Probing the Solar Dynamo by observing the Sun’s high latitude field, flows and seismic waves

35th COSPAR Scientific Assembly 18-25 July 2004

Probing the Solar Dynamo by observing the Sun’s high latitude field,

flows and seismic waves

Thierry Corbard

Observatoire de la Côte d’Azur

France


Plan

Links between the Solar interior and magnetic cycle Observed Surface Magnetic fields Solar Dynamo models

Current helioseismic probe of the dynamo and limitations Internal angular velocity from Global helioseismology 3D Subsurface flows from local helioseismology

Perspectives for Solar Orbiter


Observed Surface magnetic Fields

Courtesy: D. Hathaway; NASA/MSFC

Equatoward migration of sunspot-belt

Variation of amplitudes, duration etc..


Observed Surface magnetic Fields

Courtesy: D. Hathaway; NASA/MSFC

•Weak diffuse fields outside the sunspot drift poleward•Polar reversal takes place during sunspot maximum•Polar field take the sign of the following spots of the current cycle


6 Ingredients for Solar Dynamo Models

Parker 1970

Helical Turbulence

(-effect)

Differential rotation

Ω-effect

Poloidal Field

Toroidal Field

+ Meridional Circulation

.

+ Flux Tube dynamics, buoyancy and stabilityParker 75, Fan et al. 93, D’Silva & Choudhouri 93, Caligari et al. 95…


6 Ingredients for Solar Dynamo Models

Helical Turbulence

(-effect)

Differential rotation

Ω-effect

Poloidal Field

Toroidal Field

+ Meridional Circulation

+ Flux Tube dynamics, buoyancy and stability

2 Main Class of Dynamo models

Flux transport Dynamo (Wang et al. 91, Choudhuri et al. 95, Durney 95…)

Interface Dynamo (Parker 93, Tobias 96, Charbonneau & Mc Gregor 97….)

Dikpati & Charbonneau 99, Petrovay & Kerekes 2004


Evolution of Magnetic Fields in a Flux Transport Solar Dynamo Model

Courtesy M. Dikpati

+ Addition of a tachocline -effect is needed to satisfy Hale’s polarity rule

(Dikpati & Gilman 2001)


Global Helioseismology

Angular degree l

Fre

qu

en

cy (

mH

z)

n=0

n=1n=2n=3

:

drdθθ)Ω(r,θ)(r,Km

ωωnlm

nlmm-nl

Internal Rotation breaks spherical symmetry

=> Multiplets of 2l+1 frequencies

=> 2D Inverse Problem

observed Standard Solar Model

Unknown


Global Helioseismology Results: Internal Rotation

Tachocl

ine

Equator

Pole

Period (days)

“Polar Jet” ?

Corbard 98 Schou et al. 2002


Global Helioseismology Results: Torsional Oscillations

•Pattern found to persist from the surface down to (0.82R) Howe et al. 2000

•Indications of even deeper penetration at high latitudes Vorontsov et al. 2002

•likely a back reaction from the Dynamo generated magnetic field

Adapted from Corbard & Thompson 2001


Global HelioseismologyLimitations

Sensitive only to the part of the rotation that is symmetric about the equator.

Kernels Independent of longitude (e.g. cannot detect effect of active region on rotation)

Limited access to the polar zone

Impossible to separate the spherically asymmetric effects other than rotation (meridional circulation, magnetic fields, structural asphericity)


Local HelioseismologyAnalysis Principles

Small areas (16ºx16º) are tracked (typically between 8hrs and 28hrs)over the solar disk at a rate depending on the latitude of their center.

These areas are remapped using a Postel or transverse cylindrical projection that tend to preserve the distance along great circles.

=> Data cubes (Latitude – Longitude – time)


Local Helioseismology Main Methods

1. Time-distance analysis (Time domain)(Duvall et al. 1993, 1996)

2. Ring-Diagram analysis (Fourier domain)(Gough & Toomre 1983; Hill 1988)

3. Acoustic Holography (Phase sensitive)

(Lindsey & Braun, 1990, 1997)

Based on the local observation of global acoustic modes.


Time-distance helioseismology Principles

First developed by Duvall 1993

Employs waves travel times observed between different surface location on the Sun.

These travel times are then “inverted” to deduce:

Flow speed and direction, Sound speed perturbations [Magnetic field perturbations]

Along the ray paths of the observed modes.


Time-distance helioseismology Measuring Travel times

These travel times are obtained by cross-correlating the observed surface oscillations.

Because of the stochastic nature of excitation of the oscillations, the cross-covariance function must be averaged over some areas on the solar surface to achieve a S/N sufficient for measuring travel times.

