iaus 247, isla de margarita, venezuela, 17 - 22 september 2007
DESCRIPTION
On the frequency distribution of heating events in Coronal Loops, simulating observations with Hinode/XRT. Patrick Antolin 1 , Kazunari Shibata 1 , Takahiro Kudoh 2 , Daikou Shiota 2 , David Brooks 3 1 : Kwasan Observatory, Kyoto University - PowerPoint PPT PresentationTRANSCRIPT
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On the frequency distribution of heating events in Coronal
Loops, simulating observations with Hinode/XRT
Patrick Antolin1, Kazunari Shibata1, Takahiro Kudoh2 , Daikou Shiota2, David Brooks3
1: Kwasan Observatory, Kyoto University 2: National Astronomical
Observatory of Japan 3: Naval Research Laboratory
IAUS 247, Isla de Margarita, Venezuela, 17 - 22 September 2007
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IAUS 247
Universidad de Los Andes
International Astronomical Union Symposium 247: Waves & Oscillations in the Solar Atmosphere: Heating and Magneto-Seismology.
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How to heat and maintain the
plasma to such a high temperature?
The coronal heating problem
The Solar Corona
Grotrian, Edlén (1942)
point out existence of a 106
K plasma, 200 times hotter
than the photosphere.
Coronal Loops (~105 km long) seen by TRACE
Photosphere
coronaTransition region
height
T [
K]
Chromosphere
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•Mode conversion (Hollweg, Jackson & Galloway 1980; Moriyasu et al. 2004).
•Phase mixing (Heyvaerts & Priest 1983; Sakurai & Granik 1974; Cally 1991).
•Resonant absorption (Goedbloed 1983; Poedts, Kerner & Goossens 1989)
• Alfvén wave model: (Alfvén 1947; Uchida & Kaburaki 1974; Wenzel 1974).
- Alfvén waves can carry enough energy to heat and maintain a corona (Hollweg, Jackson & Galloway 1982; Kudoh & Shibata 1999).
- Waves created by sub-photospheric motions propagate into the corona and dissipate their energy through nonlinear mechanisms:
Plausible models
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• Nanoflare-reconnection model: (Porter et al. 1987; Parker 1988)
magnetic flux: current sheets
footpoint shuffling reconnection events
- Ubiquitous, sporadic and impulsive releases of energy (1024-1027 erg) that may correspond to the observed intermittency and spiky intensity profiles of coronal lines (Parnell & Jupp 2000; Katsukawa & Tsuneta 2001).
- However Moriyasu et al. (2004) showed that such profiles can also result naturally from nonlinear conversion of Alfvén waves.
Plausible models
((Parker, 1989)
How to recognize between the two heating mechanisms when they operate in the corona?
Yohkoh/SXT
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Observational facts
• Energy release processes in the Sun, from solar flares down to microflares are found to follow a power law distribution in frequency, (Lin et al. 1984; Dennis 1985).
• Main contribution to the heating may come from smaller energetic events (nanoflares) if these distribute with a power
law index > 2 (Hudson 1991).• Initial studies of small-scale brightenings have shown a
power law both steeper and shallower than -2 (Krucker & Benz 1998, Aschwanden & Parnell 2002). Hence, no definitive conclusion has been reached at present.
= 1.4 - 1.6
Shimizu et al. 1995
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Purpose• Propose a way to discern observationally between Alfvén
wave heating and nanoflare-reconnection heating.
• Diagnostic tool for the location of the heating along coronal loops.
Different X-ray intensity profiles & different frequency distribution of heating events between the models.
Link between the power law index of the frequency distribution and the mechanism operating in the loop.
Idea: Different characteristics of
wave modes
Different distribution of shocks and strengths
convective motions
Reconnection events
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• Initial conditions: – T0=104 K : constant – ρ0= 2.5×10-7 g cm-3, – p0= 2×105 dyn cm-2, – B0=2300 G with apex-to-base area
ratio of 1000. – hydrostatic pressure balance up to
800 km height. After: ρ (height)-4 (Shibata et al. 1989).
• 1.5-D MHD code
• CIP-MOCCT scheme (Yabe & Aoki 1991; Stone & Norman 1992; Kudoh, Matsumoto & Shibata 1999) with conduction + radiative losses (optically thin. Also optically thick approximation).
• Alfven wave model: Torsional Alfvén waves are created by a random photospheric driver.
ss φφ
Numerical model
ChromospherChromospheree
100000 km
PhotospherePhotosphere
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Nanoflare heating function
• Heating events can be:– Uniformly distributed along the
loop.– Concentrated at the footpoints
• Energies of heating events can be:– Uniformly distributed. – Following a power law
distribution in frequency.
