I have mistakenly ID'ed this star as a Linckia too as it has been called for so many years. No worries
There still is so much to learn/observe about Asteroid sea stars... very littel fo the science that has been recorded has yet to make it into popular aquarium literature. And so, for this like somany species, we are relegated to juducious experimentation and frankly educated guesses (plus a conscientious decision for most folks to avoid the animals of unknown husbandry).
This is no critique of you here though my friend. Dedicated aquarists do need to keep and experiment with these animals. I just hope to see casual reefers (those that would just throw the star in a tank and hope for the best) avoid keeping them.
My take on target feeding the purple Leiaster is akin to the orange Fromia from a recent post:
"Fromia diets run the gamut from herbivorous to detritavore and sediment feeders to "carnivore" (eating carion and living sessile invertebrates). That said, I suspect this one is not going to be inclined toward "non-reef-safe" habits (eating live sessile inverts as many other Asteroid brethren do) nor do I honestly think this star will feed much on microalgae.
Instead, do experiment with by offering small amounts of a wide variety of meats of marine origin. If you try say a half dozen or more withy little or no response, yours may favor sediments and detritus. If the matter, it will be more difficult to keep it alive in smaller (under 100 gall) or younger (under 1 year old) tanks IMO.
If you find that yours responds to any specific food or foods offered, please do post a mention of it for the benefit of all (with a picture of yours).
Feeding mixed foods (like Formula brand or Lifeline types) with some greenstuffs in them may still be helpful/necessary. Do try this as well."
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please do let us know what you discover with your specimen. Tell us what if any foods yours seems to favor and add info about husbandry, longevity, etc. as time goes by. Too many keep these animals successfully and unsuccessfully alike without reporting to other aquarists for our mutual benefit.
kindly,
Anthony