1. What can helicity redistribution in solar eruptions tell us about reconnection in these events? by Brian Welsch, JSPS Fellow (Short-Term ), Space Sciences Lab, UC-Berkeley, Non-Expert on Reconnection Image by Pevtsov & Groening 2010

2. What can helicity redistribution in solar eruptions tell us about reconnection in these events? by Brian Welsch, JSPS Fellow (Short-Term ), Space Sciences Lab, UC-Berkeley, Non-Expert on Reconnection Image by Pevtsov & Groening 2010 It’s okay for me to over interpret results, and present crazy ideas!

3. A brief review: Magnetic helicity quantifies the linkage between magnetic flux systems. Helicity is conserved if evolution is ideal, and is approximately conserved during fast reconnection. The relative helicity of coronal magnetic fields, which are anchored in the photosphere, is gauge invariant. Images by M. Berger Invariance arises from defining helicity with respect to a reference field. Potential field, used as reference B True field

4. Helicity can be decomposed into linkages between and within a flux systems: “mutual” and “self”, resp. H mut = (γ+δ) ϕ A ϕ B /π Self helicity, H self, is twist internal to a flux system. RH is positive helicity, LH is negative helicity. Mutual helicity, H mut, quantifies linkages between flux systems. Images by M. Berger

5. H mutual also has a sign given by a right-hand rule. There is a strong similarity here with magnetic configurations before and after solar eruptions. H mut < 0 H mut > 0 Image from Moore & Labonte 1980, via Hugh Hudson’s cartoon archive In a solar eruption, underlying field becomes overlying field.

6. Helicity conservation implies changes in H mutual caused by reconnection produce changes in H self, as at right. Wright & Berger 1989 Hence, we need to modify our pre- and post eruption cartoon! For instance: The linked circles here crudely denote H self. Note: downward flow of helicity would limit the ability of CMEs to remove helicity (Low 2002), but could drive subsequent eruptions.

7. Linton & Antiochos (2005) found that flux tubes can reconnect by “tunneling” through each other. Tunneling occurs when tubes can reach a lower energy by exchanging H mut with H self. Linton & Antiochos 2005 Note: perspective in (a) and (f) is face-on, but is edge- on in (b) through (e).

8. But in situations lacking artificial symmetry, how should helicity be partitioned among reconnecting flux domains? Is one partition of helicity more likely? H self in overlying flux OR H self in underlying flux

9. Back to the drawing board: a better cartoon comes with a simple quantitative, 3D theoretical model. If we take cartoons and simple models as evidence (!), then clearly the change in H mut goes primarily into H self in the ejection. Aside: There is no real debate that “flare reconnection” occurs below an erupting ejection. (Still hotly debated: (i) Does reconnection trigger eruptions? (ii) Does it directly or indirectly accelerate particles that generate X-ray emssion?) Images from Longcope & Beveridge (2007)

10. But simulations also show most helicity going into the ejection! MacNeice et al. (2006): 80% of pre-eruption helicity goes into the ejection.

11. This sequence of cartoon reconnections of a “breakout” CME illustrates that there is no helicity flux without a guide field! All reconnected field lines could form closed loops in poloidal planes, thereby linking no toroidal flux. Images from Lynch et al. (2008)

12. Observations agree, too: reconnected magnetic flux from flare ribbons matches the poloidal flux in interplanetary flux ropes. ( ASIDE: Qiu & Yurchyshyn (2005) also found a strong correlation between reconnected flux and CME speed --- evidence of hoop force from reconnected flux accelerating CME?) Qiu et al. 2006 Qiu et al. 2007

13. Simulations of undriven reconnection in Y-type, sheared fields do not clearly show upward transport of helicity. Images from Linton, DeVore, & Longcope (2009) ( But the upper boundary condition here isn’t CME-like.)

14. If CMEs are driven by an ideal MHD instability, then they drive the reconnection, rather than the other way around. In “loss of equilibrium” models, a flux rope can jump to a new altitude, driving subsequent “flare” reconnection. (Here, the hoop force from reconnected poloidal flux might still accelerate the CME – but it would be “icing on the cake.”) Forbes & Priest 1995

15. Why should reconnection primarily occur behind an erupting CME? Speculations and musings: 1.Linton & Antiochos (2005) found tunneling to be energetically favorable for high-twist flux tubes. - Is lack of tunneling evidence that pre-eruption coronal fields are not highly twisted? 2. If CMEs are triggered & driven by an ideal MHD instability, this might be “pull” reconnection. 3. Tai Phan (this meeting), citing Cowley and Owen (1989) and their own inter- planetary observations: strong shear flows inhibit reconnection. - Could the CME’s Alfvén-speed motion lead to strong shear flows along the eruption’s front? x x x v CME = v A v sh ?

16. Reconnection Onset Dependence on Velocity Shear Diffusion region Expectation: Reconnection suppressed if Velocity Shear  V L > V A [Cowley and Owen, 1989] Observed: Velocity shear  V L << V A In all solar wind reconnection events  V L = |V L1 – V L2 | V L1 V L2 L N  V L / V A A relevant slide from Tai Phan’s talk:

17. Summary 1.Reconnection redistributes helicity between mutual and self. 2.In CMEs, the large-scale mutual helicity of the coronal field changes. 3.It appears this mutual helicity primarily goes into self-helicity of the CME. 4.This might constrain pre-eruptive magnetic field configurations, as well as the reconnection process in the corona.