September 13th is the anniversary of the death of the Roman emperor Titus (Titus Flavius Vespasianus), who reigned for barely more than two years. The date is known from Suetonius’ Life 11:
Excessit in eadem qua pater villa Id. Septb. post biennium ac menses duos diesque XX. quam successerat patri, altero et quadragesimo aetatis anno.
You can find a translation of the Life here: