honestly, All corals require food of some kind, there are NO truly purely photosynthetic corals that I have ever heard of. its just many corals can subsist on photosynthesuis and available nutrients in our tanks. (aka fish poop, freefloating bacteria, nitrate, other natural microfauna etcetera), thats one reason corals are reccomended for established tanks, new tanks often dont have the naturally occuring foods in high enough numbers to support some corals so they "fade" away with no explination.
just to add to that a little IMO most corals in our closed systems are severly undernourished, while we may be thinking we are getting great growth compared the the growth rates of wild specimines we are barely growing IMO its due to lack of proper nutrtion for the coral, thats one of the reasons I have such an insne feeding ritual and water change ritual, because I feel to provide proper nutrition you need to provide each type of coral with its specific food, and you need to maintain water quality which is damn hard to combine. when you feed 5-7 times a day (like I do) water quality can suffer in a heart beat.