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the need for physics-based inversions of sunspot structure and flows D. Braun, A. Birch, A. Crouch

the need for physics-based inversions of sunspot structure and flows D. Braun, A. Birch, A. Crouch NWRA/CoRA M. Rempel NCAR/HAO. main points. goal of sunspot seismology is to determine subsurface structure, dynamics & evolution of sunspots

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the need for physics-based inversions of sunspot structure and flows D. Braun, A. Birch, A. Crouch

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  1. the need for physics-based inversions of sunspot structure and flows D. Braun, A. Birch, A. Crouch NWRA/CoRA M. Rempel NCAR/HAO

  2. main points goal of sunspot seismology is to determine subsurface structure, dynamics & evolution of sunspots after 3 decades this goal remains challenging & elusive forward, numerical, sunspot models are now reproducing helioseismic observations & suggest need to include acoustic to slow-mode conversion effects HMI/SDO provides incentive for inverse procedures demonstration of inversions around magneto-hydro-static (MHS) model faster GONG 2010-SOHO 24 2 11/30/2014

  3. issues in sunspot seismology strong & unexplained sensitivities to methodology measurements of travel-times depend on type of filtering used frequency content of cross-correlations can vary considerably between spot and quiet-Sun kernels may not contain essential physics forward models w/ mode conversion explain both absorption & phase/travel-time shifts, but disagree with pure wave-speed inversions no inversion method exists which includes mode conversion faster slower GONG 2010-SOHO 24

  4. J. Zhao & HMI team A. Birch & D. Braun ridge filters yield near-surface outflows phase-speed filters yield near-surface inflows

  5. filter sensitivities travel-times, and their inversion results, depend strongly on filtering methods & parameters Braun & Birch, 2008; Thompson & Zharkov 2008; Moradi, et al. 2009; Jackiewicz et al. 2009) positive (slower) travel-time shifts using phase-speed filters observed in simulations with only positive (faster) wave-speed perturbations sound-speed models (Birch et al. 2008) magnetic models (Moradi, Hanasoge, Cally 2009) faster slower GONG 2010-SOHO 24

  6. postive mean (sunspot-like) travel-times in Rempel simulation AR 10615 ω/k phase speed Rempel simulation frequency GONG 2010-SOHO 24

  7. discrepancies between sunspot models fundamental differences between 2-layer TD inversion and strong near-surface perturbations suggested by other models recent near-surface models include effects of mode conversion faster slower figure from Gizon, Birch & Spruit (ARAA, in press) 7

  8. a nested-magnetic-cylinder sunspot model concentric cylinders (each w/ uniform B) genetic algorithm to determine field strength & inclination within each cylinder Crouch, et al. (2005) matches both phase-shifts & absorption observed in Hankel analyses (e.g. Braun 1995)

  9. semi-empirical sunspot model Cameron, Gizon, Schunker & Pietarila 2010 • existing umbral & penumbral thermodynamic models • Maltby et al. 1996; Ding & Fang 1989 • parameterization of magnetic field • numerically propagation (SLiM) of planar wave packets (f, p1, p2) slower matches both phase-shifts & absorption of AR9286 GONG 2010-SOHO 24

  10. towards inversions including magnetic effects • construct magnetohydrostatic (MHS) AR model • surface field measurements (?) • provides reference for linearization of both measurements and kernels • measure travel-time differences between active region and MHS model • MHS travel-times determined by numerical wave propagation • derive and apply relevant kernels • horizontally variant – numerically derived • sound speed, magnetic field, flows, etc. GONG 2010-SOHO 24

  11. demonstration: inverting for sound-speed in uniform vertical field • assume reference MHS model is uniform vertical field • use TIMs (Crouch & Birch) to compute eigenfunctions, power spectra and synthetic wavefields • use B-spline representations of sound-speed perturbation • resulting travel-time maps are used to numerically solve for the kernels TD1, 3.75mHz GONG 2010-SOHO 24

  12. demonstration: inverting for sound-speed withsynthetic data (TIMs) in uniform vertical field Case 0: sound-speed perturbation, B=0 travel times referenced to model S (B=0) sound-speed kernels are referenced to model S (B=0) Case 1: sound-speed perturbation, B=3kG travel times referenced to model S w/ B=3kG sound-speed kernels are referenced to model S (B=0) GONG 2010-SOHO 24

  13. demonstration: inverting for sound-speed withsynthetic data (TIMs) in uniform vertical field Case 2: sound-speed perturbation, B=3kG travel times referenced to model S w/ B=3kG sound-speed kernels are referenced to model S w/ B=3kG GONG 2010-SOHO 24

  14. main points goal of sunspot seismology is to determine subsurface structure, dynamics & evolution of sunspots after 3 decades, this goal remains challenging & elusive forward, numerical, sunspot models are now reproducing helioseismic observations & suggest need to include acoustic to slow-mode conversion HMI/SDO provides incentive for inverse procedures demonstration of inversions around magneto-hydro-static (MHS) model faster slower supported by: NASA SDO Science Center NNH09CE41C GONG 2010-SOHO 24 14 11/30/2014

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