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Cyclic changes in the solar subsurface layers using f modes

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Cyclic changes in the solar subsurface layers using f modes

Sandrine Lefebvre

Service d’Aéronomie - Jussieu

Collaborators: P. Nghiem, S. Turck-Chièze (CEA)

A. Kosovichev (Stanford)

J.P. Rozelot (OCA)

- Leptocline
- Transition zone between Convective Zone and Photosphere
- For a long time, neglected zone due to its small mass and its physical complexity
- Important for a better understanding of the solar machine and in particular the solar cycle dynamics
- Potential origin of the solar radius variation observed at the surface
- Emergence of energetic phenomena at the Sun’s surface => solar forcing and space weather

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- Inversion of helioseimic data from SOHO/MDI : f - modes
- Changes in the subsurface stratification within the 11-year cycle
- Lefebvre & Kosovichev, 2005, ApJL, 633, L149
- Lefebvre, Kosovichev & Rozelot, 2007, ApJL, 658, L135

- Changes in the subsurface stratification within the 11-year cycle
- Use of solar models
- Influence of a radius and composition variation on the subsurface dynamics
- Lefebvre, Nghiem & Turck-Chièze, 2008, ApJ, in press (astroph 0809.1726)

- Influence of a radius and composition variation on the subsurface dynamics

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Part I: Inversion of f-modes

- Oscillation modes 3 numbers l, n, m
f-modes : n = 0 => surface wave

- Idea : compute the position of the subsurface layers by using the f-modes sensitive to the subsurface
Evolution of the stratification with depth?

Origin of the variation of the solar radius?

- Ref :
- Lefebvre & Kosovichev, 2005, ApJ, 633, L149
- Lefebvre et al., 2007, ApJ, 658, L135

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Data computed by J. Schou and available on http://quake.stanford.edu/~schou/anavw72z/

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- Dziembowski & Goode (2004)
- frequency of f-mode
- r radius of the considered layer
- l degree of f-mode
- I moment of Inertia
- eigenfrequency
- g acceleration due to gravity
- Kl kernel associated to degree l
- l mode eigenfunction
- density

r/r constant with depth

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- Inverse problem using RLS method (Regularized Least-Square) and frequencies of f-modes (Schou) with 150<l<250

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Getting ready for PICARD helioseismology program - Nice

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- Lefebvre & Kosovichev, 2005, ApJ, 633, L149
- Lefebvre et al., 2007, ApJ, 658, L135

Lefebvre et al. (2005)

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Part II: Model analysis

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- Aim : Study the influence of a radius, luminosity and composition variation on the subsurface physics
- Code CESAM
- First step : Seismic model without rotation nor B field
- |R/R| 2x10-4 => |R| 140 km
- |L/L| 1x10-3
- variation de composition 2%

- Set of 5 models

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- Leptocline :
- Transition zone between ZC et Photosphère
- f-modes => variation of the subsurface stratification with the cycle
- Double-layer structure
- The most external layers in antiphase with the cycle

- Variation of the subsurface stratification link to Hp?

- Perspectives :
- Use of dynamical model with rotation and B field
- Subsurface asphericities

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SDO

Crédit NASA

Crédit CEA

PICARD

Crédit CNES

DynaMICCS

Space perspectives

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Thank you…

Part III: A look at the asphericities

Lefebvre et al., 2004, 2006

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- Evolution of the even-a coefficients of f-modes (a2n)
- Influence of the turbulente pressure, the temperature and the magnetic field, which could be significative when looking at asphericties
- Study of the k coefficients:
- Comparison with the work of Dziembowski & Goode (2004) and their theoretical k computed from a variation of the turbulent pressure, the temperature or the magnetic field during the cycle (expression of integrals and kernels are given)

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[Hz]

[Hz]

[Hz]

[Hz]

[Hz]

[Hz]

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Effect of a magnetic perturbation

Bcycle = gaussian

Use of kernel in D&G (2004)

- Effect of a temperature perturbation
- T/T given by D&G
- Sign of T/T uncertain
- T = 0.0042 Hz

D&G (2004)

Dziembowski & Goode (2004)

Effect of a turbulent pressure perturbation

Tucycle = gaussian

D&G (2004)

D&G (2004)

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Lefebvre et al. 2006, proceedings SOHO18, CD-ROM

[Hz]

[Hz]

[Hz]

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- Schou et al. 1997
Pb1 : discrepancies for f modes with l>300

Pb2 : each mode has its own radius Rf

- Antia et al. 2000, Dziembowski et al. 2001, 2004, 2005
Rf et f are determined by a least-square fitting over frequencies

Il is the inertia momentum

l is linked to surface term

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Getting ready for PICARD helioseismology program - Nice

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- Confirmation of cyclic variations of the solar seismic radius:
- Confined in the more external layers of the Sun (Antia & Basu 2004; Dziembowski & Goode 2005).

- Double-structure layer:
- First part between 0.97 Ro et 0.99 Ro in phase with activity;
- Second part above 0.99 Ro in antiphase;
- Similar layer put in evidence by Godier & Rozelot (2001)

- Seismic radius variations at the surface in antiphase with the cycle.
- Asphericities: preliminary results
- variation of <k>
- possible influence of the turbulent pressure and/or the temperature over the cycle

- variation of <a2k/>
- amplitude of the relative variation of a2k 10x amplitude for the mean frequency
- different behavior for the variation of a2,a4 and a6 according the degree l, so according the depth

- variation of <k>

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Sofia et al. 2005, ApJL

Lefebvre et al. 2007, ApJL

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P

M2

M1

Po

r

r

r1

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http://www.techno-science.net/?onglet=glossaire&definition=8169

Equilibrium radius

req

f Mode

=

Surface wave

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- Leptocline = Transition zone between ZC et Photosphère
- f-modes => variation of the subsurface stratification with the cycle
- Double-layer structure
- The most external layers in antiphase with the cycle
- Similar layer suspected by Godier & Rozelot (2001)

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- Physics?
- Ionisation of H and He
- Basu et al. (1999) -> 2D speed analysis -> shear layer in 2 parts ( < et > à 4 Mm i.e. x 0.994)
- Corbard et al. (2001) -> 2D f-mode analysis -> inversion of the rotation gradient
- Analysis of solar models
- Variation of the subsurface stratification link to change in the parameters Hp?

- Limitations of the results :
- no magnetic field
- no rotation

- Perspectives :
- Use of dynamical model with rotation and B field
- Subsurface asphericities

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