Recent Progress in Recent Progress in Understanding The Sun’s Understanding The Sun’s

Magnetic DynamoMagnetic Dynamo

David H. HathawayDavid H. Hathaway

NASA/MSFCNASA/MSFC

National Space Science and Technology National Space Science and Technology CenterCenter

2004 April 282004 April 28

University of Texas at ArlingtonUniversity of Texas at Arlington

OutlineOutline

• Sunspot Cycle CharacteristicsSunspot Cycle Characteristics

• Magnetic Dynamo ModelsMagnetic Dynamo Models

• The Meridional CirculationThe Meridional Circulation

• Latitude Drift of Sunspot ZonesLatitude Drift of Sunspot Zones

• ConclusionsConclusions

[Schwabe, 1844][Schwabe, 1844]Dynamo models must explain the cycle period and cycle shape Dynamo models must explain the cycle period and cycle shape (asymmetric with a rapid rise and a slow decline with large cycles (asymmetric with a rapid rise and a slow decline with large cycles rising to maximum in less time than small cycles).rising to maximum in less time than small cycles).

The “11-year” Sunspot or Wolf CycleThe “11-year” Sunspot or Wolf Cycle

The Maunder MinimumThe Maunder Minimum

Dynamo models should explain the variability in cycle amplitude and Dynamo models should explain the variability in cycle amplitude and the occurrence of periods of inactivity like the Maunder Minimum the occurrence of periods of inactivity like the Maunder Minimum (1645-1715).(1645-1715).

Sunspot Latitude Drift: SpSunspot Latitude Drift: Spöörer’s Lawrer’s Law[Carrington, 1858][Carrington, 1858]

Sunspots appear in two bands on either side of the equator. These bands Sunspots appear in two bands on either side of the equator. These bands spread in latitude and then migrate toward the equator as the cycle spread in latitude and then migrate toward the equator as the cycle progresses. Cycles can overlap at the time of minimum.progresses. Cycles can overlap at the time of minimum.

Active Region Tilt: Joy’s LawActive Region Tilt: Joy’s Law[Hale [Hale et al.,et al., 1919] 1919]

Active regions are tilted so that the following polarity spots are slightly Active regions are tilted so that the following polarity spots are slightly poleward of the preceding polarity spots. This tilt increases with latitude.poleward of the preceding polarity spots. This tilt increases with latitude.

The polarity of the preceding spots in the northern hemisphere is The polarity of the preceding spots in the northern hemisphere is opposite to the polarity of the preceding spots in the southern opposite to the polarity of the preceding spots in the southern hemisphere. The polarities reverse from one cycle to the next.hemisphere. The polarities reverse from one cycle to the next.

Hale’s Polarity LawHale’s Polarity Law[Hale[Hale,, 1924] 1924]

The Sun’s Magnetic CycleThe Sun’s Magnetic Cycle

Polar Field Reversal at Cycle MaximumPolar Field Reversal at Cycle Maximum

The polarity of the polar magnetic fields reverses at about the time of The polarity of the polar magnetic fields reverses at about the time of the solar activity maximum. (Result of Joy’s Law + Hale’s Law + the solar activity maximum. (Result of Joy’s Law + Hale’s Law + Meridional Flow + Flux Cancellation across the equator?)Meridional Flow + Flux Cancellation across the equator?)

[Babcock, 1959][Babcock, 1959]

Magnetic Flux Transport (Diffusion)

Flows within the convection zone were thought to be the source of the Flows within the convection zone were thought to be the source of the solar cycle. Energy is generated in the core and transported by radiation solar cycle. Energy is generated in the core and transported by radiation outward through the core and the radiative zone. At about 70% of the way outward through the core and the radiative zone. At about 70% of the way to the surface the temperature drops from 15MK to 2MK and metals start to to the surface the temperature drops from 15MK to 2MK and metals start to recombine – increasing the opacity. Boiling convective motions carry the recombine – increasing the opacity. Boiling convective motions carry the energy the rest of the way to the surface.energy the rest of the way to the surface.

The Solar InteriorThe Solar Interior

Basic Magnetic Dynamo ProcessesBasic Magnetic Dynamo Processes

Differential rotation in radius and Differential rotation in radius and latitude amplifies the poloidal field latitude amplifies the poloidal field by wrapping it around the Sun to by wrapping it around the Sun to produce a strong toroidal field.produce a strong toroidal field.

Lifting and twisting the toroidal Lifting and twisting the toroidal field can produce a poloidal field field can produce a poloidal field with the opposite orientation.with the opposite orientation.

