If you start your car in the morning and it makes this high pitched irritating sound, after a minute it shuts off.
Guess what, it is your secondary air pump that has failed. It is part of your emissions systems.
This happens to the 740 and the E39s.
If you need to replace it, buy the pump and the valve. They are separate parts. It usually is the valve that fails, which causes the pump to eventually fail. Another diy is on www.e38.org
or a search on bimmerforums too will give you info that you need.