(The arrow symbolized the power of Abaris to fly through the air.)
Abaris was a Scythian priest of Apollo who lived during the sixth or eighth century BC. He fled to Greece from his native Scythia to avoid a plague and traveled throughout Greece for some time healing the sick with his magic. He is fabled to have performed many miracles, to have foretold the future, and to have saved the city of Sparta from being destroyed by a plague.
The magic wand of Abaris was in the form of a golden arrow said to have been given to him by the god Apollo himself. This magic talisman allowed the Scythian to fly through the air. Another legend of Abaris states that he never ate.
While wandering through Greece Abaris met the young and handsome Pythagoras. He was struck by the physical beauty of Pythagoras, who seemed to be the god Apollo incarnated in human form. Abaris gave to Pythagoras his golden arrow as a gift. In return for this magnificant gift, Pythagoras assured Abaris that he was indeed Apollo come to earth, and as proof of his godhood, he showed Abaris his "golden thigh."
There is a great deal of fantasy mixed into the legend of Abaris, but this northern magician does seem to have lived in the time of Pythagoras. In my opinion, he was probably one of Pythagoras's teachers in magic and philosophy. The golden arrow was probably a wand used to induce shamanic astral travel, which often takes the form of astral flying, during which the astral traveler can go anywhere on the earth and observe events.
The matter of the "golden thigh" of Pythagoras is more puzzling. It was probably a euphemism for the penis of Pythagoras. Homosexuality was common in ancient Greece. Pythagoras probably initiated a sexual relationship with Abaris in gratitude to the older man for teaching him the secrets of Scythian magic. I hasten to say, you will not find this explanation of the golden thigh of Pythagoras in books of history or mythology, but it seems the obvious explanation to me.
Scythia was the region of the ancient world north of the Caucasus mountains. Some accounts claim that Abaris was from the land of Hyperborea, made famous in modern times through the Conan stories of the writer Robert E. Howard. Abaris was undoubtedly a northern shaman.