The Ω-effect The α-effect

Early Dynamo ModelsEarly Dynamo Models

Kinematic dynamo models Kinematic dynamo models assumed internal profiles for both assumed internal profiles for both rotation (rotation (ΩΩ)) and helicity ( and helicity (αα) but ) but could produce 11-year cycles with could produce 11-year cycles with equatorward propagation of equatorward propagation of activity (Yoshimura, 1975).activity (Yoshimura, 1975).

MHD dynamo models produce MHD dynamo models produce internal profiles for both rotation internal profiles for both rotation ((ΩΩ)) and helicity ( and helicity (αα) but produce ) but produce short cycles cycles with poleward short cycles cycles with poleward propagation of activity propagation of activity (Glatzmaier, 1985).(Glatzmaier, 1985).

Fatal Flaws in the DynamosFatal Flaws in the Dynamos

Flows within the convection zone were previously Flows within the convection zone were previously thought to be the source of the solar cycle (for both thought to be the source of the solar cycle (for both αα- - and and ΩΩ-effects). Both dynamo types had a problem with -effects). Both dynamo types had a problem with too much too much αα-effect in the convection zone.-effect in the convection zone. Now, Now, important aspects of convection zone rotation and flux important aspects of convection zone rotation and flux tube dynamics indicate that the interface layer or tube dynamics indicate that the interface layer or “tachocline” is the seat of the solar cycle and both of “tachocline” is the seat of the solar cycle and both of the early models were fatally flawed.the early models were fatally flawed.

Dynamics of Buoyant Magnetic FluxDynamics of Buoyant Magnetic Flux

Flux tubes rise Flux tubes rise rapidlyrapidly from the tachocline (Parker 1975), move to from the tachocline (Parker 1975), move to slightly higher latitudes, are twisted slightly by the Coriolis force (as in slightly higher latitudes, are twisted slightly by the Coriolis force (as in Joy’s Law), and produce asymmetries between the preceeding and Joy’s Law), and produce asymmetries between the preceeding and following legs as they emerge through the photosphere (Fan and Fisher following legs as they emerge through the photosphere (Fan and Fisher 1996).1996).

Internal Rotation RateInternal Rotation RateHelioseismic 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 (Brown, 1985). Layers of strong radial shear are found near convection zone (Brown, 1985). Layers of strong radial shear are found near the surface and at the base of the convection zone (the tachocline). the surface and at the base of the convection zone (the tachocline). This is This is different than what was assumed and produced in the earlier dynamos.different than what was assumed and produced in the earlier dynamos.

The Meridional Circulation –The Meridional Circulation –an Added Ingredientan Added Ingredient

Hathaway (ApJ 1996) developed an image analysis technique for Hathaway (ApJ 1996) developed an image analysis technique for extracting the signal due to the meridional flow from Doppler velocity extracting the signal due to the meridional flow from Doppler velocity images. The meridional flow is largely poleward at ~20 m/s but variable.images. The meridional flow is largely poleward at ~20 m/s but variable.

The Photospheric Meridional CirculationThe Photospheric Meridional CirculationAt and near the surface the flow is largely poleward with a peak At and near the surface the flow is largely poleward with a peak velocity of about 20 m/s. There is continuing evidence that the velocity of about 20 m/s. There is continuing evidence that the strength and structure of the flow is time-dependent.strength and structure of the flow is time-dependent.

The Interior Meridional CirculationThe Interior Meridional CirculationLocal Helioseismology has recently revealed aspects of the internal Local Helioseismology has recently revealed aspects of the internal structure of the Meridional Circulation. (Giles et al., 1997; Braun and Fan, structure of the Meridional Circulation. (Giles et al., 1997; Braun and Fan, 1998; Schou and Bogart, 1998; Basu, Antia, and Tripathy 1999)1998; Schou 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” Interior Meridional CirculationDeep” Interior Meridional CirculationBraun and Fan (1998) found that the poleward flow extends at least Braun and Fan (1998) found that the poleward flow extends at least 10 to 15% into the solar interior (30 to 50% through the convection 10 to 15% into the solar interior (30 to 50% through the convection zone). By mass conservation there must be a return flow deeper in, zone). By mass conservation there must be a return flow deeper in, but probably still within the convection zone.but probably still within the convection zone.

The Meridional Circulation Return FlowThe Meridional Circulation Return FlowThe top half of the CZ The top half of the CZ contains 0.5% of the Sun’s contains 0.5% of the Sun’s mass. The rest of the CZ mass. The rest of the CZ contains over 2.5% or 5 contains over 2.5% or 5 times as much mass.times as much mass.

A poleward flow of 10 m/s in A poleward flow of 10 m/s in the outer half of the CZ the outer half of the CZ requires an average requires an average equatorward flow of just 2 equatorward flow of just 2 m/s in the lower half.m/s in the lower half.

A 2 m/s flow would carry A 2 m/s flow would carry magnetic flux from the magnetic flux from the middle latitudes to the middle latitudes to the equator in about 10 years!equator in about 10 years!