=>Averages are made on rings around the central point

T

dtrtfrtf0

21 ),(),(),(

Kosovichev & Duvall., 1997


Time-distance helioseismology Interpretation of travel time perturbations

ds.kδ1

Fermat’s Principle and ray approximation theory

Phase travel time perturbation

Ray path in the unperturbated medium

Perturbation of the wave number

Gough 1993Kosovichev 1996

Bogdan 97: wavepacket are not confined to the raypath Development of wave-theoretical sensitivity kernels: Jensen et al. (2000), Birch &

Kosovitchev (2000), Jensen & Pijpers (2002), Gizon & Birch (2002) First comparisons (e.g. Couvidat et al. (2004)) show reasonable agreement for depths

above 15Mm


Time-distance helioseismology Interpretation of travel time perturbations

22222222

222 /).(4)(

2

k)v.k(ω kckccccc AAAac

Dispersion relation:

Temperature perturbations => do not depend on the direction of propagation Flow perturbations => waves move faster along the flow Magnetic fields perturbations => waves traveling perpendicular to the field lines are

the most sensitive to B (wave speed anisotropy not yet detected) Ryutova & Scherrer 1998

4B

cA

3D velocity field Acoustic cut off frequency

Alvén velocity

(Kosovichev et al. 1997)


Time-distance helioseismology Inverting Travel Times Maps

),(rdiff

2

),(rmean

Annulus ranges: 1º19 - 1º598

Zhao 2004

dsrdiff )(c

n(r).v2

2o

ds

r

r

omean ω

k

)(c

)(c o

+Different annulus ranges sound

different depths

Inversions for sound speed perturbations and 3D flows as a function of

depth


Time-distance helioseismology Results: 3D Flows below sunspot

0-3 Mm 6-9 Mm

9-12 Mm

Zhao, Kosovichev,Duvall 2001

Downward flows

Upward flows


Time-distance helioseismology Sub sunspot dynamics and structure

Courtesy SoHO/MDI

The cluster Model of Sunspot

Parker 1979

Illustration of sound speed variations and

subsurface flow patterns of a sunspot


Ring Diagram Analysis

kx

ky

3D FFT

(, ,t) (kx,ky,)

3D Power spectra Fitting

dzzzKU yx )(v),k,ω()k,(ω yx,hoho,

2 x 1D Inversions

Vz may then be computed using the divergence of the horizontal flow and assuming mass conservation. (Komm, Corbard et al. 2004)


Ring Diagram Analysis Flow Maps


Synoptic Maps of Vorticity – Kinetic Helicity etc..

Komm, Corbard et al. 2004 (ring diagrams)

Zhao & Kosovichev 2003 (time-distance)


Time and depth variations ofMeridional Flows

Basu & Antia 2002

Gonzalez Hernandez et al.

2004


Controversial detection of a counter cell at “high latitudes” in the Northern hemisphere

Haber et al. 2002

Not found by Basu and Antia 2003

And Time-distance analysis Zhao and Kosovichev 2003


Dynamo Models and Polar Reversal

N-S asymmetry in meridional flow speed during 1996-2002 and the appearance of a reverse, high-latitude flow cell in the N-hemisphere during 1998-2001 caused the N-pole to reverse ~1 yr before the S- pole

Dikpati et al. 2003


Perspectives for The Solar Orbiter

The Visible Light-imager and Magnetograph (VIM) will provide high resolution Magnetograms and Dopplergrams from outside the ecliptic plane (up to 30º).

Immediate benefit: Reduced foreshortening and Increased sensitivity to Magnetic Fields (factor 5)

Possibility of stereoscopic observations with SDO or Earth (120º)

Observations will provide the missing parts of solar dynamo models

Polar rotation rate and torsional oscillation pattern(High latitude Jets?, lower rotation bands migrating poleward ?)

Polar meridional flows (counter cell, returning flow ?) Maps of high latitude vorticity / kinetic helicity / Small scale Dynamo Direct observations of polar reversal and flux cancellation processes Access to the deep layers (tachocline) from stereoscopic observations Access to the far side of the Sun (continuous probe of spots / far side imaging

technique)


Acoustic HolographyFar Side Imaging

Lindsey & Braun (1997)

A local acoustic depression at the focal point will shift the phase of the ingression-egression correlation.


Concluding Remarks

The field of Local Helioseismology is fairly new

A lot of efforts have been made during the last few years in:

Understanding the forward problem (wave-theoretical sensitivity kernels / Building of artificial data)

Making comparison between the different Methods (group LoHCO) Understanding errors, methods resolution and correlations Understanding effects of image misalignment / geometric effects (P-angle /

Bo angle)

First Results are very encouraging and positive First attempt of “archeo-helioseismology” using Mt Wilson data in order to

infer the meridional circulation in the past two solar cycles

There is no doubt that a lot more progress will be achieved in developing and understanding these methods before the launch of Solar Orbiter

Probing the Solar Dynamo by observing the Sun’s high latitude field, flows and seismic waves

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