The long and the short of it is that still, nobody know what they eat and they are doomed to die prematurely in an aquarium. Where thy last decades on a reef we are lucky to get months or a year out of them. For some reason, if it were a fish that was guaranteed to starve in an aquarium people would be upset at the continued importation of them, but being is it is an invert, it seem to be O.K.
From
http://www.reefkeeping.com/issues/2004-12/rs/index.php (It is the third part of a three part series if you are interested.)
Now that I am done my rant, the best part of the article was likely the last two sentences about Linckia stars which states “For large animals they are surprisingly benign. They seldom knock over rock work and do not harm most other animals while they are dying.”