The Current Status of Sunspot SeismologyH. 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”)

Sunspot SeismologySunspots – 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:

i. Near-surface flows: Outflows or inflows?

ii. The subsurface structure: Cool or hot? Shallow or deep?

iii. The subsurface field configuration: The monolithic model (a) or the cluster model (b)?

iv. 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.

Thomas & Weiss (2004)

Kosovichev, Duvall & Scherrer (2000)

?

2nd and 3rd HELAS Local Helioseismology Workshops

Overview of Key IssuesAnalysis 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 subsurface wave—speed structure.

Sunspot Models: Undertake a critical assessmentCritically 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.

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 Intensity Continuum MDI Doppler Velocity MDI Magnetic Field

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)

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)

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 9787A 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)

Subsurface Wave-speed Structure

Subsurface Wave-speed StructureAll 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.

The Different Classes of Sunspot Models

Moradi et al. (2009)

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)

SummaryKey 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)