Flows in the Solar Convection ZoneFlows in the Solar Convection ZoneFlows in the Solar Convection ZoneFlows in the Solar Convection Zone

David HathawayDavid HathawayNASA/MSFCNASA/MSFC

National Space Science and Technology CenterNational Space Science and Technology Center

2004 July 212004 July 21

David HathawayDavid HathawayNASA/MSFCNASA/MSFC

National Space Science and Technology CenterNational Space Science and Technology Center

2004 July 212004 July 21

OutlineOutlineOutlineOutline

• Non-Axisymmetric Flows – Convective FlowsNon-Axisymmetric Flows – Convective Flows• Non-Axisymmetric Flows – Flows around SunspotsNon-Axisymmetric Flows – Flows around Sunspots• Axisymmetric Flows – Differential RotationAxisymmetric Flows – Differential Rotation• Axisymmetric Flows – Meridional CirculationAxisymmetric Flows – Meridional Circulation• Solar Cycle VariabilitySolar Cycle Variability• Inter-relationshipsInter-relationships• ConclusionsConclusions

• Non-Axisymmetric Flows – Convective FlowsNon-Axisymmetric Flows – Convective Flows• Non-Axisymmetric Flows – Flows around SunspotsNon-Axisymmetric Flows – Flows around Sunspots• Axisymmetric Flows – Differential RotationAxisymmetric Flows – Differential Rotation• Axisymmetric Flows – Meridional CirculationAxisymmetric Flows – Meridional Circulation• Solar Cycle VariabilitySolar Cycle Variability• Inter-relationshipsInter-relationships• ConclusionsConclusions

Three layers of convection cells:Three layers of convection cells:1801 Granules – Surface to 1000 km1801 Granules – Surface to 1000 km1954 Supergranules – Surface to 30,000 km1954 Supergranules – Surface to 30,000 km1964 Giant Cells – Surface? to 200,000 km1964 Giant Cells – Surface? to 200,000 km GranulesGranules

SupergranulesSupergranules

Giant Cells?Giant Cells?

Convective FlowsConvective Flows

GranulationGranulation

Granulation movies from Granulation movies from the Swedish Vacuum Solar the Swedish 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 with 1000 km in diameter with lifetimes of about 20 lifetimes of about 20 minutes.minutes.

Granulation SimulationsGranulation SimulationsThe numerical simulations of The numerical simulations of Stein & Nordlund reproduce Stein & Nordlund reproduce the granulation pattern in most the granulation pattern in most details. 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 is Supergranulation is seen in Doppler seen in Doppler velocity observations velocity observations and in flow field and in flow field constructed with constructed with time-distance 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 couple lifetimes of a couple days.days.

Supergranulation in the InteriorSupergranulation in the Interior

Duvall et al. (Duvall et al. (Solar Phys.Solar Phys. 1997) used time-distance helioseismology 1997) used time-distance helioseismology to show that the supergranulation flows extend several thousand to show 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.

Supergranules and Magnetic Field DiffusionSupergranules and Magnetic Field 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 spectrum that is strongly peaked at at ℓ~120 (supergranules).ℓ~120 (supergranules).

The Photospheric Convection SpectrumThe Photospheric Convection Spectrum

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

Data Simulation Input

Data Simulation Observed

Nordlund & Stein Simulations

Correlation Tracking Results

Supergranulation as a WaveSupergranulation as a WaveRecent 3D spectral analyses Recent 3D spectral analyses of MDI Dopplergrams of MDI Dopplergrams suggest that there may be a suggest that there may be a wave-like property to wave-like property to supergranulation (Gizon, supergranulation (Gizon, Duvall, & Schou, 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.

Giant Cells?Giant Cells?

A 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 Local helioseismology (time-distance: Zhao & (time-distance: Zhao & Kosovochev, ApJ 2004;Kosovochev, ApJ 2004;Ring-diagrams: Haber et Ring-diagrams: Haber et al., ApJ 2002) shows al., ApJ 2002) shows large velocity features large velocity features below the suns surface below the suns surface that are more that are more representative of giant representative of giant cells. cells.

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.

Photospheric zonal velocity from GONG 1995.Photospheric zonal velocity from GONG 1995.

Photospheric Differential RotationPhotospheric Differential Rotation

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

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.flow were uncertain prior to helioseismology.

Photospheric Meridional flow from GONG 1995.Photospheric Meridional flow from GONG 1995.

Photospheric Meridional FlowPhotospheric Meridional Flow

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

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

Latitude Drift of Sunspot ZonesLatitude Drift of Sunspot Zones

We examined the latitude drift We examined the latitude drift of the sunspot zones by first of the sunspot zones by first separating the cycles where separating the cycles where they overlap at minimum.they overlap at 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, & [Hathaway, Nandy, Wilson, & Reichmann, ApJ 2003]Reichmann, ApJ 2003]

Drift Rate vs. LatitudeDrift Rate vs. Latitude

The drift rate in each hemisphere and for each cycle (with one exception) The drift rate in each hemisphere and for each cycle (with one exception) slows as the activity approaches the equator. This behavior follows slows as the activity approaches the equator. This behavior follows naturally from the characteristics of a deep meridional flow. The flow naturally from the characteristics of a deep meridional flow. The flow amplitude is about 2-3 m/s.amplitude is about 2-3 m/s.

Variations over the Sun’s Activity CycleVariations over the Sun’s Activity Cycle

CyclicmagnetohydrodynamichelioseismologyCyclicmagnetohydrodynamichelioseismology

Zonal Flow Variations Torsional OscillationsZonal Flow Variations Torsional OscillationsTorsional Oscillations in the rate of rotation were first observed at the Torsional Oscillations in the rate of rotation were first observed at the surface. surface.

Early surface observations Early surface observations showed high latitude showed high latitude extensions (Snodgrass, extensions (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).

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 – Internal ExtensionsTorsional Oscillations – Internal Extensions

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

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

R=-0.595% Significant

Cycle-to-Cycle VariationsCycle-to-Cycle VariationsSunspot Latitude Drift RateSunspot Latitude Drift Rate

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

Inter-Relationships:Inter-Relationships:Solar Rotation, Convection, and Axisymmetric FlowsSolar Rotation, Convection, and Axisymmetric Flows

The effects of the Sun’s rotation changes the shape and dynamics of the The effects of the Sun’s rotation changes the shape and dynamics of the convection cells – cells elongated north-south drive a rapidly rotating convection cells – cells elongated north-south drive a rapidly rotating equator (Miesch et al., equator (Miesch et al., ApJApJ 2000). The meridional flow is more complex. 2000). The meridional flow is more complex.

Effects of Weak RotationEffects of Weak RotationSolar 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.

Magnetic Features reveal the FlowsMagnetic Features reveal the Flows

ConclusionsConclusions

•Granulation is well observed and simulated with numerical models.Granulation is well observed and simulated with numerical models.

•Supergranulation still holds some surprises. – What drives it? Does it Supergranulation still holds some surprises. – What drives it? Does it have wave-like properties?have wave-like properties?

•Giant cells are still elusive. Can we observe their characteristics? Do they Giant cells are still elusive. Can we observe their characteristics? Do they match the simulations?match the simulations?

•Differential rotation and the meridional circulation throughout the bulk Differential rotation and the meridional circulation throughout the bulk of the convection zone are probably driven by giant cells.of the convection zone are probably driven by giant cells.

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

•The Tachocline is driven by…?The Tachocline is driven by…?

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

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