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

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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.

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Invariance arises from defining helicity with respect to a reference field.

Potential field, used as reference B

True field

Helicity can be decomposed into linkages between and within a flux systems: “mutual” and “self”, resp.

Hmut = (γ+δ)ϕAϕB/π

Self helicity, Hself, is twist internal to a flux system.RH is positive helicity, LH is negative helicity.

Mutual helicity, Hmut, quantifies linkages between flux systems.

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Hmutual has a sign given by a right-hand rule.

There is a strong similarity here with magnetic configurations before and after solar eruptions.

Hmut < 0 Hmut > 0

Image from Moore & Labonte 1980, via Hugh Hudson’s cartoon archive

In a solar eruption, underlying field becomes overlying field.

Helicity conservation implies changes in Hmutual caused by reconnection produce changes in Hself, as at right.

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Hence, we need to modify our pre- and post eruption cartoon! For instance:

The linked circles here crudely denote Hself.

Note: downward flow of helicity would limit the ability of CMEs to remove helicity (Low 2002), but could drive subsequent eruptions.

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 Hmut with Hself.

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5Note: perspective in (a) and (f) is face-on, but is edge-on in (b) through (e).

But in situations lacking artificial symmetry, how should helicity be partitioned among reconnecting flux domains?

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

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 Hmut goes primarily into Hself in the ejection.

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(Still hotly debated: (i) Does reconnection trigger eruptions? (ii) Does it directly or indirectly accelerate particles that generate X-ray emssion?)

But simulations also show most helicity going into the ejection!

MacNeice et al. (2006): 80% of pre-eruption helicity goes into the ejection.

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?

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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.

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Reconnection Onset Dependence on Velocity Shear

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Expectation: Reconnection suppressed if Velocity Shear DVL > VA [Cowley and Owen, 1989]

Observed: Velocity shear DVL << VA In all solar wind reconnection events

DVL = |VL1 – VL2|

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DVL / VA

The relevant slide from Tai Phan’s talk:

Summary1. 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.