ENERGY OF FORCE-FREE MAGNETIC FIELDS IN RELATION TO CORONAL MASS EJECTIONS

G.S. Choe and C.Z. Cheng

ApJ 574, L179, 2002

The Aly conjecture

“…Aly (1984), who showed that there is an upper bound of magnetic energy of FFFs in an infinite halfspacewith the same boundary normal field (Bn) distribution.Aly (1984) further conjectured that the maximum energy Of the closed FFFs should be the corresponding open-field energy.”

FFFs = force-free fields

Sturrock, P. A., Weber, M., Wheatland, M. S., and Wolfson, R., "Metastable Magnetic Configurations and Their Significance for Solar Eruptive Events,” ApJ 548, 492 (2001).

Euler potentials

…“spurious reconnection” ?

• Comment about volumes• Comment about inflation• Comment about “shackling”

Hudson, H. S., "Implosions in Coronal Transients," ApJ 531, L75-L77 (2000)

Isomagnetobars

Opened field

30% excessenergy!

From the virial theorem (Aly 1984):

• This test results in an error <9%

160

300

400

5%

1.4%

Box Error

• The effects of finite box size are < 5%

Sigmoids

• Comment: separatrix heating

So: was the conjecture wrong?

• Authorities PAS, JJA: Probably so? • Authority JL: They’ve repeated the mistake

of Barnes and Sturrock• Authority BCL: Partial opening may be a

way out. Gravity may play a role.• Spectator HSH: The implications of the

conjecture still make intuitive sense to me.