1. Magnetic Reconnection in Solar Flares

3. Loss of Equilibrium Model

5. Reconnection Electric Field for Constant Alfvén Mach Number

6. Predictive Science CME Simulation
Linker et al. (2001)

7. Flare Loop System

9. Shinkrage of Flare Loops Observed by Hinode XRT

10. Flare Reconnection Rate from Observations
NSO/Kitt Peak Magnetogram 18 Dec 1998
area s swept out
by flare ribbons
17:18 UT
18:05 UT
21:39 UT
newly re-closed flux:
voltage drop along x-line:

11. Flare Reconnection Rate
Observed Reconnection Rate for X1.6 Flare
after Qiu et al 2004

12. Observations of Reconnection Flows
Non-eruptive event of 17 Aug 2011
AIA 131
Su et al. 2013

13. Tracking of Small Features in Current Sheet
Savage et al. 2010

15. Outflow Profiles for Petschek and Sweet-Parker Reconnection

16. Early MHD Numerical Simulations
Yan et al. (1992)
Fast-Petschek solutions not observed when the resistivity is uniform.
region of enhanced resistivity

17. Incompressible Time-Dependent Nozzle Equations for Resistive MHD
a: thickness of current layer
V: outflow
b: perpendicular interior field
B: parallel exterior field
h: magnetic diffusivity
u: inflow
ba: perpendicular exterior field
a: diffusion region length
L: global scale length

18. Evolution of Non-Uniform Resistivity Solutions
a(x)
V(x) x x
b(x)
h(x) = h0 Exp[–(x/l)2]
h0 = 1/Lu =
l = x
final MA =

19. How to Calculate Reconnection Rate
Reduction to steady-state:
(equation of Vasyliunas 1975)
Most solutions of this equation have an unphysical singularity!
Taylor expand steady-state equation:
Eliminate singular solutions by requiring convergence:

20. 2D MHD Simulations for h(x) = h0 Exp[–(x/l)2]
outflow velocity
simulation
theory
rate predicted by analytical theory: MAi =
4.9% difference
rate occurring in numerical simulation: MAi =
There are no free parameters in the theory.
Baty et al. (2014)

21. Application to Simple Flare Model

22. Predicted Flow in Current Layer
early
late
symmetric field
asymmetric field

23. 2D MHD Simulation of Late Phase Reconnection
Mei et al. 2012

24. Predicted Reconnection Geometry
During Late Phase for Uniform Resistivity

25. dependent resistivity:
But What if Resistivity is Nonuniform?
Current density
dependent resistivity:
Hall MHD simulation
(Ma & Bhattacharjee 1996 ) 30 j
0.5 T j 20 25 li
hmod 10 15
– 0.5 12
– 1 1
– 4 4
0.3
0.0
– 0.3
(Yokoyama & Shibata 2001 )

26. Unanswered Questions 1.
What is the length of the region where reconnection
outflows are accelerated?
current observations           < 104 km
scale of resistivity variation 2.
Do slow shocks exist? If not, what replaces them?
late phase of flare requires
more than Sweet-Parker
How do 3D aspects change the 2D picture? 3.