Effects of the Observed Meridional Flow Variations since 1996 on the Sun’s Polar Fields

Effects of the Observed Effects of the Observed Meridional Flow Variations since Meridional Flow Variations since 1996 on the Sun’s Polar Fields1996 on the Sun’s Polar Fields

David H. HathawayDavid H. Hathaway11 and Lisa Upton and Lisa Upton2,32,3

11NASA/Marshall Space Flight Center/Science Research OfficeNASA/Marshall Space Flight Center/Science Research Office22Vanderbilt UniversityVanderbilt University

33University of Alabama, HuntsvilleUniversity of Alabama, Huntsville

2013 April 102013 April 10

Key PointsKey Points

1.1. Polar fields at cycle minimum produce and therefore Polar fields at cycle minimum produce and therefore predict the amplitude of the next cycle maximumpredict the amplitude of the next cycle maximum

2.2. Polar fields are produced by the advective transport of Polar fields are produced by the advective transport of fields from decaying active regions by near surface flowsfields from decaying active regions by near surface flows

3.3. Variations in the poleward meridional flow are the most Variations in the poleward meridional flow are the most likely cause of variations in the polar fields and solar cycle likely cause of variations in the polar fields and solar cycle amplitudesamplitudes

Four Key Characteristics of Four Key Characteristics of the Solar Cyclethe Solar Cycle

1. Sunspot Zones1. Sunspot ZonesSunspots appear in two latitude zones, one in the north and one in the Sunspots appear in two latitude zones, one in the north and one in the south. These zones drift toward the equator as each cycle progresses. south. These zones drift toward the equator as each cycle progresses. The cycles overlap at minimum – typically by 2-3 years. Cycle 24 The cycles overlap at minimum – typically by 2-3 years. Cycle 24 minimum had the smallest overlap in 130 years.minimum had the smallest overlap in 130 years.

2. Hale’s Law2. Hale’s LawIn 1919 Hale (along with Ellerman, Nicholson, and Joy) found that the In 1919 Hale (along with Ellerman, Nicholson, and Joy) found that the magnetic field in sunspots followed a definite law, “Hale’s Law” such magnetic field in sunspots followed a definite law, “Hale’s Law” such that: that: “…the preceding and following spots … are of opposite polarity, “…the preceding and following spots … are of opposite polarity, and that the corresponding spots of such groups in the Northern and and that the corresponding spots of such groups in the Northern and Southern hemispheres are also opposite in sign. Furthermore, the Southern hemispheres are also opposite in sign. Furthermore, the spots of the present cycle are opposite in polarity to those of the last spots of the present cycle are opposite in polarity to those of the last cycle”.cycle”.

3. Joy’s Law3. Joy’s LawIn that same 1919 paper Joy noted that In that same 1919 paper Joy noted that sunspot groups are tilted with sunspot groups are tilted with the leading spots closer to the equator than the following spots. This the leading spots closer to the equator than the following spots. This tilt increases with latitude but is highly variable from sunspot group to tilt increases with latitude but is highly variable from sunspot group to sunspot group.sunspot group.

4. Flux Transport4. Flux TransportMagnetic flux that emerges in active regions is transported across the Magnetic flux that emerges in active regions is transported across the sun’s surface by differential rotation (drifting prograde near the equator sun’s surface by differential rotation (drifting prograde near the equator and retrograde at high latitudes) and meridional flow (poleward from the and retrograde at high latitudes) and meridional flow (poleward from the equator).equator).

How it Works:How it Works:The Sun’s Magnetic DynamoThe Sun’s Magnetic Dynamo

The Babcock Dynamo (1961)The Babcock Dynamo (1961)a) Dipolar field at cycle minimum a) Dipolar field at cycle minimum threads through a shallow layer threads through a shallow layer below the surface.below the surface.

b) Latitudinal differential rotation b) Latitudinal differential rotation shears out this poloidal field to shears out this poloidal field to produce a strong toroidal field produce a strong toroidal field (first at the mid-latitudes then (first at the mid-latitudes then progressively lower latitudes).progressively lower latitudes).

c) Buoyant fields erupt through c) Buoyant fields erupt through the photosphere giving Hale’s the photosphere giving Hale’s polarity law and Joy’s Tilt.polarity law and Joy’s Tilt.

d) d) ProposedProposed meridional flow meridional flow away from the active latitudes away from the active latitudes gives reconnection at the poles gives reconnection at the poles and equator.and equator.

