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 http://solartheory.nrl.navy.mil/ judy.karpen@nrl.navy.mil

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?

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)

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

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)

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….

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

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

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

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

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)

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

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

Thermal Nonequilibrium: T Movie NRK run

Thermal Nonequilibrium: CDS Movie NRK run

Origin of prominence mass Are dips necessary? NO! even loops with peak heights ≈ gravitational scale height (~50-100 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…

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

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

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

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)

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

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.)

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

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

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

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

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

DOT Observations: 9 Jul 2000 30 s cadence 0.22 arcsec/pixel 45870 x 33130 km (62 x 45 arcsec)

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)

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?

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

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

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

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

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