I had the exact same symtoms when my alt went bad. It is probably a bad diode which is stuck closed I believe it is. It creates a draw while the car is not on, and drains the battery, fix it soon, or it will get really bad, really quick, trust me. You can also check out PA Performance, they have a lifetime warranty, and have lower than a 2% failure rate. If your alternator takes a complete crap, it will take your battery with it, so be prepared...good luck