Kitchen sink air gap question

We purchased an older house and are in the process of remodeling the kitchen. Both sink bowls empty into the same trap which is attached to a 1 -1/2" drain pipe coming up from the crawl space. The trap is connected to the drain with a tee. In the top of the tee there is an air gap just like the ones used for a dishwasher. We do not have a dishwasher or a disposal. I was planning on replacing the trap and lines connecting to the pipe going under the house while replacing the sink and was wondering what the air was for and if I could remove it? It is located well below the water line in sink, so, will it over flow if a full sink of water is allowed to drain out at once? The new sink is considerably deeper that the old one and would hold more water.

What it may be is an air admittance valve which is used instead of a conventional vent. It probably is needed to make the sink drain properly. My unprofessional opinion.

Sounds like that may be it. I don't remember seeing a vent stack on that side of the house. This house may very well be over 80 years old, last least parts of it are anyway and I guess the plumbing was added as needed.