How Does Free Magnetic Energy Enter the Corona? Brian Welsch, Space Sciences Lab, UC Berkeley Free magnetic energy, equivalent to departures of the coronal magnetic field from the potential field (its unique minimum energy state), is thought to drive CMEs. Non- potentiality is manifested in the coronal field by filaments and sigmoids, and in the photospheric field by magnetic shear. Observations of eruptions, and pre- and post-eruptive magnetic fields, illustrate typical properties of eruptive field configurations. Photospheric shearing flows, magnetic flux emergence, and magnetic flux cancellation (via reconnection) are three mechanisms that have been proposed to increase free magnetic energy in the corona. Reviewing observations of non- potentiality and its evolution in eruptive configurations, as well as simulations of these free energy injection mechanisms, I conclude that: 1) all three mechanisms are probably at work (a circumstance I consider unfortunate!); while photospheric shear flows and magnetic flux emergence are significant sources of non-potentiality, they are inconsistent with observations of some eruptive configurations; and 3) magnetic flux cancellation does not possess the same shortcomings, and is therefore probably primarily responsible for increasing coronal free energy leading to CMEs.

What is free magnetic energy, and who cares? U Free   dV [(B Actual ) 2 – (B Potential ) 2 ], and U Free powers flares & CMEs. How can free energy enter the corona? Emergence, shearing/twisting, convergence + cancellation, or (most likely) some combination of these. How does free energy enter the corona? All are observed. Emergence cannot explain some field configurations. Which among possible processes is… … most prevalent? Probably emergence. … most relevant to space weather? More research, with good event statistics, is needed! Hinode should help, as will useful data streams from instruments.

Free energy is the difference in energy between the actual and potential B fields. For a given field B, the magnetic energy is U   dV (B · B)/8 . The lowest energy the field could have would match the same boundary condition B n, but would be current-free (curl-free), or “potential:” B (P) = - , with  2  = 0. Then U (P)   dV (B (P) · B (P) )/8  =  dA (  ·  n  )/8  The difference U (F) = U – U (P) is the energy available to power flares and CMEs.

Observations support the hypothesis that flares release magnetic energy in non-potential fields. Schrijver et al. (2005) found “potential-looking” ARs don’t flare, but non-potential ARs do. Potential ARNon-Potential

Observations support the hypothesis that flares release magnetic energy in non-potential fields. Pevtsov et al. (1996) saw this “sigmoid- to- arcade” evolution. Sigmoids are now widely viewed as signs of non-potentiality (Canfield et al., 1999).

Empirically, strong tangential gradients in photospheric B n are associated with CMEs & flares, so imply free energy. Schrijver (submitted) all large flares originate near large patches of strong-field gradients, which can be explained by emergence. Flux cancellation can also explain large gradients in B n. from Falconer et al. (2006)

What is free magnetic energy, and who cares? U Free   dV [(B Actual ) 2 – (B Potential ) 2 ], and U Free powers flares & CMEs. How can free energy enter the corona? Emergence, shearing/twisting, convergence + cancellation, or (most likely) some combination of these. How does free energy enter the corona? All are observed. Emergence cannot explain some field configurations. Which among possible processes is… … most prevalent? Probably emergence. … most relevant to space weather? More research, with good event statistics, is needed! Hinode should help, as will useful data streams from instruments.

What is free magnetic energy, and who cares? U Free   dV [(B Actual ) 2 – (B Potential ) 2 ], and U Free powers flares & CMEs. How can free energy enter the corona? Emergence, shearing/twisting, convergence + cancellation, or (most likely) some combination of these. How does free energy enter the corona? All are observed. Emergence cannot explain some field configurations. Which among possible processes is… … most prevalent? Probably emergence. … most relevant to space weather? More research, with good event statistics, is needed! Hinode should help, as will useful data streams from instruments.

