Solar Convection Zone Dynamics
What could we learn from Solar-C?
Matthias Rempel
HAO/NCARHigh Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR)‫‏‬
The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Researchunder sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer.

Outline Our current understanding of large scale flows andmagnetic fields– Large scale convection flow (> supergranulation)– Differential rotation and meridional flow
– Large scale cyclic dynamo– Cyclic variations of diff. rot. and merid. Flow
– Magnetically induced flows at base of convectionzone
 What is the current state of the field?
 What are the key questions?
 How can Solar-C help?

Large scale convection patterns

Miesch et al.

B. Brown

 Influence of rotation changes withlatitude and depth Is this influence visible in nearsurface flows?
 Flow structure near poles– Polar vortex?
– Rossby waves?
– Any unexpected surprise?
 View on pole allows to track features
for several rotations– Study temporal evolution insteadof snapshots– Less distortion by differentialrotation

Large scale convection patterns
0.98 R

0.92 R

0.85 R

0.71 R Preferred alignment of convection cellswith respect to axis of rotation in low
latitudes (outside tangent cylinder Co-rotation of convection pattern Thermal transport toward poles ~ 5 – 10K difference between pole and midlatitudes
 Some indication of longitudinal alignmentof supergranulation?
 Primarily theoretical prediction, noobservational constraints!

Large scale flows, magnetic fields, some general
remarks Two different modeling approaches– 3D MHD simulations from ‘first principles’• No ‘free’ parameters• Limited in degree of turbulence reached• Computationally very expensive (most recent runs ~15363)– 2D axisymmetric mean field models• Computationally inexpensive• Not from first principles, strongly dependent on parametrizations

 Potential role of observational constraints– 3D MHD: Determine if models are on right track (resolution and related
to that diffusivities are the primary free parameters)– 2D meanfield: Too many degrees of freedom, need to be able to ruleout certain models

Results from 3D simulations: DR and MC
 Strong Reynolds stresses drive
differential rotation and meridional flow
 Equatorial acceleration with solar like
amplitude (almost always)
 Single celled meridional flow in highest
resolution case, multiple cells in lower
resolution case (no converged resultsyet)– Meridional flow always shows strong
temporal variability
 Solar-like rotation profiles require
equator pole entropy differences, origin
debated– Anisotropic energy transport– Coupling to tachocline
Miesch, Brun, Toomre et al. 2006, 2008

Results from 2D mean field models
 Solar-like diff. rotation requires
latitudinal entropy variation
 Entropy variation originates selfconsistently from coupling totachocline Counter-clockwise meridional flow if
inward directed angular momentum
transport (expected in limit of fast
rotation according to models by
Rüdiger & Kitchatinov) Meridional flow structure andlatitudinal temperature variation inconvection zone so far notconstrained Theoretical controversy regarding
origin of temperature perturbation(anisotropic energy transport vs.
tachocline)

Rempel, 2005

3D dynamo simulations
 Convection zone dynamo– Turbulent field, meanfield <0.03%

 Tachocline– Strong mean field ~10 kG

 Faster rotators (3x)Browning et al.
(2006)‫‏‬– Strong (~ 5 – 10 kG) field inconvection zone
– Antisymmetric over equator– Activity confined to low latitudes

 No cyclic dynamo yet– Difficult to evolve 3D runs for >10 years

 No 3D dynamo model yet
available that can bedirectly compared toobservations
Brown et al. (2008)

2D mean field dynamo models
 Main challenge– Not models from first principles, rely heavily onparameterizations– Ingredients known, but not relative importance– Variety of different models (tachocline, interface,distributed dynamos) with cyclic behavior– Progress means ruling out certain models!
– Difficult since most of the action is happening in the deep
convection zone!
 Potential ways to discriminate between different models– Meridional flow measurements in deep convection zone
– Cyclic variations of meridional flow and differential rotation– Magnetic field (direct / indirect)

Why is the meridional flow important Flux-transport dynamo– Turbulent transport weak(strong assumption thesemodels are based on!)– Meridional flow primarytransport mechanism– Meridional flow at base of
CV responsible ofequtorward propagationof activity
 Does the solar meridional
flow have the right topology
to achieve this?

M. Dikpati

Meridional flow structure

3D simulation
Miesch et al.
(2008)

 Poleward at surface (observed)
 Return flow not observable throughhelioseismology– 50 Mm depth still poleward (Gizon &Rempel 2008)
 Mass conservation– Equatorward at base Theory:– Meanfield models: equatorward– 3D simulations• Equatorward (high resolution)• Multiple flow cells (low resolution)
 Overall: Equatorward flow at base of CZ
very reasonable, observational
confirmation needed (speed of a few m/s)! Meanfield modelRempel (2005)
 Turbulent transport remains major
uncertainty: We can potentially rule out aflux-transport dynamo, but we can’t
confirm it!

