Heating the Corona and Driving the Solar Wind

1
Heating the Corona and Driving the Solar Wind
A. A. van Ballegooijen Smithsonian Astrophysical
Observatory Cambridge, MA
2
Coronal Heating
The corona has a multi-thermal structure
284 Å
195 Å
171 Å
TRACE 1998 May 19,20 (Brickhouse Schmelz 2006)
3
Coronal Heating
Differential Emission Measure Schmelz et al.
(2001) Schmelz Martens (2006)
4
Coronal Heating
Energy release occurs impulsively. There is a
power-law distribution of flare energies
From Aschwanden Parnell (2002)
5
Coronal Heating

• AIA
• Wide temperature coverage allows to determine
  DEM(T).
• Characterize spatial variability of emission as
  function of T.
• Derive number of structures N(T) along LOS,
  compare with
• prediction from current-heating model (e.g.,
  Gudiksen et al.).
• TRACE 284 observations suggest N gtgt 1 for T 2
  3 MK.
• Measure filling factors f(T) (requires density
  diagnostics).
• Isolate individual nanoflares from background
  loops.
• Study time evolution of events, especially the
  heating phase.
• Statistics, e.g. frequency distributions of
  flare energies.

6
Coronal Heating
Loops are anchored in the photosphere. Source of
energy for coronal heating lies in convection
zone
7
Coronal Heating
Magneto-convection creates flux tubes that fan
out with height and merge in the chromosphere
From Spruit (1983)
8
Coronal Heating

• Interaction of flux tubes with turbulent
  convection creates disturbances that propagate
  upward along field lines
• Periodic motions generate tube waves (e.g., kink
  modes)
• that become MHD waves in the chromosphere/corona
  .
• Random displacements of photospheric footpoints
  produce
• field-aligned electric currents (quasi-static
  disturbances)
• in coronal loops.
• Dissipation of these disturbances in the
  chromosphere/corona generally involves the
  formation of small-scale structures.

9
Wave Heating

• Slow-mode waves
• Steepen into shocks and dissipate via
  compressive viscosity.
• Important for chromospheric heating.
• Strong coupling between longitudinal and
  transverse modes
• at ß 1 surface (Bogdan et al 2003 Hasan et
  al 2005)

10
Wave Heating
Slow-mode shocks can form inside flux tubes even
for small transverse motions (1 km/s) at the
base of the photosphere
11
Wave Heating

• Alfven waves
• Flux tubes in intergranular lanes are shaken
  transversely to
• generate kink-mode waves.
• Above the height where flux tubes merge, kink
  waves are
• transformed into Alfven waves

From Cranmer van B (2005)
12
Wave Heating

• Alfven waves
• Can undergo phase-mixing and resonant absorption
  due to
• transverse variations in Alfven speed (e.g.,
  Davila 1987) or
• braided fields (Similon Sudan 1989).
• Alfven wave pressure is an important driver of
  solar wind
• (e.g., Leer, Holzer Fla 1982 Hu et al 2003).
• Wave reflection produces inward propagating
  Alfven waves.
• Nonlinear interactions between
  counter-propagating waves
• produce turbulent cascade (Matthaeus et al
  1999).

13
Wave Heating
Alfven-wave amplitudes for different outer-scale
lengths ? of the turbulence (Cranmer van
Ballegooijen 2005)
14
Wave Heating

• AIA
• Search for waves and oscillations in all AIA
  passbands.
• High cadence allows study of high-frequency
  waves.
• Search for Alfven waves track transverse motion
  of features
• in closed and open fields.
• Study evolution of coronal structures on quiet
  Sun
• Does reconnection in magnetic carpet produce
  waves that
• can drive the solar wind?

15
Current Heating
Field-aligned electric currents Required current
density in active-region loops, assuming
classical resistivity
erg s-1 cm-3
esu This would require
very thin current sheets ?B 100 G over
a distance d 0.4 km.
16
Current Heating
Formation of current sheets in closed loops
subject to random footpoint motions a)
Spontaneous formation of tangential
discontinuities by twisting or braiding of
discrete flux tubes (Parker 1972, 1983)
17
Current Heating
b) More gradual cascade of magnetic energy occurs
when footpoint mappings are continuous
functions of position (van Ballegooijen 1985,
1986 Craig Sneyd 2005)
18
Current Heating

• Dissipation of field-aligned electric currents
• Energy is released via magnetic reconnection.
• Reconnection occurs impulsively in nanoflares
  (Parker 1988)
• perhaps via resistive instabilities (e.g.,
  Galeev et al. 1981).
• Strands undergo continual heating and cooling
• observed coronal loops have an unresolved
  multi-thermal
• structure (Cargill Klimchuk 1997, 2004).
• Reconnection likely involves particle
  acceleration.
• Thermalization of energetic particles may occur
  away from
• reconnection site (e.g., at loop footpoints).

19
Current Heating
How much energy is available for
heating? Poynting flux at coronal base (L loop
length) where q 0.1 1.0 and Dcor is
random-walk diffusion const. Flux tube spreading
amplifies rotational motions
erg s-1 cm-2 consistent with
observed scaling (Schrijver et al. 2004).
20
Current Heating
Numerical simulations of current-sheet formation
and heating Mikic et al (1989) Hendrix van
Hoven (1996) ? Galsgaard Nordlund (1996)
21
Current Heating
Large-scale simulation of active region driven by
convective motions (Gudiksen Nordlund 2005)
22
Current Heating
Parallel electric currents, , at various
heights (Gudiksen Nordlund 2005)
0.0 Mm
3.0 Mm
5.6 Mm
23
Current Heating

• AIA
• Search for twisting and braiding of loops at all
  T.
• Search for evidence of small-scale reconnection.
• Relate the observed coronal structures to
  magnetic structure
• predicted by extrapolation of photospheric
  field
• Does heating occur in sheets located at
  separatrix surfaces?
• Determine how average heating depends on loop
  parameters
• (B, L, ).
• Determine how heating varies along loops.
• Evidence for energetic particles?
• Compare with theories coronal heating.