Solar Photospheric FlowsSolar Photospheric Flowsand theand the

Sunspot CycleSunspot Cycle

David H. HathawayDavid H. HathawayNASA/Marshall Space Flight CenterNASA/Marshall Space Flight Center

National Space Science and Technology CenterNational Space Science and Technology Center

9 January 20099 January 2009

OutlineOutline

• IntroductionIntroduction

• The Sun’s Magnetic CycleThe Sun’s Magnetic Cycle

• Convection Zone DynamicsConvection Zone Dynamics

• Magnetic Flux Transport ModelsMagnetic Flux Transport Models

• Modeling the Surface FlowsModeling the Surface Flows

• ConclusionsConclusions

IntroductionIntroduction

Why we study the solar cycle.Why we study the solar cycle.

The Sunspot CycleThe Sunspot Cycle

The Solar Activity Cycle is most easily seen in the number of The Solar Activity Cycle is most easily seen in the number of sunspots and sunspot groups visible on the Sun. The average cycle sunspots and sunspot groups visible on the Sun. The average cycle is about 11 years long from sunspot number minimum to minimum. is about 11 years long from sunspot number minimum to minimum. The amplitudes (average sunspot number at cycle maximum) of the The amplitudes (average sunspot number at cycle maximum) of the sunspot cycle vary widely. The Sun shows periods of inactivity like sunspot cycle vary widely. The Sun shows periods of inactivity like the Maunder Minimum and periods of high activity like the last 50 the Maunder Minimum and periods of high activity like the last 50 years. years. The solar cycle has important societal impacts.The solar cycle has important societal impacts.

The Climate ConnectionThe Climate Connection

Solar cycle related variations are evident in the terrestrial Solar cycle related variations are evident in the terrestrial temperature record.temperature record. Estimates of the variations in temperature at the Estimates of the variations in temperature at the Earth’s Surface (Mann et al. 1998, Moberg et al. 2005) show Earth’s Surface (Mann et al. 1998, Moberg et al. 2005) show significant correlations with variations in the amplitude of the significant correlations with variations in the amplitude of the sunspot cycle. The total solar irradiance has varied by about 0.1% sunspot cycle. The total solar irradiance has varied by about 0.1% over each sunspot cycle since 1975. The UV irradiance varies by over each sunspot cycle since 1975. The UV irradiance varies by about 3-4%. The precise connections between solar variability and about 3-4%. The precise connections between solar variability and climate are uncertain.climate are uncertain.

Galactic Cosmic Ray ModulationGalactic Cosmic Ray Modulation

The solar activity cycle modulates the radiation environment in the The solar activity cycle modulates the radiation environment in the inner solar system.inner solar system. While the flux of Solar Energetic Particles (SEP) While the flux of Solar Energetic Particles (SEP) from solar flares and coronal mass rises and falls with the sunspot from solar flares and coronal mass rises and falls with the sunspot number, the flux of Galactic Cosmic Rays (GCR) is low when number, the flux of Galactic Cosmic Rays (GCR) is low when sunspot number is high.sunspot number is high.

Satellite DragSatellite Drag

The solar activity cycle modulates the temperature and density of The solar activity cycle modulates the temperature and density of the thermosphere.the thermosphere. Variations in the Sun’s UV and EUV irradiance Variations in the Sun’s UV and EUV irradiance over a solar cycle produce order of magnitude changes in the over a solar cycle produce order of magnitude changes in the density at some spacecraft altitudes.density at some spacecraft altitudes.

Credit: S.Solomon

The Sun’s Magnetic CycleThe Sun’s Magnetic Cycle

A 160 year old mystery.A 160 year old mystery.

The Magnetic Field is the KeyThe Magnetic Field is the Key

Magnetic Polarity- Joy’s LawMagnetic Polarity- Joy’s Law

Active regions are tilted with the leading spots closer to the equator Active regions are tilted with the leading spots closer to the equator than the following spots. This tilt increases with latitude. This is well than the following spots. This tilt increases with latitude. This is well modeled by the effect of the Coriolis force on magnetic flux tubes modeled by the effect of the Coriolis force on magnetic flux tubes rising from deep inside the Sun. rising from deep inside the Sun.

Credit: Abbett, Fisher, & Fan (2001)

Magnetic Polarity - Hale’s LawMagnetic Polarity - Hale’s Law

The magnetic polarity of the leading sunspots in active regions The magnetic polarity of the leading sunspots in active regions switches from one hemisphere to the other and from one cycle switches from one hemisphere to the other and from one cycle to the next.to the next.

Equatorward DriftEquatorward Drift

Sunspots appear in bands on either side of the equator that drift Sunspots appear in bands on either side of the equator that drift toward the equator as each cycle progresses. Cycles overlap near toward the equator as each cycle progresses. Cycles overlap near the time of minimum. the time of minimum. Each cycle is an individual outburst.Each cycle is an individual outburst.

