yes you need a alternator..you don't need batteries..
if your alternator can supply the amp(which is ideal) adding a battery will do nothing..
if you have 3500watts you need a alternator capable of producing that power..
3500/13= 270 amp..
that's with 100% efficiency..
if you can find a 300 amp alt that would be ideal..
Batteries create a buffer for when the alternator cannot provide enough current to satisfy the draw.
What you guys need to remember is you must look at power used versus power supplied
over time, not as a single snapshot in time where the amp(s) is pulling maximum current. If the amps being used were class A, which does pull full current all the time, papermaker's math above would be spot on. But a/b and d class amps' current draw is transient, it scales with the output required/achieved.
Since the power demand goes up and down, its reasonable to assume there will be periods of time when the alternator can provide enough current, and times when it cant. If there was no battery in the circuit, the times when demand exceeds supply, system voltage would simply drop to a level that would either send the amp into protect mode, or possibly damage it. The batt is a stored power supply that will pick up the slack when the demand exceeds supply. The bigger the batt you have, or the more of them you have, the greater those periods of demand exceeding supply can be, or the greater the difference between demand and supply can be.
Ok, this is getting confusing, b/c one guy is saying i need alternator no batteries, and another one is saying batteries no alternator. I dont know.
Prepare to get more confused, this topic is more complex than people usually make it out to be. Many things factor in to how big an alt you need, how much battery storage, etc. Things like listening habits, such as how often you listen to the stereo versus how often you drive with it off, how loud you tend to listen to it, etc. Even what type of music you listen to can affect it, as some types of music tend to be more bass heavy than others. So as you can imagine, its impossible for us to give you an exact answer as to what you need. At best, in cases of extremes, like where a guy wants to run 5kw off his stock 90amp alt, daily, we can tell the person they need a bigger alt. But when the differences in supply and demand decrease, listener's habits become a bigger factor and ultimately make any math equation we offer as a guesstimate at best.
Papermaker's math above is theoretically correct, and once the 270amp is multiplied by 1.2 to factor in for the average amplifier efficiency of 80% (approx 325amp), it tells you approximately what the maximum current draw of your stereo. You then need to think about the intangible factors I mentioned above and decide if you think you are even in the ballpark of having a big enough alt. If you think you are in the ballpark, you can get a couple big batts, upgrade the big-3, and drive around with jumper cables in your trunk in case you need them. If you aren't in the ballpark, you need a new alt.
You can run a new batt in the trunk and keep your stock batt under the hood. But running two batts in parallel that dont have the same or close to the same internal resistance can cause a parasitic drain problem. I usually recommend replacing all batts in the circuit at the same time, or using an isolator to isolate the front and rear batt circuits.