Synchronic Magnetic Maps - the Inner Boundary Condition for the Heliosphere David Hathaway NASA Marshall Space Flight Center 2011 August 2 – Space Weather.

Synchronic Magnetic Maps - Synchronic Magnetic Maps - the Inner Boundary Condition the Inner Boundary Condition

for the Heliospherefor the Heliosphere

David HathawayDavid Hathaway

NASA Marshall Space Flight CenterNASA Marshall Space Flight Center

2011 August 2 – Space Weather Summer School2011 August 2 – Space Weather Summer School

http://solarscience.msfc.nasa.gov/presentations.htmlhttp://solarscience.msfc.nasa.gov/presentations.html

The Sun’s GlobalThe Sun’s GlobalMagnetic FieldMagnetic Field

The photospheric magnetic field is the inner boundary condition for virtually all The photospheric magnetic field is the inner boundary condition for virtually all space weather applications and predictions. The photospheric field extends into space weather applications and predictions. The photospheric field extends into the corona and the solar wind and provides the context for CME, SEP, and GCR the corona and the solar wind and provides the context for CME, SEP, and GCR propagation. Extrapolations of the photospheric field require the field to be propagation. Extrapolations of the photospheric field require the field to be specified over the entire surface – including both poles and the backside.specified over the entire surface – including both poles and the backside.

Field ExtrapolationsField ExtrapolationsThe magnetic field measured in The magnetic field measured in the photosphere is used in field the photosphere is used in field extrapolations to determine the extrapolations to determine the magnetic structures associated magnetic structures associated with solar eruptions.with solar eruptions.

Prominence eruption from Prominence eruption from Yeates, Mackay, & van Yeates, Mackay, & van Ballegooijen (2008).Ballegooijen (2008).

Field ExtrapolationsField ExtrapolationsThe magnetic field measured in The magnetic field measured in the photosphere is used in field the photosphere is used in field extrapolations to determine the extrapolations to determine the structure and dynamics of the structure and dynamics of the corona and the solar wind.corona and the solar wind.

Open field and high speed solar Open field and high speed solar wind from Wang, Robbrecht, & wind from Wang, Robbrecht, & Sheeley (2009).Sheeley (2009).

Synoptic Map ConstructionSynoptic Map ConstructionOne map from each rotation of the Sun using data from near the central One map from each rotation of the Sun using data from near the central meridian. They do show:meridian. They do show:

1) Bi-polar active regions are the primary sources for the field1) Bi-polar active regions are the primary sources for the field2) Diffusion (random walk in longitude and latitude)2) Diffusion (random walk in longitude and latitude)3) Differential Rotation (faster at the equator, slower near the poles)3) Differential Rotation (faster at the equator, slower near the poles)4) Meridional Flow (poleward from the equator )4) Meridional Flow (poleward from the equator )

Synoptic MapSynoptic MapData at Carrington longitude 0 is adjacent to data at Carrington longitude Data at Carrington longitude 0 is adjacent to data at Carrington longitude 360 but are acquired 27 days later. Much has changed!360 but are acquired 27 days later. Much has changed!

The GoalThe Goal: Produce instantaneous (synchronic) : Produce instantaneous (synchronic) magnetic maps of the entire surface of the Sun.magnetic maps of the entire surface of the Sun.

The ProblemThe Problem: We only see one hemisphere at : We only see one hemisphere at any time and that view excludes each pole for any time and that view excludes each pole for six months of each year.six months of each year.

A Near Term SolutionA Near Term Solution: Model the transport of : Model the transport of magnetic field at the surface of the Sun using magnetic field at the surface of the Sun using Earthside and farside information.Earthside and farside information.

A Long-Term SolutionA Long-Term Solution: Four or five spacecraft : Four or five spacecraft with magnetographs: one near Earth, one in the with magnetographs: one near Earth, one in the ecliptic 120° ahead of Earth, one in the ecliptic ecliptic 120° ahead of Earth, one in the ecliptic 120° behind Earth, and at least one more - out of 120° behind Earth, and at least one more - out of the ecliptic where it can observe the other pole. the ecliptic where it can observe the other pole.