(son Horace , not father Harold)(son Horace , not father Harold)

Polar Fields PredictionPolar Fields PredictionIn Babcock’s model, and many more since then, the strength of the In Babcock’s model, and many more since then, the strength of the Sun’s polar fields near the time of sunspot cycle minimum is the seed Sun’s polar fields near the time of sunspot cycle minimum is the seed for the next solar cycle. Polar fields have been used to reliably predict for the next solar cycle. Polar fields have been used to reliably predict the last three sunspot cycles.the last three sunspot cycles.

The weak polar fields at the last minimum indicate a weak Cycle 24 The weak polar fields at the last minimum indicate a weak Cycle 24 (Svalgaard, Cliver, & Kamide 2005; Choudhuri Chatterjee, & Jiang, (Svalgaard, Cliver, & Kamide 2005; Choudhuri Chatterjee, & Jiang, 2007; Jiang, Chatterjee, & Choudhuri,2007).2007; Jiang, Chatterjee, & Choudhuri,2007).

Polar Faculae/Polar FieldsPolar Faculae/Polar Fields

Recently, Muñoz-Jaramillo et al. (2012) Recently, Muñoz-Jaramillo et al. (2012) showed that the (corrected) number of showed that the (corrected) number of polar faculae seen on Mt. Wilson polar faculae seen on Mt. Wilson photographs by Neil Sheeley is a good photographs by Neil Sheeley is a good proxy for polar field strength and flux.proxy for polar field strength and flux.

The polar field at minimum is a good The polar field at minimum is a good predictor of the amplitude of the next predictor of the amplitude of the next cycle .cycle .

Cycle 24 Rise to (Mini) MaxCycle 24 Rise to (Mini) MaxFitting a parametric curve (Hathaway et al. 1994) to the monthly sunspot Fitting a parametric curve (Hathaway et al. 1994) to the monthly sunspot numbers indicates peak sunspot number for Cycle 24 of ~66numbers indicates peak sunspot number for Cycle 24 of ~66 – – a weak a weak cycle due to weak polar fields.cycle due to weak polar fields.

Why were the Polar Fields Why were the Polar Fields Weak?Weak?

Flux Transport and Polar FieldsFlux Transport and Polar FieldsNew regions emerge at lower and lower latitudes. Following polarity New regions emerge at lower and lower latitudes. Following polarity cancels the leading polarity that previously occupied that latitude band. cancels the leading polarity that previously occupied that latitude band. The following polarity that remains at higher latitudes is transported to The following polarity that remains at higher latitudes is transported to the poles where it reverses the old polar fields and builds up the new the poles where it reverses the old polar fields and builds up the new cycle polar fields. cycle polar fields.

The variable strength of the polar fields can depend upon variations in the The variable strength of the polar fields can depend upon variations in the active region sources and/or variations in the flux transport processes.active region sources and/or variations in the flux transport processes.

Flux TransportFlux TransportConvective motions (supergranules) quickly carry Convective motions (supergranules) quickly carry magnetic elements to their boundaries where they magnetic elements to their boundaries where they then move more slowly as the boundaries evolve.then move more slowly as the boundaries evolve.

Four days from HMI.Four days from HMI.

SupergranulesSupergranulesHathaway et al. (2000, 2006, 2008, 2010) analyzed and simulated Doppler Hathaway et al. (2000, 2006, 2008, 2010) analyzed and simulated Doppler velocity data from MDI. The simulation uses an evolving spectrum of velocity data from MDI. The simulation uses an evolving spectrum of spherical harmonics that reproduces the observed velocity spectrum, spherical harmonics that reproduces the observed velocity spectrum, the cell lifetimes, and the cell motions in longitude and latitude.the cell lifetimes, and the cell motions in longitude and latitude.

MDIMDI

SIMSIM

Axisymmetric MotionsAxisymmetric Motions

Supergranule pattern differential Supergranule pattern differential rotation profile May-July 1996.rotation profile May-July 1996.

