r = a + bθ

I’m going to refrain from using the phrase “Holy Haleakalā”, but I think I’d be perfectly justified in doing so at an image this pretty!

(click to galactify)

That mysterious looking spiral is a pre-planetary nebula* forming as the dying star LL Pegasi starts to shed its skin. The star itself is shrouded by a dense cloud of dust at the centre of the nebula. From the angle we’re seeing it, it’s essentially invisible. While a tiny amount of starlight may be responsible for some tiny amount of the illumination of this nebula, it seems to be mostly illuminated by galactic light — light from the rest of the galaxy!

The spiral shape is being created with mathematical precision (specifically, it’s an archimedian spiral**), because in the centre of this nebula are two stars. They form a binary pair, taking around 800 years to complete an orbit of each other. The material that makes up that spiral is travelling outwards at roughly 50 thousand kilometres an hour, and at that speed the spiral has a gap corresponding to 800 years or so. Mathematics really is beautiful sometimes.

Interestingly, though no one seems to have mentioned it anywhere I’ve looked, this isn’t the only place in the sky where a binary pair make such a spiral. The wolf-rayet star WR 104 and it’s companion make a very similar such spiral as they orbit each other. Seemingly any pair of stars in a roughly spherical orbit with each other, where one star is losing mass, will draw an archimedian spiral this way.

The fact that we can actually see this spiral, incidentally, is purely by chance. We’re looking straight down the central axis of the star from Earth. If we could see it from the side, it might look a lot more like other more familiar pre-planetary nebulae. The Egg Nebula, for instance. Our galaxy might be full of spirals like this, invisible to all but those who’re looking from just the right angle. In a galaxy which is itself a spiral, there’s something rather wonderfully recursive about that!

*Incidentally, for anyone who’s curious, there’s a catalog image of this object here.

**Maths geeks might already know this, and have recognised the formula in the title of this post!

Image Credit: ESA/NASA & R. Sahai

About Invader Xan

Molecular astrophysicist, usually found writing frenziedly, staring at the sky, or drinking mojitos.
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9 Responses to r = a + bθ

  1. atomicat says:

    I’m sciencing as fast as I can!
    I wonder if you might take a quick look at this and give me the benefit of yer fancy-pants book larnin’. ;D I think there’s a lot of evidence from the distribution of galaxies to the briefest “to be or not to be” of quantum physics that shows us that we are living in a fractal dimensional universe. The post that was to follow that one was going to expand on that, calling on this article for a few stones to throw at the sacred cows. So much of the mass of a proton is from the motion of it’s constituent quarks and gluons, and if there is a quark substructure then it’s reasonable to assume that most of IT’S mass is the motion of it’s constituent particles, and so on, and so on, and down the rabbit-hole we go, wheeee!!! (Go team Venture! *lol*)

  2. invaderxan says:


  3. invaderxan says:

    Or perhaps sometimes things aren’t quite as chaotic as they appear at first…

  4. invaderxan says:

    You may have mentioned before yeah… ;)
    Thanks for reading. Glad you enjoy!

  5. invaderxan says:

    Re: Recursion is a powerful concept
    Sorry — I get carried away sometimes. I usually try and keep things easy enough to understand, but I’m glad you enjoy reading anyway. Certainly rather that than dumbing things down. :)
    And catalog images… not quite. In astromomy there are a number of catalogs from surveys that have been done on various objects or with various instruments. For instance, the IRAS catalog was a catalog of objects bright in the infrared taken by the Infrared Astronomical Satellite, IRAS; and the Sharpless catalog was a collection of emission nebulae published by Stewart Sharpless in1953. Catalog numbers are the main way of identifying stars and other objects. A catalog image is simply one of the images in the catalog. :)

  6. sandalfon says:

    This is incredibly wonderful. I don’t know what I would ever do without you sharing the worlds around our world. I truly wish I could give you person – person grandmotherly hugs, you deserve all you can get.

  7. atomicat says:

    Once again, such sweet order out of such beautiful chaos. Well hell, chaos plus chaos equals order, right? :D

  8. tatjna says:

    Have I mentioned how much I enjoy your posts?

  9. maxdwolf says:

    Recursion is a powerful concept
    It’s getting to the point where I need to hit the books to keep up here (Not a complaint. I prefer material that’s over my head to that which is dumbed down.). I take it a catalog image is something like a type specimen in biology?

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