1/18

Buoyant Acceleration: from Coronal Mass Ejections to Plasmoid

P. Wu, N.A. Schwadron, G. Siscoe, P. Riley, C. Goodrich

Acknowledgement: W.J.Hughes, H.S.Spence, M.Owens, S. Mcgregor, V.Merkin

Boston University

01/09/2007 @ University of New Hampshire

New England Space Science Consortium

2/18

Siscoe Derivation of Magnetic Buoyancy: Magnetic Repulsion

Decomposition of a diverging magnetic field across a sphere into uniform and nonuniform components.

Magnetic Repulsion Force 2

0

2m a m

b a b

AK B Ka

K R

V

K R

Assuming uniformly flaring out B field

Forbes CME model

3/18

Siscoe Analytical Result

• There is no mystery about CME acceleration: Buoyancy force can fully account for propelling acceleration.

• Rather, it is the curbing acceleration results from forces such as magnetic tethering that is difficult to formulate.

4/18

SAIC MHD Model - Setup

• 2.5 – dim (simplified 3 dim: assume azimuthally symmetry)

• Non uniform Spherical Grid to minimize the effect of artificial computational boundaries

• Time step 6 min

More detail can be found from the Mikic & Linker 1994 paper

5/18

Calculating the Accelerations

• MHD acceleration: compute dv/dt from the simulated value at each time step

• Hybrid acceleration: take the simulated parameters at each time step, plug them into the Siscoe analytical equation to compute the hybrid acceleration.

Acceleration

2 2

222

2

( )( )

2 2 2

a CME esc s m a A

D CME sw CME swb b

a CME a CME a CME

M M v R K M vC a v v v vr K K rd r

dt M M M M M M

6/18

Comparison of each Hybrid Acceleration components with MHD Acceleration

+

+ =

MHDHybrid Normal Buoyancy

MHDHybrid Magnetic Buoyancy

MHDHybrid Aerodynamic Drag

MHDHybrid

7/18

Comparison of Hybrid and MHD Acceleration

Detachment height=1.55766 Rs

Buoyant

MHDHybrid

Tethered

1

Detachment height=1.55766 Rs

Teth

eredB

uo

yant

MHDHybrid

8/18

Comparison of Hybrid and MHD velocity component Vr

Hybrid velocity integrated throughout two phasesHybrid velocity integrated throughout two phases

Hybrid velocity integrated throughout two phases

BuoyantTethered

1

Detachment height=1.55766 Rs

9/18

Two Phases

Tethered Buoyant

Transition point: CME center at 1.55766 RS Height

10/18

Tethered (JXB)r

(JXB)r is

mostly

negative!

*Height 1.05771 RS

r=1.05771

11/18

Buoyant (JXB)r

(JXB)r is

mostly

positive!

*Height 2.17275 RS

r=2.017275

12/18

Transition (JXB)r

(JXB)r is

mostly

slightly more positive!

*Height 1.55766 RS

r=1.55766

13/18

(JXB)r Together

TetheredTransition

Buoyant

14/18

Suggested Advanced TheoryWhen CME is buoyant:

2,( A bom

magnetto

ticb

mbottom

Vf

R

Ka

K

3cos 2cos

3 3 ,4 / 3bottomf

where

Special Case: θ=0, fbottom=1, ftop=0 & θ=π, fbottom=0, ftop=1

Actually when CME is in Buoyant phase, as we can see from the agreement of simulation and Analytical model, f top≈0, we only need to consider the buoyant term.

1top bottomf f

Buoyant term

2, )A top

top

Vf

R

Tethered term

2 2, ,/ 4.28A bottom A topV V

Buoyant

E.g.

Tethered force is negligible

+X

X XX

XX

XX X

X

X XX

XX

XX X

Buniform

Bnon-u

Juniform = 0

1uniformB

��������������

J X Bnon-u

θ

15/18

When CME is tethered:

However, for the closed little bubble, it also feel the ram pressure from the plasmas beneath. Those plasmas are suggested to be JXB accelerated individually (inspired by the Hesse & Birn 1991 paper on Magnetotail plasmoid evolution1) and being filled into the bubble to add to the bubble’s mass and total momentum. So even as the example show that the buoyant force is only .29 of the tethered force at some point, but the bubble still goes outward radically, collecting momentum from below. That may be associated with reconnection below.

Thanks Prof. Spence for pointing this paper to me!

Suggested Advanced Theory (Continue)

E.g.

The bubble is still growing/forming. Tethered force is non-neglegible.

2 2, ,/ 0.63A bottom A topV V

Tethered The magnetic field lines in front of the bubble is being very compressed, which cause relatively larger VA,top

16/18

Conclusion

The acceleration of CME in the corona region can be divided into two phases: “Tethered phase” and “Buoyant phase”.

In the “Tethered Phase”, the CME is trying to overcome the tethering force. The kinetics are complicated.

In the “Buoyant Phase”, the CME is principally buoyant and can be approximated as a superconducting bubble. Analytical model agrees very well with MHD simulation in this phase.

17/18

Discussion-1

CMEs are on average much faster at solar maximum than at solar minimum

Solar Max: tethered magnetic field lines are on average closed at lower height. So tethered regions are smaller, CMEs are detached earlier and we can integrate velocity earlier. So the CMEs are accelerated to be faster. Solar Min is the opposite. This is consistent with observation.

CME current wedge? Will observers able to observe field aligned current along the compressed field lines? Will we be able to use it to signature the transition from “tethered phase” to “buoyant phase”. If so, we could start to use our complete buoyant phase analytical model to predict CME velocity. As we show previously, it agrees very well with MHD simulation.

Will we detect current here?

And here?

18/18

Connect CME to Magnetotail plasmoid1 to study the buoyant phase. How are CMEs and Magnetotails similar and how do they differ?

1. Note: Magnetotail Plasmoid evolution study has been done by Hesse & Birn in their1991 paper and their finding can be understood as that Plasmoid is not buoyant as a bubble, instead plasmas are accelerated by jXB force individually and being filled into the bubble to form the plasmoid. However, at 1991, the simulation magnetotail magnetic fields are constant. So they don’t have flaring out field as we have. What they see, we suspect is the tethered phase of plasmoid. The LFM model we are using is global model, we should be able to identify the buoyant phase as we will show next.

Discussion-2

Hones modelHesse & Birn 1991

19/18

Buoyancy as Universal Process: From CME to Plasmoid

X-Z planeIMF Bz=-10 after 6 UT

20/18

Analyzing vx and Acceleration to Calculate Magnetic Buoyancy

Km/s(Cm-3)

21/18

• It seems that both CME and plasmoid experience Tethered and Buoyant phases.

• It seems that in Tethered phase, micro-physics of individual plasmas plays the roles of acceleration. While in the buoyant phase, the slingshot-like mechanism of flaring out field plays the role of acceleration (buoyancy).

• Lots of things we can do to further analyze and qualify the comparison of

CME & PlasmoidTethered & Buoyant

Discussion-3