How Large-Scale Flows in How Large-Scale Flows in the Solar Convection Zone the Solar Convection Zone

May Influence Solar ActivityMay Influence Solar Activity

David H. HathawayDavid H. HathawayNASA/MSFCNASA/MSFC

National Space Science and Technology CenterNational Space Science and Technology CenterHuntsville, ALHuntsville, AL

2004 October 192004 October 19

OutlineOutline

• OutlineOutline• The Large-Scale FlowsThe Large-Scale Flows• Differential RotationDifferential Rotation• Meridional CirculationMeridional Circulation• Torsional Oscillations Torsional Oscillations • Tachocline OscillationsTachocline Oscillations• SupergranulesSupergranules• Giant CellsGiant Cells

The Large Scale Flows The Large Scale Flows AxisymmetricAxisymmetric Non-AxisymmetricNon-Axisymmetric

Differential RotationDifferential RotationMeridional CirculationMeridional CirculationTorsional OscillationsTorsional Oscillations

Tachocline OscillationsTachocline Oscillations

SupergranulationSupergranulationGiant CellsGiant Cells

Large Scale Flows from Synoptic MapsLarge Scale Flows from Synoptic MapsThis movie shows the differential rotation (faster at the equator, This movie shows the differential rotation (faster at the equator, slower at high latitudes) and both the poleward meridional flow slower at high latitudes) and both the poleward meridional flow and the equatorwad drift of the active latitudes. The non-and the equatorwad drift of the active latitudes. The non-axisymmetric flows are hard to discern with 27-day samples.axisymmetric flows are hard to discern with 27-day samples.

The Axisymmetric FlowsThe Axisymmetric Flows

Sunspot motions and direct Doppler measurements had long ago Sunspot motions and direct Doppler measurements had long ago revealed a rapidly rotating equator and more slowly rotation pole. revealed a rapidly rotating equator and more slowly rotation pole. What mechanism produces this profile? What mechanism produces this profile?

Hathaway et al 1996.Hathaway et al 1996.

Photospheric Differential RotationPhotospheric Differential Rotation

Mechanisms for MaintainingMechanisms for MaintainingThe Latitudinal Differential RotationThe Latitudinal Differential Rotation

The Coriolis force on an axisymmetric flow won’t work – The Coriolis force on an axisymmetric flow won’t work – equatorward flows get turned retrograde – slowing down the equatorward flows get turned retrograde – slowing down the equator. Poleward flows get turned prograde – spinning up the equator. Poleward flows get turned prograde – spinning up the polar regions. Possible mechanisms must counteract these polar regions. Possible mechanisms must counteract these effects.effects.

Non-axisymmetric flows are required. The resulting fluid Non-axisymmetric flows are required. The resulting fluid trajectories can have velocity correlations that produce trajectories can have velocity correlations that produce Reynolds stresses which can maintain a rapidly rotating Reynolds stresses which can maintain a rapidly rotating equator.equator.

Non-Axisymmetric ConvectionNon-Axisymmetric ConvectionAnd Angular Momentum TransportAnd Angular Momentum Transport

Cells elongated Cells elongated north-south give an north-south give an equatorward flux of equatorward flux of angular momentumangular momentum

Cells elongated east-Cells elongated east-west give a poleward west give a poleward flux of angular flux of angular momentummomentum

Non-Axisymmetric ConvectionNon-Axisymmetric ConvectionEarly non-linear Early non-linear models (Gilman & models (Gilman & Miller 1981) had Miller 1981) had distinct north-south distinct north-south cells.cells.

Recent highly non-Recent highly non-linear models linear models (Miesch et al 2000) (Miesch et al 2000) have less distinct have less distinct north-south cells north-south cells but still produce but still produce rapidly rotation rapidly rotation equators.equators.

Internal Differential RotationInternal Differential RotationHelioseismic determinations of the internal rotation rate show Helioseismic determinations of the internal rotation rate show that the latitudinal differential rotation seen at the surface that the latitudinal differential rotation seen at the surface extends through the convection zone. Layers of strong radial extends through the convection zone. Layers of strong radial shear are found near the surface and at the base of the shear are found near the surface and at the base of the convection zone (the tachocline). How is this profile maintained?convection zone (the tachocline). How is this profile maintained?

