It's 14-16" or so and by the amount of bark missing from that "branch" and the tree being healthy recently, but now dead to the top, I'd say it had a some electricity go through it from lightning. I went back and beat on it with a hammer and it sounds pretty solid. I figured out how to take it down and that will require undercutting until that "branch" is near vertical.
I'll be dropping off the Stihl at the dealer tomorrow so they can give it a good service. Cordless will by fine for a lot of stuff but a 45-50 foot tall hickory with 14-16" diameter base is a bit much.
Plenty of hickory now plus some firewood. Made my day.
Part came in for the truck but I work tomorrow and my next three days off have the 70s for a high so I'll wait.