Transcript A spectral imager for KuaFu

Observations of coronal heating
Lidia van Driel-Gesztelyi
UCL-Mullard Space Science Laboratory,UK
Observatoire de Paris, LESIA, France
Konkoly Observatory, Hungary
Solar atmospheric layers and their temperature
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Atmospheric layers of the
Sun from the photosphere
to the corona
- WL (SOHO/MDI)
- SOHO/EIT and
- Yohkoh/SXT
observations.
Chromosphere: T~104 K
During total solar eclipse the Fraunhofer absorption line spectrum of the
photosphere is replaced by an emission line spectrum – the flash spectrum.
The emission lines have dark counter-parts in the Fraunhofer spectrum but
there are differences:
• He 5876 Å is seen in the chromospheric flash spectrum.
This is collisionally excited and the gas temperature has to be ~2x104K before
there are enough free electrons with the required energy.
this tells us the chromosphere is HOT.
Corona: T~106 K
• The first clue for a hot corona:
- spectroscopic study of a total eclipse in 1869 by C.A. Young & W. Harkness
- bright emission line at 530.3 nm (green line)
- no identification with spectral lines of known elements  coronium
• several more unidentified lines found during later eclipses (i.e. 637.5 nm - red line)
• “coronium” did not easily fit in the periodic table of elements  discredited
• 1939, W. Grotrian: The “red line” was found to be due to FeIX + (FeX) T ~ 0.5 million
1942, B. Edlén - laboratory experiment of extremely hot spark sources
the “green line” was identified as due to FeXIII+ (FeXIV) which can only exist
if T ~ 1 million.
- both are “forbidden” lines resulting of highly improbable quantum-mechanical
transitions which can only occur in low-, high-T plasma  metastable levels get
overpopulated, because collisional de-excitation is rare
- other “coronium” lines were identified as due to Fe, Ni, Ca
Temperature profile
One expects the temperature to
decrease when moving away from the
energy source. However, in the Sun
where the thermonuclear reactor in the
core exerts all the energy, not all layers
behave that way:
Tphotosphere ~ 6000 K  Ttemp_min ~ 4300
K,  slow rise in the low
chromosphere, then dramatically at the
top of it reaching Tcorona ~ n x 106 K,
then slowly falls in the outer corona
and solar wind T1 AU ~ 105 K.
What is heating the corona?
Heating by conduction, radiation convection doesn’t work, because
they are not allowed by the 2nd law of thermodynamics!
The coronal heating problem - how to solve it?
The way towards solution of the coronal heating problem is to identify
and understand the physical mechanisms responsible for heating the
corona to temperatures of n x 106 MK, several hundred times hotter
than the underlying photosphere.
Undoubtedly, there are several different heating mechanisms at work in
the corona.
The real goal is to determine the dominant one both in general and in
specific situations.
Coronal heating flowchart
Identify
Determine how
Predict the spectrum of
Predict its manifestation in
Klimchuk, 2006, SP 234, 41.
Identify
Accomplish all of
these steps, an
integrated
approach is needed!
Change model parameters
to get the best match with
real observations!
Coronal heating flowchart
Multidimensional
MHD models
No info
No info
No regard for the origin
1D hydrodynamic
models (loop)
Most coronal heating
models focus on
restricted part of the
flowchart
Klimchuk, 2006, SP 234, 41.
