1. Photospheric Flows and Magnetic Fields, and Their Role in CME/Flare Initiation Brian T. Welsch Space Sciences Lab, UC-Berkeley Although CMEs and flares are coronal phenomena, magnetic evolution at the photosphere must play a key role in driving the corona into an unstable state. Unfortunately, we remain largely ignorant about how photospheric magnetic evolution destabilizes the corona. I will discuss several ways that photospheric driving might destabilize the corona, as well as how observations can reveal which are most relevant to flares/CMEs.

2. Flares and CMEs are powered by magnetic energy stored the corona. NB: This also implies Lorentz forces dominate coronal dynamics. T.G. Forbes, “A Review on the Genesis of CMEs”, JGR (2000)

3. A cartoon model helps bias the mind… A quasi-stable balance can exist between outward magnetic pressure and inward magnetic tension. From Moore et al. (2001)

4. The fact that the coronal magnetic field B cor dominates the dynamics there has several additional consequences. 1. In quiet times between flares/CMEs, no Lorentz forces must be present --- otherwise, B cor would evolve to a force-free state on the (rapid) coronal Alfvén time. ==> B cor is force-free: F L = (J x B)/c = 0, so (  x B) x B = 0. 2. Hence, if left alone, the corona would self-organize into a magnetostatic state --- implying that external driving is necessary for the corona to become unstable. 3. Such forcing must come from a region where Lorentz forces are not dominant --- namely, the denser atmospheric layers at and below the photosphere, where coronal fields are anchored. Hence, photospheric flows and magnetic fields must play a key role in driving the corona to become unstable.

5. Some active regions are said to be “born bad.” If so, does driving by photospheric evolution matter? Flares cluster in time, so all is not determined at birth! This “persistence” is useful for prediction (Wheatland 2005). RHESSI flares during the Whole Heliosphere Interval (WHI)’ from Welsch et al. (2011)

6. Is magnetic evolution, by itself, correlated with flare activity? We autocorrelated magnetogram sequences for each of 42 active regions, and estimated a decorrelation rate for each.

7. We found that rapid magnetic evolution is anti-correlated with  --- but  is known to be correlated with flares! Hence, rapid magnetic evolution, by itself, is anti- correlated with flare activity.

8. Photospheric magnetic structure and flows are complex! This 13-hr sequence of line-of- sight magnetograms from the NFI/SOT instrument aboard the Hinode satellite shows shearing flows and flux emergence prior to an X-class flare. What type of photospheric evolution matters for flares / CMEs?

9. The hypothetical coronal magnetic field with lowest energy is current-free, or “potential.” For a given coronal field B cor, the coronal magnetic energy is: U   dV (B cor · B cor )/8 . The lowest energy coronal field would have current J = 0, and Ampére says 4 π J/c =  x B, so  x B min = 0. Since B min is curl-free, B min = -  ; and since  ⋅ B min = 0 =  2, the Neumann condition from photospheric B radial determines . U min   dV (B min · B min )/8  The difference U free = [U – U min ] is “free” energy stored in the corona, which can be suddenly released in flares or CMEs.

10. Unfortunately, measurements of the vector coronal field B cor (x, y, z) --- needed to infer J cor --- cannot currently be made. Without measurements of J cor, we do not know either: – the magnitude of coronal free energy U free, or – the spatial structure of coronal currents. Studying the photospheric field B ph is useful, however, since changes in B ph will induce changes in the coronal field B cor. In addition, following active region (AR) fields in time can provide information about their history and development.

11. Consequently, our ignorance regarding free magnetic energy in the corona is profound! 1. Physically, how does free energy enter the corona? – Practically, how can we detect this buildup? 2. Physically, how is this energy stored? – Practically, how can we quantify it once it’s there? 3. Physically, what triggers its release? – Practically, how can we predict when release is imminent?

12. Short answer to #1: Energy comes from the interior! But how? Image credits: George Fisher, LMSAL/TRACE EUV image of ~1MK plasma

13. What physical processes produce the electric currents that store energy in B cor ? Three options are: (i)Currents form in the interior, then emerge across the photosphere into the corona. e.g., Leka et al. 1996, Okatmoto et al. 2008 (ii)Newly emerged flux --- even if current-free --- induces currents on separatrices between new & old flux systems. e.g., Hayvaerts et al. 1977 (iii)Photospheric evolution could induce currents in already- emerged coronal magnetic fields. e.g., Longcope et al. 1996, 2005, 2007; Kazachenko et al. 2009 All models involve slow buildup of coronal energy, then sudden release.

