1. 3D Simulations of Large-Scale Coronal Dynamics
Judy Karpen
Spiro Antiochos, Rick DeVore, Peter MacNeice, Jim Klimchuk, Ben Lynch, Guillaume Aulanier, Jimin Gao
Naval Research Laboratory

2. What is a filament channel (FC)? Why are filament channels important?
Models
FC magnetic structure (sheared arcade)
FC plasma structure (thermal nonequilibrium)
CME/flare initiation (breakout)
What will Solar B teach us about filament channels and CME initiation?

3. What is a Filament Channel?
Around neutral line (NL)
Core B ~// NL
Overlying B  NL
Exists before, after, and without visible filament
Often persists through many eruptions
Origin uncertain
(from Aulanier & Schmieder 2002)
(from Deng et al. 2002)

4. Why are filament channels important?
Development is an integral part of the Sun’s magnetic- field evolution
Energy source and driver of CMEs/eruptive flares
Insight into physics of magnetic stability and condensation processes in cosmic and laboratory plasmas

5. Sheared Arcade Model
Hypothesis: observed magnetic structure is a natural consequence of magnetic shear (B ~// NL) in a 3D topology
Initial conditions
single bipole
two bipoles along same NL with different orientations
Tests: calculations with 3D MHD fixed-grid code
References (all ApJ): Antiochos & Klimchuk 1994; DeVore & Antiochos 2000; DeVore et al. 2005; Aulanier et al. 2002, 2005 (submitted)

6. Sheared Arcade Model: Results
shearing near neutral line moves strong field out under weaker field  bulging at ends, compressed in between
field lines of interest  long, low-lying, dipped field lines near neutral line*
loci of concave upward field lines  potential sites for condensations*
3D geometry is essential!
*more about this later….

7. Prominence Linkage Simulation- +
Bipolar (one NL) initial magnetic field
Footpoint motion generates magnetic shear
Long FC field develops as shear increases
Stable despite significant expansion and reconnection

8. What have we learned about FC magnetic structure?
Modest/large shear driving an isolated bipole produces
Sigmoids (S-shaped field associated with eruptions)
General shape (prominence barbs and spine)
Mix of dipped and helical, inverse- and normal-polarity fields
Skewed overlying arcade (as seen in EUV/SXR images)
Modest shear driving two bipoles produces
Formation of large filaments by linkage of smaller ones
Dependence on chirality, relative axial-field orientation
Increased complexity and helicity accumulation due to reconnection
Stability --- sheared bipoles do not erupt

9. Objectives for Solar B
Determine origin of magnetic shear: preexisting flux rope or real-time photospheric motions
Observe and quantify filament growth through interacting segments
Detect reconnection signatures
Reconcile multiwavelength views of FCs
Establish relationship between barbs and main structure
Investigate the role of flux emergence and cancellation in FC formation and destabilization
Trace photosphere-corona coupling

10. Plasma Structure
10 Mm
Threads: length ~ 25 Mm, width ~ 200 km (SVST, courtesy of Y. Lin)
not enough plasma in coronal flux tubes  mass must come from chromosphere
plasma is NOT static  model must be dynamic

11. Thermal Nonequilibrium Model
Hypothesis: condensations are caused by heating localized above footpoints of long, low-lying loops, with heating scale << L
Assumptions
Magnetic flux tube is rigid (low coronal )
Chromosphere is mass source (evaporation) and sink
Energetics determined by heating, thermal conduction, radiation, and enthalpy (flows)
References (all ApJ): Antiochos & Klimchuk 1991; Dahlburg et al. 1998; Antiochos et al. 1999, 2000; Karpen et al. 2001, 2003; Karpen et al. 2005, 2006 (in press)

12. Why do condensations form?
chromospheric evaporation increases density throughout corona  increased radiation
T is highest within distance ~  from site of maximum energy deposition (i.e., near base)
when L > 8 , conduction + local heating cannot balance radiation
rapid cooling  local pressure deficit, pulling more plasma into the condensation
a new chromosphere is formed where flows meet, reducing radiative losses

13. Simulations of TN in sheared-arcade flux tube
ARGOS (Adaptively Refined GOdunov Solver) solves 1D hydro equations with
adaptive mesh refinement (AMR) -- REQUIRED
MUSCL+Godunov finite-difference scheme
conduction, solar gravity, optically thin radiation
spatially and/or temporally variable heating
long dipped loop
Note: Only quantitative, dynamic model for prominence plasma

14. Thermal Nonequilibrium: T Movie
NRK run

15. Thermal Nonequilibrium: CDS Movie
NRK run

16. Origin of prominence mass
Are dips necessary? NO!
even loops with peak heights ≈ gravitational scale height (~ Mm) form dynamic condensations
Flatter field lines develop longer, more massive threads and pairs that merge at high speeds (fast EUV/UV features)
Are highly twisted flux ropes consistent with dynamics? NO!
in dips deeper than f•Hg, where f measures the heating imbalance and Hg is the gravitational scale height, knots fall to lowest point and stay there (grow as long as heating is on)
Does this process still work for a field line from the sheared-arcade model? YES!
With episodic heating? YES! if not too impulsive…

17. What have we learned about FC plasma structure?
red = too short
green = too tall
black = too deep
blue = just right
Note: Distribution of field line shapes (area & height variations) dictates distribution of stationary/dynamic plasma for any model