Energy requirement
How much energy do we need?
 The combined radiative and conductive energy losses from the corona:
 Quiet Sun:
3×105 ergs cm-2 s-1
 Active regions: 107 ergs cm-2 s-1
 Coronal holes: 8×105 ergs cm-2 s-1 (QS+solar wind!) (Withbroe and Noyes, 1977)
• The total energy required to heat the corona is 0.01% of the Sun’s total luminuous
output!
Quiet Sun X-ray luminosity: 7x1027 ergs/s (Mewe, 1972; Hudson, 1991 ).
Active Sun:
2x1029 ergs/s (Vaiana and Rosner, 1978)
Heating by acoustic waves?
• Biermann (1946) and Schwarschild (1948) proposed acoustic waves for heating
the chromosphere and the corona
• The convection zone indeed generates sound waves - we see the 5 minute (3’-5’)
oscillations.
• Athay and White (1978, 1979) UV spectroscopic data from OSO-8: the acoustic
wave flux  104 ergs cm-2 s-1 , so it is insufficient to heat the corona.
• Upward propagating sound waves steepen into shocks and are dissipated in the
chromosphere
 short-period (40-60 s) are dissipated in the lower chromosphere
 long-period waves (300 s) in the upper chromosphere…
The magnetic connection
A decade of solar magnetic variability:
X-ray levels and T correlate with surface B.
Many solar-type stars seem to have X-ray corona.
Implications: structure, heating and dynamics
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Courtesy A. Winebarger
Evolution of an AR
magnetic fields (MDI)
high chromosphere
~ 80 000 K (EIT 304 Å)
corona ~ 1.6 106 K
(SOHO/EIT 171 Å )
corona ~ 2-5 106 K
(Yohkoh/SXT)
Evolution of an active region during six solar rotation from emergence through
decay (July-Nov. 1996)
Coronal heating flowchart
Identify
Klimchuk, 2006, SP 234, 41.
Footpoint shuffling
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Energy source and mechanisms
Basic requirement from any heating theory is to identify an energy source that
can sustain the observed levels of losses.
It is widely accepted that mechanical motions in and below the photosphere
are the ultimate source of the energy.
These motions displace the footpoints of coronal magnetic field lines
stress the field
(quasi-statically)
if timescale of motion is long
compared to the end-to-end
Alfven travel time
generate waves
if the timescale of the motion is short
compared to the end-to-end
Alfven travel time
DC (direct current) heating
Dissipation of stressed
magnetic fields
AC (alternating current) heating
Dissipation of waves
Importance and role of the magnetic field
• It is clear from structuring that the main contribution to the heating is in
magnetic form - regions of strong and complex magnetic field are brighter and
hotter.
• The influence of magnetic field on coronal plasma:
- exerts a force which enables it to contain the plasma with enhanced pressure
(coronal loops)
- provides magnetic energy, which is either
stored in additional wave modes that eventually dissipate
or released directly in regions where electric currents are strong
- it channels the heat along field lines
• The coronal heating problem is different from that in the chromosphere heat is not just radiated away as it is there.
- coronal hole regions with open field lines allow energy and mass loss to the
solar wind.
- closed field lines take up various forms from bright points to active regions,
where energy is lost through radiation and conduction.
DC heating
How much energy is provided by random foot-point motions?
 
