Synchronic Magnetic Maps -the Inner Boundary Conditionfor the HeliosphereSynchronic Magnetic Maps -the Inner Boundary Conditionfor 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 GlobalMagnetic FieldThe Sun’s GlobalMagnetic Field
The photospheric magnetic field is the inner boundary condition for virtually allspace weather applications and predictions. The photospheric field extends intothe corona and the solar wind and provides the context for CME, SEP, and GCRpropagation. Extrapolations of the photospheric field require the field to bespecified over the entire surface – including both poles and the backside.The photospheric magnetic field is the inner boundary condition for virtually allspace weather applications and predictions. The photospheric field extends intothe corona and the solar wind and provides the context for CME, SEP, and GCRpropagation. Extrapolations of the photospheric field require the field to bespecified over the entire surface – including both poles and the backside.
Field ExtrapolationsField Extrapolations
The magnetic field measured inthe photosphere is used in fieldextrapolations to determine themagnetic structures associatedwith solar eruptions.The magnetic field measured inthe photosphere is used in fieldextrapolations to determine themagnetic structures associatedwith solar eruptions.
Prominence eruption fromYeates, Mackay, & vanBallegooijen (2008).Prominence eruption fromYeates, Mackay, & vanBallegooijen (2008).
Field ExtrapolationsField Extrapolations
The magnetic field measured inthe photosphere is used in fieldextrapolations to determine thestructure and dynamics of thecorona and the solar wind.The magnetic field measured inthe photosphere is used in fieldextrapolations to determine thestructure and dynamics of thecorona and the solar wind.
Open field and high speed solarwind from Wang, Robbrecht, &Sheeley (2009).Open field and high speed solarwind from Wang, Robbrecht, &Sheeley (2009).
Synoptic Map ConstructionSynoptic Map Construction
One map from each rotation of the Sun using data from near the centralmeridian. They do show:One map from each rotation of the Sun using data from near the centralmeridian. 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 field
2) 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 Map
Data at Carrington longitude 0 is adjacent to data at Carrington longitude360 but are acquired 27 days later. Much has changed!Data at Carrington longitude 0 is adjacent to data at Carrington longitude360 but are acquired 27 days later. Much has changed!
The Goal: Produce instantaneous (synchronic)magnetic maps of the entire surface of the Sun.The Goal: Produce instantaneous (synchronic)magnetic maps of the entire surface of the Sun.
The Problem: We only see one hemisphere atany time and that view excludes each pole forsix months of each year.The Problem: We only see one hemisphere atany time and that view excludes each pole forsix months of each year.
A Near Term Solution: Model the transport ofmagnetic field at the surface of the Sun usingEarthside and farside information.A Near Term Solution: Model the transport ofmagnetic field at the surface of the Sun usingEarthside and farside information.
A Long-Term Solution: Four or five spacecraftwith magnetographs: one near Earth, one in theecliptic 120° ahead of Earth, one in the ecliptic120° behind Earth, and at least one more - out ofthe ecliptic where it can observe the other pole.A Long-Term Solution: Four or five spacecraftwith magnetographs: one near Earth, one in theecliptic 120° ahead of Earth, one in the ecliptic120° behind Earth, and at least one more - out ofthe ecliptic where it can observe the other pole.