The change in the actual magnetic energy is given by the Poynting flux, c(E x B)/4 . In ideal MHD, E = -(v x B)/c, so: u f  flux transport velocity (Démoulin & Berger, 2003) u f is related to induction eqn’s z-component, (1)

A “Poynting-like” flux can be derived for the potential magnetic field, B (P), too. B evolves via the induction equation, meaning (ideally) its topology is conserved. B (P) does not necessarily obey the induction equation, meaning its topology can change! But energy change is Poynting-like: from equations (1)  (2)!

The “flux” of free energy into the corona can be quantified in terms of fields, B & B (P), and flows, v, on the coronal boundary (Welsch 2006). S z (F) depends on photospheric (B x, B y, B z ), (v x,v y,v z ), and (B x (P), B y (P) ). Measuring S z (F) requires vector magnetograms, an estimated flow v, and extrapolation of the horizontal components of B (P). Possible flows: (1) emergence; (2) shearing, twisting, convergence. = flux into B – flux into B (P)

The spatially integrated free energy flux could be correlated with flares & CMEs. Knowledge of the free energy flux density S z (F) allows computation of total free energy flux, Large  t U (F) could lead to flares/CMEs. –Small flares can dissipate U (F), but should not dissipate much magnetic helicity. –Hence, tracking helicity flux is important, too!

Several techniques exist to estimate velocities that determine the free energy flux (Welsch et al. 2007). Time series of vector magnetograms can be used to compute (v z B h – v h B z ), to estimate the free energy flux. Mechanisms of free energy injection can be tested, e.g., –flux emergence –rotating sunspots; shear flows along PILs –convergence & flux cancellation Data from FPP on SOT/Hinode, & HMI on SDO should allow determination of the prevalence of each process.

This approach has been used with IVM data and ILCT (Welsch et al. 2004) to determine flows.

From B(x 1,x 2,0) and v(x 1,x 2 ), maps of the free energy flux can be computed (also Welsch & Fisher, 2006).

What is free magnetic energy, and who cares? U Free   dV [(B Actual ) 2 – (B Potential ) 2 ], and U Free powers flares & CMEs. How can free energy enter the corona? Emergence, shearing/twisting, convergence + cancellation, or (most likely) some combination of these. How does free energy enter the corona? All are observed. Emergence cannot explain some field configurations. Which among possible processes is… … most prevalent? Probably emergence. … most relevant to space weather? More research, with good event statistics, is needed! Hinode should help, as will useful data streams from instruments.

What is free magnetic energy, and who cares? U Free   dV [(B Actual ) 2 – (B Potential ) 2 ], and U Free powers flares & CMEs. How can free energy enter the corona? Emergence, shearing/twisting, convergence + cancellation, or (most likely) some combination of these. How does free energy enter the corona? All are observed. Emergence cannot explain some field configurations. Which among possible processes is… … most prevalent? Probably emergence. … most relevant to space weather? More research, with good event statistics, is needed! Hinode should help, as will useful data streams from instruments.

Free energy can enter the corona directly, by emergence of non-potential magnetic fields (Leka et al., 1996). The emergence of a current-carrying flux tube would lead to long, parallel, opposite-flux fibrils in magnetic fields. AR 8100

Free energy can enter the corona indirectly, by introducing new flux into a pre-existing B field. Generally, currents flow along the separatrix between the new & old flux systems, even if both flux systems are current free. Longcope et al. (2005) studied an observed emergence that created currents. Abbett et al. (2004 [JASTP]) also studied emergence with differently oriented pre-existing B fields, and resulting currents.

