What is a Good Capacitor?

On most newer cars, adding a 1000w amp would probably not require an alternator upgrade right.  That's 1000w peak so RMS is probably less than 500w.  I'm running a RF P8002 with a 4ohm load which RMS 400W and I have 2 smaller RF amps with 45w x2 RMS.  That's 600W RMS and my lights are not dimming on my huyndai elantra.  I have a second battery which I installed for playing with the car off. 

Every car is different so maybe they designed mine with a bit more reserve.  Does a cap really improve bass responce or are the internal caps of an amplifier sufficient for spontaneous bass notes?

I suppose in a very general, basic layman's terms sort of way it could, but the two are entirely different types of devices and operate in entirely different ways.  A battery produces energy through an electro-chemical reaction, releasing voltage potential from the interaction of several compounds, while a capacitor simply stores a difference in charge potential.  A battery actually converts physical matter into electricity and back through a chemical reaction, while a capacitor does nothing more than allow an electric charge to build up on a plate.  A battery will generate its voltage all by itself, a cpacitor must be continually supplied with energy to maintain the charge potential across its plates.  A battery is a generator, a capacitor holds static electricity.  Without external influences, a battery can sit for very long periods of time and still have its ability to convert chemisrty into electricity, while a capacitor will eventually dissipate the temporary chages it stores on one plate to the other and it will equalize.  So, wihile on a very, very basic usage level both devices "store energy," a battery is considered an actual power source while a capacitor is simply a temporary storage area.

I would start with a bigger alt. everthing electrical in a car depends on the alt (radio, amp, battery, cap) it all is supported by the alt. Thats were I would start anyway..