How Does Free Magnetic Energy Enter the Corona?

1
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.
2

• What is free magnetic energy, and who cares?
• UFree ? ?dV (BActual) 2 (BPotential) 2, and
  UFree 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.

3
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 Bn, 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.

4
Observations support the hypothesis that flares
release magnetic energy in non-potential fields.
Potential AR
Non-Potential
Schrijver et al. (2005) found potential-looking
ARs dont flare, but non-potential ARs do.
5
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).

6
Empirically, strong tangential gradients in
photospheric Bn are associated with CMEs
flares, so imply free energy.
from Falconer et al. (2006)

• 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 Bn.

7

• What is free magnetic energy, and who cares?
• UFree ? ?dV (BActual) 2 (BPotential) 2, and
  UFree 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.

8

• What is free magnetic energy, and who cares?
• UFree ? ?dV (BActual) 2 (BPotential) 2, and
  UFree 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.

9
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
• uf ? flux transport velocity (Démoulin Berger,
  2003)
• uf is related to induction eqns z-component,

(1)
10
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)!

11
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).

flux into B flux into B(P)
Possible flows (1) emergence (2) shearing,
twisting, convergence.
Sz(F) depends on photospheric (Bx, By, Bz),
(vx,vy,vz), and (Bx(P), By(P)). Measuring Sz(F)
requires vector magnetograms, an estimated flow
v, and extrapolation of the horizontal components
of B(P).
12
The spatially integrated free energy flux could
be correlated with flares CMEs.

• Knowledge of the free energy flux density Sz(F)
  allows computation of total free energy flux,
• Large ?tU(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!

13
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 (vzBh vhBz), 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.

14
This approach has been used with IVM data and
ILCT (Welsch et al. 2004) to determine flows.
15
From B(x1,x2,0) and v(x1,x2), maps of the free
energy flux can be computed (also Welsch
Fisher, 2006).
16

• What is free magnetic energy, and who cares?
• UFree ? ?dV (BActual) 2 (BPotential) 2, and
  UFree 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.

17

• What is free magnetic energy, and who cares?
• UFree ? ?dV (BActual) 2 (BPotential) 2, and
  UFree 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.

18
Free energy can enter the corona directly, by
emergence of non-potential magnetic fields (Leka
et al., 1996).
AR 8100

• The emergence of a current-carrying flux tube
  would lead to long, parallel, opposite-flux
  fibrils in magnetic fields.

19
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.

20
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
• Simulationobservation 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)

21
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.

22
Flux emergence might drive some eruptions, but is
neither sufficient nor necessary for every
eruption.

• Sometimes CMEs occur after emergence but over
  1 day following. (The coronal Alfvén crossing
  time is 102 sec.)
• Further, decayed active regions (showing no
  emergence) can erupt repeatedly.

From The Initiation of Coronal Mass Ejections
by Newly Emerging Flux, by J. Feynman and S.
Martin, JGR, v. 100, p. 3355-3367 (1995).
23
From Filament Eruptions near Emerging Bipoles,
Wang, Y.-M., and Sheeley, N. R., ApJ v. 510, p.
L157

• 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.

24
The majority of quiescent filaments form between
bipolar regions (BRs), not within them.
Data from Quiescent prominences - Where are they
formed? by Frances Tang, Solar Physics, v.
107, p. 233 (1987).

• Filaments that form between active regions were
  probably not formed by emergence. Flux
  cancellation is a possibility.

25
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.

26
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.

27
Circular filaments are also difficult to explain
in terms of emergence.
Link to a TRACE movie

• In a delta-spots sheared field, converging
  flows could easily build a circular filament over
  the PIL.

28

• What is free magnetic energy, and who cares?
• UFree ? ?dV (BActual) 2 (BPotential) 2, and
  UFree 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.

29
Aside A useful data stream of magnetograms is
essential for data driving, and entails

• Vector magnetograms LOS wont do.
• Departures from potentiality in BHORIZ must be
  observationally determined.
• A high duty cycle magnetograph, for adequate
  temporal coverage.
• Practically, space-borne magnetographs are best.
• Low cadence is probly okay
• v 1 km/s ? 10 min. for ?x 1 arc. sec.

30
Random Thoughts

• Emergence is most often observed, but aint
  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/Uf),
  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.