Synchronic Map ConstructionSynchronic Map Construction
•Data assimilation•Data assimilation
–Magnetic data from full disk–Magnetic data from full disk
–Active region data from farside helioseismology–Active region data from farside helioseismology
–Active region data from active region decay–Active region data from active region decay
•Flux transport•Flux transport
–Differential rotation structure and variations–Differential rotation structure and variations
–Meridional flow structure and variations–Meridional flow structure and variations
–Supergranule diffusion (random walk) model–Supergranule diffusion (random walk) model
Surface Flux TransportSurface Flux Transport
Surface magnetic flux transport models were developed in the early1980s by the Naval Research Laboratory (NRL) group including NeilSheeley, Yi-Ming Wang, Rick DeVore, and Jay Boris. They found thatthey could reproduce the evolution of the Sun’s surface magnetic fieldusing active region flux emergence as the only source of magnetic flux– that flux is then transported across the Sun’s surface by:Surface magnetic flux transport models were developed in the early1980s by the Naval Research Laboratory (NRL) group including NeilSheeley, Yi-Ming Wang, Rick DeVore, and Jay Boris. They found thatthey could reproduce the evolution of the Sun’s surface magnetic fieldusing active region flux emergence as the only source of magnetic flux– that flux is then transported across the Sun’s surface by:
1.Differential Rotation, U(θ)1.Differential Rotation, U(θ)
2.Meridional Flow, V(θ)2.Meridional Flow, V(θ)
3.Supergranule Diffusion, 3.Supergranule Diffusion,
∂B/∂t + 1/(R sinθ) ∂(BV sinθ)/∂θ + 1/(R sinθ) ∂(BU)/∂ = 2B + S(θ,)∂B/∂t + 1/(R sinθ) ∂(BV sinθ)/∂θ + 1/(R sinθ) ∂(BU)/∂ = 2B + S(θ,)
Neither the meridional flow nor the supergranule diffusion were wellconstrained at that time – so they used what worked.Neither the meridional flow nor the supergranule diffusion were wellconstrained at that time – so they used what worked.
Characterizing theAxisymmetric FlowsCharacterizing theAxisymmetric Flows
We (Hathaway & Rightmire 2010, Science, 327, 1350) measured theaxisymmetric transport of magnetic flux by cross-correlating11x600 pixel strips at 860 latitude positions between ±75˚ frommagnetic images acquired at 96-minute intervals by MDI on SOHO.We (Hathaway & Rightmire 2010, Science, 327, 1350) measured theaxisymmetric transport of magnetic flux by cross-correlating11x600 pixel strips at 860 latitude positions between ±75˚ frommagnetic images acquired at 96-minute intervals by MDI on SOHO.
Average Flow ProfilesAverage Flow Profiles
Average (1996-2010) differentialrotation profile with 2σ errorlimits.Average (1996-2010) differentialrotation profile with 2σ errorlimits.
Average (1996-2010) meridionalflow profile with 2σ error limits.Average (1996-2010) meridionalflow profile with 2σ error limits.
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’sequator. We extracted differential rotation and meridional flow profilesfrom over 60,000 image pairs from May of 1996 to September of 2010.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’sequator. We extracted differential rotation and meridional flow profilesfrom 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 NRLgroup (Wang et al.). It is similar at low latitudes to that used by othergroups but differs by not vanishing at high latitudes.The Meridional Flow we measure is very unlike that still used by the NRLgroup (Wang et al.). It is similar at low latitudes to that used by othergroups but differs by not vanishing at high latitudes.
Solar Cycle Variations in theAxisymmetric FlowsSolar Cycle Variations in theAxisymmetric Flows
While the differential rotation does vary slightly over the solar cycle, it isthe meridional flow that shows the most significant variation. TheMeridional Flow slowed from 1996 to 2001 but then increased in speedagain after maximum. The slowing of the meridional flow at maximumseems to be a regular solar cycle occurrence (Komm, Howard, & Harvey,1993). The greater speed up after maximum is specific to Cycle 23.While the differential rotation does vary slightly over the solar cycle, it isthe meridional flow that shows the most significant variation. TheMeridional Flow slowed from 1996 to 2001 but then increased in speedagain after maximum. The slowing of the meridional flow at maximumseems to be a regular solar cycle occurrence (Komm, Howard, & Harvey,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 FlowStructureSolar Cycle Variations in FlowStructure
Differential rotation profilesDifferential rotation profiles
Meridional flow profilesMeridional flow profiles
The differential rotation and meridional flow profiles for each solarrotation also show that the differential rotation changes very little whilethe meridional flow changes substantially. Note, in particular, thepresence of countercells with equatorward flow near the poles.The differential rotation and meridional flow profiles for each solarrotation also show that the differential rotation changes very little whilethe meridional flow changes substantially. Note, in particular, thepresence of countercells with equatorward flow near the poles.
