It's very difficult to see what you mean by the light rings, but I'm guessing you mean the slightly different shades of grey on the darker part of the background?

If that is what you mean, I think it's due to a small variation of tone over a large area. Because there are limited colour values available (in greyscale 256 from black to white), small variations over a large area can only be represented by adjacent bands of different shade.

Unfortunately, the human eye (or rather, brain) plays a trick on you by accentuating the contrast between one band and the next: it makes each band appear darker where it adjoins the lighter shade, and lighter where it adjoins the darker shade. So it looks like you have light and dark bands across that area.

You can eliminate this with some blur in postwork, or in the render with a bit of Gaussian post-filter, or on the background material shader by adding a little noise.

"If I were a shadow, I know I wouldn't like to be half of what I should be."
Mr Otsuka, the old black tomcat in Kafka on the Shore (Haruki Murakami)