i noticed that when i did not have the air pump running for a day or two, the goldfish poop seems to not go away and swirls around the bottom....however, when i turn on the air, all the poop disappears with a few hours.

is air (oxygen) required for the effective breakdown of waste, even in a fully cycled tank?

Just throwing a thought out there. The air pump could be creating a different current pattern in your tank that better moves the waste into the filter intake.

I agree - the air pump helps to create more water movement which in turn helps to keep waste suspended for longer allowing it to be sucked into your filter intake rather than settling on the bottom of the tank.

So, in terms of mechanical filtration the added water movement provided by an air pump can certainly assist your filtration system.

However, in another aspect the added oxygenation the air pump creates also aids the the biological filtration element by ensuring an oxygen rich, ammonia laiden water flow passes over the filter media and "feeds" the beneficial bacterial. The nitrogen cycle requires the presence of oyxgen - aerobic bacteria.

So I'd say all in all whilst non-essential provided your filter outputs create enough surface aggitation on it's own - air pumps are certainly a positive contribution to a healthy aquarium. Positioning of filter intakes can certainly make a difference to waste collection too. As can thinning out the substrate in a goldfish aquarium too

thanks...that is why im thinking of adding a submerged powerhead to get the water moving around near the bottom.

plus, the fishies love to play in the bubbles!