Evolution of Magnetic Helicity

in the Corona During FluxEmergence

Anna Malanushenko, Humed Yusuf, Dana Longcope

AR’s 9002/9004:

• Old AR 9002

• Emerging AR 9004:

- Footpoints rotate and spin about each other

Longcope et. al., 2007

Helicity injected by motion of footpoints

• Simple model:

+

-

br

Welsch & Longcope, 2003

Helicity injected by motion of footpoints

• Simple model:

+

-

br

Longcope et. al., 2007

How does the coronal field change?

If a flux rope is twisted too much… something like that

could happen:

(another event – for illustration purposes)

Fan & Gibson (2003)TRACE 195A

Twisted thin flux tube

“Tw” full revolutions per length L

Force-free: J=B=B

In this special case:

2TwL/2

The problem…

• …twist is defined for thin flux tubes

• Solution: helicity

Tw: turns about the axis Twgen?

Relative Helicity

• For a domain of connectivity: two potential fields, two helicities

Htot HTw

(Longcope & Malanushenko, 2008)

HTw=Twgen2

(Malanushenko, Yusuf, Longcope, 2011)

(Malanushenko, Longcope, Fan, Gibson, 2009)

(Longcope & Malanushenko, 2008)

(e.g., Gold & Hoyle. 1960; Hood & Priest, 1979)

Twisted field: generalizations

Thin uniformly twisted tube: 2TwL/2

For domains of arbitrary shape: Twgen=HTw/2

In a const- domain: HTw/2<Li>/2

Proposal: in general, 2Twgen<iLi>/2

Force-free field: B=B

Can we guess from shapes of field lines?

>00 <0…sometimes yes.

Use coronal loops: fit them to lines of constant- fields

(Malanushenko et. al, 2009b)

Try many field lines along the line of sight for many

constant- fields

Find a best-fitting constant- field for each

individual loop

L&Lfield lines

const-field lines

If ≠const – seems to work on Low&Lou fields

(Malanushenko et. al, 2009b)

Recovered from projections of L&L lines

and photospheric Bz

If ≠const – seems to work on Low&Lou fields

(Malanushenko et. al, 2009b)

Use coronal loops: fit them to lines of constant- fields

(Malanushenko et. al, 2009b)

Try many field lines along the line of sight for many

constant- fields

Find a best-fitting constant- field for each

individual loop

Use coronal loops: fit them to lines of constant- fields

(Malanushenko, Yusuf, Longcope, 2011)

Accessing twist in the corona

• Procedure:

• Repeat for many time frames; keep track of iLi

(Malanushenko, Yusuf, Longcope, 2011)

Accessing twist in the corona

• Procedure:

• Repeat for many time frames; keep track of iLi

(Malanushenko, Yusuf, Longcope, 2011)

(Longcope et. al., 2007)

Accessing twist in the corona

• Footpoints inject twist at 0.016 rad/hr• Observe Twgen increasing at 0.021 rad/hr!

(Malanushenko, Yusuf, Longcope, 2011)

Accessing twist in the corona

• Footpoints inject twist at 0.016 rad/hr• Observe Twgen increasing at 0.021 rad/hr• Uncertainty: different fits and bootstrapping

method

0.016 ≤ Twgen ≤ 0.038 rad/hr

Side remark: free energy estimate…

…could be made from reconstructed field lines via Monte Carlo sum:

Side remark: free energy estimate

Tests on Low & Lou fields seem fine:

(Longcope & Malanushenko, 2011, in review)

Side remark: free energy estimate

[preliminary] timeline for AR’s 9002/9004:

Conclusions

• Could measure twist in coronal fields• However noisy, this measurement seems to

agree with the injection rate• Such loop reconstructions could in principle be

used to estimate free energy in AR’s