The Current Status of Sunspot Seismology

1. The Current Status of Sunspot Seismology H. Moradi, H. Schunker, L. Gizon (Max Planck Institute for Solar System Research, Katlenburg-Lindau, Germany) + HELAS Local Helioseismology Collaboration (see poster “The Subsurface Structure of Sunspots”)

2. Sunspot Seismology • Sunspots – why are we so interested in them? • Theories about their formation, subsurface structure, thermal properties, and deep magnetic field topology are still controversial. • There are 4 outstanding issues: • Near-surface flows: Outflows or inflows? • The subsurface structure: Cool or hot? Shallow or deep? • The subsurface field configuration: The monolithic model (a) or the cluster model (b)? • The anchoring problem: At which depth, and by which agent is the sunspot flux bundle kept together? • Local/sunspot helioseismology is the only means by which we can investigate subphotospheric structure. ? Kosovichev, Duvall & Scherrer (2000) Thomas & Weiss (2004)

3. 2nd and 3rd HELAS Local Helioseismology WorkshopsOverview of Key Issues • Analysis of AR 9787: using all available helioseismic tools • Time-distance, helioseismic holography, ring-diagrams, Hankel analysis. • Issues addressed: Helioseismic travel times, the effects of filtering, acoustic power absorption, moat flow, subsurface vorticity and active region helicity, acoustic halos, subsurface flows and subsurfacewave—speed structure. • Sunspot Models: Undertake acritical assessment • Critically asses all sunspot models and identify those which can be used in the forward modelling process. • What properties should ideally be included in these models? • Numerical Simulations: Forward modelling of waves through model sunspots • Comparison of observed cross-covariances with simulations.

4. AR 9787 • Why AR 9787? • The sunspot is fairly isolated and axisymmetric. • Observed continuously by SOHO-MDI during 20-28 January 2002. • Showed little evolution during this time. MDI Magnetic Field MDI Intensity Continuum MDI Doppler Velocity

5. AR 9787 – The Moat Flow • The sunspot is surrounded by a region of horizontal outflow (the moat flow). • The motion of the moving magnetic features (MMFs) were measured from hourly averages of the magnetograms using a local correlation tracking method. • The moat flow has a peak amplitude of 230 m/s and extends to about 45 Mm. Gizon et al. (2009)

6. Linear Inversion for Subsurface Flows • Near-surface Flows: • Linear inversion for flows below AR 9787 using ring-diagrams (left) and ridge-filtered time-distance travel times (right) and show a horizontal outflow in the upper 4 Mm that is consistent with the moat flow deduced from the surface motion of MMFs. Moradi et al. (2009)

7. Linear Inversion for Subsurface Structure • As in the case of the subsurface flows, alternate and conflicting inferences have been produced from linear inversions of subsurface structure. • Common practice to treat the regions of magnetism as perturbations to the background wave speed. • Subsurface waves-speed perturbations – The case of AR 9787 • A comparison of structural inversions for AR 9787 using ring-diagram analysis and (phase-speed filtered) time-distance helioseismology. • Also compare the helioseismic models with some numerical/phenomenological models: • Fourier-Hankel Phenomenological Model (Fan, Braun & Chou 1995) • Nested Magnetic Cylinders (Crouch et al. 2005) • Semi-empirical Model of the Sunspot in AR 9787 (Cameron et al. 2010) • Radiative MHD Simulation of a Sunspot (Rempel et al. 2009)

8. Subsurface Wave-speed Structure

9. Subsurface Wave-speed Structure • All methods, expect for time-distance (phase-speed filters), show an increased wave speed in the top 2 Mm, with wave-speed perturbations of amplitudes less than about 2% at greater depths. • What could cause the inconsistency between the inversions for wave-speed? • Details of the measurement procedure: • The effects of the data analysis filtering in Fourier space (e.g., phase-speed filters) in the time-distance measurements are not fully accounted for. • Ring inversions include a contribution from changes in the first adiabatic index, as well as a treatment of near-surface effects which is different than in the time-distance inversions • Sensitivity functions: • Both methods use sensitivity functions that do not explicitly include the direct effects of the magnetic field, also assume that wave-speed perturbations are small. • The time-distance sensitivity functions may not model the reference power spectrum sufficiently accurately (convective background, mode frequencies, relative mode amplitudes, line widths and asymmetries). • Direct simulation of wave propagation through sunspot models is essential to test the validity of these models.

10. The Different Classes of Sunspot Models Moradi et al. (2009)

11. A semi-empirical model of the sunspot in AR 9787 (Cameron et al. 2010) • Thermodynamics: a combination of existing semi-empirical models of sunspot structure: the umbral model of Maltby et al. (1986) and the penumbral model of Ding and Fang (1989). • Magnetic field: vertical component is assumed to have a Gaussian horizontal profile, with a maximum surface field strength fixed by observations (3 kG). • Forward modelling: the helioseismic signature of the model sunspot has been studied using numerical simulations of the propagation of f, p1, and p2 wave packets (Hannah Schunker’s talk). • Simulations show the sunspot model gives a helioseismic signature that is similar to the observations (see poster by Cameron et al.) – perhaps the strongest argument in favour of shallow, fast-wave speed model. Cameron et al. (2010)

12. Summary • Key Findings Regarding Subsurface Structure: • Subsurface Flows: agreement between TD (ridge-filters) and RD, showing horizontal outflows, consistent with observations. • Subsurface Structure: the sunspot most likely introduces a (one-layered) shallow positive wave-speed perturbation. • Forward Modelling: using a “shallow” sunspot model to model the wave-field around a sunspot produces results that match actual observations very closely. • Detailed analysis can be found in the proceedings from the HELAS Local Helioseismology Workshops: Gizon et al. (2009, Space Sci. Rev.) and Moradi et al. (2009, Solar Phys.) • The way forward: • Continue to develop methods that incorporate appropriate physical models of the interaction of waves with strong magnetic fields near the surface (need good sunspot models/parametric studies here). • Realistic radiative simulations of sunspot-like structure will provide the ultimate test to validate the forward and inverse methods. • The deep structure: surface magnetic effects must be accounted for before we can detect and study the magnetic field below the photosphere. • SISI Project – Seismic Imaging of the Solar Interior (ongoing ERC Project at MPS, PI Gizon)