The airstone in my fish tank broke?

An airstone doesn't *add* any air to the water. What it does is create a disturbace along the surface so the top layer of water that absorbs the oxygen from the air circulates around your tank.

What an airstone does is to make the bubbles that come out of the tubing smaller. You can just leave the tubing in, it will still create the water disturbance.

But if you have a filter in your tank, then you don't need to use an airstone at all, the filter cleans food, feces and other material in your water, but it creates the water disturbance too.

Yes you do need the air stone, but you can leave it off if you like. If you leave it off then the bubbles will just be a lot bigger. Making the water move a lot more. The air stone is used to put air into the water. It is not actually the air bubbles that put the air in the water. It is the move meant at the top of the water that puts the oxygen into the water.