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). Introduction. Leptocline

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Cyclic changes in the solar subsurface layers using f modes

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)


Introduction
Introduction

  • 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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Outlines
Outlines

  • 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

  • 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)

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Part i inversion of f modes

Part I: Inversion of f-modes


Principle
Principle

  • 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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Variation of the f mode frequency during the solar cycle
Variation of the f-mode frequency during the solar cycle

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

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Mathematical formalism 1
Mathematical formalism (1)

  • 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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Mathematical formalism 2
Mathematical formalism (2)

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

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Kernels
Kernels

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Variations of frequencies with the cycle
Variations of frequencies with the cycle

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Variation of the position of subsurface layers
Variation of the position of subsurface layers

  • 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

Part II: Model analysis


Schematic view of the leptocline
Schematic view of the Leptocline

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Principle1
Principle

  • 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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Difference between models
Difference between models

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Relative difference of the theoretical frequencies
Relative difference of the theoretical frequencies

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Inversion of the theoretical frequencies
Inversion of the theoretical frequencies

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Radial displacement of the modeled profiles
Radial displacement of the modeled profiles

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Conclusions
Conclusions

  • 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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Part iii a look at the asphericities

Part III: A look at the asphericities


Solar asph ericities at the surface
Solar asphericities at the surface

Lefebvre et al., 2004, 2006

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Asphericities 1
Asphericities (1)

  • 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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Asphericities 2
Asphericities (2)

[Hz]

[Hz]

[Hz]

[Hz]

[Hz]

[Hz]

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Asphericities 3
Asphericities (3)

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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Asphericities 4
Asphericities (4)

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

[Hz]

[Hz]

[Hz]

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What has been done before
What has been done before…

  • 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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Diff rence relative entre les mod les
Différence relative entre les modèles

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Radius variation at the surface
Radius variation at the surface

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Conclusions our results
Conclusions: our results

  • 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

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Results of sofia et al 2005
Results of Sofia et al. (2005)

Sofia et al. 2005, ApJL

Lefebvre et al. 2007, ApJL

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Procedure

P

M2

M1

Po

r

r

r1

Procedure

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Link with the physical parameters
Link with the physical parameters

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Link with the physical parameters 2

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

Equilibrium radius

req

Link with the physical parameters (2)

f Mode

=

Surface wave

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Conclusions 1
Conclusions (1)http://www.techno-science.net/?onglet=glossaire&definition=8169

  • 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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Conclusions 2 perspectives
Conclusions (2) & perspectiveshttp://www.techno-science.net/?onglet=glossaire&definition=8169

  • 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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