high pitched whine for 45 seconds after starting
 

I have a 07 DTS just changed the water pump . I actually thought it may have been the problem with the whine, it was leaking and when I replaced it the whine was still there. It sound like the starter staying engaged for a while after the engine starts, but it lasts about the same amount of time and it stays if you blip the throttle. I thought maybe it was the electric booster pump, but it seems to come from higher up. Any ideas on a possible cause?