Judy Karpen, Spiro Antiochos, Rick DeVore, and Mark Linton MHD Simulations of Flux Cancellation on the Sun* *Work supported by ONR and NASA

Outline What is flux cancellation? What is flux cancellation? Origins Origins Methodology Methodology Results Results Conclusions Conclusions Questions Questions

What is Flux Cancellation? Observational definition: the disappearance of the line-of-sight component of magnetic flux where opposite polarities meet. Observational definition: the disappearance of the line-of-sight component of magnetic flux where opposite polarities meet. Each magnetogram measures the field at 1 height (photosphere or chromosphere); rarely obtained at 2 or more heights at the same time (e.g., Harvey et al. 1993). Each magnetogram measures the field at 1 height (photosphere or chromosphere); rarely obtained at 2 or more heights at the same time (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 Cancellation emergence of concave-upward flux (U loops) emergence of concave-upward flux (U loops)  Can result from reconnection below the photosphere/ chromosphere, but only the shallowest U loops can overcome mass loading submergence of concave-downward flux (Omega loops) submergence of concave-downward flux (Omega loops)  If due to reconnection above the photosphere/ chromosphere, then the lower (concave-downward) region of newly reconnected flux must submerge completely below the magnetogram level. Magnetic reconnection in the photosphere/ chromosphere itself Magnetic reconnection in the photosphere/ chromosphere itself  unlikely to occur only in those few layers observed by magnetographs). Role of reconnection assumed but not well tested

Cancellation and Filament Channel Formation Van Ballegooijen & Martens (1989) Problem: do required surface flows exist?

Flux Emergence and Sheared Arcades Strongly sheared flux rope is mainly trapped by mass loading. What emerges forms a sheared arcade, but shear is not concentrated enough at PIL (Magara et al. 2007).Strongly sheared flux rope is mainly trapped by mass loading. What emerges forms a sheared arcade, but shear is not concentrated enough at PIL (Magara et al. 2007). Weakly sheared flux rope emerges more, but shear is weaker than observed (Magara 2006).Weakly sheared flux rope emerges more, but shear is weaker than observed (Magara 2006). Can flux cancellation concentrate magnetic shear at the PIL in our sheared 3D arcade model?

Methodology 3D MHD simulations with ARMS*: 3D MHD simulations with ARMS*:  Finite-difference FCT  Cartesian geometry  Adaptive mesh refinement with PARAMESH  Numerical resistivity  No radiation, heating, or thermal conduction Visualization with HelioSpace* Visualization with HelioSpace* *developed, tested, and used extensively under DoD CHSSI and HPCM programs, and NASA’s HPCC

Initial Conditions Magnetic Field: Lundquist flux tube embedded in potential arcade 1.5 < |B| max < 600 G Plasma: hydrostatic equilibrium atmos- phere, -1.8 < log  8 Closed boundaries System size: 20 Mm x 20 Mm x 10 Mm (symmetry in z) Fieldlines and plasma 

Imposed Subphotospheric Flow Subsurface Flow: two- cell convection-like pattern below photosphere (  1), converging at polarity inversion line Subsurface Flow: two- cell convection-like pattern below photosphere (  1), converging at polarity inversion line max. V y = +2.3 km s -1 max. V x = -6.0 km s -1 max. V y = +2.3 km s -1 max. V x = -6.0 km s -1 Cosine fall-off in z so V x and V y = 0 at z max Cosine fall-off in z so V x and V y = 0 at z max Streamlines and |B|

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

Early development (t= s) |B| jzjzjzjz |v|

Plasmoid formation (t= s) log  1000 s 1600 s 1200 s 1400 s 1800 s 2000 s

Asymmetry develops (t= s) |j| 2800 s 2600 s 2500 s

Late Development (t= s) |B|=300 G |v| jzjzjzjz jzjzjzjz

t=6000 s

Magnetograms |B x | < 100 G; height = -2.5 Mm (photosphere) 2000 s 100 s 3000 s 4000 s 5000 s 6000 s

Preliminary Conclusions Subsurface flows acting on unsheared flux can produce reconnection and magnetographic signatures of cancellation at photosphere Subsurface flows acting on unsheared flux can produce reconnection and magnetographic signatures of cancellation at photosphere Cancellation of unsheared flux yields complex magnetic structure both below the photosphere and in the corona above Cancellation of unsheared flux yields complex magnetic structure both below the photosphere and in the corona above Classical signature of reconnection (jets) does not occur, perhaps due to strong downflows Classical signature of reconnection (jets) does not occur, perhaps due to strong downflows Need better resolution -- turn adaptivity on Need better resolution -- turn adaptivity on

Adaptive Gridding Initial grid: 3 levels, magenta is finest

Adaptive Gridding t=1000 s: 4 levels, magenta is finest

Adaptive Gridding t=2000 s: 4 levels, magenta is finest

Questions 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 z? Source of periodic structure in z? How much flux cancels at the photosphere? How much flux cancels at the photosphere? What happens when sheared flux is cancelled? Tune in next time…. What happens when sheared flux is cancelled? Tune in next time….

Importance of Flux Cancellation Associated with many forms of solar activity, from “magnetic carpet” recycling to X-ray BPs to CMEs Associated with many forms of solar activity, from “magnetic carpet” recycling to X-ray BPs to CMEs Counterbalance to flux emergence; otherwise flux increases indefinitely! Counterbalance to flux emergence; otherwise flux increases indefinitely! Nonthermal velocity in transition region vs. time, during flux cancellation (solid line) and without cancellation (dotted line). (Chae et al. 1998)

HPC information Systems used: Jaws (MHPCC) and Kamala (NRL) Systems used: Jaws (MHPCC) and Kamala (NRL) Number of PEs per run: 128 Number of PEs per run: 128 Timestep: ~0.05 s Timestep: ~0.05 s Typical number of cells: 6.82 x 10 6 Typical number of cells: 6.82 x 10 6 Processor time Processor time  t= s: CPU-s  t= s: 188,300 CPU-s Machine speed: Gflops (I/O frequency dependent) Machine speed: Gflops (I/O frequency dependent) Number of CPU-hours used (as of 9/19): ~300,000 on Jaws Number of CPU-hours used (as of 9/19): ~300,000 on Jaws THANK YOU HPCMP!