Sun Dogs – what would they look like on Mars?

I was in Dorset last weekend when I saw a beautiful sundog (I took the picture on my phone – so apologies for the bad quality!) :

The sun dog (also known as a parhelion) is evidenced by a thin red line – which I added in paint by the way, it is not an atmospheric phenomenon!!! These lines form when light is diffracted by ice crystals as shown in this figure, which I borrowed from hyperphysics:

Why are parhelions formed at 22 degrees? It is because the ice crystals act as little 60 degree prisms,  as we all know the angle of minimum deviation of a prism \delta   is determined by the formula:

n=\frac{sin(\sigma+\delta)/2}{sin(\sigma)}

where n is the refractive index and \sigma is the angle of the prism. For a \sigma of 60 degrees and an n of 1.333 (the index of ice), \delta is 22 degrees. Hence the position of the parahelion.

As soon as I captured this picture I thought this would make a great blog post – but surely it’s a bit trite. I could spice it up a little by conjecturing on what would sun dogs look like on MARS! Clearly they would be different – Mars does not have much water in its atmosphere, in fact it does not have much of an atmosphere! So any refraction is likely to occur from solid CO2 – dry ice to me and you. Solid CO2 has a similar refractive index to ice, but it has a very different crystal structure and therefore results in different shape crystals – they tend to be cuboctahedra or octahedra. These shapes would actually be quite challenging to model – so I thought I would dig around a little on the internet to see if I could find any more info. To my shock I realised that not only has this been an active area of research, with one of the aims of the 1999 Mars Polar lander to find them, but that someone has even written code to predict them! Check it out on AtmoPhysics, they have the most amazing compute generated simulations.

Unfortunately the Mars Polar Lander failed to make it to the surface, so I guess we are going to have to keep wondering: are there sun dogs on Mars?

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About jakirkpatrick

I am a researcher in solar energy at the University of Oxford. I am interested in mathematics, programming and trying to understand why things work. I also like the great outdoors and riding my bike.
This entry was posted in geometry, physics. Bookmark the permalink.

2 Responses to Sun Dogs – what would they look like on Mars?

  1. Pete W says:

    Nice post, although I think it’s ‘parhelion’ not ‘para’, check out this Youtube video of spectaular sun dogs in Canada! http://bit.ly/jKaE2l

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