Summary-2 (?)
Takashi Sakurai
National Astronomical Observatory of Japan
Two Summaries:
Two Basic Problems in Solar MHD

Parker’s Hypothesis
 coronal heating (nanoflare theory)

Aly&Sturrock’s Hypothesis
 CME
Parker Problem and Parker’s Hypothesis

hypothesis
 uniform
initial field
 regular boundary motion (but not preserving
winding pattern)
 creates discontinuity
 leads to dissipation (by reconnection)
Parker: ApJ 174, 499, 1972
Parker: ApJ 264, 635, 1983
Parker: Solar Phys. 121, 271, 1989
Ideal MHD
magnetic
field
uniform
boundary create
motion
discontinuity?
singular yes
discontinuity regular
yes
with nulls
regular
yes
dipping field
lines
uniform
regular
yes
regular
no
Parker: ApJ 407, 342, 1993
discontinuous field
regular motion
magnetic null and
singular mapping
dipping field lines and
singular mapping
Mikic, Schnack, and van Hoven: ApJ 338, 1148, 1989
Discontinuity is not created.
See also
Galsgaard and Nordlund,
JGR 1996
Craig and Sneid, Solar Phys.,
in press
real life (with finite resistivity)
uniform field, regular boundary motion
 nulls created by diffusion
 singular mapping of field lines
 shear layer is created
 dissipation by reconnection

Dennis: Solar Phys. 100, 465, 1985
Shimizu, PASJ 47, 251-263, 1995
N(E)
limited by micro physics
small scale events
slope< −2 ?
new physics
“flare” population
slope ~ −1.5
limited
by finite
size of
the sun
1026 erg
1032 erg
E
Aschwanden: Solar Phys. 190, 223, 1999
Arbitrarily small flare loops cannot exist.
What is “new physics?”
purely coronal events? no conduction loss
 new regime of reconnection?
 new component of magnetic field?
 new component of driving motion?
 ????
 forget this and go to waves?

Aly&Sturrock’s Hypothesis
closed field lines (loops)+footpoint motion
 energy increases and asymptotically
approaches an upper limit
 the upper limit is attained by the open field
 the energy of the closed field can never
exceed the open field energy
 hence eruption to the open field is
impossible

Energy
Energy of
open field
Energy of
potential
field
Shear
Exceptions
two interacting flux tubes (Choe and
Cheng 2002)
 configuration with a detached flux tube (a
filament) (Li and Hu 2003)

Choe and Cheng: ApJ, 574, L179, 2002
I wonder if the existence of a field-free volume
separating the two flux tubes is essential.
Can more general conditions be formulated to
obtain E>Eopen?
Li and Hu: Chinese J. Astron. Astrophys. 3, 555, 2003
Field with floating flux rope has energy
exceeding the open field energy.
In this case the excess is 1.5% of open field,
2.4% of closed dipole field energy.
Y.Q.Hu: ApJ 607, 1032, 2004
octapole field
central arcade opens,
asymptotically approaching
partially open field
Y.Z.Zhang et al.: ApJ 626, 1096, 2005
With floating flux rope, the
open field energy is exceeded
Energy
Energy of
open field
Energy of
potential
field
S hear
Three Major Problems in Solar Physics

flares and CMEs
 Solar-B
launch in activity minimum,,,
 high resolution, trigger mechanism

heating of the atmosphere (and solar-wind
acceleration)
 waves
or superposition of small explosions?
 the main target of Solar-B
 carefully-designed observing plans (not trivial)

magnetic field generation (dynamo)
 important
hints (diffusion, surface dynamo,,,)