1. Estimating the magnetic energy in solar magnetic configurations Stéphane Régnier Reconnection seminar on Thursday 15 December 2005

2. Goals: estimating the magnetic energy in a magnetic configuration, finding the amount of magnetic energy which can be released during an eruption, determining where and how the magnetic energy is stored in the corona Plan: 1) What can we learn from the potential field extrapolations? 2) How does the magnetic energy differ from on model to another (potential-linear force-free, nonlinear force-free fields)? 3) What is the evolution in time of the magnetic energy in a flaring active region using the nonlinear force-free approximation?

3. Definition

4. 1) What can we learn from the potential field extrapolations? Halloween event: X17 flare on Oct. 28, 2003 The solar X-ray flux measured by GOES-10 exhibits a peak on Oct 28 at 11:10 UT characterizing the X17 flare which occurred in AR 0486 As shown by the 195Å EIT image at 11:12 UT, the X-class flare occurred in AR0486. A CME was observed by LASCO C2-C3. In addition, a fast emerging active region (AR 0488) was observed. AR0486 AR0488

5. Background image: smoo- thed MDI magnetograms on the computational grid (215x150x150) Field lines: red (green) field lines coming from the positive (negative) polarity Potential field extrapolations of AR 10486 10:00 UT 11:05 UT 11:15 UT 11:10 UT 11:20 UT

6. Potential field extrapolation of AR 10486 at 11:10 UT on Oct. 28, 2003

7. Magnetic energy of AR 0486 from the potential field We compute the magnetic energy of the potential field for every 96 min MDI magnetograms from Oct. 27 to Oct 29 and for every 1 min MDI magnetograms on Oct. 28 before and after the flare. Over this three day period, the magnetic energy (or the unsigned magnetic flux) is rising by a factor of 1.6 (from 1.1 10 34 erg to 1.8 10 34 erg). Solid line: flare time, Dashed lines separate each day (AR0486 crossed the disk center around 18:00 UT on Oct. 29) Magnetic energy of the potential field from 1 min cadence MDI magnetogram

8. Time series of 1 min cadence SOHO/MDI magnetograms during the eruption “parasitic” polarities are observed in the active region starting from the flare site and propagating away in strong field regions. Conclusion: instrumental effect

9. 2) How does the magnetic energy differ from on model to another (potential-linear force-free, nonlinear force-free fields)? Ordering: E pot < E lff, E nlff ; E lff (dH m ) < E nlff ; E m < E open

10. 3) What is the evolution in time of the magnetic energy in a flaring active region using the nonlinear force-free approximation?

11. A Moving feature Flare site Overview of AR 8210 X-ray flux: observed on May 1, 1998, site of numerous flares (4 C-class and 2 B-class flares) H  events: blue-shift events were observed at location A before and during the first series of C-class flares from 17:07 UT to 17:56 UT Photospheric motions Clockwise rotation of the sunspot Fast moving parasitic polarity IVM movie of AR8210 Vector magnetograms: time series of 15 magnetograms averaged over 15 min, observed by IVM on May 1 from 17:13 UT to 21:29 UT

12. EEEAEEeEEEAEEe Rotating sunspot Scenario of the flares: Topology of the field: dome-like separatrice surface above the red field lines Photospheric motion: clockwise rotation of the negative main polarities Reconnection process: field lines moving toward the separatrice surface due to the rotation can reconnect from the red domain to the green domain Signatures: blue-shift events at one foot-point of the reconnected field lines dome

13. Emerging and moving parasitic polarity Pre-existing magnetic configuration Emerging and moving parasitic polarity Separatrix Scenario of the flux emergence: Pre-existing topology: red field lines inside two different connectivity domains (NE and SW) separate by a separatrice surface Emergence: flux emergence of a parasitic polarity close to the separatrice Photospheric motion: fast motion of the parasitic polarity toward the South-West Reconnection process: field lines in NE approaching the separatrice surface are reconnected into SW NE SW

14. Time evolution of the magnetic energy in AR 10486 - Magnetic energy of the potential field (dashed line) - Magnetic energy of the nonlinear force-free field (solid line) Measurement of the rate of change (10 29 erg.s -1 )

15. Time evolution of the magnetic energy in AR 10486 - Magnetic energy due to transverse motion on the photosphere (Longcope 2004, MEF -Minimum Energy Fit- technique) - Free magnetic energy budget: difference between the magnetic energy of the nonlinear force-free field and of the potential field

16. Relevant quantities to study the evolution and the differences of active regions: the magnetic energy in the corona and the relative magnetic helicity (relative to the potential field). Twisted flux tubes Confined flares Two- ribbon flare Comparison between different active regions

17. Conclusions Magnetic energy budget, flare and reconnection - The most relevant quantity is: the free magnetic energy budget - The combination of 3D magnetic field geometry and magnetic energy values gives information on the nature and the location of the flare and the reconnection site - Small scale flares do not modify significantly the magnetic energy budget - The transverse photospheric motions contribute to injection of magnetic energy in the corona, they seem to be precursors of flaring activity Space Weather - Need first to understand the capabilities of the instrument ….