It's likely you have a mix of fescue and Kentucky bluegrass in your turf. KBG needs full sun to thrive. In the shade of a tree it will brown and thin out. The remaining fescue is not the kind of grass that fills in by itself. It must be reseeded in the fall to fill in.

Are you watering one inch per week, all at one time, in the summer heat? If not then that's a problem, too. And did you fertilize in late May?

Yes I can see how that could be true. Even though tree isn't big it does cast some shade. But it definitely moves throughout the day.
I fertilized early June. I water at least 1 inch. We've had a lot of rain this summer.
What variety can I seed here?

Hmm thinking some more. Why would I only have blue grass under the tree? The other areas as you can see are a heavy mix of fescue I think, or am I not seeing the bluegrass in the healthy picture?

could this also be a fairy ring? How could I tell?

Glad you mentioned fairy ring. I had not really noticed it in the first picture even though you mentioned it. Great chance it is a fairy ring. Not all fairy rings are bad, by the way. Can you take another picture? Stand as close as you can to still get the entire ring in the picture. I'm not sure I would do anything at this point. If you want to try an otherwise harmless organic approach you could apply ordinary ground corn all around the area and at least 20 feet out from the tree. Apply at 20 pounds per 1,000 square feet. Repeat in 3 weeks. Corn meal doubles as an organic fertilizer so there will be some benefit to the soil regardless of whether the disease disappears. Corn meal works by attracting a predatory fungus that feeds on the disease fungus. Again, it does not look terrible at least not from the angle you took the distance picture. If it looks much worse in the next photo, then you might want to try a chemical fungicide. I try to stay away from those, but the often work when properly applied. Also, what has been your daily high temp for the past week?

Also you need to pull the mulch back off the trunk of your tree. That will eventually develop into a fungal attack on the tree bark which stops the flow of nutrients up to the leaves. The tree canopy will get thinner and thinner until there are no leaves left and it dies. It can take years, but it is pretty consistent on trees with the trunks buried like that. You should be able to see the part of the trunk where the roots flare out away from the trunk.

Thank you dchall for the post and advice.
Daily high temp has barely been 82 for the past couple of weeks.
Yes I know the photo doesn't look too bad, but the grass is definitely as bad as it is in the close up photo.
Thanks for the advice on the tree. I didn't realize that the top of those main roots should show.
what chemical fungicides work? I will dry the corn meal