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.

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