K. Galsgaard1, A.L. Haynes2, C.E. Parnell2 How complicated can the reconnection process be in a simple MHD flux interaction problem? K. Galsgaard1, A.L. Haynes2, C.E. Parnell2 1 Niels Bohr Institute 2 University of St Andrews Workshop on Magnetic Reconnection and Plasma turbulence Uppsala 29th May 2007

Solar “Magnetic field” TRACE - SOHO Complicated structures Potential B-model Magnetic field lines!? Localised sources

Numerical Experiment – + Negative Source Positive Source Simple magnetic setup with two sources and overlying field Lower boundary: Negative Source – Overlying Field Overlying Field + Positive Source Upper boundary: Closed Side boundaries: Periodic Galsgaard et al (2000)

Equations and Numerical Code ∂(𝜌𝑢 ∂𝑡 =−∇.(𝜌𝐮𝐮+𝜏 −∇ 𝑝+𝐽×𝐵 𝐸=−𝑢×𝐵+𝜂𝐽 ∂𝑒 ∂𝑡 =−∇.(𝑒𝑢 − 𝜌(𝑇− 𝑇 0 𝑡 𝑐𝑜𝑜𝑙 + 𝑄 𝑣𝑖𝑠𝑐 + 𝑄 𝑗𝑜𝑢𝑙𝑒 𝐽=∇×𝐵 ∂𝐵 ∂𝑡 =−∇×𝐸 𝑒= 𝑝 𝛾−1 ∂𝜌 ∂𝑡 =−∇.(𝜌𝑢 𝑝=𝜌𝑇 Finite difference resistive MHD code of size (1, 1, ¼) with (128, 128, 66) grid points. Third order predictor-corrector method. Sixth order spacial derivatives. Fifth order spacial interpolation. Hyper viscosity and magnetic diffusion. Combined 2ed and 4th order + Shock diffusion.

Magnetic Field Structure of Magnetic Field: 4 Sources (P1, P∞, N1, N∞) 4 Source Pairs: N∞ to P∞ (overlying) N1 to P∞ (negative open) N∞ to P1 (positive open) N1 to P1 (closed) 2 Null points (on base) Evolution of source flux: Open → Closed → Reopened.

Evolution of 3D Magnetic Skeleton Positive Separatrix Surface Negative Separatrix Surface Separators Haynes et al (2007)

Phases of Skeleton (cuts at y=0.5) D=3 Phase 2 D=5 Phase 3 D=4 Phase 4 D=8 Phase 5 D=6 Separatrix Surfaces: Negative Positive Separators: The skeleton evolves due to reconnection What is the nature of the reconnection? Haynes et al (2007)

Separator Labels XC XR XL

Movement of particles Trace fieldline to plane y=0.5 Plot point on y=0.5 Particle moving with plasma flow XC XL XR Distance of fieldline to nearest separator determines colour of point on y=0.5.

Particles near Separators (Phase 5) Particle fieldlines near XL near XC near XR XC XL XR

Recursive Reconnection Particles fieldlines about to change connectivity are all coloured  separator reconnection XC XL XR Closing Reopens Reopens

Particles near Separators (Phase 5)

Flux in Domains tR Examine reconnection at highest rate of change. Flux in (original) open tails off due to recursive reconnection tR

But we want to understand more… Current Sheet (t = tR) Twisted Current Sheet But we want to understand more…

Central Separator (XC): Where Does Reconnection Occur? Use time slices of E|| along the separator XC. Reconnection occurs at 0.5 of the normalised separator length Time (tR) of fastest reconnection rate

Planes of Properties (t = tR) Plane – fixed at 0.5 of separator XC's length. Set plane perpendicular to separator Dots – connectivity (closed, -ve open, +ve open, overlying) normal Thin current sheet visible on XC.

XC: Radial velocity from separator (t=tR) Reconnection is closing magnetic field Strong subalfvénic outflow jets

What drives reconnection? Possible Mechanisms: Plasma Pressure/Magnetic Pressure. Magnetic Tension.

Plasma Pressure Little/no change of pressure at XC. Significant pressure gradient at XL and XR. XC XL XR

Magnetic Pressure Generally opposite to plasma pressure. Still little pressure change at XC, high at XL and XR. XC XL XR

Total Pressure Central reconnection is not pressure driven. Side separators are pressure driven. XC XL XR

Magnetic Tension Only reconnection at central separator driven by magnetic tension. XC XL XR

Conclusions Separator reconnection. Closing of field driven by magnetic tension force. Reopening driven by total pressure force. Reconnection is complex. Multiple separator reconnection. Isolated region(s) of diffusion along each separator. Fronts in outflow jets. Unlikely to be shocks. Possible contact discontinuity. Recursive reconnection. Flux is closed ↔ reopened multiple times.

Introduction to Magnetic Skeletons 2D magnetic skeleton Sources and sinks. Null points (B = 0). Separatrix curves. 3D magnetic skeleton Separatrix surfaces Separators (intersection of separatrix surfaces). 3D

Evolution of 3D Magnetic Skeleton Negative Separatrix Surface Positive Separatrix Surface Separators Many separators implies many reconnection sites. Haynes et al (2007)

XC: Current Thin current sheet visible on XC.

Plasma Flows Expect reconnection to occur at stagnation-like point. Direction of plasma flow shows direction of reconnection.

XC: Magnetic tension (t = tR) Closing Driven by Magnetic Tension

Conclusions Shown reconnection is separator reconnection. Multiple separators imply: Multiple heating sites. Recursive reconnection: Flux is repeatedly closed ↔ reopen. Each separator has an isolated diffusion region. Central separator (XC): Closing magnetic field. Tension driven reconnection. Subalfvénic jets.