Searching for Alfvén Waves
John Yoritomo
The Catholic University of America
Mentor: Dr. Adriaan van Ballegooijen
The Smithsonian Astrophysical Observatory
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Coronal Heating Problem
• Walter Grotrian in 1939 and
Bengt Edlén in 1943
discovered that the
temperature in the corona is a
few million degrees Kelvin.
• If the only process involved
was thermal in nature, this
would violate the second law of
thermodynamics, namely that
heat cannot flow from a colder
area to a hotter one.
• There must be some other
physical mechanism that heats
the corona to such high
temperatures.
Two Main Heating Theories
• Direct Current (DC) Heating Models
– Magnetic Reconnection, i.e. dissipation of magnetic stresses
– Nanoflares
– First developed by Eugene Parker (1972)
• Alternating Current (AC) Heating Models
– Waves
– Transverse Alfvén Waves are created in the photosphere and travel
up to the corona where they dissipate their energy
– First proposed by Evry Schatzman (1949) and Hannes Alfvén (1947)
– Random footpoint motion
QuickTime™ and a
YUV420 codec decompressor
are needed to see this picture.
Magnetohydrodynamic (MHD) Waves
Phase velocity perpendicular vph,x/vA
• Three modes
– Fast mode: compressional Alfvén
waves, modified by plasma pressure
– Slow mode: sound wave, modified by
the magnetic field
– Intermediate mode: Alfvén Waves
• Alfvén Waves
– Transverse waves (like waves
on a string).
– Incompressible, so no density or
pressure changes related to it.
– The magnetic tension force is
the sole driving force.
image: http://www.aldebaran.cz/astrofyzika/plazma/waves_en.html
My Research
• Look at an active region with SDO/AIA images to
find signs of transverse motions that may be
evidence for Alfvén waves.
• Using the Alfvén wave heating model developed by
van Ballegooijen et al. (2011), create models of
certain coronal loops.
• Compare the models to the observations.
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Active Region: May 19, 2012
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Observations: Loop 5 Selected
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Intensity vs. position and time
Time
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Observations: Loop 5 Selected
Plot of position of max intensity for reach time step
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Modeling Magnetic Loops
Magnetogram
• Using Coronal Modeling
System (CMS2) software, a
potential field model is
created from a magnetogram
and the corresponding
magnetic synoptic map.
• From this potential field,
models of coronal loops are
made.
Synoptic Map
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Potential Field Model
Contour of magnetogram. Red is positive polarity, green is negative polarity
Overlaid image of active region in 171 Å
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Potential Field Model
5
3
2
1
4
Included five field lines traced through potential field
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Braid Program
• Taking the loops from the CMS2
program, 3D MHD models for the
Alfvén waves in the loops are
constructed.
• Simulations yield estimate for
heating rate Q0 along with other
parameters.
Interactions of magnetic flux tube
footpoint with convective flows in the
photospheric granules. The flows distort
the shape of the flux tube, generating
transverse motions upward into the
corona.
Cross-sectional contour of different patterns of motion along any part of the loop.
Arrows point at the driver modes of the footpoints in the photosphere.
Images: van Ballegooijen et al.13
(2011)
Various Quantities Describing Model 5
The X axis of all plots is distance in Alfvén travel time:
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Movie Display of Heating Rate
Photosphere
Corona
Photosphere
QuickTime™ and a
GIF decompressor
are needed to see this picture.
• Displays the heating produced by the Alfvén waves
• Top row shows side view with respect to the x position; middle shows side
view for y position
• Blue arrows indicate where the transition region is.
• Bottom row shows cross section of heating rate at various locations.
• Waves coming from both sides; one can clearly see reflection at both
transition regions.
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Results for Loop Model 5
• Results for minimum heating rate, Qmin, and exponent, m, are
put back into another part of the CMS2 program. A new
temperature and density are calculated with these parameters
using a one dimensional loop model.
Initial temperature determined by RTV scaling laws
Nu is the damping rate (s-1)
m is exponent in expression for time averaged heating rate Q0
rstart is height in solar radii, i.e. 0.03 solar radii above the photosphere
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Coronal Loops in Center of Region
We wanted to see at what critical height the loops become thermally unstable.
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Coronal Loops in Center of Region
As height increases, the heating rate and density decrease. Interestingly, F9,
F7, and F5 are thermally stable, even as the temperature goes below 2 MK.
Loops at these heights that are not in the center become thermally unstable.
One possible explanation for this stableness is that these loops are rooted in
strong fields (i.e. sunspots), preventing thermal non-equilibrium from occurring.
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Results from Models
• There is a large increase in temperature and Alfvén
speed for loops as they go from the photosphere to the
corona. Also a large decrease in heating rate and
density.
• The heating rate is intermittent in the loops, and there is
strong reflection at the transition region.
• Thermal non-equilibrium is reached at lower heights in
the periphery of the active region than in the center.
• As height increases, the heating rate and density
decrease for center loops.
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•Perhaps the biggest obstacle for
any coronal heating model is to
match the model predictions to
the actual observations.
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Relating the Model to Observations
Top figure is a cutout of previous plot of loop 5. Bottom figure is plot of the heating rate
variations as function of time and position along the loop. Position is in Alfvén travel time.
200
2.6
1000
Time (s)
2000
2.4
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Conclusions
• There are signs that some loops may have a long wavelike structure with short waves superimposed onto it.
This agrees with the predictions for the loop heating from
the model.
• There are clear visual signs of movement in the coronal
loops, but whether these movements are Alfvén waves is
yet to be conclusively decided.
• Our model has produced interesting results that looks
towards an agreement with observations, but it is still a
long ways off.
• More work needs to be done on making the model more
realistic, and especially on extracting information from
the observations.
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The Search Continues!
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Special Thanks
•
•
•
•
Aad van Ballegooijen
Mah Asgari-Targhi
Kathy Reeves and Ed DeLuca
Trae Winter, John Sattelberger and other SAO Solar
Staff
• Fellow Solar Interns and Astro Interns and Admins
• NSF REU Grant ATM-0851866
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Further Reading
• “Heating of the Solar Chromosphere and Corona by Alfvén
Wave Turbulence” (2011) by A.A. van Ballegooijen, M.
Asgari-Targhi, S.R. Cranmer, and E.E. Deluca
• “Model for Alfvén Wave Turbulence in Solar Coronal
Loops: Heating Rate Profiles and Temperature
Fluctuations” (2012) by M. Asgari-Targhi, A.A. van
Ballegooijen.
• Physics of the Solar Corona (2004), Chapters 7-9, by M.
Aschwanden
• Solar Magnetohydrodynamics (1982), Chapters 1,2,4,6 by
E.r.Priest
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