heating the corona and driving the solar wind

Feb. 2006 HMI/AIA Science Team Mtg. 1

Heating the Corona and Driving the Solar Wind

A. A. van BallegooijenSmithsonian Astrophysical Observatory

Cambridge, MA


Coronal HeatingThe corona has a multi-thermal structure:

TRACE1998 May 19,20(Brickhouse &Schmelz 2006)

284 Å195 Å171 Å


Coronal HeatingDifferential Emission Measure:

Schmelz et al. (2001)

Schmelz & Martens (2006)


Coronal HeatingEnergy release occurs impulsively.There is a power-law distribution of flare energies:

From:Aschwanden &Parnell (2002)


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 >> 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.


Coronal Heating

Loops are anchored in the photosphere.Source of energy for coronal heating lies in convection zone:


Coronal HeatingMagneto-convection creates “flux tubes” that fan out with height and merge in the chromosphere:

From: Spruit (1983)


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.


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 β = 1 surface (Bogdan et al 2003; Hasan et al 2005):


Wave Heating

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


Wave HeatingAlfven 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)


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).


Wave Heating

Alfven-wave amplitudes for different outer-scale lengths Λ of the turbulence (Cranmer & van Ballegooijen 2005):


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?


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:

ΔB = 100 G over a distance δ = 0.4 km.

Current Heating

110

3102 LH

5.010

6106/ Lj clasH


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):


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):


Current HeatingDissipation 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).


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).

Current Heating

LBqDvBBF corzz /241

LqB

LBBqDF photphotz

/10

/15


Current Heating

Numerical simulations of current-sheet formation and heating:

Mikic et al (1989)Hendrix & van Hoven (1996) Galsgaard & Nordlund (1996)


Current HeatingLarge-scale simulation of active region driven by convective motions (Gudiksen & Nordlund 2005):


Current Heating

Parallel electric currents, , at various heights(Gudiksen & Nordlund 2005):

Bj

0.0 Mm 3.0 Mm 5.6 Mm


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.

heating the corona and driving the solar wind

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