Learjet 45 Captain reported a bird strike and engine roll back after takeoff. The flight crew requested priority handling and made an air turn back and precautionary landing at departure airport.

Narrative

Departing Runway X at ZZZ; crew only to pickup passengers. Normal engine start/taxi & lineups. Rolling takeoff with full fuel (6;040 pounds). As I rotated the aircraft to initiate the climb; something flashed past the right window and we heard an impact. I elected to continue the takeoff; but at a lower deck angle than normal. Shortly after the right engine started making an unusual buzzing sound and the FO (first officer) said we had a bird strike. I pushed the engines into APR for and told the tower we hit a bird; right engine was rolling back; we were entering left traffic for an immediate landing and to roll the trucks. Tower cleared us to land on Runway X. After I felt the aircraft had a safe energy state I reduced power to [tracking] and then to idle on the right engine. The buzzing stopped as the engine slowed to near idle. I chose not to shut it down as there was no indication of fire and no significant vibration at that time. I continued a normal traffic pattern and completed a full flap single engine landing at slightly higher than normal weights (~800 pounds over maximum landing weight). Using full TR on the left engine and moderate braking; I easily made the turnoff at the end of the runway. I shut down the right engine as we turned off the runway and taxied back to the ramp on the left engine. ZZZ1 followed us in and did not find any indications of hot breaks or evidence of fire in the right engine. The City airport staff found bird remains near taxiway (appeared to be some sort of hawk); and the right engine fan displayed significant damaged to several blades and stators. Initial inspection appears to show the bird went through the bypass fan and missed the engine core. All engine/cowling parts still appear to be attached to the aircraft. ZZZ airport staff has additional details and pictures.