Judy Karpen, Spiro Antiochos, Rick DeVore, and Judy Karpen, Spiro Antiochos, Rick DeVore, and Mark LintonMark Linton

MHD Simulations of Flux MHD Simulations of Flux Cancellation on the Sun*Cancellation on the Sun*

*Work supported by ONR and NASA*Work supported by ONR and NASA

OutlineOutline

• What is flux cancellation?What is flux cancellation?

• OriginsOrigins

• MethodologyMethodology

• ResultsResults

• ConclusionsConclusions

• QuestionsQuestions

What is Flux Cancellation?What is Flux Cancellation?• Observational definitionObservational definition: :

the disappearance of the the disappearance of the line-of-sight component of line-of-sight component of magnetic flux where magnetic flux where opposite polarities meet. opposite polarities meet.

• Each magnetogram Each magnetogram measures the field at 1 measures the field at 1 height (photosphere or height (photosphere or chromosphere); rarely chromosphere); rarely obtained at 2 or more obtained at 2 or more heights at the same time heights at the same time (e.g., Harvey et al. 1993).(e.g., Harvey et al. 1993).

Time series of magnetograms showing the magnetic flux changes (crosses show explosive event locations). The tick interval is 5” (3600 km). The brighter features are positive (north) polarity magnetic fluxes, and the darker features are negative (south) polarity fluxes. The positive magnetic flux indicated by the arrow is decreasing with time. [images from BBSO]

Possible Origins of Flux CancellationPossible Origins of Flux Cancellation• emergence of concave-upward flux (U loops)emergence of concave-upward flux (U loops)

Can result from reconnection below the photosphere/ Can result from reconnection below the photosphere/ chromosphere, but only the shallowest U loops can chromosphere, but only the shallowest U loops can overcome mass loading overcome mass loading

• submergence of concave-downward flux submergence of concave-downward flux (Omega loops)(Omega loops) If due to reconnection above the photosphere/ If due to reconnection above the photosphere/

chromosphere, then the lower (concave-downward) region chromosphere, then the lower (concave-downward) region of newly reconnected flux must submerge completely of newly reconnected flux must submerge completely below the magnetogram level. below the magnetogram level.

• Magnetic reconnection in the photosphere/ Magnetic reconnection in the photosphere/ chromosphere itself chromosphere itself unlikely to occur only in those few layers observed by unlikely to occur only in those few layers observed by

magnetographs).magnetographs).

Role of reconnection assumed but not well testedRole of reconnection assumed but not well tested

Cancellation and Filament Cancellation and Filament Channel FormationChannel Formation

Van Ballegooijen & Martens (1989)Van Ballegooijen & Martens (1989)

Problem: do required surface flows exist?Problem: do required surface flows exist?

Flux Emergence and Sheared ArcadesFlux Emergence and Sheared Arcades

• Strongly sheared flux Strongly sheared flux rope is mainly trapped by rope is mainly trapped by mass loading. What mass loading. What emerges forms a sheared emerges forms a sheared arcade, but shear is not arcade, but shear is not concentrated enough at concentrated enough at PIL PIL (Magara et al. 2007)(Magara et al. 2007). .

• Weakly sheared flux rope Weakly sheared flux rope emerges more, but shear emerges more, but shear is weaker than observed is weaker than observed (Magara 2006)(Magara 2006)..

Can flux cancellation concentrate magnetic shear at Can flux cancellation concentrate magnetic shear at the PIL in our sheared 3D arcade model?the PIL in our sheared 3D arcade model?