Internal rotation profile from SOHO/MDI (Howe)Internal rotation profile from SOHO/MDI (Howe)

Mechanisms for MaintainingMechanisms for MaintainingThe Radial Differential RotationThe Radial Differential Rotation

The Coriolis force on an axisymmetric flow won’t work – outward The Coriolis force on an axisymmetric flow won’t work – outward flows get turned retrograde – slowing down the surface. Inward flows get turned retrograde – slowing down the surface. Inward flows get turned prograde spinning up the interior. Possible flows get turned prograde spinning up the interior. Possible mechanisms must counteract this effect.mechanisms must counteract this effect.

Gilman & Miller (1981)Gilman & Miller (1981) Miesch et al. (2000)Miesch et al. (2000)

Non-axisymmetric con-Non-axisymmetric con-vection gives profiles vection gives profiles with rotation constant with rotation constant on cylinders – close – on cylinders – close – but not good enough.but not good enough.

Although penetration Although penetration into the stable radiative into the stable radiative interior is included, no interior is included, no evidence for a evidence for a tachocline is seen.tachocline is seen.

The surface layers are The surface layers are not included.not included.

Surface Shear LayerSurface Shear LayerThe surface shear layer is probably due to the effects of rotation The surface shear layer is probably due to the effects of rotation on supergranulation. Foukal and Jokipii (1975), Foukal and on supergranulation. Foukal and Jokipii (1975), Foukal and Gilman (1979), Hathaway (1982), and DeRosa, Gilman, & Toomre Gilman (1979), Hathaway (1982), and DeRosa, Gilman, & Toomre (2002) find similar shear layers. The fluid tends to conserve its (2002) find similar shear layers. The fluid tends to conserve its angular momentum as it moves rapidly (compared to a rotation angular momentum as it moves rapidly (compared to a rotation period) across the layer.period) across the layer.

DeRosa, Gilman, & Toomre (2002)DeRosa, Gilman, & Toomre (2002)

Effects of Differential RotationEffects of Differential Rotationon Solar Activityon Solar Activity

•Key dynamo mechanism – Key dynamo mechanism – converts poloidal fields into converts poloidal fields into intense toroidal fieldsintense toroidal fields

•Advects active regionsAdvects active regions

•Shears unipolar regionsShears unipolar regions

The direction, the strength, and the structure of the meridional The direction, the strength, and the structure of the meridional flow were uncertain prior to helioseismology. It is now well flow were uncertain prior to helioseismology. It is now well established that the flow is predominantly poleward at ~20 m sestablished that the flow is predominantly poleward at ~20 m s-1-1. . But it appears to be variable and may have countercells at high But it appears to be variable and may have countercells at high latitudes. What drives this flow?latitudes. What drives this flow?

Hathaway et al (1996)Hathaway et al (1996)

Photospheric Meridional FlowPhotospheric Meridional Flow

Polar Field Reversal at Cycle MaximumPolar Field Reversal at Cycle MaximumThe polarity of the polar magnetic fields reverses at about the time of the The polarity of the polar magnetic fields reverses at about the time of the solar activity maximum. solar activity maximum.

Internal Meridional FlowInternal Meridional FlowLocal Helioseismology has revealed aspects of the internal Local Helioseismology has revealed aspects of the internal structure of the Meridional Circulation. (Giles et al., 1997; Braun structure of the Meridional Circulation. (Giles et al., 1997; Braun and Fan, 1998; Schou and Bogart, 1998; Basu, Antia, and Tripathy and Fan, 1998; Schou and Bogart, 1998; Basu, Antia, and Tripathy 1999)1999)

All of these investigations find All of these investigations find a poleward meridional flow of a poleward meridional flow of about 20 m/s that persists with about 20 m/s that persists with depth.depth.

Deep Meridional FlowDeep Meridional Flow(Giles 2001)(Giles 2001)

• Inversion of travel times with Inversion of travel times with mass-conservation constraint mass-conservation constraint through the whole convection through the whole convection zone (Giles PhD thesis).zone (Giles PhD thesis).

• For r/R>0.8 the mean For r/R>0.8 the mean meridional circulation is meridional circulation is poleward in both hemispheres poleward in both hemispheres and peaks around 25 deg and peaks around 25 deg latitude.latitude.

• The data are consistent with a The data are consistent with a 3 m/s return flow at the base 3 m/s return flow at the base of the convection zone.of the convection zone.

