Only the "hard" classified astrals, meaning the even numbers or s3 (fabled).
s3 gives the most sovereign per run done.
You only get it for killing the 4th boss on the allod.
leaving an incomplete allod or leaving too soon before the system recognizes that the 4th boss has been killed, will result in a debuff that lasts 30m where you will not get sovereign if you ENTER an allod with that buff active.
s2 is irrelevant so don't run that ever. it's previous patch (lv84 gear (current gear: 87))
Goodluck!