Synchronic Map ConstructionSynchronic Map Construction

• Data assimilationData assimilation– Magnetic data from full diskMagnetic data from full disk– Active region data from farside helioseismologyActive region data from farside helioseismology– Active region data from active region decayActive region data from active region decay

• Flux transportFlux transport– Differential rotation structure and variationsDifferential rotation structure and variations– Meridional flow structure and variationsMeridional flow structure and variations– Supergranule diffusion (random walk) modelSupergranule diffusion (random walk) model

Surface Flux TransportSurface Flux Transport

Surface magnetic flux transport models were developed in the early Surface magnetic flux transport models were developed in the early 1980s by the Naval Research Laboratory (NRL) group including Neil 1980s by the Naval Research Laboratory (NRL) group including Neil Sheeley, Yi-Ming Wang, Rick DeVore, and Jay Boris. They found that Sheeley, Yi-Ming Wang, Rick DeVore, and Jay Boris. They found that they could reproduce the evolution of the Sun’s surface magnetic field they could reproduce the evolution of the Sun’s surface magnetic field using active region flux emergence as the only source of magnetic flux using active region flux emergence as the only source of magnetic flux – that flux is then transported across the Sun’s surface by:– that flux is then transported across the Sun’s surface by:

1.1. Differential Rotation, U(Differential Rotation, U(θθ))2.2. Meridional Flow, V(Meridional Flow, V(θθ))3.3. Supergranule Diffusion, Supergranule Diffusion,

∂∂B/∂t + 1/(R sinB/∂t + 1/(R sinθθ) ∂(BV sin) ∂(BV sinθθ)/∂)/∂θθ + 1/(R sin + 1/(R sinθθ) ∂(BU)/∂) ∂(BU)/∂ = = 22B + S(B + S(θθ,,))

Neither the meridional flow nor the supergranule diffusion were well Neither the meridional flow nor the supergranule diffusion were well constrained at that time – so they used what worked.constrained at that time – so they used what worked.

Characterizing the Characterizing the Axisymmetric FlowsAxisymmetric Flows

We (Hathaway & Rightmire 2010, We (Hathaway & Rightmire 2010, ScienceScience, 327, 1350) measured the , 327, 1350) measured the axisymmetric transport of magnetic flux by cross-correlating axisymmetric transport of magnetic flux by cross-correlating 11x600 pixel strips at 860 latitude positions between ±75˚ from 11x600 pixel strips at 860 latitude positions between ±75˚ from magnetic images acquired at 96-minute intervals by MDI on SOHO. magnetic images acquired at 96-minute intervals by MDI on SOHO.

Average Flow ProfilesAverage Flow Profiles

Average (1996-2010) differential Average (1996-2010) differential rotation profile with 2rotation profile with 2σσ error error limits.limits.

Average (1996-2010) meridional Average (1996-2010) meridional flow profile with 2flow profile with 2σσ error limits. error limits.

Our MDI data included corrections for CCD misalignment, image offset, Our MDI data included corrections for CCD misalignment, image offset, and a 150 year old error in the inclination of the ecliptic to the Sun’s and a 150 year old error in the inclination of the ecliptic to the Sun’s equator. We extracted differential rotation and meridional flow profiles equator. We extracted differential rotation and meridional flow profiles from over 60,000 image pairs from May of 1996 to September of 2010.from over 60,000 image pairs from May of 1996 to September of 2010.

Meridional Flow ComparisonsMeridional Flow Comparisons

The Meridional Flow we measure is very unlike that still used by the NRL The Meridional Flow we measure is very unlike that still used by the NRL group (Wang et al.). It is similar at low latitudes to that used by other group (Wang et al.). It is similar at low latitudes to that used by other groups but differs by not vanishing at high latitudes.groups but differs by not vanishing at high latitudes.

Solar Cycle Variations in the Solar Cycle Variations in the Axisymmetric FlowsAxisymmetric Flows

While the differential rotation does vary slightly over the solar cycle, it is While the differential rotation does vary slightly over the solar cycle, it is the meridional flow that shows the most significant variation. The the meridional flow that shows the most significant variation. The Meridional Flow slowed from 1996 to 2001 but then increased in speed Meridional Flow slowed from 1996 to 2001 but then increased in speed again after maximum. The slowing of the meridional flow at maximum again after maximum. The slowing of the meridional flow at maximum seems to be a regular solar cycle occurrence (Komm, Howard, & Harvey, seems to be a regular solar cycle occurrence (Komm, Howard, & Harvey, 1993). The greater speed up after maximum is specific to Cycle 23.1993). The greater speed up after maximum is specific to Cycle 23.