 Poynting flux:
1
F
4
BV Bh  Vh
(Note that emerging and submerging flux is not taken into account…)
Observational constraints (after Klimchuk, 2006):
• Most of the photospheric flux is in small tubes of kG strength
(e.g. Solanki,
 1993; Socas-Navarro and Sánchez Almeida, 2002)
• Most of the mixed polarity inter- network loops are low; the majority of “magnetic carpet”
loops do not reach the corona (Close et al., 2003)
 B measurements with modest resolution (pixel size  4”)
• Bv = 100 G in AR plage areas (Schrijver and Harvey, 1994)
Bv = 5-10 G in the quiet Sun (López Fuentes, p.c. by Klimchuk, 2006)
Vh = 1.0x105 cm s-1(Mueller et al., 1994; Berger & Title, 1996)
assume: Bv = Bh (not really true! Bh  tg 20º Bv = 0.36  Bv)
• Use these values in the Eq.  Poynting flux into the corona is adequate to cover the
observed energy losses both in the quiet Sun (1-3x105) and in ARs (3-8x107 ergs cm-2 s-1)
More shuffling, hotter loop…
Support for the
role of random
footpoint motions
in providing
energy for coronal
heating!
Katsukawa & Tsuneta, 2005
Hot (SXR; 2MK) loops:
Lower magnetic filling factor at
footpoints, more room to shuffle
Cool (TRACE; 1MK) loops:
Higher magnetic filling factor at
footpoints, less room to shuffle
AC heating
The energetic feasibility of AC heating is less certain…
Turbulent convection also generates a large flux of upward propagating waves:
acoustic, Alfvén, fast and slow magnetosonic plane waves, torsional, kink and sausage
flux tube (both body and surface) waves. Valery’s lecture
Theoretical and observational estimates suggest energy fluxes on the top of the
convection zone of ~ nx107 ergs cm-2 s-1 (Narain and Ulmschneider, 1996) adequate?
However, only a small fraction of waves can pass through the steep  and T gradients in
the chromosphere and transition region!
- acoustic and slow-mode waves form shocks and are strongly damped
- fast-mode waves are strongly refracted and reflected (Narain and Ulmschneider, 1996)
 Alfvén waves (incl. Alfvén-like torsional and kink tube waves) are best to penetrate into
the corona. They don’t form shocks (being transverse) and their energy is channeled
along the magnetic field (no refraction).
 Energy flux of Alfvén waves: ≤ 107 ergs cm-2 s-1 in regions of strong magnetic field.
(Ulrich, 1996; based on observed magnetic and velocity fluctuations with the correct
phase relationship for Alfvén waves).
AC heating
 Energy flux of Alfvén waves: ≤ 107 ergs cm-2 s-1 in regions of strong magnetic field.
Would be ~ sufficient to heat ARs, and more than sufficient to heat QS areas in case of
100% transmission efficiency.
However, Alfvén waves are strongly reflected in the chromosphere and TR, where vA
changes dramatically with height.
Significant transmission is possible in narrow frequency ranges, where loop resonance
conditions are satisfied (Hollweg, 1984; Ionson, 1982)
Enough for long loops (>100 Mm), but insufficient wave flux to heat the short ones
(unless they are twisted)! (Hollweg, 1985; Litwin & Rosner, 1998).
Waves generated in the corona by e.g. magnetic reconnection events have no
transmission problem (e.g. Moore et al., 1991, Longcope, 2004).
Energy in stressed m.f. is converted to wave energy in such case… DC  AC
Such waves can be very important in heating the corona away from DC energy release
sites and provide heating to the “diffuse corona”.
Coronal heating flowchart
Identify
Klimchuk, 2006, SP 234, 41.
Energy conversion
Since classical dissipation coefficients are very small in the corona, significant heating requires:
• very steep gradients
- magnetic gradients  strong currents  Ohmic dissipation, reconnection
- velocity gradients  heating by viscous dissipation
• very small spatial scales
Steep gradients are linked to:
• magnetic topology (separatrix surfaces, nulls, QSLs, separators)
• complex flow patterns
• instabilities (e.g. kink)
• loss of equilibrium
• turbulence
• resonant absorption
• phase mixing
Anomalously large transport coefficients (e.g. electrical resistivity) may be required for
significant heating (even if steep gradients are present).
Petschek-type fast reconnection requires >1000 x electrical resistivity increase (Parker, 1973,
Bishkamp, 1993), and it must be spatially localised (Kulsrud, 2001).
Coronal heating flowchart
May affect the subsequent heating!
Close coupling between the corona
and the transition region (moss,
flows during flares…)
Resonant wave absorption is
affected by the plasma response!
Klimchuk, 2006, SP 234, 41.
Coupling with the TR
In static equilibrium thermal conduction transports more than half of coronal heating
energy down to the transition region, where it is more efficiently radiated away (>, <T).
(Vesecky et al., 1979). The corona can not be treated in isolation!
 e.g. moss!
Katsukawa & Tsuneta, 2005
Time-dependent heating ((nano)flares): suddenly increased downward heat-flux +
radiation saturation  chromospheric evaporation (heated upward plasma flow)
 decreasing heating  cool condensations flow down.
 Field-aligned thermal conduction is an important factor…
Chromospheric evaporation: highest-speed upflows are short-lived and
faint  small Doppler (blue) shift (Warren & Doschek, 2005)