Supergranule pattern meridional Supergranule pattern meridional flow profile May-July 1996.flow profile May-July 1996.

Hathaway et al. (2010) and Hathaway (2012a, 2012b) measured and Hathaway et al. (2010) and Hathaway (2012a, 2012b) measured and simulated the longitudinal and latitudinal motions of the supergranule simulated the longitudinal and latitudinal motions of the supergranule pattern.pattern.

As the supergranules themselves are advected by these larger flows As the supergranules themselves are advected by these larger flows they carry the magnetic elements at their boundaries and impart to them they carry the magnetic elements at their boundaries and impart to them this differential rotation and meridional flow (Hathaway & Upton 2013).this differential rotation and meridional flow (Hathaway & Upton 2013).

Magnetic Element MotionsMagnetic Element MotionsHathaway & Rightmire (2010, 2011) measured the axisymmetric Hathaway & Rightmire (2010, 2011) measured the axisymmetric transport of magnetic flux by cross-correlating 11x600 pixel strips at transport of magnetic flux by cross-correlating 11x600 pixel strips at 860 latitude positions between ±75˚ from 60,000 magnetic images 860 latitude positions between ±75˚ from 60,000 magnetic images acquired at 96-minute intervals by MDI on SOHO. acquired at 96-minute intervals by MDI on SOHO.

Axisymmetric Flow ProfilesAxisymmetric Flow Profiles

The average Differential Rotation The average Differential Rotation profiles with 2profiles with 2σσ error limits for the error limits for the MDI/HMI overlap interval.MDI/HMI overlap interval.

The average Meridional Flow The average Meridional Flow profiles with 2profiles with 2σσ error limits for the error limits for the MDI/HMI overlap interval.MDI/HMI overlap interval.

Rightmire-Upton, Hathaway, & Kosak (2012) extended the measurements Rightmire-Upton, Hathaway, & Kosak (2012) extended the measurements to HMI data and compared the results to the MDI measurements. The to HMI data and compared the results to the MDI measurements. The flow profiles are in good agreement but with small, significant, flow profiles are in good agreement but with small, significant, differences – DR is faster in HMI, MF is slower in HMI.differences – DR is faster in HMI, MF is slower in HMI.

These profiles can be well fit with 4These profiles can be well fit with 4thth order polynomials in sin(latitude). order polynomials in sin(latitude).

Flow Profile HistoriesFlow Profile HistoriesDifferential Rotation hardly changes. Meridional Flow changes substantially!Differential Rotation hardly changes. Meridional Flow changes substantially!

The Meridional Flow at Cycle 24 minimum was ~20% faster than it was at The Meridional Flow at Cycle 24 minimum was ~20% faster than it was at Cycle 23 minimum. A fast Meridional Flow produces weak polar fields in Cycle 23 minimum. A fast Meridional Flow produces weak polar fields in surface flux transport models (c.f. Wang, Robbrecht, & Sheeley, 2009).surface flux transport models (c.f. Wang, Robbrecht, & Sheeley, 2009).

Surface Flux Transport via Observed FlowsSurface Flux Transport via Observed FlowsWe are constructing 1024x512 Synchronic Maps every 15We are constructing 1024x512 Synchronic Maps every 15mm using evolving using evolving supergranules and the observed axisymmetric flows to transport flux with supergranules and the observed axisymmetric flows to transport flux with data assimilated from MDI and HMI at 96data assimilated from MDI and HMI at 96mm and 60 and 60mm intervals respectively. intervals respectively.

Note that the flux elements are transported by the observed flows to the Note that the flux elements are transported by the observed flows to the positions they are found when the data is assimilated.positions they are found when the data is assimilated.

Effects of Meridional Flow Effects of Meridional Flow Variations (Upton’s Thesis)Variations (Upton’s Thesis)

The Plan: The Plan: 1.1. Produce a baseline set of synchronic maps assimilating data Produce a baseline set of synchronic maps assimilating data

from all latitudes.from all latitudes.2.2. Produce a second set of synchronic maps assimilating data Produce a second set of synchronic maps assimilating data

from the equatorial regions (active region sources) and using from the equatorial regions (active region sources) and using a constant, average, north/south symmetric meridional flow.a constant, average, north/south symmetric meridional flow.

