Wild kingdom
I think this is a red tailed hawk; I got this picture of it perching in our neighbor's tree about twenty minutes ago, after I noticed it swooping overhead. There have been a number of sightings of this bird or its buddy (there are sometimes two of them) over the last several months in our rather built-up suburban area of Arlington, Virginia. I have no idea what they're doing here, but they seem to be doing it reasonably well.
These birds are supposed to be highly territorial.
Perhaps it's a male/female pair that's been seen.
Like you, I would wonder what they are living on.
The one thing I've noticed is how adept our ravens are at driving these birds away -- it takes just two or three ravens working together to chase a red-tailed hawk (if I've correctly identified it) away.
As to what they're living on -- there are all kinds of little critters (mice, moles, shrews, rabbits) that our cat catches out back of our house. There are also some critters our cat doesn't mess with -- possum and racoons -- that the hawks will try to eat. I would be willing to bet a predatory bird could do quite well on squirrel meat alone...