Comments on Reconnection at the Sun

L. A. Fisk

University of Michigan

Three-Dimensional Perspective

Footpoint Motions on the Solar Surface

Questions Asked

• What kind of values are expected for the spatial scales of reconnection events and the time scales for the reconnection?

• How certain are we of the values today?

• How important is it to know these values?

Fisk (ApJ, 626, 563, 2007)

• The interaction among the flux concentrations lends itself naturally to the principles of particle diffusion theory.

• A simple theory is possible for describing what happens when loops emerge on the solar surface, expand into the network lanes, move along the lanes, coalesce to form new loops, or reconnect with and displace open field lines.

Results• The frequency of collisions between two flux

concentrations is

Here

is the diffusion coefficient forrandom convective motions.is the surface number densityof target flux concentrations.

• Same result as Schrijver, et al. (1997).

1

τ c

=34

δh2

δtNt

δh2 / 2δt

Nt

Results

• The mean square separation between the footpoints of loops is found to be:

is the average amount of magnetic flux in a flux concentration.

is the mean field strength of the open magnetic flux.

h 2 =8ϕ3Bo

ϕ

Bo

Results• If we know the mean square separation between the

footpoints of loops, and the frequency of reconnections, we can find the diffusion coefficient for the transport of open flux due to the reconnection with loops:

is the mean field strength of the loops.

κ =h 2

4τ c=

1

4

8ϕ

3Bo

3

4

δh2

δt

Blϕ

=δh2

2δt

BlBo

Bl

Some numbers

• Reasonable to use the diffusion coefficient for random convective motions of Wang & Sheeley

• The typical value for the magnetic flux in a flux concentration is

δh2

2δt≈ 6g1012cm2s−1

ϕ ≈3g1018Maxwells

Some numbers

Coronal Holes• Take open magnetic

flux to be 8 G; field strength in loops, 1 G

• Mean reconnection time between open flux and loops is 40 hours.

• Mean loop size, 10mm.• Diffusion of open flux

mainly by random convective motions

Outside Coronal Holes• Take open magnetic

flux to be 1 G; field strength in loops to be 3 G.

• Mean reconnection time between open flux and loops is 13 hours.

• Mean loop size, 30mm.• Diffusion of open flux

mainly by reconnection with loops

Some complications• There are some complications for open flux

embedded in closed field regions.• The open flux must penetrate through the

overlying loops and can reconnect in the corona, as opposed to reconnection at the photospheric base.

• We have referred to reconnection in the corona as canopy diffusion -- diffusion in the overlying canopy of loops.

Some complications• Have not found a good way to determine diffusion

coefficient for transport of open flux by canopy diffusion.

• Must be consistent with global motions of open flux driven by over expansion from coronal holes and differential rotation.

• In Fisk & Zurbuchen (JGR,111, A09115, 2006 ), where we used canopy diffusion to predict distribution of open flux outside of coronal holes, not necessary to know canopy diffusion coefficient.

• These are not issues for coronal holes.

How important is it to know these values?

• Depends on what else you think is happening.• We have argued that reconnection between an open

field line and a loop will release material from the loop onto the open field line and can contribute to or even determine the mass flux of the solar wind.

• We have argued that the process of an open field line reconnecting with a loop and being displaced can contribute to and may even determine the heating of the solar corona and the acceleration of the solar wind.

The final speed of the solar wind• If we use these simple concepts, and the

theory for how emerging loops evolve, coalesce, and reconnect with open flux, we can derive that:

is the magnetic energy in open flux in a

flux tube of cross section A. is the mass flux of the solar wind.

u f2

2=

1τopen

+1

τ loop

⎡

⎣⎢⎢

⎤

⎦⎥⎥

WB

ρuA⎛

⎝⎜⎞

⎠⎟−

GMo

ro

WB

ρuA