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Searching for Alfvén Waves

John Yoritomo

The Catholic University of America

Mentor: Dr. Adriaan van Ballegooijen

The Smithsonian Astrophysical Observatory

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

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Magnetohydrodynamic (MHD) Waves

• 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

Phase velocity perpendicular vph,x/vA

Phase velo city pa ral lel vp h, z /v

A

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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

Time

Posi

tion

Intensity vs. position and 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

• 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.

Magnetogram

Synoptic Map

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Potential Field Model

Contour of magnetogram. Red is positive polarity, green is negative polarityOverlaid image of active region in 171 Å

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3

5

2

1

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Potential Field Model

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.

Images: van Ballegooijen et al. (2011)

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.

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.

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Various Quantities Describing Model 5The X axis of all plots is distance in Alfvén travel time:

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Movie Display of Heating Rate

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• 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.

Photosphere PhotosphereCorona

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Results for Loop Model 5

Initial temperature determined by RTV scaling lawsNu 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

• 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.

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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

200 1000 20002.6

2.4

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.

Time (s)

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Conclusions• There are signs that some loops may have a long wave-

like 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!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