Magnetic Helicity and Energetics in Solar Active Regions: Can we calculate them – why do we need them? Manolis K. Georgoulis JHU/APL Whistler, CA, 08/01/07 Partial Support by LWS/TR&T Grant NNG05-GM47G

Why is magnetic helicity physically important to calculate? Some evidence of the importance of magnetic helicity Linear force-free calculations of energy/helicity in solar ARs Preliminary further work Conclusions / Future work Whistler, 08/01/07 02/17 Outline

Why is helicity important to calculate? Whistler, 08/01/07 03/17 Free magnetic energy is due to electric currents Electric currents imply twisted and tangled (helical) field lines

Phillips et al. (2005)Fan (2005) Whistler, 08/01/07 04/17 Free magnetic energy vs. magnetic helicity Free magnetic energy and relative magnetic helicity both reflect departures from potentiality. However, they have one fundamental difference: Magnetic helicity is a signed quantity. Free magnetic energy is not! Large total (relative) helicity means large free energy. The opposite is not always true Both situations are capable of triggering eruptions

Whistler, 08/01/07 05/17 Some evidence of helicity’s involvement in solar eruptions Nindos & Andrews (2004) Rust & LaBonte (2005) Preflare values of constant a are higher for active regions with eruptions The helical kink instability is viewed to have triggered the above filament eruption BUT CAN WE CALCULATE HELICITY QUANTITATIVELY TO INVESTIGATE ITS IMPORTANCE?

Whistler, 08/01/07 06/17 Calculation of the helicity’s injection rate … There are concerns about u LCT. As a result, sufficient statistics might help

Whistler, 08/01/07 07/17 and the statistics of the calculation … There appears to be a threshold for (dHm/dt) below which an AR does not give a X-class flare LaBonte, Georgoulis, & Rust (2007) 393 ARs in total 57 X-flaring ARs

and the statistics of the calculation … Whistler, 08/01/07 08/17 LaBonte, Georgoulis, & Rust (2007) 393 ARs in total 57 X-flaring ARs X-flaring ARs accumulate 2 x Mx 2 of helicity within a few hours to a few days. Typical times for non X-flaring ARs range from tens to hundreds of days

Whistler, 08/01/07 09/17 Calculation of the magnetic energy and helicity budgets Georgoulis & LaBonte (2007): Derived expressions for the energy and helicity budgets (not rates) in the constant-  approx. Applied it to a sequence of VMGs from an eruptive AR (9165) and a noneruptive AR (8844) Data from Mees/IVM

Whistler, 08/01/07 10/17 Results – energy and helicity budgets Ratios (eruptive / noneruptive) For nearly identical  : The ratio of total magnetic energies scales ~  The ratios of the free magnetic energy and the relative helicity scale ~  2 THE LFF APPROXIMATION IS UNREALISTIC ! BUT MANY OF YOU MIGHT RIGHTFULLY SAY THAT…

Whistler, 08/01/07 11/17 Nonlinear force-free energy/helicity calculation From a single flux tube: To a collection of flux tubes: THIS IS ONLY THE SELF TERM

Nonlinear force-free energy/helicity calculation (cont’d) Whistler, 08/01/07 12/17 Demoulin et al. (2006) provide the mutual terms: [from Demoulin et al. (2006)]   unknown where   known from geometry To calculate L i,j close, we keep E c(mutual) positive and the minimum possible: THIS IS THE MUTUAL TERM

Whistler, 08/01/07 13/17 Preparing a vector magnetogram for calculation Partition the flux distribution using the MCT model of Barnes et al. (2005) Calculate the boundary connectivity using simulated annealing (Georgoulis & Rust 2007) Ignore connections closing beyond the FOV – focus on closed connections For each flux concentration, find average  -value from total current –  = (4  /c) (I/  ) For two connected concentrations with  -values  1 and  2, assign the mean to the connection Data from Mees/IVM

Whistler, 08/01/07 14/17 And applying the calculation to the same ARs Ratios (eruptive / noneruptive) The ratios of total magnetic energies remain nearly identical The ratio of the free magnetic energies drops to ~5, but The ratio of the total helicities remains at ~8

Whistler, 08/01/07 15/17 Actual calculation results NOAA AR 8844NOAA AR 9165 MUTUAL HELICITY DOMINATES OVER SELF HELICITY

Whistler, 08/01/07 16/17 Actual calculation results NOAA AR 8844NOAA AR 9165 MUTUAL ENERGY TERMS DOMINATE OVER SELF TERMS

A Quiz, instead of Conclusions Q: Is it possible to estimate magnetic energy / helicity budgets of ARs? A: We believe so, adopting the nonlinear force-free approximation Q: Do we need a full-fledged nonlinear force-free field extrapolation for that? A: From preliminary results, extrapolation may not be necessary, assuming a minimum magnetic free energy for the ARs Q: Is knowledge of helicity budgets important in solar ARs? A: YES – it complements the quantitative knowledge of nonpotentiality Q: Have we proved that helicity is important in solar eruptions? A: NOT YET – However, we have brought some evidence in favor of the idea Q: When can we speak with greater confidence? A: We need to determine whether: Eruptive ARs can be distinguished from noneruptive ones in terms of their helicity budgets Significant variations of helicity exist before and after eruptions

Future Work Q: Is it possible to estimate magnetic energy / helicity budgets of ARs? A: We believe so, adopting the force-free approximation Q: Do we need a full-fledged nonlinear force-free field extrapolation for that? A: From preliminary results, extrapolation may not be necessary, assuming a minimum magnetic free energy for the ARs Q: Is knowledge of helicity budgets important in solar ARs? A: YES – it complements the quantitative knowledge of nonpotentiality Q: Have we proved that helicity is important in solar eruptions? A: NOT YET – However, we have brought some evidence in favor of the idea Q: When can we speak with greater confidence? A: We need to determine whether: Eruptive ARs can be distinguished from noneruptive ones in terms of their helicity budgets Significant variations of helicity exist before and after eruptions