For some reason the coral Tubastraea micrantha is referred to in English as the black sun coral even though it is obviously green in color.
As a sun coral it lacks zooxanthellae thus it is not photosynthetic. Thus the black sun coral needs to be fed regularly small meaty pieces of seafood otherwise it will die.
The specimen in the picture has lived in my reef tank for years and then some change in water chemistry has killed it. I have purchased another specimen when it became available (they are rare and expensive in the aquarium trade) but it got wiped out with the rest of the inhabitants of my tank in the 2013 power blackout.
I just gave up, and concentrate on my Dendrophyllia — another relatively expensive coral which has similar apperance and needs as a sun coral — which did survive the same disaster.
Aquarium Corals: A Look at the Sun Corals — Advanced Aquarist – Aquarist Magazine and Blog.