Fractional radius r/R

Mechanisms for MaintainingMechanisms for MaintainingThe Meridional CirculationThe Meridional Circulation

Hathaway (1984)Hathaway (1984) Miesch at al. (2000)Miesch at al. (2000)

Coriolis force on differential rotation Coriolis force on differential rotation gives a different structure. Reynolds gives a different structure. Reynolds stresses due to correlation between stresses due to correlation between outward and poleward flow works well. outward and poleward flow works well. Latitudinal pressure gradients may also Latitudinal pressure gradients may also contribute.contribute.

Effects of Meridional CirculationEffects of Meridional Circulationon Solar Activityon Solar Activity

•Key dynamo mechanismKey dynamo mechanism

•Carries following polarity Carries following polarity flux to the polesflux to the poles

•May carry toroidal fields in May carry toroidal fields in the tachocline equatorwardthe tachocline equatorward

We examined the latitude We examined the latitude drift of the sunspot zones by drift of the sunspot zones by first separating the cycles first separating the cycles where they overlap at where they overlap at minimum.minimum.

We then calculated the We then calculated the centroid position of the daily centroid position of the daily sunspot area averaged over sunspot area averaged over solar rotations for each solar rotations for each hemisphere.hemisphere.

[Hathaway, Nandy, Wilson, & Reichmann, [Hathaway, Nandy, Wilson, & Reichmann, ApJApJ 589. 665-670 2003 & 589. 665-670 2003 & ApJApJ 602, 543-543 602, 543-543 2004]2004]

Latitude Drift of Sunspot ZonesLatitude Drift of Sunspot Zones

The drift rate in each hemisphere and for each cycle (with one The drift rate in each hemisphere and for each cycle (with one exception) slows as the activity approaches the equator. exception) slows as the activity approaches the equator.

Drift Rate vs. LatitudeDrift Rate vs. Latitude

The sunspot cycle period is anti-correlated with the drift velocity The sunspot cycle period is anti-correlated with the drift velocity at cycle maximum. The faster the drift rate the shorter the period. at cycle maximum. The faster the drift rate the shorter the period.

R=-0.595% Significant

Cycle-to-Cycle VariationsCycle-to-Cycle Variations

The drift velocity at cycle maximum is correlated to the cycle The drift velocity at cycle maximum is correlated to the cycle amplitude but a stronger and more significant correlation is with the amplitude but a stronger and more significant correlation is with the amplitude of the second following (N+2) cycle.amplitude of the second following (N+2) cycle.

Both of these results were anticipated by the Dikpati & Charbonneau, Both of these results were anticipated by the Dikpati & Charbonneau, ApJApJ 1999, dynamo paper. 1999, dynamo paper.

R=0.598% Significant

R=0.799% Significant

Drift Rate – Amplitude CorrelationsDrift Rate – Amplitude Correlations

Torsional Oscillations in the rate of rotation were first observed at Torsional Oscillations in the rate of rotation were first observed at the surface (Howard and LaBonte, 1980). the surface (Howard and LaBonte, 1980).

Early surface observations Early surface observations showed high latitude exten-showed high latitude exten-sions (Snodgrass, sions (Snodgrass, ApJ ApJ 1985).1985).

More recent observations More recent observations show detatched polar spin-show detatched polar spin-ups at cycle maximum (Ulrich, ups at cycle maximum (Ulrich, ApJApJ 2001). 2001).

Torsional OscillationsTorsional Oscillations

Kosovichev & Schou (1997) Kosovichev & Schou (1997) found the torsional oscillation found the torsional oscillation signal below the surface.signal below the surface.

Antia & Basu (2001) follow the Antia & Basu (2001) follow the equatorward drift in GONG data equatorward drift in GONG data at 15 Mm depth and see high at 15 Mm depth and see high latitude spin up.latitude spin up.

Howe et al. (2000) see Howe et al. (2000) see extensions to 60-70 Mm depth.extensions to 60-70 Mm depth.

Torsional Oscillations in the InteriorTorsional Oscillations in the Interior

Torsional OscillationsTorsional Oscillationsand Solar Activityand Solar Activity

•The may be a symptom of, or The may be a symptom of, or reaction to, solar activityreaction to, solar activity

•Spruit (2003) suggests that they Spruit (2003) suggests that they are a dynamical result of are a dynamical result of thermal shadows from AR flux thermal shadows from AR flux tubestubes

Howe et al. 2002 found that the shear across the tachocline grew Howe et al. 2002 found that the shear across the tachocline grew and decayed with a period of about 18 months.and decayed with a period of about 18 months.

