplify matters, we will consider the spheroidal mode equations in the Cowling approximation where we include all buoyancy terms but ignore perturbations to the gravitational potential

Spheroidal modes w/ self grav (three times slower than for Cowling approx)

Red > 1%; green .1--1%; blue .01--.1%

Red>5; green 1--5; blue .1--1 microHz

Mode energy densities

Normalized radius Dash=shear, solid=compressional energy density

(black dots are observed modes)

All modes for l=1

(normal normal modes)

hard to compute ScS --not observed (not-so-normal normal modes)