ComplicationsComplications
The axisymmetric flows we(Hathaway & Rightmire 2010, 2011)measured were for magneticelements with |B| < 500G.The axisymmetric flows we(Hathaway & Rightmire 2010, 2011)measured were for magneticelements with |B| < 500G.
Lisa has discovered that if shelimits the data to weaker magneticelements she finds fastermeridional flow and slowerdifferential rotation.Lisa has discovered that if shelimits the data to weaker magneticelements she finds fastermeridional flow and slowerdifferential rotation.
The weaker magnetic elements areanchored closer to the surfaceshear layer where the rotation isslower and meridional flow faster.The weaker magnetic elements areanchored closer to the surfaceshear layer where the rotation isslower and meridional flow faster.
This makes magnetic flux transportmore complicated!This makes magnetic flux transportmore complicated!
Supergranules and theMagnetic NetworkSupergranules and theMagnetic Network
Tracking the motions of granules (correlation tracking with 6-minute timelags from HMI Intensity data) reveals the flow pattern within supergranulesand the relationship with the magnetic pattern – the magnetic networkforms at the supergranule boundaries (convergence zones).Tracking the motions of granules (correlation tracking with 6-minute timelags from HMI Intensity data) reveals the flow pattern within supergranulesand the relationship with the magnetic pattern – the magnetic networkforms at the supergranule boundaries (convergence zones).
Flux Transport DetailsFlux Transport Details
Four days of HMI data drive home the fact that flux transport isdominated by the cellular flows. The extent to which this can berepresented by a diffusion coefficient and a Laplacian operator is to bedetermined.Four days of HMI data drive home the fact that flux transport isdominated by the cellular flows. The extent to which this can berepresented by a diffusion coefficient and a Laplacian operator is to bedetermined.
300 Mm300 Mm
500 Mm500 Mm
Characterizing SupergranulesCharacterizing Supergranules
We (Hathaway et al. 2010, ApJ 725, 1082) analyzed and simulatedDoppler velocity data from MDI to determine the characteristics ofsupergranulation. These cellular flows have a broad spectrumcharacterized by a peak in power at wavelengths of about 35 Mm.We (Hathaway et al. 2010, ApJ 725, 1082) analyzed and simulatedDoppler velocity data from MDI to determine the characteristics ofsupergranulation. These cellular flows have a broad spectrumcharacterized by a peak in power at wavelengths of about 35 Mm.
MDIMDI
SIMSIM
Measuring their motionsMeasuring their motions
The axisymmetric flows can be measured using the Doppler velocitypattern using the same method used with the magnetic pattern. A keydifference is the use of several different time lags between images.The axisymmetric flows can be measured using the Doppler velocitypattern using the same method used with the magnetic pattern. A keydifference is the use of several different time lags between images.
Reproducing the LifetimesReproducing the Lifetimes
The cellular structures are given finite lifetimes by adding randomperturbations to the phases of the complex spectral coefficients. Theamplitude of the perturbation was inversely proportional to a lifetimegiven by the size of the cell (from its wavenumber) divided by its flowvelocity (from the amplitude of the spectral coefficient).The cellular structures are given finite lifetimes by adding randomperturbations to the phases of the complex spectral coefficients. Theamplitude of the perturbation was inversely proportional to a lifetimegiven by the size of the cell (from its wavenumber) divided by its flowvelocity (from the amplitude of the spectral coefficient).
This process can largely reproduce the strength of the cross-correlation as a function of both time and latitude.This process can largely reproduce the strength of the cross-correlation as a function of both time and latitude.
