Photospheric Flows and Magnetic Fields, and Their Role in CME/Flare Initiation

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. The fact that the coronal magnetic field Bcor dominates the dynamics there has several additional consequences. 1. In quiet times between flares/CMEs, no Lorentz forces must be present --- otherwise, Bcorwould evolve to a force-free state on the (rapid) coronal Alfvén time. ==> Bcoris force-free: FL = (JxB)/c = 0, so (xB) xB= 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.

4. 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)

5. 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.

6. 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.

7. 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?

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

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

10. 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?

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

12. What physical processes produce the electric currents that store energy in Bcor? Three options are: • Currents form in the interior, then emerge across the photosphere into the corona. e.g., Leka et al. 1996, Okatmoto et al. 2008 • Newly emerged flux --- even if current-free --- induces currents on separatrices between new & old flux systems. e.g., Hayvaerts et al. 1977 • 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.

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

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

15. 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

16. 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?

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? 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?

18. 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, vhBR2 (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.

19. 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?

20. In principle, electric fields derived from magnetogram evol-ution can quantify the energy flux into the corona. • The Poynting flux of magnetic energyinto the corona depends upon E =-(vxB)/c: dU/dt = ∫ dASz= c∫ dA (ExB)z /4π • Coupling of Bcor to Bph beneath the corona implies estimates of E there can provide boundary conditions for data-driven,time-dependent simulations of Bcor.

21. One can use either tBz or, better, tB to estimate E orv. • “Component methods” derive vor Eh from the normal component of the ideal induction equation, Bz/t = -c[ hxEh ]z= [ x(vx B) ]z • But the vectorinduction equation can place additional constraints on E: B/t = -c(xE)= x(vx B), where I assume the ideal Ohm’s Law,*so v<--->E: E = -(vx B)/c==>E·B = 0 *One can instead use E = -(vx 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.)

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

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

24. 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.

25. For instance, the “PTD” method (Fisher et al. 2010, 2011) can be used to estimate E: • In addition to tBz, PTD uses information from tJz 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).

26. Quantitative tests with “data” from MHD simulations show Doppler information improves recovery of E-field and Poynting flux Sz. Upper left: MHD Szvs. PTD Sz. Lower left: MHD Szvs. PTD + FLCT Sz. Upper right: MHD Szvs. PTD + Doppler Sz. Lower right: MHD Szvs. PTD + Doppler + FLCT Sz. Poyntingflux units are in [105 G2 km s−1]

27. 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?

28. “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.

29. The hot, “chewynougat” in the core of thisnon-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! Non-potential structures can persist for weeks, then flare or erupt suddenly. Hudson et al. (1999)

30. 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

31. 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?

32. 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)

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

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

35. The assumption that h·Eh = 0 results in little free energy.

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

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? 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.

38. 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!

39. The End