About Me

I currently attend the University of St. Andrews and will receive my M.Maths at the end of the 2006-2007 academic year. I used to attend Willamette University. I was raised in Portland, OR, which is why I turned out to be a fairly dedicated portlandophile. I read too much, listen to way too much music, and watch way too many movies. You can contact me at ac362 (at) st-andrews (dot) ac (dot) uk



The Project: Measuring Twist

This summer I have been working with Dr. Nandi and Dr. Canfield at Montana State University to measure twist in solar active regions. Traditionally the force-free field parameter alpha has been used in the force-free field equation (curl B = alpha * B) to measure twist. This assumes that the magnetic field in the photosphere is force free which is not necessarily true - the plasma beta is roughly equal to one. We attempted to determine the twist in solar ARs from numerical flux-tube fitting. We were also interested in investigating the twist of substructures inside the flux-tubes.



Steps Toward Finding Twist

Previous work by Jessica Windschitl had been done on a program to compute both the twist and the kink in vector magnetograms. My first task was to determine ways to better analyze the data. For instance, the center of the tube was found through simple flux weighting after removing all values below the 3-sigma level (300 G). After looking at a wide range of magnetograms and looking at every threshold between 50G and about 2/3 of the maximum flux, we determined that a cutoff of 50% of the maximum flux was the best way to determine the flux weighted centroid. Another important consideration we found was which method we were using to fit the data with. After reviewing the fitting programs we had access to we found which were most appropriate to our equations and data.

We next tried looking at every pixel surrounding our flux weighted centroid. Perhaps these were better choices for the actual center of the flux tube? Looking at each of these pixels, we were faced with two methods of determining which is the "best" pixel. The first was a simple statistical consideration. Maybe we should choose the pixel with the lowest residual? The other was a theoretical consideration. In our fitting of twist, we used the formula Btheta / Bz = q * r + c, where q represents twist, r represents distance from the center, and c is simply a fitting constant. Clearly the smallest c fits with theory best (since, in theory, c should equal 0). Upon examining the two options we came to the conclusion to use the smallest c value. This did indeed lead to better estimates of the center of the flux tube.



Steps Toward Finding Kink

Once we determined where the center was, we could determine the kink. The equation to determine kink is a Taylor series approximation of another equation. This series is Bz = B0 * (1 - mu * r^2 - p * r^4 - ...). We had been using a lowest-order truncation, only keeping the r^2 term. We considered retaining higher order terms in our fits. It was found that not only did fitting procedures have occasional trouble with it but that it often led to fits that were unrealistic. Thus, we decided to keep only the r^2 term.



Analyzing The Data

Next, we decided to analyze the data using our procedure. Along with a function to determine alpha-best and several other parameters, we ran our code on all the HSP magnetograms available to us. We initially trimmed the data by removing all active regions above a latitude of +/- 40 degrees and with a CMD of more than +/- 50 degrees. Additionally, all analyzed magnetograms that could not converge on a kink or twist value were removed. After, we ran another program that gave us the total flare flux for each active region, giving us more data to play with.



Looking At Fragments

An important consideration in all this is the fragmentation of the flux tubes. Using code from Alex Russell, I ran a tessellation program on the HSP magnetograms.