14. For (i), note that currents can emerge in two distinct ways! a)emergence of new flux (increases total abs. flux) b) vertical transport of cur- rents in already-emerged flux NB: This does not increase total unsigned photospheric flux. Ishii et al. 1998 NB: New flux only emerges along polarity inversion lines! Fan & Gibson 2007

15. For (ii), emergence of new flux can induce currents on separatrices, even if the emerging flux is current-free. Hale’s Law implies that new flux is typically positioned favorably to reconnect with old flux. titftitf Within one hemisphere:Trans-equatorial: Not a new idea! See, e.g., Hayvaerts et al. 1977  But “interaction energy” is a new way to quantify U free :

16. For (iii), if coronal currents induced by post-emergence photospheric evolution drive flares and CMEs, then: The evolving coronal magnetic field must be modeled! NB: Induced currents close along or above the photosphere --- they are not driven from below. ==> All available energy in these currents can be released. Longcope, Sol. Phys. v.169, p.91 1996

17. Back to the catalog of our ignorance regarding free magnetic energy in the corona: 1. Physically, how does free energy enter the corona? – Practically, how can we detect this buildup? 2. Physically, how is this energy stored? – Practically, how can we quantify it once it’s there? 3. Physically, what triggers its release? – Practically, how can we predict when release is imminent?

18. Back to the catalog of our ignorance regarding free magnetic energy in the corona: 1. Physically, how does free energy enter the corona? – Practically, how can we detect this buildup? Statistically? 2. Physically, how is this energy stored? – Practically, how can we quantify it once it’s there? 3. Physically, what triggers its release? – Practically, how can we predict when release is imminent?

19. Statistical methods have been used to correlate observables with flare & CME activity, including: Total flux in active regions, vertical current (e.g., Leka et al. 2007) Flux near polarity inversion lines (PILs; e.g., Falconer et al. 2001-2009; Schrijver 2007) “Proxy” Poynting flux, v h B R 2 (e.g., Welsch et al. 2009) Subsurface flows from helioseismology (e.g., Reinard et al. 2010, Komm et al. 2011) Magnetic power spectra (e.g., Abramenko & Yurchyshyn, 2010) It’s challenging to infer physics from correlations, so I will emphasize more deterministic approaches here.

20. Back to the catalog of our ignorance regarding free magnetic energy in the corona: 1. Physically, how does free energy enter the corona? – Practically, how can we detect this buildup? Catch it in the act! 2. Physically, how is this energy stored? – Practically, how can we quantify it once it’s there? 3. Physically, what triggers its release? – Practically, how can we predict when release is imminent?

21. In principle, electric fields derived from magnetogram evol- ution can quantify the energy flux into the corona. The Poynting flux of magnetic energy into the corona depends upon E =-(v x B)/c: dU/dt = ∫ dA S z = c ∫ dA (E x B) z /4 π Coupling of B cor to B ph beneath the corona implies estimates of E there can provide boundary conditions for data-driven, time-dependent simulations of B cor.

22. One can use either  t B z or, better,  t B to estimate E or v. “Component methods” derive v or E h from the normal component of the ideal induction equation,  B z /  t = -c[  h x E h ] z = [  x (v x B) ] z But the vector induction equation can place additional constraints on E:  B/  t = -c(  x E)=  x (v x B), where I assume the ideal Ohm’s Law,* so v E: E = -(v x B)/c ==> E·B = 0 *One can instead use E = -(v x B)/c + R, if some model resistivity R is assumed. (I assume R might be a function of B or J or ??, but is not a function of E.)

