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

1. Two energy release processes for CMEs: MHD catastrophe and magnetic reconnectionYao CHENDepartment of Space Science and Applied Physics Shandong University at Weihai China In collaboration with You-Qiu HU, Li-Dong XIA, & Shu Ji SUN

2. 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

3. 1、A brief Introduction Motion on the photosphere < 1km/s, CME speed: 100-1000 km/s The energy is stored in the corona before the eruption Magnetic-energy storage processes: Flux emergence, surface flow/footpoint shear motion flux 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

4. Two energy release processes for CMEs: flux rope catastrophe & mag. reconnec. } } After catastrophe, the system evolves from a meta-stable state to an eruptive state the ejecta are accelerated by unbalanced Lorentz forces energy released without current dissipation/Ohmic heating (ideal) • resistive process • further release the magnetic energy Extended, well-developed current sheets can form during the eruption, which provide appropriate conditions for fast magnetic reconnection.

5. The magnetic reconnection in addition to flare phenomena, f-associated SEPs also causes an enhanced CME acceleration a reduction of the retarding magnetic forces provided by the background field confining arcades, and/or the current in the current sheet Both the catastrophe and reconnection are thought to 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

6. 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. An example Color map: velocity

7. (2.1) impact of reconnection on the rope dynamics Left: a polytropic solar wind background (γ=1.05) Right: swelling streamer after flux rope emergence The solar wind - c.s. - streamer swelling streamer! • 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.

8. shock wave driven by CMEs Snapshots at a given time after the catastrophe for the ideal (left) and resistive (right) calculations • Two main differences: • existence (absence) of a well-developed current • sheet below the rope in the ideal (resistive) case • 2. the resistive case is generally faster

9. B0=6 G Resistive Resistive Cusp point Rope top Rope axis Rope bottom Ideal Ideal temporal profiles of distances & vel: Ideal V.S. Resistive • Monotonic decrease of velocities from leading to trailing edges: rapid expansion with eruption • 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.)

10. (2.2) Fast & slow eruptions produced with different b.g. field B0=10 G resis. thin: ideal B0=2 G resis. thin: ideal Cusp point Rope top Rope axis Rope bottom • 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…)

11. B0=10 G resis. thin: ideal B0=2 G resis. thin:ideal Cusp point Rope top Rope axis Rope bottom Comparison with observations: Zhang, J. et al., 2001, 04, ApJ Solid: X-ray flux profile Dotted: CME velocity profile

12. 10G B0=10G resis. Kinetic energy increase (∆Ek) unit: 5.38X1031 ergs 6G B0=6G resis. ∆Ek after reconn. sets in B0=10G ideal B0=6G ideal 2G ∆Ek without Reconnections B0=2G resis. B0=2G ideal Increase in the total kinetic energy over the initial meta-stable state before the eruption Reconnections & catastrophe may have comparable significance on CME dynamics/energetics.

13. 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…)

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