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 SourcesTearing 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 pictureSolar flares: Global picture

26th GA IAU, JD01 “Cosmic Particle Acceleration”, Prague, August 16, 2006

2.5D MHD

X-ray loop-top source produced by electrons X-ray loop-top source produced by electrons accelerated in collapsing magnetic trap accelerated in collapsing magnetic trap

26th GA IAU, JD01 “Cosmic Particle Acceleration”, Prague, August 16, 2006

Karlicky & Barta, ApJ 647, 1472Karlicky & Barta, 26th 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 conditionsalong y and z directions

GeometryGeometry

Dimensions of the domain:-lx < x < lx, 0 < y < 2ly, 0 < z < 2lz

Description of the simulationDescription of the simulationIncompressible, viscous, dimensionless MHD equations:

0

0

1)(

1)()(

2

2

V

B

BBVB

VBBVVV

M

v

Rt

RP

t

B B is the magnetic field, is the magnetic field, VV the plasma velocity and the plasma velocity and PP the the kinetic pressure.kinetic pressure.

MR vRand are the magnetic and kinetic Reynolds are the magnetic and kinetic Reynolds numbersnumbers.

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

Three-dimensional structure of the electric field Three-dimensional structure of the electric field

Isosurfaces of the electric filed at different times

t=50 t=200

t=300 t=400

Time evolution of the electric fieldTime evolution of the electric field

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

-31.5 10E= x

-37 10E= x

-21.7 10E= x

P(E)

t=200

t=300

t=400

Distribution function of the electric fieldDistribution function of the electric field

E

Kinetic energy distribution function of electrons Kinetic energy distribution function of electrons

P(Ek)

Ek (keV) Ek (keV)

t=50 TA T=400 TA

Kinetic energy as a function of timeKinetic energy as a function of time

Ek (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=B0 (x,y,-2z)

• We consider the spine reconnection configuration

3D null point - test particles

Priest and Titov (1996)

S Dalla and PK Browning

2D

3Dspine

Energy spectrum of particles

Strong acceleration Steady state after

few 1000s Power law spectrum

over ≈ 200 – 106 eV

92.0 Ef

Number of particles and energetics of the monolithic current sheet

e2 , e4 : negative chargese1 , e3 : positive charges

Motion of the charges=> Current sheet at separator=> Reconnection (with E//)=> Flux exchange between domains

III

IIIIV

Configuration with 4 magnetic polarities

separatorNull

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

F x /x x /y

y /x y /y

Jacobi matrix :

Field line mapping to the “boundary” :

x,y x ,y : x x,y , y x,y

Corona: - low beta plasma- vA~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

N ||F ||1

Q||F ||2

Bn, /Bn,

1

( Démoulin et al. 1996 )

( Titov et al. 2002 )

Q QSame value of Q at both feet of a field line :

Squashing degree

Example of an eruption

( Williams et al. 2005 )

MDI1:57 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 tocontinuous 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. 1997 )

H (Pic du Midi)

Soft X-rays (SXT)

Arch Filament System

QSL chromospheric footprint

~ H ribbons

X-ray loops27 Oct. 1993

Formation of current layers at QSLs (1)

(Titov, Galsgaard & Neukirch. 2003 )

Surface Q = constant ( = 100 )

Formation ofcurrent 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. 1997 )

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