Two energy release processes for CMEs: MHD catastrophe and magnetic reconnection

Yao CHEN

Department of Space Science and Applied Physics Shandong University at Weihai China

In collaboration with You-Qiu HU, Li-Dong XIA, & Shu Ji SUN

Outline:1. A brief intro. to the two energy release processes for CMEs: catastrophe & magnetic reconnection

2. Preliminary calculations to disentangle their contributions to CME dynamics with a flux rope catastrophe model in the corona & solar wind

3. Summary

1、 A brief IntroductionMotion on the photosphere < 1km/s, CME speed: 100-1000 km/sThe energy is stored in the corona before the eruptionMagnetic-energy storage processes:Flux emergence, surface flow/footpoint shear motionflux rope: a product of these energy build-up processes.

Total energy that can be stored in a flux rope system has an upper bound. Beyond this bound, the whole system loses equilibrium a global MHD instability, also called the flux rope catastrophe, models developed:Analytical ones (Forbes et al., 95; Lin et al., 98 … )Numerical ones (Hu et al., 03; Chen et al., 06; … )

• Most models, including the present one, use axisymmetric approx. (2.5d) assuming length>>diameter

A 3-D flux rope sketch:Low, B. C., 2000

}

After catastrophe, the system evolves from a meta-stable state to an eruptive statethe ejecta are accelerated by unbalanced Lorentz forcesenergy released without current dissipation/Ohmic heating (ideal)

resistive process further release the magnetic energy

}Two energy release processes for CMEs:flux rope catastrophe & mag. reconnec.

Extended, well-developed current sheets can form during the eruption, which provide appropriate conditions for fast magnetic reconnection.

The magnetic reconnectionin addition to flare phenomena, f-associated SEPsalso causes an enhanced CME accelerationa reduction of the retarding magnetic forces provi

ded by the background field confining arcades, and/or the current in the current sheet

Both the catastrophe and reconnection are thoughtto be important to CME dynamics and energetics.

To disentangle their contributions we compare solutions in two situations:(1) ideal MHD: only catastrophe to release energy(2) resistive MHD: catastrophe + reconnection

An example

Color map: velocity

Numerical reconnections do take place!How to eliminate/prohibit numerical reconnection to obtain the ideal MHD solution?Taking advantage of the fact that the magnetic flux function along the current sheet is invariant, which is a local minimum or maximum, known a priori. Any reconnection across the sheet changes it.

We therefore reassign the flux function along the current sheet to the known constant value at each time step.

Left: a polytropic solar wind background (γ=1.05)Right: swelling streamer after flux rope emergence

(2.1) impact of reconnection on the rope dynamics

1. locate the catastrophic point, or the meta-stable critical state.2. the instability can be easily triggered by a slight modification to many system parameters, like footpoint shear, flux cancellation of the b.g. field, change of the flux rope para., flux emergence, etc.

swelling streamer!The solar wind- c.s. - streamer

Two main differences:1. existence (absence) of a well-developed current sheet below the rope in the ideal (resistive) case2. the resistive case is generally faster

shock wave driven by CMEs

Snapshots at a given time after the catastrophe for the ideal (left) and resistive (right) calculations

1. Monotonic decrease of velocities from leading to trailing edges: rapid expansion with eruption

2. A multi-phased evolution of the CME acceleration: an initial slow rise phase, a main acceleration phase,

and a propagation phase (J. Zhang et al.)

temporal profiles of distances & vel: Ideal V.S. Resistive

Resistive

IdealCusp pointRope topRope axisRope bottom

Resistive

Ideal

B0=6 G

• Stronger b.g. field enable faster CMEs

Fast & slow CMEs: driven by one mechanism?(Recent observational analyses seem to be supportive:Yurchyshyn et al. 05; Zhang & Dere, 06; Vrsnak et al.05…)

B0=2 G resis.

thin: ideal

B0=10 G resis.

thin: ideal

(2.2) Fast & slow eruptions produced with different b.g. field

Cusp pointRope topRope axisRope bottom

Comparison with observations: Zhang, J. et al., 2001, 04, ApJ

Solid: X-ray flux profileDotted: CME velocity profile

B0=2 G resis.

thin:ideal

B0=10 G resis.

thin: ideal

Cusp pointRope topRope axisRope bottom

Increase in the total kinetic energy over the initial meta-stable state before the eruption

B0=10G resis.

B0=6G resis.

B0=10G ideal

B0=6G idealB0=2G resis.

B0=2G ideal

Reconnections & catastrophe may have comparable significance on CME dynamics/energetics.

∆Ek after reconn. sets in

10G

6G

2G ∆Ek withoutReconnections

Kinetic energy increase(∆Ek) unit:5.38X1031

ergs

Summary:With a flux rope catastrophe model for CMEs in the corona and solar wind

I: Preliminary cal. to disentangle the contributions of the two energy release processes (catastrophe and reconnection) to CME dynamics & energetics.

Magnetic reconnections & catastrophe may have comparable significance on CME accelerations.

II: Stronger b.g. fields, where more magnetic free energy can be accumulated and released, enable faster CMEs

Fast and slow CMEs: one identical driving mechnism?(Recent observational analyses seem to be supportive:Yurchyshyn et al. 05; Zhang & Dere, 06; Vrsnak et al.05…)

References: Chen, Hu & Xia, 2007, ASR, in pressChen, Hu & Sun, 2007, ApJ, 665, 1421Chen, Li & Hu, 2006, ApJ, 649, 1093

Thanks!