And the stars never rise, but I feel the bright eyes Of the beautiful Annabel Lee; (lines 36-37)
This is definitely a supernatural moment, even though it doesn't mention angels or ghosts or demons. Look carefully at the words the speaker uses. He doesn't say that he thinks about her when the stars rise, or that he imagines she is there. He says that he can feel her eyes on him. It's an intense, scary moment, and it plays into the sense that Annabel might not really be gone, just lurking somewhere, waiting for us to find her. This line suggests that the speaker might be a little unbalanced, but it also lets us know that he's straining to keep Annabel's memory alive.