The Magnetic CycleThe Magnetic Cycle

Polar Field ReversalsPolar Field Reversals

The magnetic polarities of the Sun’s poles reverse from one cycle to The magnetic polarities of the Sun’s poles reverse from one cycle to the next at about the time of sunspot cycle maximum. The source of the next at about the time of sunspot cycle maximum. The source of these reversals is the transport of following (higher latitude by Joy’s these reversals is the transport of following (higher latitude by Joy’s Law) polarity magnetic elements to the poles by a meridional flow.Law) polarity magnetic elements to the poles by a meridional flow.

Convection Zone DynamicsConvection Zone Dynamics

The fluid flow controls the The fluid flow controls the magnetic field.magnetic field.

The Sun’s Internal StructureThe Sun’s Internal Structure

Energy is created in the Sun’s core by hydrogen burning and is Energy is created in the Sun’s core by hydrogen burning and is carried outward by radiation (photons) through the core and radiative carried outward by radiation (photons) through the core and radiative zone. The energy is carried outward by convective motions from a zone. The energy is carried outward by convective motions from a depth of about 200 Mm to the surface (the photosphere).depth of about 200 Mm to the surface (the photosphere).

Measuring CZ FlowsMeasuring CZ Flows1. Feature Tracking1. Feature Tracking

Measure the apparent motion of intensity (sunspots, granulation) or Measure the apparent motion of intensity (sunspots, granulation) or magnetic features. This gives both components of horizontal flow magnetic features. This gives both components of horizontal flow but depends upon availability of features (sunspots) and/or size of but depends upon availability of features (sunspots) and/or size of window for cross-correlations. Sunspots are known to have motions window for cross-correlations. Sunspots are known to have motions that do not reflect the actual surface flows.that do not reflect the actual surface flows.

Measuring CZ FlowsMeasuring CZ Flows2. Doppler Measurements2. Doppler Measurements

Measure the Doppler shift of photospheric spectral lines. This only Measure the Doppler shift of photospheric spectral lines. This only gives the line-of-sight velocity but can provide data from the entire gives the line-of-sight velocity but can provide data from the entire disc at rapid cadence.disc at rapid cadence.

Measuring CZ FlowsMeasuring CZ Flows3. Helioseismic Measurements3. Helioseismic Measurements

Measure the rotation of global oscillation modes (global helio-Measure the rotation of global oscillation modes (global helio-seismology) or differences in travel times for acoustic waves seismology) or differences in travel times for acoustic waves moving from point A to point B (local helioseismology). Gives moving from point A to point B (local helioseismology). Gives horizontal flows as functions of latitude, longitude, and depth.horizontal flows as functions of latitude, longitude, and depth.

The Axisymmetric FlowsThe Axisymmetric Flows

All three methods give similar results – the rotation rate is faster at All three methods give similar results – the rotation rate is faster at the equator and slower at the poles and the fluid flows from the the equator and slower at the poles and the fluid flows from the equator to the poles at the surface.equator to the poles at the surface.

Internal Rotation ProfileInternal Rotation Profile

Helioseismology gives the internal rotation profile. There are Helioseismology gives the internal rotation profile. There are shear layers at the top and bottom of the convection zone. The shear layers at the top and bottom of the convection zone. The latitudinal variation seen at the surface vanishes at the CZ base.latitudinal variation seen at the surface vanishes at the CZ base.

Internal Meridional FlowInternal Meridional Flow

The poleward meridional flow persists to depths of at least 20 Mm. A The poleward meridional flow persists to depths of at least 20 Mm. A slow return flow below 0.8 Rslow return flow below 0.8 R is suggested by mass flow constraints. is suggested by mass flow constraints.

Non-Axisymmetric FlowsNon-Axisymmetric Flows

GranulesGranulesDawes (1864)Dawes (1864)

SupergranulesSupergranulesHart (1954)Hart (1954)

GranulesGranules• Cellular flow patternCellular flow pattern• Characteristic Width ~ 1 MmCharacteristic Width ~ 1 Mm• Characteristic Lifetime ~ 10Characteristic Lifetime ~ 10mm

• Typical flow velocities ~ 3 km/sTypical flow velocities ~ 3 km/s• Magnetic elements form in the Magnetic elements form in the

downdrafts at the cornersdowndrafts at the corners• Flow velocities can become Flow velocities can become

supersonic ( > 7 km/s) and supersonic ( > 7 km/s) and generate acoustic wavesgenerate acoustic waves

• Size is characteristic of Size is characteristic of pressure scale height at pressure scale height at photospherephotosphere

