Stars are Synthesis Materials that can be found in both Bafabon and Dr. Diaper's Mission. Clearing Dr, Diaper's Mission Yields chances of getting certain Stars.
They are used in Mix Machine No.54 (it must be upgraded to that state) at Accessory Alchemy to create accessories from it.
If the Star creation is successful, you receive a certain accessory from the core you used to alchemize. If failed, you either recieve a random material, or a Broken fragment.
These Stars are the beta image before they got visual upgraded from it.