Supergranule DiffusionSupergranule Diffusion
We can use the evolving supergranule flow field from the simulation totransport magnetic elements from an initial magnetic map and use this todetermine the diffusion coefficient, . (Lisa Rightmire)We can use the evolving supergranule flow field from the simulation totransport magnetic elements from an initial magnetic map and use this todetermine the diffusion coefficient, . (Lisa Rightmire)
Reproducing their RotationReproducing their Rotation
The motions of the cellular patterns in longitude can be reproduced bymaking systematic changes to the complex spectral coefficient phases(Hathaway et al. 2010).The motions of the cellular patterns in longitude can be reproduced bymaking systematic changes to the complex spectral coefficient phases(Hathaway et al. 2010).
Reproducing their Meridional FlowReproducing their Meridional Flow
The motions of the cellular patterns in latitude can be reproduced bymaking systematic changes to the complex spectral coefficient amplitudes(Hathaway et al. 2010).The motions of the cellular patterns in latitude can be reproduced bymaking systematic changes to the complex spectral coefficient amplitudes(Hathaway et al. 2010).
Supergranules Rule!Supergranules Rule!
Surprisingly, if we add differential rotation and meridional flow on top ofsupergranules that don’t move with those flows we get magnetic elementmotion with no differential rotation or meridional flow. The differentialrotation and meridional flow velocities are too small to overpower theflows in the supergranules themselves!Surprisingly, if we add differential rotation and meridional flow on top ofsupergranules that don’t move with those flows we get magnetic elementmotion with no differential rotation or meridional flow. The differentialrotation and meridional flow velocities are too small to overpower theflows in the supergranules themselves!
Supergranules Rule!Supergranules Rule!
The magnetic elements experience differential rotation and meridionalflow only to the extent that supergranules are transported by these flows- as in this simulation.The magnetic elements experience differential rotation and meridionalflow only to the extent that supergranules are transported by these flows- as in this simulation.
Data AssimilationData Assimilation
Data from the entire visible hemisphere should be assimilated – but withweights inversely proportional to the noise level.Data from the entire visible hemisphere should be assimilated – but withweights inversely proportional to the noise level.
Knowledge of the growth and decay of active regions can allow forestimates of active region evolution after they rotate off of the west limb.Knowledge of the growth and decay of active regions can allow forestimates of active region evolution after they rotate off of the west limb.
Farside imaging from helioseismology can provide information aboutthe emergence of new active regions on the farside of the Sun.Farside imaging from helioseismology can provide information aboutthe 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 anddecay exponentially with time. Flux is transport by differential rotation bytaking the FFT in longitude of the data (and weights) at each latitude andadding a phase shift representing the longitudinal displacement.Full disk data assimilated with weights that vary inversely with noise anddecay exponentially with time. Flux is transport by differential rotation bytaking the FFT in longitude of the data (and weights) at each latitude andadding a phase shift representing the longitudinal displacement.
ConclusionsConclusions
1.To produce synchronic magnetic maps for heliosphericconditions we need to transport magnetic flux and assimilatedata from multiple sources.1.To produce synchronic magnetic maps for heliosphericconditions we need to transport magnetic flux and assimilatedata from multiple sources.
2.To do the axisymmetric transport we need to measure andmonitor the structure and variations in the flow components –differential rotation and meridional flow.2.To do the axisymmetric transport we need to measure andmonitor the structure and variations in the flow components –differential rotation and meridional flow.
3.To do the non-axisymmetric transport (diffusion) we need tocharacterize the supergranule flow properties.3.To do the non-axisymmetric transport (diffusion) we need tocharacterize the supergranule flow properties.
4.Magnetic elements experience differential rotation andmeridional flow via the differential rotation and meridionalmotion of supergranules.4.Magnetic elements experience differential rotation andmeridional flow via the differential rotation and meridionalmotion of supergranules.