the need for physics-the need for physics-based inversions of based inversions of

sunspot structure and sunspot structure and flowsflows

D. Braun, A. Birch, A. CrouchD. Braun, A. Birch, A. Crouch

NWRA/CoRANWRA/CoRA

M. RempelM. Rempel

NCAR/HAONCAR/HAO

04/18/23 2GONG 2010-SOHO 24

main pointsmain 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

04/18/23 3GONG 2010-SOHO 24

issues in sunspot seismologyissues in sunspot seismology strong & unexplained sensitivities to strong & unexplained sensitivities to

methodologymethodology measurements of travel-times depend on type of measurements of travel-times depend on type of

filtering usedfiltering used frequency content of cross-correlations can vary frequency content of cross-correlations can vary

considerably between spot and quiet-Sunconsiderably between spot and quiet-Sun kernels may not contain essential physicskernels may not contain essential physics

forward models w/ mode conversion explain both forward models w/ mode conversion explain both absorption & phase/travel-time shifts, but absorption & phase/travel-time shifts, but disagree with pure wave-speed inversionsdisagree with pure wave-speed inversions

no inversion method exists which includes mode no inversion method exists which includes mode conversionconversion

faster

slower

phase-speed filtersphase-speed filters

yield near-surface yield near-surface inflowsinflows

ridge filtersridge filters

yield near-surface yield near-surface outflowsoutflows

J. Zhao & HMI teamJ. Zhao & HMI team A. Birch & D. BraunA. Birch & D. Braun

04/18/23 5GONG 2010-SOHO 24

filter sensitivitiesfilter sensitivities travel-times, and their inversion results, depend travel-times, and their inversion results, depend

strongly on filtering methods & parametersstrongly on filtering methods & parameters

Braun & Birch, 2008Braun & Birch, 2008; ; Thompson & Zharkov 2008Thompson & Zharkov 2008; ; Moradi, et al. 2009; Jackiewicz et al. 2009)Moradi, et al. 2009; Jackiewicz et al. 2009)

positive (slower) travel-time shifts using phase-positive (slower) travel-time shifts using phase-speed filters observed in simulations with only speed filters observed in simulations with only positive (faster) wave-speed perturbationspositive (faster) wave-speed perturbations sound-speed models (Birch et al. 2008)sound-speed models (Birch et al. 2008) magnetic models (Moradi, Hanasoge, Cally 2009)magnetic models (Moradi, Hanasoge, Cally 2009)

faster

slower

04/18/23 6GONG 2010-SOHO 24

postive mean (sunspot-like) travel-times in Rempel simulation

AR 10615

Rempel simulation

ω/k

ph

ase

speed

frequency

7

discrepancies between sunspot discrepancies between sunspot models models

fundamental fundamental differences differences between 2-layer between 2-layer TD inversion and TD inversion and strong near-strong near-surface surface perturbations perturbations suggested by other suggested by other modelsmodels

recent near-recent near-surface models surface models include effects of include effects of mode conversionmode conversion

figure from Gizon, Birch & Spruit (ARAA, in press)

faster

slower

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)

04/18/23 9GONG 2010-SOHO 24

semi-empirical sunspot modelsemi-empirical sunspot model

slower

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)

matches both phase-shifts & absorption of AR9286

04/18/23 10GONG 2010-SOHO 24

towards inversions towards inversions including magnetic effectsincluding magnetic effects

construct magnetohydrostatic (MHS) AR model construct magnetohydrostatic (MHS) AR model surface field measurements (?)surface field measurements (?) provides reference for linearization of both measurements provides reference for linearization of both measurements

and kernelsand kernels measure travel-time differences between active measure travel-time differences between active

region and MHS modelregion and MHS model MHS travel-times determined by numerical wave MHS travel-times determined by numerical wave

propagation propagation derive and apply relevant kernels derive and apply relevant kernels

horizontally variant – numerically derivedhorizontally variant – numerically derived sound speed, magnetic field, flows, etc.sound speed, magnetic field, flows, etc.

04/18/23 11GONG 2010-SOHO 24

demonstration: inverting for sound-demonstration: inverting for sound-speed in speed in

uniform vertical fielduniform vertical field

assume reference MHS model is uniform vertical fieldassume reference MHS model is uniform vertical field use TIMs (Crouch & Birch) to compute use TIMs (Crouch & Birch) to compute

eigenfunctions, power spectra and synthetic eigenfunctions, power spectra and synthetic wavefieldswavefields

use B-spline representations of sound-speed use B-spline representations of sound-speed perturbationperturbation

resulting travel-time maps are used to numerically resulting travel-time maps are used to numerically solve for the kernelssolve for the kernels

TD1, 3.75mHz

04/18/23 12GONG 2010-SOHO 24

demonstration: inverting for sound-demonstration: inverting for sound-speed withspeed with

synthetic data (TIMs) in uniform synthetic data (TIMs) in uniform vertical fieldvertical field

Case 0: Case 0: sound-speed sound-speed perturbation, B=0perturbation, B=0travel times referenced to model travel times referenced to model S (B=0)S (B=0)sound-speed kernels are sound-speed kernels are referenced to model S (B=0)referenced to model S (B=0)

Case 1: Case 1: sound-speed perturbation, sound-speed perturbation, B=3kGB=3kGtravel times referenced to model S travel times referenced to model S w/ B=3kGw/ B=3kGsound-speed kernels are referenced sound-speed kernels are referenced to model S (B=0)to model S (B=0)

04/18/23 13GONG 2010-SOHO 24

demonstration: inverting for sound-demonstration: inverting for sound-speed withspeed with

synthetic data (TIMs) in uniform synthetic data (TIMs) in uniform vertical fieldvertical field

Case 2: sound-speed perturbation, B=3kGCase 2: sound-speed perturbation, B=3kGtravel times referenced to model S w/ B=3kGtravel times referenced to model S w/ B=3kGsound-speed kernels are referenced to model S sound-speed kernels are referenced to model S w/ B=3kGw/ B=3kG

04/18/23 14GONG 2010-SOHO 24

main pointsmain 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:supported by:NASA SDO Science Center

NNH09CE41C