Free energy can be introduced to the coronal field by flows that act on fields that have already emerged. Twisting motions, e.g., rotating sunspots –Observed: Nightingale et al. (this session) Shearing along polarity inversion lines –Simulations: Lynch et al. (this session) –Observations: Deng (this session) General footpoint displacements –Simulation+observation: Longcope (this session) Convergence & flux cancellation –Observations: Martin (1998) cancellation is “essential” for filament formation –Simulations: Linker et al. (2001), Amari et al. (2003a,2003b)

There are varied and complex ways free energy enters the solar corona. Emergence is probably the most frequently observed process, but is not necessarily the proximate cause of flares or CMEs. No single process can explain all observed eruptive configurations. Therefore, one should not talk about “the” trigger of flares or CMEs – there are many. Rather, we should determine which process is dominant.

Flux emergence might drive some eruptions, but is neither sufficient nor necessary for every eruption. From “The Initiation of Coronal Mass Ejections by Newly Emerging Flux,” by J. Feynman and S. Martin, JGR, v. 100, p (1995). Sometimes CMEs occur after emergence – but over ~1 day following. (The coronal Alfvén crossing time is ~10 2 sec.) Further, decayed active regions (showing no emergence) can erupt repeatedly.

“It has been suggested in previous studies that quiescent prominences and filaments erupt preferentially in the vicinity of emerging magnetic flux. … Because eruptions sometimes occur in the absence of any observable flux emergence, however, we conclude that new flux may act as a strong catalyst but is not a necessary condition for filament destabilization.” From “Filament Eruptions near Emerging Bipoles,” Wang, Y.-M., and Sheeley, N. R., ApJ v. 510, p. L157:

The majority of quiescent filaments form between bipolar regions (BRs), not within them. Filaments that form between active regions were probably not formed by emergence. Flux cancellation is a possibility. Data from “Quiescent prominences - Where are they formed?” by Frances Tang, Solar Physics, v. 107, p. 233 (1987).

Many examples of such inter-active-region filatments can be found. An overlay of the line- of- sight magnetic field and a chromospheric H  image reveals filaments between ARs.

Quiescent filaments are longer- lived than AR filaments, but can also produce halo CMEs. Two filaments from the previous slide erupted on 05 June 1998.

Circular filaments are also difficult to explain in terms of emergence. In a delta-spot’s sheared field, converging flows could easily build a circular filament over the PIL. Link to a TRACE movie

What is free magnetic energy, and who cares? U Free   dV [(B Actual ) 2 – (B Potential ) 2 ], and U Free powers flares & CMEs. How can free energy enter the corona? Emergence, shearing/twisting, convergence + cancellation, or (most likely) some combination of these. How does free energy enter the corona? All are observed. Emergence cannot explain some field configurations. Which among possible processes is… … most prevalent? Probably emergence. … most relevant to space weather? More research is needed! Hinode should help. To get good event statistics, user-friendly data streams from instruments are also necessary.

Aside: A “useful” data stream of magnetograms is essential for data driving, and entails: Vector magnetograms; LOS won’t do. –Departures from potentiality in B HORIZ must be observationally determined. A high “duty cycle” magnetograph, for adequate temporal coverage. –Practically, space-borne magnetographs are best. Low cadence is prob’ly okay –v ~ 1 km/s  10 min. for  x ~ 1 arc. sec.

Random Thoughts Emergence is most often observed, but ain’t necessarily the “relevant” process. (Eruptions come days later, or occur without flux emergence.) Distinguish flux ropes that emerge to form ARs from flux ropes that are observed in CMEs --- these latter flux ropes can form in the eruption. Submergence is both inferred (no infinite pileup) and observed (Chae et al. 2004). Address Lites (2005): observation of concave-up field at PIL prior to filament formation does not imply emergence of a flux rope. Would expect convex  concave evolution as top, core, then bottom emerge. And how do filaments reform in the same channel? Does Longcopean free energy monotonically increase? A type of topological entropy, if you will? No clear reason why free energy should drive an eruption, cf., Boltzmann factor, exp(-  U/U f ), where  U is energy required to expel a flux rope. Review Schrijver et al. (2005): strong gradients, emergence. Free energy is not enough! Helicity is conserved, but small flares can disspate free energy. Only ejection can remove helicity.