1. Evolution of Magnetic Helicity in the Corona During Flux Emergence Anna Malanushenko, Humed Yusuf, Dana Longcope

2. Talk Plan: Emerging dipole Simple model Helicity injection Response of the corona? (N)LFFF Relation to helicity Results

3. AR’s 9002/9004: Old AR 9002 Emerging AR 9004: -Footpoints rotate and spin about each other Longcope et. al., 2007

4. Helicity injected by motion of footpoints Simple model: ++ --  br Welsch & Longcope, 2003

5. Helicity injected by motion of footpoints Simple model: ++ --  br Longcope et. al., 2007 How does the coronal field change?

6. If a flux rope is twisted too much… something like that could happen: (another event – for illustration purposes) Fan & Gibson (2003) TRACE 195A

7. Twisted thin flux tube “Tw” full revolutions per length L Force-free: J=  B=  B In this special case: 2  Tw  L/2

8. The problem… …twist is defined for thin flux tubes Solution: helicity Tw: turns about the axisTw gen ?

9. Relative Helicity For a domain of connectivity: two potential fields, two helicities H tot H Tw (Longcope & Malanushenko, 2008) H Tw =Tw gen  2

10. (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: 2  Tw  L/2 For domains of arbitrary shape: Tw gen =H Tw /  2 In a const-  domain:H Tw /  2  /2 Proposal: in general, 2  Tw gen  /2

11. Force-free field:  B=  B Can we guess  from shapes of field lines?   >0 0  <0 …sometimes yes.

12. 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

13. L&L field 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 B z

14. If  ≠const – seems to work on Low&Lou fields (Malanushenko et. al, 2009b )

15. 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

16. Use coronal loops: fit them to lines of constant-  fields (Malanushenko, Yusuf, Longcope, 2011 )

17. Accessing twist in the corona Procedure: Repeat for many time frames; keep track of  i L i (Malanushenko, Yusuf, Longcope, 2011 )

18. Accessing twist in the corona Procedure: Repeat for many time frames; keep track of  i L i (Malanushenko, Yusuf, Longcope, 2011 )

19. (Longcope et. al., 2007 ) Accessing twist in the corona Footpoints inject twist at 0.016 rad/hr Observe Tw gen increasing at 0.021 rad/hr! (Malanushenko, Yusuf, Longcope, 2011 )

20. Accessing twist in the corona Footpoints inject twist at 0.016 rad/hr Observe Tw gen increasing at 0.021 rad/hr Uncertainty: different fits and bootstrapping method 0.016 ≤ Tw gen ≤ 0.038 rad/hr

21. Side remark: free energy estimate… …could be made from reconstructed field lines via Monte Carlo sum:

22. Side remark: free energy estimate Tests on Low & Lou fields seem fine: (Longcope & Malanushenko, 2011, in review )

23. Side remark: free energy estimate [preliminary] timeline for AR’s 9002/9004:

24. 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