A couple of days ago, the alternator died. Tried to make it home, but the pulley let go and took the tensioner and serpentine belt with it. I replaced all three today. (And for once, did not have an extra parts leftover

Engine fired right up and run for about 1 minute and then died. Now restarts and will run for at most 10 seconds and then dies. Exhaust smells of incomplete combustion / running rich.
Start poking around under the hood and noticed humming / buzzing sound from the top of the engine on the passenger side. This sound continues if the engine is off and key removed. Does not appear to stop until the battery cable is pulled.
Pulled the cover of the area next to the timing belt and isolated the sound to the device shown. Appears to be two of then. I pulled the power to the one closest to to the firewall and the sound stopped.
What is this devices and would it cause to engine to experience the issues described?