18. Objectives for Solar B
Determine how prominence mass is brought up from the chromosphere: jets, levitation, or evaporation
Coincident multiwavelength observations of condensation formation and evolution
Reconcile H and EUV measurements of plasma motions
Deduce spatial and temporal characteristics of coronal heating in filament channel

19. CME/eruptive flare initiation
Eruption requires that
Energy is stored in the coronal magnetic field
FC is the only place where the field is sufficiently nonpotential to contain this energy
Overlying field must be removed
Hypothesis: multipolar field provides a natural mechanism for meeting these requirements

20. 2.5D Breakout Model
MHD simulations with ARMS (adaptive mesh, massively //)
Add 2D (axisymmetric) “AR” dipole to global dipole
Global evolution controlled by small-scale diffusion region
References (ApJ except as noted): Antiochos 1998; Antiochos et al. 1999; Lynch et al. 2004; MacNeice et al. 2004; Phillips et al. 2005; Gao 2005 and Lynch 2005 (PhD theses, in preparation)

21. 3D Asymmetric Breakout Model
Eruption similar to axisymmetric case, but all field lines remain connected to photosphere
V > 1000 km/s
Simulation with outer boundary at 30 Rsun in progress

22. Breakout Flare Ribbons (2D)
Ribbons appear after eruption on either side of a neutral line
Breakout model reproduces generic current-sheet flare-loop geometry
Loops grow in height and footpoints separate with time
(from Fletcher et al.)

23. Roles of Reconnection Initial breakout reconnection
Removes overlying flux by transfer to adjacent system
Feedback loop between plasmoid acceleration and reconnection rate
Two phases of flare reconnection
Initial (impulsive?) reconnection in low-, strong guide-field region (sheared): shocks, particle acceleration, HXR/wave bursts
Main phase (gradual?) reconnection in neutral sheet below prominence (unsheared flux): magnetic islands, flare ribbons, and “post-flare” EUV/SXR loops

24. What have we learned about FC eruption?
Energy for CMEs stored in sheared 3D field held down by overlying unsheared field
Breakout model yields unified explanation for
pre-eruption prominence structure
fast eruption (reconnection rate grows exponentially)
magnetic energy above that of the open state
“post-flare” loops
flux ropes in heliosphere
Flux ropes are formed by flare reconnection

25. Objectives for Solar B
Search for signatures of breakout reconnection: jets, crinkles, energetic particles, etc.
Establish temporal and spatial relationships among eruption features (e.g., reconnection signatures, EUV dimmings, flare ribbons)
Determine whether flux rope forms before or after eruption
Test correlation between flare phase and amount of shear on reconnecting flux

26. Summary
Sheared arcade model: filament magnetic structure is produced by strong shear (NOT twist) near and parallel to neutral line
Thermal nonequilibrium model: dynamic and static condensations are produced by normal coronal heating localized at base of loops
Breakout model: eruptions are produced by shearing of filament channel (inner core) within multipolar topologies
Progressing toward a complete, self-consistent, 3D model of filament-channel lifecycle

27. Our Goals for Solar B
Reveal origin and evolution of magnetic structure of filament channels
Test sheared arcade model
Determine primary source of filament mass
Test thermal nonequilibrium model
Establish the roles of multipolarity and reconnection in CME+flare initiation/ evolution
Test magnetic breakout model

28. DOT Observations: 9 Jul 2000 30 s cadence 0.22 arcsec/pixel
45870 x km
(62 x 45 arcsec)

29. Breakout Model Topology: Tests:
sheared dipolar field + neighboring flux systems = multipolar field with coronal null
Tests:
3D MHD simulations with ARMS (Adaptively Refined MHD Solver)
References: Antiochos et al. 1999, ApJ; MacNeice et al. 2004, ApJ; Gao (PhD thesis, in preparation); Lynch (PhD thesis, in preparation); MacNeice et al. 2000, Comp. Phys. Comm. 126, 330 (PARAMESH)

30. 2.5D Asymnmetric Breakout Model
Breakout reconnection results in jets, fast plasmoid ejection
Flare reconnection produces rising arcade of loops, fast upward/downward flows – shocks – energetic particles?

31. 3D Reconnection in Breakout Model
Breakout reconnection occurs over large area
Requires strong deformation of null
Flare reconnection appears very efficient

32. 3D Breakout Model Add 3D “active region” dipole to global dipole+ - - + + -
Add 3D “active region” dipole to global dipole
Two-flux system with null point – generic coronal topology
Preserve shear width/length ratio, overlying arcade

33. Footpoint heating on 2 sides
Heat + enthalpy fluxes transport energy through corona
Heating drives evaporation from both footpoints
Increased radiation vs heat + enthalpy fluxes

34. Why does thermal nonequilibrium occur?
Constraints: P1 = P2 , L1 + L2 = L
Scaling Laws: E ~ PV ~ T7/2 L ~ P2 L / T2+b
Key Result: P ~ E(11+2b)/14 L (2b-3)/14
e.g., for b = 1, P ~ E13/14 L -1/14 ,
equilibrium position: L1 / L2 = (E1 / E2 ) (11+2b)/(3-2b) ,
for b = 1, L1 / L2 = (E1 / E2 ) 13 !!
for b  3/2, no equilibrium is possible

35. What have we learned about FC plasma structure?
Steady footpoint heating produces no (significant) condensations in
Overlying arcade rooted outside the sheared zone (too short for TN)
Loops higher than the gravitational scale height (condensations too small and short-lived)
No dynamic condensations on deeply dipped field lines
Distribution of field line shapes (area and height variations) dictates distribution of stationary and dynamic condensations