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 with input from Mark G. Linton Naval Research Lab, Washington, D.C. Source of Crazy Ideas Voice of Reason Image by Pevtsov & Groening 2010

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 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? Which partition of helicity is most likely? H self in overlying flux OR H self in underlying flux

9. Back to the drawing board, to consider a better cartoon – this one with four panels! There is no real debate that “flare reconnection” occurs below an erupting ejection. If we take cartoons as evidence, then clearly the change in H mut goes primarily into H self in the ejection. Moore et al. 2001 xxx (Still hotly debated: (i) Does reconnection trigger eruptions? (ii) Does it directly or indirectly accelerate particles that generate X-ray emssion?)

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. Observations agree, too: reconnected magnetic flux from flare ribbons matches the poloidal flux in interplanetary flux ropes. 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

12. Why should reconnection primarily occur behind an erupting CME? 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 aren’t highly twisted? 2.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? 3. CMEs seem similar to “pull” reconnection. x x x ? ? vAvA

13. 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 The relevant slide from Tai Phan’s talk:

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

15. “Recurrence Process of a Large Earthquake,” from the Univ. of Tokyo’s Earthquake Prediction Research Center: Large earthquakes repeatedly occur along a large-scale fault, and the entire recurrence process includes the following stages: (I) fault healing and re-strengthening just after the previous earthquake occurred, (II) accumulation of the elastic strain energy with tectonic stress loading, (III) local concentration of deformation and rupture nucleation at the final stage of tectonic stress buildup in which an enough amount of the strain energy has been stored, (IV) mainshock earthquake rupture, and (V) rupture arrest and its aftereffect. http://wwweprc.eri.u-tokyo.ac.jp/ENG_HP/recurren/main.html

16. This slow forcing  sudden release process in flares & CMEs closely resembles that in earthquakes. Earthquake terms  Flare terms earthquakes  flares/CMEs fault  (quasi-) separator (elastic) strain energy  free magnetic energy tectonic stress loading  photospheric evolution deformation  magnetic diffusion rupture  fast reconnection mainshock earthquake rupture  flare reconnection fault healing and re-strengthening  diffusivity quenching

17. Large earthquakes flares repeatedly occur along a large-scale fault (quasi-) separator, and the entire recurrence process includes the following stages: (I) fault healing and re-strengthening diffusivity quenching just after the previous earthquake flare occurred, (II) accumulation of the elastic strain energy free magnetic energy with tectonic stress loading photospheric evolution, (III) local concentration of deformation magnetic diffusion and rupture fast reconnection nucleation at the final stage of tectonic stress buildup photospheric evolution in which an enough amount of the strain free magnetic energy has been stored, (IV) mainshock earthquake rupture flare reconnection, and (V) rupture reconnection arrest and its aftereffect. “Recurrence Process of Large Solar Flares:”