23. Tracking with “component methods” constrains ψ by estimating u in the source term (  h x u B z ) · z. Methods to find ψ via tracking include, e.g.: – Local Correlation Tracking (LCT, November & Simon 1988; ILCT, Welsch et al. 2004; FLCT Fisher & Welsch 2008) – the Differential Affine Velocity Estimator (DAVE, and DAVE4VM; Schuck 2006 & Schuck 2008) (Methods to find ψ via integral constraints also exist, e.g., Longcope’s [2004] Minimum Energy Fit [MEF] method.) Welsch et al. (2007) tested some of these methods using “data” from MHD simulations; MEF performed best. Further tests with more realistic data are underway. ^

24. While  t B provides more information about E than  t B z alone, it still does not fully determine E. Faraday’s Law only relates  t B to the curl of E, not E itself; a gauge electric field  ψ is unconstrained by  t B. (Ohm’s Law does not fully constrain E.) Doppler data can provide additional info.

25. While  t B provides more information about E than  t B z alone, it still does not fully determine E. Faraday’s Law only relates  t B to the curl of E, not E itself; a gauge electric field  ψ is unconstrained by  t B. (Ohm’s Law does not fully constrain E.) Doppler data can provide additional info.

26. Doppler data helps because emerging flux might have little or no inductive signature at the emergence site. Schematic illustration of flux emergence in a bipolar magnetic region, viewed in cross-section normal to the polarity inversion line (PIL). Note the strong signature of the field change at the edges of the region, while the field change at the PIL is zero.

27. Aside: Flows v || along B do not contribute to E = -(v x B)/c, but do “contaminate” Doppler measurements. v LOS v v v =

28. Aside: Dopplergrams are sometimes consistent with “siphon flows” moving along B. MDI Dopplergram at 19:12 UT on 2003 October 29 superposed with the magnetic polarity inversion line. (From Deng et al. 2006) Why should a polarity inversion line (PIL) also be a velocity inversion line (VIL)? One plausible explanation is siphon flows arching over (or ducking under) the PIL. What’s the DC Doppler shift along this PIL? Is flux emerging or submerging?

29. For instance, the “PTD” method (Fisher et al. 2010, 2011) can be used to estimate E: In addition to  t B z, PTD uses information from  t J z in the derivation of E. No tracking is used to derive E, but tracking methods (ILCT, DAVE4VM [next talk!] ) can provide extra info! Using Doppler data improves PTD’s accuracy! For more about PTD, see Fisher et al. 2010 (ApJ 715 242) and Fisher et al. 2011 (Sol. Phys. in press; arXiv:1101.4086).

30. The “PTD” method employs a poloidal-toroidal decomposition of B into two scalar potentials. B =  x (  x B z) +  x J z B z = -  h 2 B, 4 π J z /c =  h 2 J,  h ·B h =  h 2 (  z B ) Left: the full vector field B in AR 8210. Right: the part of B h due only to J z. ^^  t B =  x (  x  t B z) +  x  t J z  t B z =  h 2 (  t B ) 4 π  t J z /c =  h 2 (  t J )  h ·(  t B h ) =  h 2 (  z (  t B )) ^^

31. How accurate is PTD? We tested it with MHD simulations of emerging flux also used by Welsch et al. (2007). Top row: Three components of E and S z from MHD code. 2nd row: PTD E and S z 3rd row: PTD + Doppler E and S z. (Note the dramatic improvement in the estimate of S z !) 4th row: PTD + FLCT E and S z. 5th row: PTD + Doppler + FLCT E and S z (Note good recovery of E x, E y, and S z, and reduction in artifacts in weak-E regions.)

32. Quantitative tests with “data” from MHD simulations show Doppler information improves recovery of E-field and Poynting flux S z. Upper right: MHD S z vs. PTD + Doppler S z. Lower right: MHD S z vs. PTD + Doppler + FLCT S z. Poynting flux units are in [10 5 G 2 km s −1 ] Upper left: MHD S z vs. PTD S z. Lower left: MHD S z vs. PTD + FLCT S z.

33. Problem: With real observations, convective blueshifts must be removed! There’s a well-known intensity-blueshift correlation, because rising plasma (which is hotter) is brighter (see, e.g., Gray 2009; Hamilton and Lester 1999; or talk to P. Scherrer). (Helioseismology uses time differences in Doppler shifts, so this issue isn’t a problem.) Because magnetic fields suppress convection, lines are redshifted in magnetized regions. Consequently, absolute calibration of Doppler shifts is essential. From Gray (2009): Bisectors for 13 spectral lines on the Sun are shown on an absolute velocity scale. The dots indicate the lowest point on the bisectors. (The dashed bisector is for λ6256.) Lines formed deeper in the atmosphere, where convective upflows are present, are blue- shifted.

