Solar Flares: A Brief Look into 2D Modelling

Though I am trying to pass the one-post-a-year thing by, it seems that it shall continue for a while longer. Meanwhile, let me tell you that last semester amused me greatly with respect to the lecturers allowing us to choose our own project to model. So, I went all out and thought of the most hideously complex thing I could. Magnetohydrodynamics in a solar flare (or rather, a solar flare including the magnetohydrodynamics) was what won the competition, so I set out to think about them in some detail — not too much detail though, since that would be well beyond me. Indeed, I was quite happy keeping the level of detail rather obscure and low.

However, what I found was good fun all round. Previously, for some reason I had thought that solar flares are rather well known. Now, I am far better educated — indeed, we know so little it is amusing how we do not strive to know more. After all, flares (and coronal mass ejections) control so much of our climate (even if on a ‘short term’ basis). But then, were that question up to the scientists we would probably have a network of satellites around every celestial body in our star system, measuring as much as we can and enjoying the constant influx of data.

I will keep today’s introduction short (having planned to write it since the very beginning of October), so I shall only continue with a brief description of the modelling methods I used. Namely, since solar flares take place in an environment that is very difficult to directly observe, the majority of our models are tested based on incomplete sets of observations. These models therefore can be of varying degrees of complexity, with the easiest division lying between 2D and 3D models (where 2D actually implies a 2.5D situation). These again subdivide, but I shall not go into that (this time round).

Magnetic reconnection is a term which needs to be introduced before all that. Magnetic reconnection has been described in many ways, but as it is relevant to the flares, it should be understood as the process in which magnetic flux lines break apart due to plasma stresses and other factors (the majority of which are not known) and then later reconnect at some other point in space and time. This reconnection is measured (calculated and modelled, that is) by a value that is dimensionless, and which is known as the rate of magnetic reconnection. The 2D models rely on calculating this rate, and then comparing it to observed values to assess the model’s degrees of accuracy.

The 2D models of the simplest construction were first created by Mr Sweet (I would not dare guess whether he was a Professor or a Doctor). Soon, corrections were suggested by Parker, and this model is known as the Sweet-Parker model. Their model is generally found to be too slow to accurately model the magnetic reconnection that goes on in the flare. The approximations that are made allow it to be one of the easier models to be used to study flares though.

Soon after, a slightly more complex model was created by Petschek. The Petschek model is generally considered to be more accurate, achieving rates for magnetic reconnection that are closer to the the observed values than the Sweet-Parker ones by a few orders of magnitude. The results can also be very accurate, but based on my experiments (inherently flawed in so many different ways) they are not necessarily so.

In effect, it can be said that the assumptions that the Petschek model makes are not inherently more complicated than the Sweet-Parker ones but the results are of a higher degree of accuracy. And that is the thought at which I would like to leave you today.

Reflection Geophysics

Reflection geophysics, or at least how we apply reflection in the modern day, has made me think quite a bit of how they used to do it back in the day. I have a fair idea how gravity and magnetic anomalies were interpreted and modelled in those dark times, but when we get to reflection and refraction, similar construction models are already quite a bit more computationally intensive.

If anyone does know how the first reflection surveys were modelled and interpreted in the ’20’s and ’30’s, please do inform me, but until I learn some more either through educated guesses or finding it out, I’ll try to bring up what strikes me as the difficult part there, at least when I look at it and see how we do it in the modern day.

Firstly, a number of shots in different points along a line are shot and recorded. I can imagine this recording device being a simple seismograph at some point in the beginning (or a device operating like a seismograph would, with a needle mapping the perturbations).

Secondly, we need to stack these shots, after removing noise. Now this is the difficult part — admittedly, noise removal would not be that complex although I would believe there’s trouble to be had when we’d try to use a seismograph to map a direct arrival vs a refracted/reflected one. But, this could be possible depending on how it is set up. But stacking? Without the ability to automatically add up different shot results from various locations, the method that remains possible is manually going through seismograph records and adding up the measured amplitudes to create an approximated stack (which would be, naturally, wrong in a variety of ways due to the inherent inaccuracy of manually re-graphing data which is not that accurate by itself, but it probably went through a function like this).

Thirdly, once we do have a stack, we should actually be able to base something on it, and try some interpretation.

Or, it could also be that the guys involved knew that the equipment and method was not refined enough and they met the above process somewhere half-way through with a proposed model that they then tried to fit into the ground. Say, for simplicity and ease of explanation that the scientist thought there would be largely four different layers, one of which relevant to the purposes of what he was looking for. He would then, based on the locations of shot-points and shot-gathers, calculate what those shots would look like if the subsurface actually looked like what he thought it looked like.

I am unsure how many tries and tests the second way would have to go through, but I guess that it would truly be part of one of those older things that people speak of when science was half art, and the best scientists could guess and then approximate based on their guesses so that in essence they were just proving themselves correct with data. And if it was anything like this, then I am both sorry and happy that I can use a variety of complex programs for the same purpose. Happy because I have quite a bit easier a life for myself with less chance of going horribly wrong for fifty times in a row; and sadder because the cultivation of such a skill as guessing anything as complex as that must have been very very interesting.

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