Sol, in Roman religion, was the name of two distinct sun gods at Rome. The Original Sol (Sol Indiges) had a shrine on the Quirinal, and another shrine, together with Luna, the moon goddess, in the Circus Maximus. Roman poets equated him with the Greek sun god Helios. The Roman Emperor, Elagabalus, during his short reign between 218-222, built a temple to him as The Unconquered Sun (Sol Invictus), on the Palatine and attempted to make his worship the principal religion at Rome. Later, Aurelian, who reigned between 270-275, erected a magnificent temple to Sol Invictus in the Campus Agrippae. Aurelian chose December 25th in 274 to dedicate the new temple of Sol in an effort to use the winter solstice to make a political statement and elevate the sun god to a higher status among the divinities of Rome.
For more information on Sol Invictus, here are some helpful links:
Connected study article: December 25: Christian Or Pagan Origin?