Intermittent drone and shaky steering

I have 2005 Subaru Outback. Rarely - every few hundred miles - I hear a low frequency noise that builds up over 30 sec and seems to come from the front. Usually happens driving straight on highway. First time I heard it I thought I might be getting a flat tire. The engine seems to be running fine. Car handles OK, eg not pulling to side etc. The noise stays the same as I slow down and if I put car in neutral while moving. I pull over and the steering wheel shakes just before stopping. The sound goes away when stopped and the car is seemingly completely fine again when I start driving, as if something has been re-set back to normal. Has happened about 5 times, now I just stop and then go again. I also noted very recently that power steering is off - when I turn wheels to extreme eg when parking the wheel shudders somewhat, but otherwise steering is fine; not sure if this is related. Would really appreciate any ideas on what this could be!