Artificial energy injectionPhotospherePhotosphere
(Taroyan et al. 2006, Takeuchi & Shibata 2001)
= 1.5
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Alfvén wave heating
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Alfvén wave heating
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Alfvén wave heating
• Heating mechanism
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
Alfvén waves Slow/fast modes
Non-linear effects
Shock heating
Develop into shocks
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Alfvén wave heating
For <v2>1/2 ≿ 2 km/s a corona is created.
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Nanoflare heating
20 Mm10 Mm~ 2
Conductive flux
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Nanoflare heating
footpoint
uniform
energy input
Slow modes
Gas pressure
Fast dissipation
Shock heating
Top of TR Apex
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Alfvén wave
Simulating observations with Hinode/XRT
1”x1” F.O.V.
Apex
Top of TR
Ubiquitous strong slow
and fast shocks
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Nanoflare footpoint
Simulating observations with Hinode/XRT
1”x1” F.O.V.
Apex
Top of TR
Small peaks are levelled
out
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Nanoflare uniform
Simulating observations with Hinode/XRT
1”x1” F.O.V.
Apex
Top of TR
Flattening by thermal conduction
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Intensity histograms
I1
I2
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Alfvén wave
Intensity histograms
1”x1” F.O.V.
Apex
Top of TR
= 2.53 = 2.44
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Nanoflare footpoint
Intensity histograms
1”x1” F.O.V.
Apex
Top of TR
= 1.86 = 1.48
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Nanoflare uniform
Intensity histograms
1”x1” F.O.V.
Apex
Top of TR
= 2.66 = 0.90
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Power law index
~ close to the footpoint; decreases approaching the apex due to fast dissipation of slow modes & to
thermal conduction
= 2.1
Input:
Output:
- Footpoint- Power law spectrum in
energies
Measurement of power law index depends strongly on the location along the loop, hence on the formation temperature of the observed
emission line.
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Conclusions• Alfvén wave heated coronas:
– Ubiquitous mode conversion -> ubiquitous fast and slow strong shocks.
– Intensity profiles are spiky and intermittent throughout the corona.– Power law distribution in energies. Steep index ( > 2), roughly
constant along the corona: heating from small dissipative events.
• Nanoflare heated coronas:– Uniform heating along the loop:
• weak shocks everywhere. • Flat, uniform intensity profile everywhere: Power law index ~ 1.
– Footpoint heating:• Strong slow shocks only near the transition region. Fast dissipation and
thermal conduction dampingonly weak shocks at apex.• Spiky intensity profiles near the transition region, flattening at apex:
power law index becomes shallower the farther we are from the transition region.
• If power law energy spectrum at input, the measured index matches original input power law index ( ~ ) only near the transition region.
– Measurement of power law index is strongly dependent on location along loops, hence on temperature.
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Thank you for your attention!
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• Mass conservation
• Momentum equation (s-component)
• Momentum equation (-component)
• Induction equation( -component)
• Energy equation
1.5-D MHD Equations
Alfvén wave
generator
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• Radiative losses:- For T > 4 x 104 K:
Optically thin plasmas- For T < 4 x 104 K:
Optically thick plasmas
χTTQ =)(
(Landini & Monsignori-Fossi 1990, Anderson & Athay
1989).
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Nanoflare heating function
Localization of heating
∑=
=
=n
ii
i
stHH
stH
1
),(
),(
0
,||
expsin0 ⎟⎟⎠
⎞⎜⎜⎝
⎛ −−⎟⎟
⎠
⎞⎜⎜⎝
⎛ −
h
i
i
i
ssstt
Eτ
π ti < t < ti + τi
otherwise
• Model parameters:
E0 ={ 0.01, 0.05, 0.5 } erg cm-3 s-1; sh={ 200, 500, 1000} km;
frequency:{ 1 / 50, 1 / 34, 1 / 7 } s; τi ={ 2η, 10η , 40η } s, with η a
random number in [0,1].• Heating events can be:
– Uniformly (randomly) distributed along the loop (above 2 Mm height).
– Concentrated at the footpoints: randomly distributed in [2,20] Mm, [2,12] or [1,10] Mm height.
• Heating events can have their energies:
– Uniformly distributed: <E0> = constant
– Following a power law distribution in frequency. <E0>
(Taroyan et al. 2006)
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SXT/XRT Intensities
Filter Thin Be in XRT similar to filter Mg 3mm in SXT (used in Moriyasu et al. 2004).
2 = 2.08
1 = 1.84
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Catastrophic cooling events
Intensity flux seen with Hinode/XRT
Loss of thermal equilibrium at apex due to footpoint heating (Mueller et al. 2005, Mendoza-Briceño 2005).
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Power law index Alfvén wave
Nanoflare footpointNanoflare uniform
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Power law index
Input:
Output:
= 2.2
= 2.1
= 2.0
= 1.9
= 1.8
= 1.7
= 1.6
= 1.5