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Solar sound speed inversion using a nonlocal convection model

Solar sound speed inversion using a nonlocal convection model. Chunguang Zhang National Astronomical Observatories, CAS. Outline. Nonlocal convection theory Our solar model Sound speed inversion Discussion. Stellar convection. Energy transpotation & Material mixing Nonlocal phenomenon

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Solar sound speed inversion using a nonlocal convection model

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  1. Solar sound speed inversion using a nonlocal convection model Chunguang Zhang National Astronomical Observatories, CAS

  2. Outline • Nonlocal convection theory • Our solar model • Sound speed inversion • Discussion

  3. Stellar convection • Energy transpotation & Material mixing • Nonlocal phenomenon • Convection theory Mixing-length theory (MLT) Xiong’s nonlocal convetion theory Figure 2: The distribution of pulsating stars in the H-R diagram. (Xiong, & Deng, 2007, MNRAS, 378,1270) Figure 1: Cut-away of the solar interior showing the location of the convection zone. (Demarque, P. & Guenther, D. B. 1999, PNAS, 96, 5356)

  4. Xiong’s nonlocal convection theory • Basic equations of hydrodynamics • Write any physical quantity as the sum of averaged and turbulent fluctuated components

  5. Substitute these expressions into basic equations to obtain equations of the auto- and cross-correlations of turbulent velocity and temperature fluctuation • Form closure with a gradient type approximation

  6. Solar envelope model • Chemical composition GN93 abundance, Grevesse & Noels 1993 • Equation of state OPAL EOS 2005 • Opacity OPAL opacity, Iglesias & Rogers 1996 Low temprature opacity, Ferguson et al. 2005

  7. Comparison with Model S Figure 3: Temperature gradient versus fractional radius around the bottom of solar convection zone. The solid line is that of Xiong’s model, and the dashed line is Model S using MLT.

  8. Figure 4: Sound speed difference between Xiong’s model and Model S.

  9. Frequency comparision • ADIPLS – the Aarhus adiabatic oscillation package • 2060 observed frequencies from SOHO satellite from l = 0 to l = 300 Figure 5: Frequency differences between observations and Xiong’s model: + for l=20;  for l=40;  for l=70;  for l=100;  for l=130 ;  for l=160.

  10. Sound speed inversion • Helioseismology • SOLA method Figure 6: Solar oscillation modes (Montgomery, 2008, Science, 322,536) Figure 7: The sound speed inversion result of Model S.(Christensen-Dalsgaard, J. 2003)

  11. Figure 8: Sound speed difference between Xiong’s model and Model S (solid line) .

  12. Figure 9: The l- diagram of the data used in sound speed inversion, with 1000 error bars.

  13. Figure 10: Sound speed inversion result of the nonlocal solar model (filled circles), compared with that of Model S (empty circles).

  14. Discussion • About standard solar model • Further improvements of the model • New stellar evolution code using nonlocal convection theory

  15. Nonlocal convection model for solar-like stars Figure 11: H-R diagram of stars in which solar-like oscillations have been detected. (Aerts et al. 2008, Solar Phys. 251. 3)

  16. Thank you!

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