 Solar-B: look in the hottest lines!
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Coronal heating flowchart
If plasma is in ionisation
equilibrium state, CHIANTI
can be used; problems:
Doppler shifts integrated,
elemental abundances
unknown…
Even more complicated in
non-equilibrium case.
Klimchuk, 2006, SP 234, 41.
Observables
• Real data detect bits of pieces of the emitted spectrum, average it over space, time
and wavelength  ambiguity leading to confusion. Care is needed!
• Sub-resolution structures in , T (Orall et al., 1990; Brosius et al, 1996; Schmelz,
2002)
• Line-of-sight path in the optically thin corona can cross different large-scale structures
with different properties.
• T determination (filter-ratio method) is only valid, if the plasma is isothermal (it is not!)
(Reale & Peres, 2000; Martens et al., 2002; Schmelz et al, 2003; also Noglik et al.,
2004, 2005, Patsourakos and Klimchuk, 2005)
• Simulated observations (with model parameters varied) matched with real
observations.
DC heating
Nanoflares
Parker (1983)
• Parker (1988) proposed that the corona would be heated by the dissipation of many tangential
discontinuities arising spontaneously in the coronal magnetic field that is stirred by random
photospheric footpoint motions.
The theoretically estimated energy dissipated in a single burst was 3x1023 ergs,
10-9 times the energy of a great flare of 1032 -1033 ergs  nanoflares
• Parker noted that the mean input to the gas is not large: 3 ergs/cm3 over the reconnected
volume, 1/3 of the thermal energy density, but it is concentrated…
At the heating rate required, this would mean 30 nanoflares over a granule-size
area (1016 cm2) are present at different stages of development at any one time…
• It is beyond doubt that reconnection events occur in the corona, but also in the transition
region and chromosphere.
• A key question:
Can we detect unambiguous observational signatures of the reconnection events and quantify
their energy input and realise their efficiency for coronal heating?
Surface magnetic field
Footpoint shuffling…
The magnetic “carpet”
Démoulin &
Priest (1997)
QSLs in a bipolar region formed by 200
magnetic field concentrations.
At QSL location, the field line linkage
changes drastically, and these are preferred
places for magnetic current formation.
 reconnection, dissipation of
currents
Conditions for current generation and dissipation
• A slow random walk of flux tubes can lead to distortion of the coronal
magnetic field, producing field aligned currents that can dissipate resistively.
This only applies to closed magnetic structures where stresses can build up over time.
Field aligned currents appear when <<1
recall:  = L2/ diffusion time in the corona is only effective at length scales of a
few meters, then it is a few seconds.
• Currents may dissipate
- directly by Joule heating
- by a chain of events
involving reconnection
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Tangled coronal magnetic field
TRACE
Electric current sheet
Impulsive energy release: nanoflare in loops
Nanoflare can also be defined as impulsive
heating in a single, probably unresolvable,
loop strand.
 frequency of recurrence in a given strand
relative to the cooling time define the plasma
properties , T (e.g. Kopp & Poletto, 1993,
Tesla et al., 2005)  could result in loops in
quasi-equilibrium.
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When thinking of micro- and nano-flares, do
not only consider brightenings in small-scale
loops: XBPs or EUV BPs…
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Small-scale EUV brightenings
30,000 x 74,000 km, t= 1min.
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Simultaneous observations of the distribution and mixing of magnetic
polarities as observed by MDI (displayed as yellow and blue in the left panel)
and the EUV emission observed by CDS from plasma at the temperature of
250 000 K. The field of view is 5’ x 4’ and the actual duration is 1.5 hours.The
observations were obtained at disk center on 15 August 1996.
Explosive events and nanoflares
• Explosive events: just velocity events (red- and blueshift in spectral lines, with no
observable brightening - they also result from magnetic reconnection (Innes et al, 1997).
Energy and T of different flare classes
Eth (erg)
T (MK)
ne (cm-3 )
detection (Tmax)
Large flares
1030 - 1032
8 - 40
0.2-2 x 1011
HXR, SXR, EUV
Microflares
1027 - 1030
2-8
0.2-2 x 1010
SXR, EUV (HXR!)
Nanoflares
1024 - 1027
1-2
0.2-2 x 109
EUV
Flare distribution function
The number of flares falls off with increasing power as a flat power law
with a slope of ~-1.8 (SXR, EUV, microwave, HXR bursts, optical flares)
(e.g. Drake, 1971; Dennis, 1985, see refs. in Hudson, 1991)
dN/dW=A.W- (ergs s)-1
the normalisation factor A varies with the level of activity (Kreplin et al, 1977, Wagner, 1988)
Then the total power released by flares is:
P
Wmax
 (dN/dW)WdW 
Wmin
A
max
W  2 |W
Wmin
  2
If the power is flat (distribution of microflares have the same distribution as large
flares) and  < 2, then the total power depends on the most energetic events and
Microflares or nanoflares do not contribute much to the total power (Hudson, 1991).

