Ay 123 Lecture 9 - Helioseismology Contour plots of spherical harmonic function Yl,m (, ) - ignoring phase factor (-1)m =0 axis is inclined 45º towards you each panel labeled l,m l defines horizontal waveno. kh = L/R, where L = [l (l+1)]0.5 surface wavelength 2/ kh m gives phase -1<m<l (2l+1 values) 1,0 1,1 2,0 2,1 2,2 3,0 3,1 3,2 3,3 10,10 5,5 10,5

Types of Solar Oscillations Modes characterized by frequency  and angular degree l - l=0 are radial modes; can detect l<3 in integrated light (stellar seismology) high frequency waves are acoustic or p-modes; well-characterized low frequency waves are buoyancy or g-modes; hard to detect on surface but valuable probes of interior f-modes are surface versions of g-modes

Refraction of Acoustic (p-) Waves (3 mHz) Waves can be refracted and reflected by the change in cS and density with depth - effect more pronounced for large angular degrees l (marked) surface reflection due to density change internal effects due to changes in cS 75 25 20 2

Model Predictions of ,l distribution Excellent match between p-mode data and solar models

Fourier Power Spectrum of p-modes

Derived Sound Speed vs Model

Inferred Internal Rotation (as fn of latitude)