4400w rms is a continuous draw of 314 amps at 14V, chances are that the normal current draw will be in the 50 amp range with short bursts of over 150 under normal 20 something listening habits. (Not taking into account losses from the amp)
That at said if you do a lot of freeway driving then a second battery is the way to go. If you just drive here and there on short trips then batteries and alternator.
i have run 1500 watts rms (class A and an A/B) with a 63 amp alternator and when I did at least a 40 mile drive a day everything was fine but on Friday and Saturday night I would ride with my friends down the strip and the normal kid route and set off car alarms at the movie theater and crap like that. I would come out on Sunday to a dead battery. Happened 3 weeks in a row so I added a second battery and a PAC 80 amp relay instead of an isolator and never had another problem.
Jeff