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Sol Invictus ("the unconquered sun") or, more fully, Deus Sol Invictus ("the unconquered sun god") was a religious title applied to three distinct divinities during the later Roman Empire.
Unlike the earlier, agrarian cult of Sol Indiges ("the sun in-the-earth"), the title Deus Sol Invictus was formed by analogy with the imperial titulature pius felix invictus ("dutiful, fortunate, unconquered").
The cult of Sol Invictus continued to be a cornerstone of the emperors until Theodosius I's decree on Feb 27, 390 that only Nicene Christianity was acceptable.
The equivalent of Helios in Roman mythology is Sol.
On the Quirinalis, he was worshipped as Sol Indiges.
His epithet Phoebus 'shining' was later applied by Latin poets to the sun-god Sol also, perhaps from such connections as well as from its obvious appropriateness.