These are definitely carpenter ants. They have been identified by the
exterminator and by pictures on the internet. But reading these
replies, I realize that I have bushes that are right up against my
house, as well as a tree that overhangs directly over my chimney and my
attic. Maybe the flying guys are getting sucked into my fireplace or
vents? Unfortunately it's not my tree, but my neighbors, so I'd have
to negotiate cutting off the branches.
Anyway, thanks everyone for the help. Maybe when the exterminator
comes tomorrow, he'll really be able to do something. I still have not
seen any of the regular ants, just the winged ones, and they all seem
half dead.
I swear I'm moving to Siberia. I bet there are no carpenter ants
there.