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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. Leptocline

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Cyclic changes in the solar subsurface layers using f modes

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  1. 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)

  2. 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 Getting ready for PICARD helioseismology program - Nice

  3. 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) Getting ready for PICARD helioseismology program - Nice

  4. Part I: Inversion of f-modes

  5. 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 Getting ready for PICARD helioseismology program - Nice

  6. Variation of the f-mode frequency during the solar cycle Data computed by J. Schou and available on http://quake.stanford.edu/~schou/anavw72z/ Getting ready for PICARD helioseismology program - Nice

  7. 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 Getting ready for PICARD helioseismology program - Nice

  8. Mathematical formalism (2) • Inverse problem using RLS method (Regularized Least-Square) and frequencies of f-modes (Schou) with 150<l<250 Getting ready for PICARD helioseismology program - Nice

  9. Kernels Getting ready for PICARD helioseismology program - Nice

  10. Variations of frequencies with the cycle Getting ready for PICARD helioseismology program - Nice

  11. Variation of the position of subsurface layers • Lefebvre & Kosovichev, 2005, ApJ, 633, L149 • Lefebvre et al., 2007, ApJ, 658, L135 Lefebvre et al. (2005) Getting ready for PICARD helioseismology program - Nice

  12. Part II: Model analysis

  13. Schematic view of the Leptocline Getting ready for PICARD helioseismology program - Nice

  14. 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 Getting ready for PICARD helioseismology program - Nice

  15. Difference between models Getting ready for PICARD helioseismology program - Nice

  16. Relative difference of the theoretical frequencies Getting ready for PICARD helioseismology program - Nice

  17. Inversion of the theoretical frequencies Getting ready for PICARD helioseismology program - Nice

  18. Radial displacement of the modeled profiles Getting ready for PICARD helioseismology program - Nice

  19. 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 Getting ready for PICARD helioseismology program - Nice

  20. SDO Crédit NASA Crédit CEA PICARD Crédit CNES DynaMICCS Space perspectives Getting ready for PICARD helioseismology program - Nice

  21. Thank you…

  22. Part III: A look at the asphericities

  23. Solar asphericities at the surface Lefebvre et al., 2004, 2006 Getting ready for PICARD helioseismology program - Nice

  24. 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) Getting ready for PICARD helioseismology program - Nice

  25. Asphericities (2) [Hz] [Hz] [Hz] [Hz] [Hz] [Hz] Getting ready for PICARD helioseismology program - Nice

  26. 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) Getting ready for PICARD helioseismology program - Nice

  27. Asphericities (4) Lefebvre et al. 2006, proceedings SOHO18, CD-ROM [Hz] [Hz] [Hz] Getting ready for PICARD helioseismology program - Nice

  28. Getting ready for PICARD helioseismology program - Nice

  29. 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 Getting ready for PICARD helioseismology program - Nice

  30. Différence relative entre les modèles Getting ready for PICARD helioseismology program - Nice

  31. Radius variation at the surface Getting ready for PICARD helioseismology program - Nice

  32. 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 Getting ready for PICARD helioseismology program - Nice

  33. Results of Sofia et al. (2005) Sofia et al. 2005, ApJL Lefebvre et al. 2007, ApJL Getting ready for PICARD helioseismology program - Nice

  34. P M2 M1 Po r r r1 Procedure Getting ready for PICARD helioseismology program - Nice

  35. Link with the physical parameters Getting ready for PICARD helioseismology program - Nice

  36. 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 Getting ready for PICARD helioseismology program - Nice

  37. Conclusions (1) • 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) Getting ready for PICARD helioseismology program - Nice

  38. Conclusions (2) & perspectives • 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 Getting ready for PICARD helioseismology program - Nice

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