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

Imag

e by

Pev

tsov

& G

roen

ing

2010

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

Imag

e by

Pev

tsov

& G

roen

ing

2010

It’s okay for me to over interpret results, and present crazy ideas!

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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y M

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ger

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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y M

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Hmutual also 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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on &

Anti

ocho

s 200

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?

Is one partition of helicity more likely? Hself in overlying flux OR Hself in underlying flux

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 Hmut goes primarily into Hself 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?)

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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.

(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 a

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07

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.)

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.”)

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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

vCME = vA

vsh?vsh?

Summary1. 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.