## 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