• Well modeled in radiative-MHD Well modeled in radiative-MHD simulationssimulations

SupergranulesSupergranules

• Cellular flow patternCellular flow pattern• Characteristic Width ~ 30 MmCharacteristic Width ~ 30 Mm• Characteristic Lifetime ~ 1Characteristic Lifetime ~ 1dd

• Typical flow velocities ~ 300 m/sTypical flow velocities ~ 300 m/s• The magnetic network forms at The magnetic network forms at

their boundariestheir boundaries• They drive the surface shearThey drive the surface shear• NOT well modeled in any NOT well modeled in any

simulationssimulations• Rotation Rate mysteriesRotation Rate mysteries

– Faster for longer time lagsFaster for longer time lags– Faster for bigger cellsFaster for bigger cells– Faster than the internal Faster than the internal

rotation?rotation?• Open Question: What Open Question: What

determines their characteristic determines their characteristic size?size?

Giant CellsGiant CellsGiant cells – convection Giant cells – convection cells that span the CZ – cells that span the CZ – were proposed in the were proposed in the 1950s and 1960s.1950s and 1960s.

They appear in numerical They appear in numerical simulations. Their north-simulations. Their north-south alignments are south alignments are critical to driving the critical to driving the differential rotation.differential rotation.

Their existence is Their existence is suggested by suggested by observations but definitive observations but definitive characteristics have not characteristics have not been determined. been determined.

MesogranulesMesogranulesMesogranules – cells Mesogranules – cells intermediate in size intermediate in size between granules and between granules and supergranules – were supergranules – were proposed in the 1981 by proposed in the 1981 by November, Toomre, and November, Toomre, and Gebbie.Gebbie.

They filtered out the They filtered out the granules and then the granules and then the supergranules and found a supergranules and found a residual pattern with residual pattern with typical sizes of 10 Mm and typical sizes of 10 Mm and lifetimes of hours.lifetimes of hours.

Magnetic Flux Transport ModelsMagnetic Flux Transport Models

Basic Dynamo ProcessesBasic Dynamo Processes

Two basic dynamo processes are common to most models – Two basic dynamo processes are common to most models – shearing of poloidal field lines by differential rotation and lifting shearing of poloidal field lines by differential rotation and lifting and twisting of toroidal field lines. The emerging field must still and twisting of toroidal field lines. The emerging field must still be transported poleward by diffusion and/or meridional flow.be transported poleward by diffusion and/or meridional flow.

In/CCWIn/CCW

Out/CWOut/CW

Dikpati & Charbonneau DynamoDikpati & Charbonneau Dynamo

This is a 2D kinematic dynamo which uses the observed internal This is a 2D kinematic dynamo which uses the observed internal differential rotation, a realistic meridional circulation, a low differential rotation, a realistic meridional circulation, a low diffusivity, and a parameterized diffusivity, and a parameterized αα-effect. It produces a reversing -effect. It produces a reversing magnetic field configuration with a 22-year period and an equator-magnetic field configuration with a 22-year period and an equator-ward propagation of active zones. ward propagation of active zones. Strong Meridional flow gives Strong Meridional flow gives strong polar fields. strong polar fields. This model is used in predicting Cycle 24.This model is used in predicting Cycle 24.

Surface Flux TransportSurface Flux Transport

Surface flux transport models take emerging active regions as Surface flux transport models take emerging active regions as input and transport the magnetic flux by differential rotation, input and transport the magnetic flux by differential rotation, meridional flow, and diffusion. meridional flow, and diffusion. Strong Meridional flow gives weak Strong Meridional flow gives weak polar fields. polar fields. This model is use to give historical field estimates.This model is use to give historical field estimates.

Modeling the Surface FlowsModeling the Surface Flows

Spherical Harmonic AnalysisSpherical Harmonic Analysis

Years ago I developed an analysis technique based on spherical Years ago I developed an analysis technique based on spherical harmonics. The axisymmetric flows are determined and extracted. harmonics. The axisymmetric flows are determined and extracted. The nonaxisymmetric flows are projected onto spherical harmonics.The nonaxisymmetric flows are projected onto spherical harmonics.

•Calculate vector velocities using input spectrum of complex Calculate vector velocities using input spectrum of complex spectral coefficients, spectral coefficients, R, S, R, S, andand T T (Chandrasekhar, 1961). (Chandrasekhar, 1961).

•Project velocities into the line-of-sight, integrate over pixels, Project velocities into the line-of-sight, integrate over pixels, add noise, and blur with MDI MTF to get the observed signaladd noise, and blur with MDI MTF to get the observed signal

Data SimulationsData Simulations

m

mm

mm

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mm

mm

m

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Visual ComparisonVisual Comparison

Spectral ComparisonSpectral Comparison

Observed kinetic energy perObserved kinetic energy perwavenumber matches.wavenumber matches.

