Hi there, thanks for asking. It could be related to high cholestrol level. You can ask your doctor to send a blood test to see of your triglyceride or cholestrol are elevated. Especially, people who have familial type of cholestrol problem will have this ring in their eyes.
There are some other situations which may cause ring around the pupil which is not white. Those situations are accompanied with depression, and other mental symptoms. It appears that the ring you are observing is white.
It is a god observation and I hope that if it is related to your metabolism and cholestrol, you take care of that. I wish you a good health.

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