MethodologyMethodology

• 3D MHD simulations with 3D MHD simulations with ARMSARMS**:: Finite-difference FCTFinite-difference FCT

Cartesian geometryCartesian geometry

Adaptive mesh refinement with PARAMESHAdaptive mesh refinement with PARAMESH

Numerical resistivityNumerical resistivity

No radiation, heating, or thermal conductionNo radiation, heating, or thermal conduction

• Visualization with Visualization with HelioSpace*HelioSpace*

*developed, tested, and used extensively under DoD *developed, tested, and used extensively under DoD CHSSI and HPCM programs, and NASA’s HPCCCHSSI and HPCM programs, and NASA’s HPCC

Initial ConditionsInitial Conditions

• Magnetic Field: Lundquist flux tube embedded in potential arcade

• 1.5 < |B|max < 600 G

• Plasma: hydrostatic equilibrium atmos- phere, -1.8 < log8

• Closed boundaries

System size: 20 Mm x 20 Mm x 10 Mm (symmetry in System size: 20 Mm x 20 Mm x 10 Mm (symmetry in zz))

Fieldlines and plasma Fieldlines and plasma

Imposed Subphotospheric FlowImposed Subphotospheric Flow

• Subsurface Flow: two-cell Subsurface Flow: two-cell convection-like pattern convection-like pattern below photosphere (below photosphere (1), 1), converging at polarity converging at polarity inversion lineinversion line

• max. Vmax. Vyy = = ++2.3 2.3 km skm s-1 -1

max. Vmax. Vxx = -6.0 = -6.0 km skm s-1-1

• Cosine fall-off in Cosine fall-off in zz so V so Vxx

and Vand Vyy = 0 at z = 0 at zmaxmax

Streamlines and |B|Streamlines and |B|

Global PropertiesGlobal Properties

• Break in KE at 1000s Break in KE at 1000s because subsurface because subsurface flow was ramped up flow was ramped up from 0 to 1000 s, held from 0 to 1000 s, held steady thereaftersteady thereafter

Early development Early development (t=1000-2000 s)(t=1000-2000 s)

|B||B| jjzz |v||v|

Plasmoid formation Plasmoid formation (t=1000-2000 s)(t=1000-2000 s)

loglog

1000 s1000 s

1600 s1600 s

1200 s1200 s 1400 s1400 s

1800 s1800 s 2000 s2000 s

Asymmetry develops Asymmetry develops (t=2500-3000 s)(t=2500-3000 s)

|j||j|

2800 s2800 s

2600 s2600 s

2600 s2600 s

2600 s2600 s2500 s2500 s

Late Development (t=3000-5000 s)Late Development (t=3000-5000 s)

|B|=300 G|B|=300 G

|v||v| jjzzjjzz

t=6000 st=6000 s

MagnetogramsMagnetograms

|B|Bxx| | << 100 G; height = -2.5 Mm (photosphere) 100 G; height = -2.5 Mm (photosphere)

2000 s2000 s100 s100 s 3000 s3000 s

4000 s4000 s 5000 s5000 s 6000 s6000 s

Preliminary ConclusionsPreliminary Conclusions

• Subsurface flows acting on Subsurface flows acting on unshearedunsheared flux can flux can produce reconnection and magnetographic produce reconnection and magnetographic signatures of cancellation at photospheresignatures of cancellation at photosphere

• Cancellation of Cancellation of unshearedunsheared flux yields complex flux yields complex magnetic structure both below the photosphere magnetic structure both below the photosphere and in the corona aboveand in the corona above

• Classical signature of reconnection (jets) does Classical signature of reconnection (jets) does not occur, perhaps due to strong downflowsnot occur, perhaps due to strong downflows

• Need better resolution -- turn adaptivity onNeed better resolution -- turn adaptivity on

Adaptive GriddingAdaptive Gridding

Initial grid: 3 levels, magenta is finestInitial grid: 3 levels, magenta is finest

Adaptive GriddingAdaptive Gridding

t=1000 s: 4 levels, magenta is finestt=1000 s: 4 levels, magenta is finest

Adaptive GriddingAdaptive Gridding

t=2000 s: 4 levels, magenta is finestt=2000 s: 4 levels, magenta is finest

QuestionsQuestions

• Any plasmoids (flux ropes) fully in corona? Any plasmoids (flux ropes) fully in corona?

• No reconnection jets?No reconnection jets?

• Source of periodic structure in Source of periodic structure in zz??

• How much flux cancels at the photosphere?How much flux cancels at the photosphere?

• What happens when What happens when shearedsheared flux is flux is cancelled? Tune in next time….cancelled? Tune in next time….