Differential rotation variationsDifferential rotation variations Meridional flow variationsMeridional flow variations

Solar Cycle Variations in Flow Solar Cycle Variations in Flow StructureStructure

Differential rotation profilesDifferential rotation profiles Meridional flow profilesMeridional flow profiles

The differential rotation and meridional flow profiles for each solar The differential rotation and meridional flow profiles for each solar rotation also show that the differential rotation changes very little while rotation also show that the differential rotation changes very little while the meridional flow changes substantially. Note, in particular, the the meridional flow changes substantially. Note, in particular, the presence of countercells with equatorward flow near the poles. presence of countercells with equatorward flow near the poles.

ComplicationsComplications

The axisymmetric flows we The axisymmetric flows we (Hathaway & Rightmire 2010, 2011) (Hathaway & Rightmire 2010, 2011) measured were for magnetic measured were for magnetic elements with |B| < 500G.elements with |B| < 500G.

Lisa has discovered that if she Lisa has discovered that if she limits the data to weaker magnetic limits the data to weaker magnetic elements she finds faster elements she finds faster meridional flow and slower meridional flow and slower differential rotation.differential rotation.

The weaker magnetic elements are The weaker magnetic elements are anchored closer to the surface anchored closer to the surface shear layer where the rotation is shear layer where the rotation is slower and meridional flow faster. slower and meridional flow faster.

This makes magnetic flux transport This makes magnetic flux transport more complicated!more complicated!

Supergranules and the Supergranules and the Magnetic NetworkMagnetic Network

Tracking the motions of granules (correlation tracking with 6-minute time Tracking the motions of granules (correlation tracking with 6-minute time lags from HMI Intensity data) reveals the flow pattern within supergranules lags from HMI Intensity data) reveals the flow pattern within supergranules and the relationship with the magnetic pattern – the magnetic network and the relationship with the magnetic pattern – the magnetic network forms at the supergranule boundaries (convergence zones).forms at the supergranule boundaries (convergence zones).

Flux Transport DetailsFlux Transport DetailsFour days of HMI data drive home the fact that flux transport is Four days of HMI data drive home the fact that flux transport is dominated by the cellular flows. The extent to which this can be dominated by the cellular flows. The extent to which this can be represented by a diffusion coefficient and a Laplacian operator is to be represented by a diffusion coefficient and a Laplacian operator is to be determined.determined.

300 Mm300 Mm

500 Mm500 Mm

Characterizing SupergranulesCharacterizing SupergranulesWe (Hathaway et al. 2010, We (Hathaway et al. 2010, ApJApJ 725, 1082) analyzed and simulated 725, 1082) analyzed and simulated Doppler velocity data from MDI to determine the characteristics of Doppler velocity data from MDI to determine the characteristics of supergranulation. These cellular flows have a broad spectrum supergranulation. These cellular flows have a broad spectrum characterized by a peak in power at wavelengths of about 35 Mm.characterized by a peak in power at wavelengths of about 35 Mm.

MDIMDI

SIMSIM

Measuring their motionsMeasuring their motionsThe axisymmetric flows can be measured using the Doppler velocity The axisymmetric flows can be measured using the Doppler velocity pattern using the same method used with the magnetic pattern. A key pattern using the same method used with the magnetic pattern. A key difference is the use of several different time lags between images.difference is the use of several different time lags between images.

Reproducing the LifetimesReproducing the LifetimesThe cellular structures are given finite lifetimes by adding random The cellular structures are given finite lifetimes by adding random perturbations to the phases of the complex spectral coefficients. The perturbations to the phases of the complex spectral coefficients. The amplitude of the perturbation was inversely proportional to a lifetime amplitude of the perturbation was inversely proportional to a lifetime given by the size of the cell (from its wavenumber) divided by its flow given by the size of the cell (from its wavenumber) divided by its flow velocity (from the amplitude of the spectral coefficient).velocity (from the amplitude of the spectral coefficient).