3.3. Produce a third set of synchronic maps assimilating data Produce a third set of synchronic maps assimilating data from the equatorial regions (active region sources) but using from the equatorial regions (active region sources) but using the observed and variable meridional flow.the observed and variable meridional flow.

This will quantify the effects of meridional flow variations on the This will quantify the effects of meridional flow variations on the polar fields in cycles 23 and 24.polar fields in cycles 23 and 24.

The Problems:The Problems:1.1. Data from MDI and HMI have different magnetic sensitivities.Data from MDI and HMI have different magnetic sensitivities.2.2. Data from MDI and HMI have image distortionsData from MDI and HMI have image distortions3.3. MDI did not produce data from June 1998 to February 1999MDI did not produce data from June 1998 to February 1999

ConclusionsConclusions

The cause of this low minimum and long cycle can be attributed to The cause of this low minimum and long cycle can be attributed to the wimpy size of Cycle 24 itself.the wimpy size of Cycle 24 itself.

The cause of this wimpy cycle was the weak polar fields produced The cause of this wimpy cycle was the weak polar fields produced during Cycle 23.during Cycle 23.

The likely cause of the weak polar fields in Cycle 23 was the fast The likely cause of the weak polar fields in Cycle 23 was the fast meridional flow late in the cycle (but this still needs to be quantified).meridional flow late in the cycle (but this still needs to be quantified).

We gratefully acknowledge support from the CCMSC Program.We gratefully acknowledge support from the CCMSC Program.

Secondary FlowsSecondary FlowsRemoving the average meridional Removing the average meridional flow profile reveals inflows toward flow profile reveals inflows toward the active latitudes (weaker in cycle the active latitudes (weaker in cycle 24).24).

Removing the average differential Removing the average differential rotation profile reveals the rotation profile reveals the “torsional oscillations” – faster “torsional oscillations” – faster than average on the equatorward than average on the equatorward sides and slower than average sides and slower than average on the poleward sides of the on the poleward sides of the active latitudes.active latitudes.

Our Meridional Flow Measurements are Our Meridional Flow Measurements are NOTNOT Substantially Influenced by Supergranule Substantially Influenced by Supergranule

“Diffusion”“Diffusion”

1.1. In Hathaway & Rightmire (2011) we found that In Hathaway & Rightmire (2011) we found that NONO measureable meridional flow signal was measureable meridional flow signal was produced by evolving supergranules with produced by evolving supergranules with observed properties advecting the magnetic observed properties advecting the magnetic field elements that produced an observed field elements that produced an observed magnetic field map.magnetic field map.

2.2. The observed effects of the active latitudes is The observed effects of the active latitudes is a superimposed flow a superimposed flow TOWARDTOWARD the active the active latitudes not away as would be produced by latitudes not away as would be produced by diffusion.diffusion.

Our Legendre Polynomial Coefficients Our Legendre Polynomial Coefficients DODO Capture the Evolution of the Meridional Flow Capture the Evolution of the Meridional Flow

PatternPattern

Raw, individual meridional flow profiles Raw, individual meridional flow profiles since May of 1996.since May of 1996.

Individual meridional flow profiles since Individual meridional flow profiles since May of 1996 with the Legendre May of 1996 with the Legendre Polynomial fits removed.Polynomial fits removed.

(Weaker) Statistical Expectations(Weaker) Statistical Expectations

Typically, small cycles start late and leave behind a long cycle and a Typically, small cycles start late and leave behind a long cycle and a low minimum (Hathaway low minimum (Hathaway et al. et al. 2002.)2002.)

The last cycle was 147 months The last cycle was 147 months long – suggesting that Cycle 24 long – suggesting that Cycle 24 maximum will be maximum will be 86±3086±30. .

The sunspot number at Cycle 24 The sunspot number at Cycle 24 minimum was 1.7 – suggesting that minimum was 1.7 – suggesting that Cycle 24 maximum will be Cycle 24 maximum will be 87±3387±33..

South Pole Field Reversal 2001South Pole Field Reversal 2001