While somewhat variable, in no case does light alone supply anywhere near the total energy budget of any zoanthid. "Furthermore, much of the carbon products produced by photosynthesis are used in the production of mucus, making external sources of carbon containing compounds, in addition to non-photosynthate material imperative to the health and survival of zoanthids. Zoanthids feed on particulate matter, organic macromolecules, bacteria, plankton, and even larger prey. To what degree each food item can theoretically comprise the natural dietary intake of zoanthids is anyone's guess, but it would appear that most tank conditions are able to supply the required external nutrition to a tolerable level based on the success of colonies in the aquarium" Eric Borneman.

If you like zoas and palys you should read this article:
Reefs.org: Where Reefkeeping Begins on the Internet - Zoanthids by Eric Borneman Aquarium.Net January 1998