Hawk in the barn

We have a hawk in our barn, and I'm happy about that and hope he will stay.  I'm not sure what kind it is as the barn is pretty dark, but it does have a striped tail and is medium large sized.   He (she?) was there yesterday and all the pigeons were gone.   Dane thought the hawk might be trapped, so he opened the barn doors wide.  Well, he is still there today and just as I went in I saw him make a dive for a pigeon and miss.   As long as he sticks to pigeons and stays out of the ducks and chickens I'll be happy.    We have far too many of the winged rats and they make horrible messes in there.