Summary-2 (?)Summary-2 (?)

Takashi SakuraiTakashi SakuraiNational Astronomical Observatory of JapanNational 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

hypothesisuniform initial fieldregular 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 MHDmagnetic field

boundary motion

create discontinuity?

uniform singular yes

discontinuity regular yes

with nulls regular yes

dipping field lines

regular yes

uniform 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 alsoGalsgaard and Nordlund, JGR 1996Craig 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

“flare” populationslope ~ −1.5

small scale eventsslope< −2 ?

new physics

N(E)

E

limited by micro physics

1032 erg1026 erg

limited by finite size of the sun

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 ofopen field

Energy ofpotentialfield

S hear

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 ofopen field

Energy ofpotentialfield

Shear

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-Bcarefully-designed observing plans (not trivial)

magnetic field generation (dynamo) important hints (diffusion, surface dynamo,,,)