Magnetic Flux Tube Reconnection: Tunneling Versus Slingshot

The highly discrete nature of the solar magnetic field as it emerges into the corona through the photosphere, where it is predominantly concentrated into sunspots and magnetic pores, indicates that the magnetic field exists as discrete, isolated flux tubes in the convection zone, and will remain as discrete flux tubes in the corona until it collides and reconnects with other coronal fields. Collisions of these flux tubes, both in the convection zone and in the corona, will in general be three dimensional as the flux tubes will collide at random angles, and in many cases this will lead to reconnection, both rearranging the magnetic field topology in fundamental ways, and releasing magnetic energy. With the goal of better understanding these dynamics, we carry out a set of numerical experiments exploring fundamental characteristics of three dimensional magnetic flux tube reconnection. We first show that reconnecting flux tubes at opposite extremes of twist behave very differently: in some configurations, low twist tubes slingshot while high twist tubes tunnel. We then discuss a theory explaining these differences: by assuming helicity conservation during the reconnection one can show that at high twist, tunneled tubes reach a lower magnetic energy state than slingshot tubes, whereas at low twist the opposite holds. We test three predictions made by this theory. 1) We find that the level of twist at which the transition from slingshot to tunnel occurs is about two to three times higher than predicted on the basis of energetics and helicity conservation alone, probably because the dynamics of the reconnection play a large role as well. 2) We find that the tunnel occurs at all flux tube collision angles predicted by the theory. 3) We find that the amount of magnetic energy a slingshot or a tunnel reconnection releases agrees reasonably well with the theory, though at the high resistivities we have to use for numerical stability, a significant amount of magnetic energy is lost to diffusion, independent of reconnection. We find that, while the slingshot reconnection is generally applicable to flux tubes of all twist, the level of twist needed for tunneling reconnection is relatively high compared to observations of the twist of large coronal loops. Therefore the tunnel is mainly relevant for the Space Science Division, Naval Research Laboratory, Washington, DC 20375-5352