Tachocline OscillationsTachocline Oscillations

Tachocline OscillationsTachocline Oscillationsand Solar Activityand Solar Activity

•They also may be a symptom of They also may be a symptom of solar activitysolar activity

•However, the time scale of the However, the time scale of the oscillations is similar to that of oscillations is similar to that of other solar activity indicatorsother solar activity indicators

Three layers of convection cells:Three layers of convection cells:1801 Granules – Surface to 1000 km1801 Granules – Surface to 1000 km1954 Supergranules – Surface to 10,000 km1954 Supergranules – Surface to 10,000 km1964 Giant Cells – Surface? to 200,000 km1964 Giant Cells – Surface? to 200,000 km GranulesGranules

SupergranulesSupergranules

Giant Cells?Giant Cells?

The Convective FlowsThe Convective Flows

GranulationGranulation

Granulation movies Granulation movies from the Swedish from the Swedish Vacuum Solar Vacuum Solar Telescope in La Palma Telescope in La Palma illustrate the evolving illustrate the evolving granulation pattern.granulation pattern.

Typical cells are about Typical cells are about 1000 km in diameter 1000 km in diameter with lifetimes of about with lifetimes of about 20 minutes.20 minutes.

Granulation SimulationsGranulation SimulationsThe numerical simulations of The numerical simulations of Stein & Nordlund reproduce Stein & Nordlund reproduce the granulation pattern in the granulation pattern in most details. most details.

A “Cork” movie by Fausto A “Cork” movie by Fausto Cattaneo shows magnetic Cattaneo shows magnetic elements might be advected elements might be advected into downdrafts.into downdrafts.

SupergranulationSupergranulationSupergranulation Supergranulation is seen in Doppler is seen in Doppler velocity observa-velocity observa-tions and in flow tions and in flow fields constructed fields constructed with time-distance with time-distance helioseismology.helioseismology.

Typical cells are Typical cells are about 30,000 km in about 30,000 km in diameter and have diameter and have lifetimes of a lifetimes of a couple days.couple days.

Supergranulation in the InteriorSupergranulation in the InteriorDuvall et al. (1997) used time-distance helioseismology to show Duvall et al. (1997) used time-distance helioseismology to show that the supergranulation flows extend several thousand that the supergranulation flows extend several thousand kilometers into the sun.kilometers into the sun.

Supergranulation SimulationsSupergranulation SimulationsNumerical simulations Numerical simulations of supergranulation are of supergranulation are not as mature as those not as mature as those for granulation. for granulation.

The mechanism that The mechanism that selects cells the size of selects cells the size of supergranules is still supergranules is still uncertain. uncertain.

Data simulations can, Data simulations can, however, provide however, provide important information important information about the properties of about the properties of supergranules.supergranules.

The Photospheric Convection SpectrumThe Photospheric Convection SpectrumThe spectrum has two peaks: one at The spectrum has two peaks: one at ℓ~120 (supergranules) and ℓ~120 (supergranules) and one at ℓ~4000 (granules). There is nothing to indicate an one at ℓ~4000 (granules). There is nothing to indicate an additional component (mesogranules).additional component (mesogranules).

Data Simulation Input

Data Simulation Observed

Nordlund & Stein Simulations

Correlation Tracking Results

Supergranular DiffusionSupergranular Diffusion

A Diffusivity constructed from the A Diffusivity constructed from the data simulation input spectrum data simulation input spectrum (velocity x wavelength) gives a (velocity x wavelength) gives a spectrum that is strongly peaked at spectrum that is strongly peaked at ℓ~120 (supergranules).ℓ~120 (supergranules).

Supergranulation as a WaveSupergranulation as a WaveRecent 3D spectral Recent 3D spectral analyses of MDI Doppler-analyses of MDI Doppler-grams suggest that there grams suggest that there may be a wave-like prop-may be a wave-like prop-erty to supergranulation erty to supergranulation (Gizon, Duvall, & Schou, (Gizon, Duvall, & Schou, NatureNature 2003; Schou, 2003; Schou, ApJApJ 2003).2003).

Cells of different sizes Cells of different sizes rotate at different rates.rotate at different rates.

Rotation Effects on SupergranulesRotation Effects on SupergranulesSolar Rotation (27Solar Rotation (27dd) is slow for ) is slow for supergranules (40supergranules (40hh) and ) and granules (20granules (20mm).).

