1. 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

2. 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

3. 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

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

5. Fourier Power Spectrum of p-modes

6. Derived Sound Speed vs Model

7. Inferred Internal Rotation (as fn of latitude)