It is important to measure It is important to measure the meridional flow at the the meridional flow at the base of the convection zone.base of the convection zone.

Dynamo Wave Vs. Meridional FlowDynamo Wave Vs. Meridional Flow

With meridional flow the activity With meridional flow the activity moves in the flow direction with moves in the flow direction with period ~ 1/Velocityperiod ~ 1/Velocity

Dynamo waves travel along surfaces Dynamo waves travel along surfaces of constant angular velocity in a of constant angular velocity in a direction determined by the sign of direction determined by the sign of αα·· and a p and a period ~ 1/eriod ~ 1/√√ααωω

ωω-effect ~ d-effect ~ dΩΩ/dr/dr

αα-effect ~ u·curl u-effect ~ u·curl u

Dynamo Wave Vs. Meridional FlowDynamo Wave Vs. Meridional FlowButterfly DiagramsButterfly Diagrams

RRüdiger & Brandenberg (1995)üdiger & Brandenberg (1995) Dikpati & Charbonneau (1999)Dikpati & Charbonneau (1999)

Dynamo wave solutions have a Dynamo wave solutions have a poleward moving branch at high poleward moving branch at high latitudes and drift rates that are latitudes and drift rates that are nearly constant with latitude.nearly constant with latitude.

Solutions with meridional flow Solutions with meridional flow do not have the poleward do not have the poleward moving branch and have drift moving branch and have drift rates that are slower nearer the rates that are slower nearer the equator.equator.

Time (years) Time (years)

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]

Centroid Position vs. TimeCentroid Position vs. Time

The centroid of the sunspot area drifts toward the equator and slows to The centroid of the sunspot area drifts toward the equator and slows to a stop at a latitude of about 8a stop at a latitude of about 8°. The sunspots do not show evidence for °. The sunspots do not show evidence for the poleward branch at higher latitudes expected from dynamo waves.the poleward branch at higher latitudes expected from dynamo waves.

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 (1-2 m/s) is consistent with helioseismology (Giles, 2000).amplitude (1-2 m/s) is consistent with helioseismology (Giles, 2000).

Drift Rate – Period Anti-correlationDrift Rate – Period Anti-correlation

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. This is cycle maximum. The faster the drift rate the shorter the period. This is precisely what is predicted by dynamo models with deep meridional precisely what is predicted by dynamo models with deep meridional flow.flow.

R=-0.595% Significant

Drift Rate – Amplitude CorrelationsDrift Rate – Amplitude Correlations

The drift velocity at cycle maximum is correlated to the cycle amplitude The drift velocity at cycle maximum is correlated to the cycle amplitude (Wang, Lean, & Sheeley, 2002) but a stronger, and more significant (Wang, Lean, & Sheeley, 2002) but a stronger, and more significant correlation is with the correlation is with the amplitude of the second following (N+2) cycleamplitude of the second following (N+2) cycle. . This is a feature of dynamo models with fluctuating meridional flow This is a feature of dynamo models with fluctuating meridional flow (Charbonneau & Dikpati, 2000) and it offers a prediction for the (Charbonneau & Dikpati, 2000) and it offers a prediction for the amplitude of the next cycle.amplitude of the next cycle.

R=0.598% Significant

R=0.799% Significant

Dikpati & Charbonneau DynamoDikpati & Charbonneau Dynamo

Cycle 24 PredictionCycle 24 Prediction

The fast drift rates at the maximum of the last cycle (red oval – northern The fast drift rates at the maximum of the last cycle (red oval – northern hemisphere, yellow oval – southern hemisphere) indicate a larger than hemisphere, yellow oval – southern hemisphere) indicate a larger than average amplitude for the next cycle.average amplitude for the next cycle.

ConclusionsConclusions

• The drift rate of the sunspot area centroid favors The drift rate of the sunspot area centroid favors dynamo models with deep meridional flowdynamo models with deep meridional flow

1.1. No poleward drifting sunspot activity componentNo poleward drifting sunspot activity component2.2. Slower drift rate at lower latitudesSlower drift rate at lower latitudes3.3. Anti-correlation between drift rate and cycle periodAnti-correlation between drift rate and cycle period4.4. Correlation between drift rate and N+2 cycle amplitudeCorrelation between drift rate and N+2 cycle amplitude5.5. Flow rate of ~1 m/s consistent with helioseismologyFlow rate of ~1 m/s consistent with helioseismology

• The fast drift rates from the last cycle indicate that The fast drift rates from the last cycle indicate that the next cycle will be a large amplitude cyclethe next cycle will be a large amplitude cycle

Supported by NASA/OSS Solar and Heliospheric Physics SR&TSupported by NASA/OSS Solar and Heliospheric Physics SR&T

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