This process can largely reproduce the strength of the cross-This process can largely reproduce the strength of the cross-correlation as a function of both time and latitude.correlation as a function of both time and latitude.

Supergranule DiffusionSupergranule DiffusionWe can use the evolving supergranule flow field from the simulation to We can use the evolving supergranule flow field from the simulation to transport magnetic elements from an initial magnetic map and use this to transport magnetic elements from an initial magnetic map and use this to determine the diffusion coefficient, determine the diffusion coefficient, . (Lisa Rightmire). (Lisa Rightmire)

Reproducing their RotationReproducing their RotationThe motions of the cellular patterns in longitude can be reproduced by The motions of the cellular patterns in longitude can be reproduced by making systematic changes to the complex spectral coefficient making systematic changes to the complex spectral coefficient phasesphases (Hathaway et al. 2010).(Hathaway et al. 2010).

Reproducing their Meridional FlowReproducing their Meridional Flow

The motions of the cellular patterns in latitude can be reproduced by The motions of the cellular patterns in latitude can be reproduced by making systematic changes to the complex spectral coefficient making systematic changes to the complex spectral coefficient amplitudesamplitudes (Hathaway et al. 2010).(Hathaway et al. 2010).

Supergranules Rule!Supergranules Rule!Surprisingly, if we add differential rotation and meridional flow on top of Surprisingly, if we add differential rotation and meridional flow on top of supergranules that supergranules that don’t movedon’t move with those flows we get magnetic element with those flows we get magnetic element motion with no differential rotation or meridional flow. The differential motion with no differential rotation or meridional flow. The differential rotation and meridional flow velocities are too small to overpower the rotation and meridional flow velocities are too small to overpower the flows in the supergranules themselves!flows in the supergranules themselves!

Supergranules Rule!Supergranules Rule!The magnetic elements experience differential rotation and meridional The magnetic elements experience differential rotation and meridional flow flow onlyonly to the extent that supergranules are transported by these flows to the extent that supergranules are transported by these flows - as in this simulation.- as in this simulation.

Data AssimilationData Assimilation

Data from the entire visible hemisphere should be assimilated – but with Data from the entire visible hemisphere should be assimilated – but with weights inversely proportional to the noise level.weights inversely proportional to the noise level.

Knowledge of the growth and decay of active regions can allow for Knowledge of the growth and decay of active regions can allow for estimates of active region evolution after they rotate off of the west limb.estimates of active region evolution after they rotate off of the west limb.

Farside imaging from helioseismology can provide information about Farside imaging from helioseismology can provide information about the emergence of new active regions on the farside of the Sun.the emergence of new active regions on the farside of the Sun.

Synchronic Map ExamplesSynchronic Map Examples

Updated 15 times per dayUpdated 15 times per day

Full disk data assimilated with weights that vary inversely with noise and Full disk data assimilated with weights that vary inversely with noise and decay exponentially with time. Flux is transport by differential rotation by decay exponentially with time. Flux is transport by differential rotation by taking the FFT in longitude of the data (and weights) at each latitude and taking the FFT in longitude of the data (and weights) at each latitude and adding a phase shift representing the longitudinal displacement.adding a phase shift representing the longitudinal displacement.

ConclusionsConclusions1.1. To produce synchronic magnetic maps for heliospheric To produce synchronic magnetic maps for heliospheric

conditions we need to transport magnetic flux and assimilate conditions we need to transport magnetic flux and assimilate data from multiple sources.data from multiple sources.

2.2. To do the axisymmetric transport we need to measure and To do the axisymmetric transport we need to measure and monitor the structure and variations in the flow components – monitor the structure and variations in the flow components – differential rotation and meridional flow.differential rotation and meridional flow.

3.3. To do the non-axisymmetric transport (diffusion) we need to To do the non-axisymmetric transport (diffusion) we need to characterize the supergranule flow properties.characterize the supergranule flow properties.

4.4. Magnetic elements experience differential rotation and Magnetic elements experience differential rotation and meridional flow via the differential rotation and meridional meridional flow via the differential rotation and meridional motion of supergranules.motion of supergranules.