Scaling laws
From physical parameters of flares, microflares and nanoflares in the
EUV, SXR and HXR wavelength groups the deduced approximate
scaling laws are:
L(T)  T1
ne(T)  T2
(neL  T2 )
p(T)  T3
(p  nexT  T2xT=T3)
EM(T)  T5
(EM  ne2x L  (T2)2xT= T5)
Eth(T)  T6
(Eth=3nekBTeV)
Aschwanden et al (2000)
Consequences:
• Correlated increase of T and EM
• Nano- and pico-flare events would be much cooler, so it is a question
whether they remain relevant for coronal heating.
However, it is the energy added which counts!!!
Flare statistics
Results are controversial,  values
found range between -1.5 and -2.6.
Are the slopes based on data obtained
in a narrow T range overestimated?
<1-hour dataset!
(Aschwanden & Charbonneau, 2002)
=-1.8
Aschwanden et al, (2000)
Discrepancies could be due to
• systematic errors in the
conversion to total flare energy
and/or to
• actual variability of the solar
event rate.
• Integration over the l.o.s.
decrease of slope.
Note that such statistics can only
be valid over a long time…
Is the power law really flat????
Uncertainties: event definition
Moving plasma clouds (in emission and absorption), oscillating and swaying
loops, propagating sound waves, rotating helical spicules, coronal dimming,
temperature changes due to cooling and thermal conduction introduce time
variability which may be completely unrelated to flare/microflare/nanoflare
processes.
Moving absorption features
Oscillating loops
Not every detected brightness change is a nanoflare
!
The power-law slope is different
for all events (2.08) and for
“flares” (1.80-1.85).
Aschwanden et al. 2000.
Observing cadence and exposure time
Data with full time resolution
Flux
Data with limited cadence
Time
Typical cadences:
30-200 sec (TRACE, EIT)
Typical exposure times: 5-20 sec (TRACE, EIT)
- The exposure time smears fast time scales out
- Poor time cadence under-samples the data
flux and number of small events is underestimated
Multi-Temperature
structure of the Sun
Blue:
EIT 171 A
T=1.0 MK
Green:
EIT 195 A
T=1.5 MK
Red:
EIT 284 A
T=2.0 MK
T
True peak temperature
Detected temperature in 171 A
What temperature response do we see in the filters ?
The flux peaks when flare temperature matches the
filter peak temperature !
Correction of Temperature bias
power-law slopes (of narrowband EUV filters)
Observations:
Uncorrected
Corrected
TRACE 171 (Aschwanden & Parnell 2002)
TRACE 171 (Parnell & Jupp 2000)
EIT 171 (Krucker & Benz 1988)
1.86+0.06
1.84-2.08
1.77-1.94
1.62+0.06
1.69+0.09
1.62+0.07
TRACE 195 (Aschwanden & Parnell 2002):
1.81+0.10
1.59+0.09
SXT (Aschwanden & Parnell 2002)
SXT (Shimizu 1995)
1.57+0.05
1.6-1.7
1.57+0.05
1.65+0.05
Nanoflares - verdict (by Marcus Aschwanden)
Since the observational value is below the critical limit of =2, this implies
that there is more total energy content in the large (catastrophic) flare events
than in small-scale energy releases, and thus the small-scale events can be
neglected in the total energy budget of energy releases, as possible
power source for coronal heating.
However, many researchers do not agree with this!
Marcus also remarks (Aschwanden, 2003):
The integrated energy flux of dissipation events should be a better measure
of the effectiveness of nanoflare heating, so the finding that the powerlaw
slope <2 is not decisive for the heating budget.
Gudiksen & Nordlund (2002)
MHD simulations of magnetic reconnection,
driven by (convective) random motion of chromospheric
loop footpoints, reproduces the filling of coronal loops with
heated plasma  a likely mechanism for coronal heating
