Limb Darkening in AGN Jets

While writing my first astronomy paper, I just typed the following sentence:

As expected, the profiles are roughly gaussian in shape due to line of sight effects analogous to solar limb darkening.

It makes life easier for everyone when you can refer to a well known phenomenon like limb darkening to explain some point in your paper. In this case, the analogy only saved a few words, but it’s still fun. What is limb darkening? It’s this (from Wikipedia’s entry on the subject):

Notice that all around the edges, or limb, the sun appears to be less bright, or darkened. That’s the phenomenon and you might be able to guess at the explanation. When you look at the middle of the sun you’re seeing photons that have been emitted within a few hundred kilometers of it’s surface.  As you look closer to the edge, the photons are traveling through just as much material (a few hundred kilometers), but they are coming from a part of the Sun closer to the surface, further away from the Sun’s center. This part is further away from the core of the sun where all the hot nuclear reactions take place, and thus it’s cooler (and, for other reasons less dense). Since your looking at cooler, less dense gas, it’s less bright, or more darkened. Here’s another wikipedia image to help explain limb darkening:

The distance the photons travel through the sun is represented by L in this image.   As you can see, the place where the photons are coming from along the edge of the sun (point B) is cooler than the place where the photons are coming from at the sun’s center (point A).

This effect is the well known to astronomers, which is why I use it to explain this:

This is an AGN jet originating from the galaxy NGC1052 as it appears at different frequencies (Matthias Kadler took this image). Notice that along the edges of the jet the brightness dims.  By “edge of the jet” I’m referring not to the end of the jet (located on the upper left and and lower right side of the image), but to the “sides” of the jet.  This image is what I meant by limb darkening in my paper, except this time I’m referring to an AGN jet, which is much more poorly understood than our Sun! Still, most (including me) would say the limb darkening we see in AGN jets can be understood in a similar way* as the Sun’s limb darkening. However, the most well known and well studied AGN jet (emanating from galaxy M87) shows us there’s more to this story:

Notice that the center of the jet is not as bright as the edges (especially the parts of the jet on the left), thus this jet is limb brightened. So, as usual in science and especially in astronomy, there are exceptions to the rule and we have another astronomical mystery to add to the pile.

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* There are also some key differences between the limb darkening in the Sun and AGN jets.  First, solar limb darkening occurs because toward the edges of the Sun your seeing photons that have been emitted from cooler gas than when you look at the center of the Sun.  With AGN jets, it’s not clear if the plasma/gas is cooler or hotter in the outer part of the jet.   So really the only analogy that AGNs limb darkening has with solar limb darkening is that both phenomena are the result of the curvature of the surface we’re looking at (where the sun is spherical and the jet is roughly cylindrical).

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