Measuring Meridional Circulation

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Measuring Meridional Circulation

• Markus Roth
• SPD Summer School on Helioseismology
• Boulder, July 27, 2005

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Meridional Circulation
Definition from the Arctic Climatology and
Meteorology Primer.
Meridional Circulation An atmospheric
circulation in a vertical plane oriented along a
meridian. It consists, therefore, of the vertical
and the meridional (North or South) components of
motion only.
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Role of the meridionalcirculation in the Sun
Mass transport from one latitude to another !
transport of angular momentum and magnetic
field Important for solar convection zone
dynamics and solar dynamo mechanism Theoretic
ally multi-cellular structure possible Direction
of the flow not clear (poleward or equatorward at
the surface?)
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Mass Conservation and Flux Transport Time
Top half of convection zone contains 0.25 of
stellar mass. Lower CZ contains ¼ 5 times as
much mass. Poleward flow of 10 m/s in the outer
half of the CZ requires an equatorward return
flow of just 2 m/ s in the lower convection
zone. At the bottom of the CZMagnetic flux
transport time from middle latitudes to equator
10 years
Velocity of meridional circulation determines
length of the cycle. Important for the solar
cycle! But hard to detect.
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Feature Tracking
Motion of sunspots, magnetic elements, Problems
sunspots limited to low latitudes, no sunspots
during solar minimum Morphology of the features
makes determination of exact location
difficult (Wöhl Brajsa 2000)
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Doppler Measurements
At the surface the flow is poleward. Maximum
velocity ¼ 20 m/s. Strength and structure of the
flow are time-dependent.
Problems include additional signals
(Hathaway et al. 1996)
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Quasi-Degenerate Perturbation Theory
Perturbing the equilibrium model with a slow flow
(small perturbation)
Mode Coupling Perturbation matrix elements for
calculation of new eigenvalues
Eigenvalues of perturbation matrix are frequency
corrections
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Effect of Rotation
Toroidal Flow
Differential rotation (s odd, t0)
?k(m)?k(m0)??(m) with ??(m)?s1,3,5,cn
l,s?ls(m) where cnl,ss0R ws(r) Knl,s(r) r2
dr and ?nl,s orthogonal functions
(Clebsch-Gordon coefficients) ! Inversion
possible
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Differential Rotation
Lifting of degeneracies ! Multiplets
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Inversion of Real Data
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Effect of Meridional Circulation
Meridional cirulation
frequency shift
basis functions are squared Clebsch-Gordon
coefficients! Not orthorgonal!
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Additional Frequency Shifts
Meridional circulation leaves ist signature in
global data Mode coupling leads to a kind of
actio-reactio effect Real effect is very
small in comparison to rotational splitting.
Inversion possible?
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Inverting for Meridional Circulation
Inverted Flow
Input Flow (s2, t0)
Mode Coupling
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Signatures of the Meridional Circulation in Real
Global Data
Components of meridional circulation (averaging
data over 1 yr)
Temporal variation of flow componets Can this be
correct? Effect of asphericity? Crosstalk?
Rel. number of multiplets with signature of
meridional flow
Next step Inversion of the coefficients !
Depth dependence
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Ring Diagrams
Power of oscillations averaged over visible solar
surface
2D power spectrum of section of solar
surface Horizontal sections give
rings. Underlying flow tilts the trumpets !
ellipses
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Meridioncal Flow from Ring Diagram Analysis
Haber et al. 2002
Basu, Antia, Tripathy 1998
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Time Distance Helioseismology
At depth 3-4.5 Mm (solid) and 6-9 Mm
(dashed) Relation to solar activity zones.
Zhao Kosovichev 2004
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Frequency Shifts
Doppler effect changes frequency of poleward and
equatorward traveling waves. A measured frequency
shift between these waves can be accounted to
meridional flow
Result Poleward flow extends at least 30 to 50
into the convection zone Return flow must be
deeper in, but probably still within the
convection zone.
Braun Fan, 1998
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Conclusions

• Meridional Circulation
• Coupling effects can be used to develop inversion
  methods for global data
• Local helioseismology has revealed aspects of the
  internal structure of the meridional
  circulation.All these investigations indicate a
  poleward flow of ¼ 20 m/s that persists with
  depth but shows a high variation.
• Investigations of solar cycle dependencies show
  variations of the meridional circulation within a
  year! solar dynamo?

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Collaborations
http//www.kis.uni-freiburg.de/mroth
National Solar Observatory, GONG-Group, Tucson
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Meridional Circulation

• Probing the Solar Convection Zone
• Relations of structural changes to the Solar Cycle

• Meridional Circulation
• Where is the return flow?
• Geometric structure (one cell, two cells, more
  cells)?
• Devolpment of new data analysis tools