Cyclic flow variations
Simulation, Rempel (2006)(R. Howe, global)(L. Gizon, local)
Torsional oscillation

Meridional flow

 Torsional oscillations most likely linked to dynamo, provide information about global
energy budget Global inversions loose sensitivity in high latitudes
 Global inversions less sensitive to meridional flows
 Origin of torsional oscillations can only be understood if zonal and meridional flow
variations are observed at same time (required to disentangle Lorentz force andthermal forcing)– High latitude local helioseismic observations required

Structure of magnetic field at base of convectionzone
 In most dynamo models base of convection zone is essential fororganization of large scale toroidal field Disagreement regarding field strength– Rising flux tube models require ~ 100 kG– Differential rotation can energetically produce up to ~10 kG– Meridional flow can transport field of up to 30 kG– 3D simulations with tachocline ~ 10 kG
 Observational constraints on field strength very helpful, but can we tell thedifference between a 100 kG intermittent and a 10 kG homogeneous
field?
– Direct magnetic effect ~ 10-7 - 10-5
– Possibility of detection through zonal flow variations?

Equilibrium and instability of magnetic field at thebase of the convection zone Force equilibrium requires balance ofmagnetic curvature force by pressure,buoyancy and Coriolis force
 Low filling factor field preferentially inbalance between tension, buoyancy andCoriolis force:– Prograde jets in strong field regions– Potentially observable if B~100 kG– If B~ 100 kG filling factor most likely
small (0.1)

Flow variations during rise of flux tubes
 Zonal flow changes from prograde
to retrograde in middle of convection
zone (angular momentumconservation)
 Large rise velocities (~ km/s) inupper most 10-20 Mm, however,timescale shortThin/thick flux tube simulation (Y. Fan)

HD/MHD tachocline instabilities produce non-axisymmetric flow
2D MHD model of tachocline shows
tipping & deformation of a toroidal
band; flows channeled through themagnetic fields produce large-scale
non-axisymmetry in the flow field(Cally, Dikpati and Gilman, 2003)‫‏‬

3D models also produce tipping(Miesch et al. 2007a, 2007b)‫‏‬

A snap-shot of the non-axisymmetric flow Global inversions show that axisymmetric variations at the base of theconvection zone with ~ 5 m/s amplitude are detectable– Can we detect jet-like feature at the base of the convection zone?
– Can we constrain non-axisymmetric variations of the zonal flow withsimilar accuracy?

Summary Helioseimic measurements of flows– Influence of rotation on convection (latitude/depth)• Constraint on global convection models• Long term tracking of temporal evolution– Structure of meridional flow
• Constraint on global convection models (constrains turbulent
angular momentum flux parallel to axis of rotation)• Constraint of flux-transport dynamo models– ‘unfavorable’ flow can rule out flux transport dynamo– ‘favorable’ flow is not sufficient due to uncertainty of role of turbulent
transport processes– High latitude zonal and meridional flow pattern• Better understanding of the origin of torsional oscillations and theirrelation to the dynamo process• Unknown territory, polar vortex, Rossby waves?

Summary Helioseismic measurements of flows at base of CZ– Zonal jets at base of convection zone/tachocline• Indirect detection of strong magnetic field? (100 kG is a 10-5change in pressure, but a 10% change in flow speed)– Non-axisymmetric flows• Tachocline instabilities?
• Indirect detection for strong magnetic field?

 High precision photometric measurements– Pole equator temperature variation• Predicted by most convection models• Essential ingredient for solar-like differential rotation in currentmodels

Summary Photospheric flow/field measurements– Better understanding of flux-transport anddispersial, point of return of meridional flow
– Detailed measurements of low order nonaxisymmetric field components needed for nonaxisymmetric dynamo models under development– Quantification of magnetic helicity fluxes
potentially very important for operation of dynamo– Detailed structure of photospheric field might beless important for large scale dynamo since
dynamo region about a factor of 105 in density
stratification away from photoshpere

Conclusion
 Understanding the large scale dynamo is strongly linked to understanding
convection and large scale flows– All of our current knowledge on structure of convection is based on numericalsimulations– Strong need for observational constraints (a lot can be learned frommeasurements in the upper half of the convection zone) Dynamo theory is a field that suffers strongly from insufficient observational
constraints, but the observations we need are very challenging:– Can we differentiate between a 10 kG (f~1) and a 100 kG (f<0.1) field at baseof CZ– Can we measure ~1-5 m/s meridional flow at base of convection zone?
– Can we see signatures of the flux emergence process?
 A mission such as Plan A combined with a major effort in numerical modeling (andalso further investigation of the solar stellar connection) is the only path I see wecan make progress in this field– The question is not if, but when we should do it?