Does this contradict Marcus’ conclusion?
Marcus: There is a continuous distribution from large-scale loops
(L>600,000 km) to small-scale loops (L<2000 km) that
show brightening (emission measure increase) as a result
of filling with heated plasma.
The basic heating mechanism has therefore to occur in the
transition region, driven by either magnetic reconnection or particle
precipitation.
Unresolved coronal nanoflares (Parker 1988) cannot explain
the emission measure increase in isothermal coronal loops.
Nanoflares are important: loop argument
• Warm (TRACE and EIT) loops are over dense to what is expected for static equilibrium
(Aschwanden et al., 1999, 2001; Winebarger et al., 2003)
or steady flow equilibrium (Patsourakos et al., 2004).
• Hot (> 2 MK; Yohkoh) loops are under dense to what is expected for static equilibrium
(Porter & Klimchuk, 1995).
• Loops of intermediate T (SXI on GOES-12) have ~ the right density (Lopez-Fuentes et al.,
2004)
Are they physically different classes of loops? There may be a different explanation…
Over and under densities are related to the ratio of the radiative and conductive cooling times:
 rad
T7/2
7
 2.9 10 2 2
 cond
n L (T)
where (T) is the optically-thin radiative loss function. For loops in equilibrium the ratio is 1
(Vesecky et al., 1979).
Cooling Time Ratio vs. Temperature (multi-stranded loop)
Hot loops:
thermal conduction
dominates over
radiation
Simulated
observations
Static
Equilibrium
Cooling track
Cooler loops:
radiation dominates
over thermal
conduction
TRACE
Yohkoh
rad/cond = T4 / (nL)2
+ Actual observations
Klimchuk (2006)
Cooling loops?
However, both SXR and EUV loops live
longer than their cooling times!!!
(Porter & Klimchuk, 1995; Winebarger et
al., 2003; Lopez Fuentes et al., 2004)
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 Loops are not monolitic structures, but a
bunch of individually heated strands, which
evolve rapidly, while their ensemble is slowevolving…
 Yohkoh detects the hottest strands in
their early, conduction-dominated phase of
cooling
 TRACE detects the warm strands in the
later, radiation-dominated phase.
Problem: Yohkoh and TRACE loops should
be co-spatial…
Large literature to show the opposite!
Cooling loops?
Repetition of nanoflare along each strand
quasi-static equilibrium conditions
• Larger events and frequencies maintain
hot strands
• Smaller events and lower frequencies
warm strands
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Hot and warm loops are not at the same
place!
However, this does not explain the under
densities of hot and over densities of warm
loops…
Aschwanden & Nightingale (2005): thin
TRACE loops are isothermal.
Where is the truth?
AC Heating
Detectability of various MHD Wave Types
MHD wave type
Observables of Oscillations
Fast MHD kink mode
x(t), transverse displacements
Fast MHD sausage mode
A(t), n_e(t), EM(t)
cospatial flux variations
Slow MHD (acoustic mode)
Acoustic waves
n_e(x-vt), EM(x-vt)
propagating density compression
Alfvenic waves
B(x-v_A*t), v1(x-v_A*t)
line broadening
Magnetoacoustic waves
(intermediate between acoustic
and Alfvenic waves)
n_e(x-vt), EM(x-vt)
(but weaker signal than for
acoustic waves)
Wave observations
Most of the theoretically known MHD oscillation and propagating
wave modes have been detected recently (since 1999), except for
the torsional mode. We can know identify the modes and measure
the periods, amplitudes, phase speeds, and propagation speeds.
Energy flux carried by MHD waves
Kinetic energy associated with a wave disturbance propagating with v1
1 2
d kin   v1 dV
2