The input spectrum has twoThe input spectrum has twoLorentzian-shaped components:Lorentzian-shaped components:

supergranules and granules.supergranules and granules.

Evolving the Flow PatternEvolving the Flow Pattern

• The velocity pattern is evolved using the advection equationThe velocity pattern is evolved using the advection equation

• where, for example,where, for example,

• plus random changes in the phases of the complex coefficients so plus random changes in the phases of the complex coefficients so that the accumulated changes are of order 1 for a turnover timethat the accumulated changes are of order 1 for a turnover time

u

rV

u

rV

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uV

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)(sin,cossin,0 rDV

Rotation Profiles fromRotation Profiles fromCross-Correlation StudiesCross-Correlation Studies

Near the equator faster rotation rates are obtained for larger Near the equator faster rotation rates are obtained for larger separations in time. This was previous noted by Duvall (1980) separations in time. This was previous noted by Duvall (1980) and by Snodgrass & Ulrich (1990).and by Snodgrass & Ulrich (1990).

Rotation Profile ComparisonsRotation Profile Comparisons

They match at virtually all latitudes and time differences.They match at virtually all latitudes and time differences.

Lifetime ComparisonsLifetime Comparisons

The correlation match extremely well for separations of 8The correlation match extremely well for separations of 8hh and and 1616hh. The correlations are a bit too high for the shortest . The correlations are a bit too high for the shortest separations – suggesting faster evolution or more noise.separations – suggesting faster evolution or more noise.

Rotation Rate vs. WavenumberRotation Rate vs. Wavenumber

Beck & Schou (2000) Figure 4Beck & Schou (2000) Figure 4 10-day Simulation Results10-day Simulation Results

The increase in rotation rate at small wavenumbers – to rotation The increase in rotation rate at small wavenumbers – to rotation rates greater than the maximum measured by helioseismology in rates greater than the maximum measured by helioseismology in the surface shear layer – suggested a wave-like nature for the surface shear layer – suggested a wave-like nature for supergranules. The rotation rate we use DOES NOT exceed the supergranules. The rotation rate we use DOES NOT exceed the maximum. The faster rates are an illusion due to the line-of-sight maximum. The faster rates are an illusion due to the line-of-sight projection of the Doppler observations.projection of the Doppler observations.

Wave-Like Properties?Wave-Like Properties?Schou (2003) found evidence for prograde and retrograde moving Schou (2003) found evidence for prograde and retrograde moving components after adjusting for projection effects, applying weighting components after adjusting for projection effects, applying weighting and apodizing functions, and tracking at an appropriate rotation rate.and apodizing functions, and tracking at an appropriate rotation rate.

MDI – 60MDI – 60dd @ 1/60 @ 1/60mm SIM – 10SIM – 10dd @ 1/15 @ 1/15mm

Key PointsKey Points

• We simulate photospheric velocity fields We simulate photospheric velocity fields that accurately reproduce the MDI that accurately reproduce the MDI observations. They show:observations. They show:

1.1. Only two cellular flows are implicated: granules Only two cellular flows are implicated: granules and supergranules.and supergranules.

2.2. The cellular flows need not rotate faster than the The cellular flows need not rotate faster than the layers they are embedded in.layers they are embedded in.

3.3. The simulated velocity fields are useful for other The simulated velocity fields are useful for other studies, e.g. magnetic element diffusion.studies, e.g. magnetic element diffusion.

Magnetic Element DiffusionMagnetic Element Diffusion

The simulated flows can be used to advect passive elements to The simulated flows can be used to advect passive elements to determine the characteristics of diffusion.determine the characteristics of diffusion.

Meridional Flow VariationsMeridional Flow Variations

19961996 20002000

2003200320082008

I have started measuring the meridional flow using feature tracking I have started measuring the meridional flow using feature tracking on weak field magnetic elements and find variations over the on weak field magnetic elements and find variations over the course of cycle 23 (min. in 1996, max. in 2000, min. in 2008).course of cycle 23 (min. in 1996, max. in 2000, min. in 2008).

ConclusionsConclusions

1.1. There are two components to the surface cellular There are two components to the surface cellular flows - supergranules and granules.flows - supergranules and granules.

2.2. Supergranules do not actually rotate more rapidly Supergranules do not actually rotate more rapidly than the peak rotation rate in the surface shear than the peak rotation rate in the surface shear layer.layer.

3.3. The simulated flow fields can now be used to study The simulated flow fields can now be used to study the magnetic field diffusion characteristics.the magnetic field diffusion characteristics.

4.4. Variations in the flows over time can be used to Variations in the flows over time can be used to distinguish between different flux transport distinguish between different flux transport models.models.