Look at this photo. It is a pretty lousy photo, but it was made with a pretty lousy camera for low light conditions. But it still captured a very faint aurora (in South Carolina) in a 1/6th second exposure. With a better camera (like your Galaxy has) and brighter aurora (which your location should have) I’m guessing that you wouldn’t need to crack 1 second for the exposure.
What I kick myself for is not taking a large number of the shots a second or so apart to make a time-lapse video of the aurora as it shifts (as low quality as that would be). If I were you having the chance to do it again I’d try a few shots to see what a good shutter time is, then leave the camera be to do a long timelapse video.
(ETA, I should be aiming that comment at commasense.)