Foukal & Jokipii, Foukal & Jokipii, ApJApJ 1975, 1975, suggested that with slow suggested that with slow rotation fluid will tend to rotation fluid will tend to conserve angular momentum conserve angular momentum and produce a shear layer with and produce a shear layer with rotation increasing inward.rotation increasing inward.

Simulations by Gilman & Simulations by Gilman & Foukal, Foukal, ApJApJ 1979, and by 1979, and by Hathaway, Hathaway, Solar Phys.Solar Phys. 1982, 1982, confirmed this for confirmed this for supergranulation.supergranulation.

A poleward meridional flow at A poleward meridional flow at the surface is also produced.the surface is also produced.

SupergranulesSupergranulesand Solar Activityand Solar Activity

•They sweep magnetic elements to their They sweep magnetic elements to their boundaries and across the surfaceboundaries and across the surface

•They likely play important roles in both They likely play important roles in both the growth and decay of active regionsthe growth and decay of active regions

•They likely produce the surface shear They likely produce the surface shear layer and a faster meridional flow right at layer and a faster meridional flow right at the photospherethe photosphere

Giant CellsGiant CellsA 3D spectral analysis A 3D spectral analysis of MDI Dopplergrams of MDI Dopplergrams shows a ridge of shows a ridge of power that extends power that extends down to the lowest down to the lowest wavenumbers.wavenumbers.

This represents large This represents large Doppler features Doppler features rotating with the Sun.rotating with the Sun.

However, the characteristics of these Doppler However, the characteristics of these Doppler features are inconsistent with actual flows and features are inconsistent with actual flows and do not exhibit other characteristics expected do not exhibit other characteristics expected from Giant cells.from Giant cells.

Giant Cells as “Sub-Surface Weather”Giant Cells as “Sub-Surface Weather”Local helioseismology (time-distance: Zhao & Kosovochev, ApJ Local helioseismology (time-distance: Zhao & Kosovochev, ApJ 2004; Ring-diagrams: Haber et al., ApJ 2002) shows large velocity 2004; Ring-diagrams: Haber et al., ApJ 2002) shows large velocity features below the suns surface that are more suggestive of features below the suns surface that are more suggestive of giant cells. giant cells.

Giant Cells from SimulationsGiant Cells from Simulations

The highly nonlinear simulations of Miesch et al. (2000) produce The highly nonlinear simulations of Miesch et al. (2000) produce complex and rapidly evolving convection patterns. If this is a complex and rapidly evolving convection patterns. If this is a good represention of giant cell convection on the sun then giant good represention of giant cell convection on the sun then giant cells cannot be responsible for solar activity phenomena such as cells cannot be responsible for solar activity phenomena such as active longitudes and activity nests.active longitudes and activity nests.

How would threads of intense magnetic fields alter this situation?How would threads of intense magnetic fields alter this situation?

Giant CellsGiant Cellsand Solar Activityand Solar Activity

•They sweep magnetic elements to their They sweep magnetic elements to their boundaries and across the surfaceboundaries and across the surface

•They likely play important roles in both the They likely play important roles in both the growth and decay of active regionsgrowth and decay of active regions

•They likely produce the latitudinal and radial They likely produce the latitudinal and radial differential rotation as well as the meridional differential rotation as well as the meridional circulation through out much of the convection circulation through out much of the convection zonezone

•Are they responsible for active longitudes and Are they responsible for active longitudes and activity nests?activity nests?

ConclusionsConclusions

•Differential rotation and the meridional circulation are probably Differential rotation and the meridional circulation are probably driven by giant cells.driven by giant cells.

•The surface shear layer and excess surface meridional flow is The surface shear layer and excess surface meridional flow is probably driven by supergranulation.probably driven by supergranulation.

•The Tachocline shear layer is produced by…?The Tachocline shear layer is produced by…?

•Torsional oscillations may be driven by thermal shadows from Torsional oscillations may be driven by thermal shadows from rising flux tubes (Spriut, 2003).rising flux tubes (Spriut, 2003).

•Tachocline oscillations may be driven by…?Tachocline oscillations may be driven by…?

•Granulation is driven by the ionization/recombination of hydrogenGranulation is driven by the ionization/recombination of hydrogen

•Supergranulation is driven by…?Supergranulation is driven by…?

•Giant cells are driven by the ionization/recombination of metalsGiant cells are driven by the ionization/recombination of metals

•What roles do giant cells play in solar activity?What roles do giant cells play in solar activity?

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Zonal Momentum EquationZonal Momentum Equation