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Exploring Cyclic Changes in Solar Subsurface Layers Using f-Modes: Insights from Helioseismology

This study examines the transient nature of the solar subsurface layers to enhance our understanding of solar dynamics, particularly the solar cycle. Emphasizing the Leptocline and Transition zone, it discusses the significance of these typically overlooked regions in interpreting solar radius variations and energetic surface phenomena. Utilizing helioseismic data inversion (f-modes), we analyze how subsurface stratification evolves across the 11-year solar cycle. This research serves as a foundation for the PICARD helioseismology program, aiming to deepen our knowledge of solar behavior and space weather impacts.

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Exploring Cyclic Changes in Solar Subsurface Layers Using f-Modes: Insights from Helioseismology

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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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