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• Convection theory Mixing-length theory (MLT) Xiong’s nonlocal convetion theory

Figure 1: Cut-away of the solar interior showing the location of the convection zone.

(Demarque, P. & Guenther, D. B. 1999, PNAS, 96, 5356)Figure 2: The distribution of pulsating stars

in the H-R diagram.

(Xiong, & Deng, 2007, MNRAS, 378,1270)

Xiong’s nonlocal convection theory

• Basic equations of hydrodynamics

• Write any physical quantity as the sum of averaged and turbulent fluctuated components

• 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

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

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.

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

Frequency comparision

• ADIPLS – the Aarhus adiabatic oscillation package

• 2060 observed frequencies from SOHO satellite from = 0 to= 300

Figure 5: Frequency differences between observations and Xiong’s model: + for =20; for =40; for =70; for =100; for =130 ; for =160.

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)

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

Figure 9: The diagram of the data used in sound speed inversion, with 1000 error bars.

Figure 10: Sound speed inversion result of the nonlocal solar model (filled circles),

compared with that of Model S (empty circles).

Discussion

• About standard solar model

• Further improvements of the model

• New stellar evolution code using nonlocal convection theory

• 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)

Thank you!