What causes the circles on the greens at Carnoustie?

Sprinkler system?

Probably. Or it could be the current drought revealing the remnants of ancient settlements. It’s more likely to be the sprinklers though.

I think it’s Fairy Ring: https://en.wikipedia.org/wiki/Fairy_ring

I’m pretty sure they are discolouration caused by a fungal growth.
A fairly common phenomenon, I’ve seen loads on playing pitches and golf courses.