Yup in a $1500 sound system there's no need for a second battery, just dont leave the system cranking with the ignition off for too long. If headlight dimming is your main concern there's a few things you can look at:
*Make sure your wiring to the amp is big enough (for a decent mono block you'll need atleast 4Gauge, some of the bigger ones are going to need 0 Gauge) - What this does is ensure a minimal resistance in the power wire. Too much resistance results in a voltage drop when the amp is sucking power, which means the amp will need to suck more current in order to get the same power to the sub.
*Make sure your wire from the amp to sub is a decent sized wire, I went from 12Ga to 10Ga wire for my Kicker L7 and the difference was very noticeable. again like the power wire the larger the wire, the more efficient the amp can push power to the sub
*Make sure the earthing point is good: ie make sure it's a clean and unpainted surface with good metal to metal contact, try and keep the ground lead form the amp as short as possible. This minimizes the restistance and keeps the voltage drop down, a reliable ground is also important for the electronics inside the amp to function as they usually reference to ground for signal processing.
*If after looking at this you are still getting dimming then upgrade your battery to something like a Optima Yellowtop, not only do these store more charge (Ampere hours) than a regular battery they also have lower internal resistances, this means they provide a more steady voltage output when they are loaded up. For example a standard battery unloaded may provide 14.6V when the car and alternator is running but when the sub hits full bass the voltage may drop to around say 14V. If it were a yellowtop though the voltage drop wont be asmuch and for example purposes may be still 14.3V under load from the sub.
You'll get alot of people saying that you dont need your battery once your engine is running so a yellowtop wont make any difference, but generally thoser people are noobs. Because an amp for a sub draws fluctuating amounts of power (ie. lots of power when the sub punches and then minimal power inbetween) there is no way the alternator can supply that, it simply doesn't respond fast enough. The power when the sub hits is drawn from the battery, the voltage regulator then realises the voltage of the battery drops and it ups the current output of the alternator to replenish the battery. Just by listening to my exhaust note I can tell that's how my CJ definitely does it.
As for capacitors they still do store power, just not as much as a battery does. The primary role of a power capacitor those is to try and keep the voltage in a circuit steady. When the sub hits full base the voltage drops which in turn makes the capacitor discharge its power quickly so that it keeps the voltage to the amp up. That's probably the easiest way I can really explain it, but summing up it preferrable to upgrade your wiring and battery before you even look at getting a capacitor as they are really a band-aid solution....