34. HMI data clearly exhibit this effect. How can this bias best be corrected? PILs (found by an automated method) in AR 11117 are color- coded by HMI’s Doppler shift. Note predominance of redshifts.

35. Changes in LOS flux are quantitatively related to PIL Doppler shifts multiplied by transverse field strengths. From Faraday’s law, Since flux can only emerge or submerge at a PIL, From LOS m’gram: Summed Dopplergram and transverse field along PIL pixels. (Eqn. 2) In the absence of errors, ΔΦ LOS /Δt =ΔΦ PIL /Δt. (Eqn. 1)

36. So we must determine and correct for the bias in the zero-velocity v 0 in Doppler shifts. ΔΦ LOS /Δt should match ΔΦ PIL /Δt, but with a bias velocity v 0, := “magnetic length” of PIL

37. Back to the catalog of our ignorance regarding free magnetic energy in the corona: 1. Physically, how does free energy enter the corona? – Practically, how can we detect this buildup? Catch it in the act! 2. Physically, how is this energy stored? – Practically, how can we quantify it once it’s there? Infer existence of energy from coronal observations… 3. Physically, what triggers its release? – Practically, how can we predict when release is imminent?

38. “Potentiality” should imply little free energy, and little likelihood of flaring. Schrijver et al. (2005) found potential ARs were relatively unlikely to flare.

39. “Non-potentiality” should imply non-zero free energy, and increased likelihood of flaring. Schrijver et al. (2005) found non-potential ARs were more likely to flare, with fields becoming more potential over 10-30 hours.

40. Non-potential structures can persist for weeks, then flare or erupt suddenly. Hudson et al. (1999) The hot, “chewy nougat” in the core of this non-potential structure --- visible in SXT --- persists for months. Evidently, the corona can store free energy for long times! Some perturbation must cause this to erupt! Detecting coronal free energy is not enough to predict its release!

41. Non-potential fields are evinced by filaments / prominences, and sheared H- α fibrils & coronal loops. Non-potential structures can remain stable, even in the presence of strong perturbations. AIA movie courtesy of Tom Berger

42. Back to the catalog of our ignorance regarding free magnetic energy in the corona: 1. Physically, how does free energy enter the corona? – Practically, how can we detect this buildup? Catch it in the act! 2. Physically, how is this energy stored? – Practically, how can we quantify it once it’s there? Requires quantitative modeling of coronal field. 3. Physically, what triggers its release? – Practically, how can we predict when release is imminent?

43. The Minimum Current Corona (MCC) approach can be used to identify unstable separators. Method: Determine linkages from initial magnetogram, infer coronal currents (and free energy) based upon magnetogram evolution. Separators with large currents have been related to flare sites. Kazachenko et al. (2011)

44. Mark Cheung has been running magnetogram-driven coronal models.

45. Accurate driving of the model requires accurate estimation of the boundary electric field E.

46. The assumption that  h ·E h = 0 results in little free energy.

47. Mark gets more free energy with an ad-hoc assumption for  h ·E h -- estimates of E from observations would be better!

48. Back to the catalog of our ignorance regarding free magnetic energy in the corona: 1. Physically, how does free energy enter the corona? – Practically, how can we detect this buildup? Catch it in the act! 2. Physically, how is this energy stored? – Practically, how can we quantify it once it’s there? Requires quantitative modeling of coronal field. 3. Physically, what triggers its release? – Practically, how can we predict when release is imminent? Again, quantitative modeling of the coronal field is needed.

49. Summary We are still ignorant of the physical processes that triggers CMEs and flares. We are, however, hard at work developing the quantitative tools necessary to determine how photospheric evolution drives the corona to become unstable. Stay tuned!

50. The End

51. The ideal induction equation is:  t B x = (-  y E z +  z E y )c =  y (v x B y - v y B x ) -  z (v z B x - v x B y )  t B y = (-  z E x +  x E z )c =  z (v y B z - v z B y ) -  x (v x B y - v y B x )  t B z = (-  x E y +  y E x )c =  x (v z B x - v x B z ) -  y (v y B z - v z B y )