The 3D picture of a flare Loukas Vlahos

Points for discussion  When cartoons drive the analysis of the data and the simulations….life becomes very complicated  Searching for truth in the “standard model”  The 3D picture of a flare and were the loop and loop top meet  The multi scale phenomena in complex magnetic topologies and solar flares  The limits of MHD and the beginning of a big physics challenge

When cartoons drive the analysis  In the recent solar flare literature it is hard to distinguish the real data from the implied interpretation. We have seen many examples in the preceding presentations.  Let me discuss the monolithic cartoon in detail  Let me tell you from the start that I believe that the Loop top sources are embedded in the acceleration volume and their not

High Coronal X-ray Sources Tearing Mode Instability? 23:13:40 UT 23:16:40 UT Sui et al. 2005

The 2D simulations of a cartoon

Jets and shocks in the 2D picture

Solar flares: Global picture 26 th GA IAU, JD01 “Cosmic Particle Acceleration”, Prague, August 16, D MHD

X-ray loop-top source produced by electrons accelerated in collapsing magnetic trap 26 th GA IAU, JD01 “Cosmic Particle Acceleration”, Prague, August 16, 2006 Karlicky & Barta, ApJ 647, 1472 Karlicky & Barta, 26 th GA IAU, JD01 (poster) 2.5D MHD Test particles (GC approx. + MC collisions)

Radiation from the cartoon

The MHD incompressible equations are solved to study magnetic reconnection in a current layer in slab geometry: Periodic boundary conditions along y and z directions Geometry Dimensions of the domain: -l x < x < l x, 0 < y < 2  l y, 0 < z < 2  l z

Description of the simulation Incompressible, viscous, dimensionless MHD equations: B is the magnetic field, V the plasma velocity and P the kinetic pressure. and are the magnetic and kinetic Reynolds numbers are the magnetic and kinetic Reynolds numbers.

Numerical results: B field lines and current at y=0

Three-dimensional structure of the electric field Isosurfaces of the electric filed at different times t=50t=200 t=300 t=400

Time evolution of the electric field Isosurfaces of the electric field from t=200 to t=400

P(E) t=200 t=300 t=400 Distribution function of the electric field E

Kinetic energy distribution function of electrons P(E k ) E k (keV) t=50 T A T=400 T A

Kinetic energy as a function of time E k (keV) t (s) electrons protons

Numerically integrate trajectories of particles in em fields representative of reconnection Widely studied in 2D (e.g. X-type neutral line, current sheet), but few 3D studies B=B 0 (x,y,-2z) We consider the spine reconnection configuration 3D null point - test particles Priest and Titov (1996)

S Dalla and PK Browning 2D 3D spine

Energy spectrum of particles  Strong acceleration  Steady state after few 1000s  Power law spectrum over ≈ 200 – 10 6 eV

Number of particles and energetics of the monolithic current sheet

e 2, e 4 : negative charges e 1, e 3 : positive charges Motion of the charges => Current sheet at separator => Reconnection (with E // ) => Flux exchange between domains I II III IV Configuration with 4 magnetic polarities separator Null 4 connectivity domains Separatrices: 2 intersecting cupola (Sweet 1969, Baum & Brathenal 1980, Gorbachev & Somov 1988, Lau 1993 )

Main properties Global bifurcations : Skeleton : (Gorbachev et al. 1988, Brown & Priest 1999, Maclean et al. 2004) Null points + spines + fans + separators “summary of the magnetic topology” Classification of possible skeletons (with 3 & 4 magnetic charges) They modify the number of domains - separator bifurcation (2 fans meet) - spine-fan bifurcation (fan + spine meet) (Molodenskii & Syrovatskii 1977, Priest et al. 1997, Welsch & Longcope 1999, Longcope & Klapper 2002) (Beveridge et al. 2002, Pontin et al. 2003, 1980, Gorbachev & Somov 1988, Lau 1993 )

Definition of Quasi-Separatrix Layers Jacobi matrix : Field line mapping to the “boundary” : Corona: - low beta plasma - v A ~1000 kms -1 Photosphere & below: - high inertia, high beta - low velocities (~0.1 kms -1 ) - line tying Initial QSL definition : regions where Better QSL definition : regions where ( Démoulin et al ) ( Titov et al ) Same value of Q at both feet of a field line : Squashing degree

Example of an eruption ( Williams et al ) MDI 1:57 UT 2:04 UT quadrupolar reconnection (breakout) 4 ribbons reconnection behind the twisted flux rope (with kink instability) 2 J-shaped ribbons

Brief summary Discret photospheric field : (Model with magnetic charges) Generalisation to continuous field distribution : More still to come…. --> Photospheric null points --> Skeleton Separatrices Separator Quasi-Separatrix Layers Hyperbolic Flux Tube Indeed, a little bit more complex…..

A different type of flaring configuration ( Schmieder, Aulanier et al ) H  (Pic du Midi) Soft X-rays (SXT) Arch Filament System QSL chromospheric footprint ~ H  ribbons X-ray loops 27 Oct. 1993

Formation of current layers at QSLs (1) (Titov, Galsgaard & Neukirch ) Surface Q = constant ( = 100 ) Formation of current layers Example of boundary motions Expected theoretically : - with almost any boundary motions - with an internal instability Using Euler potential representation: magnetic shear gradient across QSL ( Démoulin et al )

The 3D picture of a flare  Assume that ant time neighboring field lines are twisted more than θ the current sheet becomes unstable and the resistivity jumps up  The E=-vxB+ηJ  Distributed E-fields do the acceleration and the tangled field lines do create local trapping producing the anomalous diffusion

Eruption and stresses (Kliem et al)

Emerging Flux Current Sheet

Emerging flux Current Sheet

The multi scale phenomena in solar flares  The Big structure is due to magnetic field extrapolation. This extrapolated field has build in already magnetic filed anisotropies and small scale CS providing part of the coronal heating  The numerous loops and arcades are now stressed further from photospheric motions  Compact Loops form CS internally (see Galsgaard picture) and some loops erupt forming even more stresses magnetic topologies (see Amari picture)  Pre-impulsive phase activity and post impulsive phase activity is an indication of these stresses  What causes the impulsive flare? The sudden formation of a big structure and its cascade.

The multi scale phenomena in solar flares  The ideal MHD predicted coronal structures are long and filled with many CS covering many scales.  A few CS are becoming UCS due to resistivity changes  A typical Multi scale phenomenon  Suggestion: “Loop-top” and foot points are connected with acceleration source.

A new big physics challenge  How can we build a multi code environment where most structures are predicted by Ideal MHD. From time to time small scales appear were we depart from MHD and move to kinetic physics  Drive such a code from photosphere (fluid motions and emerging flux)  We are currently attempting to model this using a CA type model, as prototype and will follow by MHD/Kinetic models