1. Searching for the Magnetic Fields at the Base of the Convection Zone Dean-Yi Chou Institute of Astronomy & Department of Physics Tsing Hua University, Taiwan (March 2003, Seoul)

2. 0.96 R < r < R Mode Frequency (c, v) Time-Distance (c, v) Acoustic Imaging (c) 0.9 R < r < R Time-Distance (v) r  0.7 R Time-Distance (c) Probing Subsurface Magnetic Fields

4. MOTIVATION 1.The change in frequency by magnetic fields near the surface depends on frequency only. 2.The change in frequency by magnetic fields deep in the convection zone depends on horizontal phase velocity. 3.To study magnetic fields at the base of the convection zone, we have to separate these two dependences.

5. Modeling 1.Simulating effects of magnetic fields by perturbing sound speed in a standard solar model. 2.Two perturbed regions: One is near the surface; another is near the base of the convection zone. 3.The mode frequencies are computed from the perturbed solar model. 4.The change in frequency due to the perturbed sound speed is studied.

6. Procedure 1.The dependence of mode mass is removed by multiplying frequency change by mode mass. 2.Using the modes with low horizontal phase velocity as a reference, the frequency dependence of frequency change is removed. 3.The frequency change of modes in a range of 2.5-3.5 mHz is plotted vs. horizontal phase velocity. 4.To see small variation in frequency change as a function of horizontal phase velocity, modes in certain range of horizontal velocity are averaged.

7. Frequency changeFrequency change * mode mass

9. What we learn from modeling. The frequency change remains constant for modes which can not penetrate into the base of the convection zone. The frequency change increase rapidly for modes whose lower turning points are located near the base of the convection zone. For modes which can penetrate into the radiative zone, the frequency change drops a little.

10. MDI Central Frequency MDI central frequencies are used in this study. The frequency change relative to the solar minimum in different periods along the solar cycle is computed for each mode. The frequency change is analyzed as in modeling.

13. N is the number of bounces which takes the wave packet travel around the Sun. N is anti-correlated with the horizontal phase velocity.

14. Conclusion from Studies of Central Frequency No anomaly in frequency change is found at horizontal phase velocity corresponding to the base of the convection zone. A upper limit of change in sound speed, about one millionth, can be given from this study. This limit is smaller than previous studies.

15. m=l modes 1.Since the power of mode m=l is concentrated near the equator, the probability to detect the effect of the magnetic fields at the base of the convection is higher. 2.The frequency change is analyzed as the central frequency. 3.We use MDI and GONG frequencies.

18. Conclusion An anomaly near N=8, which corresponds to the base of the convection zone, is seen in both MDI and GONG frequencies. It is unlikely due to the measurement artifacts. It is not clear what causes this anomaly.