TRACKING MOVEMENT OF CORONAL HOLES USING MCINTOSH ARCHIVE DATA

By Jacob Harris

Mentored by Ian Hewins, Sarah Gibson and Mausumi Dikpati

Coronal Holes

• Coronal holes are regions in Corona that are cooler and less dense than the surrounding plasma.
• They can easily be seen as dark patches in extreme ultraviolet and soft x-ray images.
• These regions are created from open magnetic field lines from the sun.
• Because the field is open more particles from the corona are free to escape as solar wind.

Why Tracking Coronal Holes are Important

• Tracking coronal holes will help us better understand how the suns magnetic field works.
• Finding the rotation rates of these features, will help us make deductions of phenomena in the suns interior.
• Understanding how coronal holes migrate will help us better understand phenomena of space weather and make better predictions.

Sunspots and Relationship to Solar Cycle

• Sunspots are regions on the photosphere that are cooler than the surrounding plasma.
• These regions are created by intense magnetic flux that prevents convection and heat transfer from occurring.
• Sunspots are more common during solar maximum and less common during solar minimum.
• The number of sunspots increases and decreases through an average cycle of 11 years.

Rossby Waves

• Rossby waves are a type of inertial hydrodynamic wave that naturally occur in rotating fluids.
• They can be found on Earth and were recently discovered beneath the suns photosphere as well.
• Rossby waves on Earth are mainly driven by the Coriolis effect, both in the sea and air. However the sun’s Rossby can be magnetically driven as well.
• Magnetohydrodynamic Rossby waves, when they move retrograde, tend to be faster than hydrodynamic Rossby waves.

Differential Rotation and Carrington Rate

• The sun is not a rigid body like the Earth, so the photosphere will have different angular velocities depending on it’s latitude.
• However like the Earth, the sun will rotate fastest at the equator and slowest at the poles.
• Overall rotation rate of sun is arbitrarily defined at 26 degrees as the Carrington rate and the period of that is called a Carrington rotation.
• A Carrington Rotation is about 27.2753 days on average in a synodic frame of reference, i.e. relative to the Earth.
• The sidereal period of the Carrington rotation is about 25.38 days.

Our Main Question

How do low latitude long lived coronal holes migrate throughout solar cycle 23 and is there evidence that Rossby waves influence their motion?

Mapping Suns Magnetic Features

• In 1964, Patrick Mcintosh, a former scientists at NOAA’s Space Science Center, started creating hand-drawn maps of the sun's magnetic features.
• Over the course of his life, he made over 45 years (about 4 solar cycles) worth of maps.
• This data gave us a unique record solar activity and the evolution of the suns magnetic field.
• Recently he passed away, and his life's work was in danger of being lost.
• Thankfully, NOAA and NCAR, under the funding of the NSF, have now digitalized most if not all of these maps.

SYNOPTIC MAPS: WHAT ARE THEY?

• Map of suns solar features
• Coronal holes
• Filaments
• Magnetic polarity
• Sunspots
• Polarity Inversion Lines

HOW WE TRACK CORONAL HOLES

Calculating the Centroids of Coronal Holes

• Before we can find the slopes of the coronal holes, we must first calculate the centroids of the coronal holes in the stack plots.
• I developed a new method to do this and implemented it in Mathematica.
• The method can be broken down into a simple two step process.
1. Mathematically represent the coronal holes with parametric equations.
2. Use line integration to calculate the x and y coordinates of the coronal holes.

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PARAMETRIZING ANYTHING (USING FAST FOURIER TRANSFORM)

How These Equations are Made

• Images of the stack plots are put through a color filter to isolate the positive and negative coronal holes.
• Each stack plot image is split into smaller images, showing the latitude bands during each Carrington rotation.
• Mathematica then extracts the pixel coordinates at the edges of each of the coronal holes and performs Fourier transformations on these points.
• This creates pairs of trigonometric equations for the x and y values.
• Together these equations create curves that model the contours of the coronal holes.

Calculating Centroids Using Line Integration

• To calculate the centroid of 2-D objects it is common to use double integration.
• However, these integrals are not compatible with parametric equations.
• Fortunately, it is possible to use line integrals as a substitute.
• All we need to do is convert between the two, which can be done with Green’s Theorem.

Calculating Centroids Using Line Integration

Recall Green’s Theorem

Result

Calculating Centroids Using Line Integration

Calculating Centroids Using Line Integration

Finding the Slopes

• After the centroids of the coronal holes are calculated the coordinates the x values are converted to longitude.
• The longitudes are then plotted on Longitude vs Time Plots.
• Then to get the slopes we found the line of best fit.
• We found the slopes for all coronal hole patterns (coronal holes close together on 4 or more Carrington rotations.)

Results

• Coronal holes don’t just move from differential rotation they sometimes have local migration speeds as well.
• Seeing how much the rotation rates of these coronal holes differs from the differential rotation will tell us how much its movement is being influenced by other phenomena.
• The main cause of local migration we hypothesis is Magnetohydrodynamic Rossby waves. There is a correlation in the data which appears to support this, at least for low latitude coronal holes.

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Example (Longitude vs time plot in Carrington Rotations)

Differential Rotation Rate (Green) vs Actual Migration Rate

Final Result

Final Result

• We find on average the difference in migration velocities is 110 m/s retrograde.
• It turns out that the Rossby waves can move retrograde at velocities very similar to this.
• In particular, Magnetohydrodynamic Rosby waves can move up to 170 m/s retrograde.
• This correlation seems to imply that Rosby waves do in fact effect local migration of coronal holes.
• Higher latitude coronal holes and more solar cycles need to be analyzed to see if this relationship holds.

QUESTIONS