Energy flux flowing through volume dV with footpoint area dA
along field line ds with phase speed vph
dV  dA ds  dA dt  v ph
 Energy flux F per unit area dA and time dt :
F
d kin  1 2 
  v1 v ph
dAdt  2

mass density (mean molecular weight m=1.27 for H:He=10:1)
  mn  mp ne
mean velocity v1 of disturbed mass is quantified by displacement
amplitude a and period P,
 4a 
v1   
 P
phase speed of wave vph propagating over 4 node half-lengths L:
 4L 
v ph   
 P
define velocity ratio
qa 
v1 a

v ph L
 wave energy flux
Fwave
1
 n
 q 
 m p ne qa2v 3ph  1.06105  9 e 3  a 
2
 10 cm  0.01
2
3
 v ph 

 [erg  cm2  s 1 ]
 1Mm / s 
Radiative loss rate:
Frad  ne2(T ) L
Thermal conduction rate:
Fcond  T 5 / 2
dT
2 T 7/2
 
ds
7
L
Wave energy flux compared with radiative and conductive loss rates :
in
Fwave
Frad
out
 ne  qa 
 1.0610  9 3 

 10 cm  0.01
5
 ne 
 1.0 10  9 3 
 10 cm 
Fcond
2
6
 T 
 2.6 10 

 1MK 
4
2
3



 [erg  cm 2  s 1 ]
 1Mm / s 
v ph
 L   
2
1

 22 [erg  cm  s ]
 100Mm  10 
7/2
1
 L 
2
1

 [erg  cm  s ]
 100Mm 
Alfvenic MHD Oscillations and Waves
Fast MHD
kink mode
Fast MHD
Propagating
sausage mode Alfven wave
Aschwanden et al.2002 Asai et al. 2001
Nakariakov et al. 2003
Doyle et al. 1999
Electron density ne [cm-3]
0.6 x 109
0.7x1011
0.11x109
Loop half length L =
110 Mm
10 Mm
47 Mm
Electron temperature T=
1.0 MK
15 MK
Displacement qa=a/L
0.02
0.01
Phase speed vph~vA
1.0 MK
0.015
1400 km/s
4600 km/s
Wave energy flux Fwave
7x105
7x108
1.6x105
Radiative loss rate 2Frad
8x105
4x108
6x103
Conductive loss rate 2Fcond
0.5x105
7x109
6x104
7x105
Solar wind flux Fwind
Input/output
1800 km/s
0.82
0.09
0.21
Acoustic MHD Oscillations and Waves
Slow MHD
(acoustic) mode
Wang,T.J. et al. 2002
Propagating
acoustic wave
DeMoortel et al. 2002
Electron density ne [cm-3]
1.0 x 109
0.24x109
Loop half length L =
95 Mm
8.9 Mm
Electron temperature T=
6.3 MK
1.0 MK
Displacement qa=a/L
0.05
0.02
Phase speed vph~vA
370 km/s
147 km/s
Wave energy flux Fwave
1.3x105
3.2x102
Radiative loss rate 2Frad
0.8x106
5x103
Conductive loss rate 2Fcond
3.4x107
3x105
Solar wind flux Fwind
Input/output
0.09
0.04
Wave heating - verdict
Alfvenic MHD waves carry a wave energy flux that is comparable
with radiative and conductive losses, and thus could potentially
account for coronal heating, while acoustic waves and oscillations
fall short of the heating rate requirement by ~2 orders of magnitude.
Conclusions
• The exact details of the mechanisms heating the solar corona are still unclear,
but the heating must have a magnetic origin.
• Different mechanisms may dominate in different regions.
• Coronal heating is probably due to a combination of wave and electric
current dissipation - both have ~ enough energy flux…
- (nano)flares heat the corona supplying a large fraction of the energy
- they also generate waves that propagate into extended loops and dissipate
there to provide extra heat for these large-scale structures
- waves generated by (nano)flares help to dissipate other MHD waves.
Useful observables with new instruments:
current heating
•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 or QSL 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.
Useful observables with new instruments:
waves
•Search for waves and oscillations in all SOLAR-B and 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?
I thank Jim Klimchuk and Marcus Aschwanden for their help
with the preparation of this lecture…