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##### Helioseismology (III)

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**Probing Magnetic Fields and Flows**in the Solar Convection Zone with Helioseismology Helioseismology (III) 周定一 Dean-Yi Chou 台灣清華大學，物理系 (2010.08, 北京)**Helioseismolgy**Using solar p-mode oscillations (waves) measured on the solar surface to probe the solar interior.**Basic Principle to probe Solar Interiors**Different modes penetrate into different depths.**Observations in Helioseismology**Using solar p-mode oscillations (waves) measured on the solar surface to probe the solar interior. Observations setr = R But it still gives the same dispersion relation:**How to Probe Magnetic Fields**Deep in the Solar Convection Zone? Interaction of acoustic waves with magnetic fields. changes in rotation, sound speed, and flow. Look for: 1. Solar-cycle variations of rotation 1. Solar-cycle variations of sound speed 2. Solar-cycle variations of meridional flows**Probing Subsurface Magnetic Fields**0.96 R < r < R Ring diagram Time-Distance Acoustic Imaging 0.8 R < r < R Time-Distance r 0.7 R ???**Probing Magnetic Fields with Multiple-Bounce Travel Time**(Chou & Serebryanskiy 2002)**Another Approach:**Solar Cycle Variations of Frequencies (Chou & Serebryanskiy 2005)**Perturbation at BCZ**Perturbation at surface**Perturbation at BCZ**Perturbation at surface**Perturbations at BCZ and surface**Error added**Perturbations at BCZ and surface**Error added**Data & Analysis**• MDI frequencies (72-day data). • GONG frequencies (36-day data). • Average over minimum (1996.06 - 1997.07) as the reference frequency. • Compute the frequency shift relative to the reference frequency.**δΓ/Γ = 2 – 6 x 10^-5 , if FWHM = 0.05R**• r = 0.65 – 0.67 R • B = (8πP δΓ/Γ)^(-1/2) = 0.17 – 0.29 M Gauss Upper limit set by inversion (Eff-Darwich et al. 2002) δc/c = 3 x 10^-5 (δΓ/Γ = 1.5 x 10^-5 ) Why don’t we see the signals in the inversion study?**Meridional flow with time-distance (Giles et al. 1997)**• Cross-correlation is computed for pairs in the north-south direction. • Cross-correlation functions are averaged over longitude. • Determine travel time from cross-correlation function. different distances different depths latitude longitude**relates to the flow velocity in the north-south direction.**from TON data 2- 6 deg. r = 0.962 – 0.987 R 1 sec ～ 10 m/s The sine-shape time shift corresponds to the one-cell pole ward circulation pattern in each hemisphere.**Solar-Cycle Variations of Meridional Flows**• Use data taken with Taiwan Oscillation Network(TON) • K-line full-disk images (1994-2004) • Time series of each site each day (~ 512 images) is analyzed separately. • 1676 time series (~ 0.8M images) are analyzed.**Solar-Cycle Variations of Meridional Flows (chou & Dai**2001) Δ= 2 – 6 deg r = 0.962 – 0.987 R 1 sec ≈ 10 m/s**Solar-Cycle Variations of Meridional Flows (chou & Dai**2001) Δ= 6 – 10 deg r = 0.938 – 0.962 R 1 sec ≈ 10 m/s**Solar-Cycle Variations of Meridional Flows (chou & Dai**2001) Δ= 6 – 10 deg r = 0.938 – 0.962 R 1 sec ≈ 10 m/s**Solar-Cycle Variations of Meridional Flows (chou & Dai**2001) 2000 - 1997 2- 6 deg, r = 0.962 – 0.987 R 6-10 deg, r = 0.938 – 0.962 R 10-16 deg, r = 0.900 – 0.938 R 1 sec ≈ 10 m/s**Solar-Cycle Variations of Meridional Flows (chou & Dai**2001) Giles et al. 1997 solar minimum max - min solar maximum additional component created at maximum**Beck et al. (2002)**• Confirm the result of Chou & Dai (2001). • The location of the divergent flow coincides with magnetic field and torsional oscillations. Δ= 17 deg r = 0.9 R meridional flow torsional oscillations from time-distance torsional oscillations from f-modes magnetic field**Questions:**• Does the divergent flow decrease as activities decrease? • How deep does it go? • How is it created?**Chou & Ladenkov (2005)**• Improve data analysis to go deeper. • Study the decline phase of cycle 23. Findings: • The divergent flow decreases with activities. • It extends at least down to 0.8 R. • It amplitude peaks at about 0.9 R.**Temporal variations of divergent flows**Correlation between divergent flow & sunspot number 6-16 deg**Depth Variations**2- 6 deg, r = 0.962 – 0.987 R 6-10 deg, r = 0.938 – 0.962 R 10-16 deg, r = 0.901 – 0.938 R 16-22 deg, r = 0.864– 0.901R 22-32 deg, r = 0.793– 0.864R**Conclusion on Meridional Flow**• Meridional flows extend through the entire CZ (Giles et al. 1999). • A divergent flow is generated in each hemisphere as activities develop. • The location of the divergent flow coincides with active latitude and torsional oscillations. • The magnitude of the divergent flow correlates with activities. • The divergent flow peaks at about 0.9 R. • It could be a tool to probe the magnetic field deep in the CZ.