Do I need a capacitor or a second battery?

The alternator charges the battery and the battery runs the car and its accessories. You need a second battery unless you want to keep replacing overworked alternators. The second battery should be isolated so it doesn t drag the main battery down as it is used. Alternators were never intended to run accessories or even supplement the battery. The alternator actually uses the battery to energize its electromagnet so it can produce more current. With a weak battery, or no battery and alternator will run its electromagnet into a meltdown of a sort, as why you never run a car without a battery and why weak batteries destroy alternators.

Capacitors only filter the power you have. They do not create power, so if you need to bolster your power supply because of deficiency, a capacitor is not the answer. If there is plenty of power a capacitor can tighten up the transient response, but never provide sustained power.

For starters, capacitors look really cool. Capacitors don't do anything in a car audio system. They are absolutely garbage. Don't even look at them.

The most important thing is the alternator because that's where all of your power is generated from.

High output alternators are an ideal solution for cars with high output sound systems. That 1000 watt Hifonics amp will run just fine on a 100A - 130A stock alternator.

So no, you don't need a second battery.

Generally 1000w isn't enough power to cause electrical system issues that require attention.

If you're getting excessive Vdrop (and 2+v is fairly excessive) I have to wonder about the amp's settings.

Where is the gain? Where is the bass boost?

I've been running 1200-1500w rms for ~10 yrs. Alts from 75-140A. Never any day-to-day problems.