What Kind of Pigment Would Allow Basic Photosynthesis and Give the Skin a Blue Color

Question

Let's say there is a planet orbiting a star. The planet is much like our own, with a similar atmosphere. However, the star this planet orbits differ from out star. It differs in such a way that it emits more UV light than ours does.

On the planet orbiting this star are a race of humanoids. These humanoids have light blue skin with flushes of yellow-green. Their hair is a deep blue. They can also see in the visible light spectrum as well as the UV spectrum. These Aliens, which I'll call Silox, absorb UV light to provide extra energy. They do eat food, but this Pseudo-Photosynthesis allows them to spend more time on other tasks.

My question is, "Is there any kind of pigment that would give the skin a blue color and allow them to absorb UV light to produce energy?"

Answer 1

These Aliens, which I'll call Silox, absorb UV light to provide extra energy

So, assuming you haven't already seen this a bajillion times, read the relevant XKCD what-if on green cows. TL;DR: animals need a lot of calories, and photosynthesis doesn't supply it.

Next, regarding UV: it is very strongly attenuated by the atmosphere. Assuming your aliens live under an Earth-like atmosphere, 3-5% of the sunlight striking the earth will be UV (eg. under 400nm wavelength). Solar irradiance at the equator is about 1kW/m², so that's 30-50W of energy per square metre. The complete human body surface area is about two square metres, so that's 100W of energy max. Terrestrial photosynthetic efficiency is about 3-6%, so that's 6W of energy. A single banana contains something like 600kJ of energy, which is nearly 23 years worth of photosynthesis, at that efficiency. Even with 100% UV collection efficiency, it'd still take over 16 months to get a banana-equivalent of energy.

So, important things:

• Don't just use UV photosynthesis. There's not enough UV light.
• In fact, UV flux is basically a rounding error. You can ignore it entirely in favour of visible light photosynthesis.
• Unless you have the surface area of a tree, photosynthesis isn't going to do much for you.

There are other questions and answers on photosynthetic animals on this site that might be worth a look... if you'll forgive me for tooting my own horn, I'll point you at one of my answers on the matter, which combined larger (but not tree-size) surface area with cold-blooded metabolism, producing something that was not totally implausible.

Is there any kind of pigment that would give the skin a blue color and allow them to [photosynthesise]?

Concentrating merely on the "looks blue, does photosynthesis" bit of the question: there aren't really any naturally occurring photosynthetic pigments on Earth that would fit your needs (the closest is chlorophyll a, though that's still too green, really), but there's absolutely no reason why a blue-coloured photosynthetic organism coudl not exist, You should feel free to handwave the existence of such a pigment, and name it yourself, without fear of implausibility.

Just skip the UV bit.