The Venkatachala Mahatmya of the Skanda Purana describes the story of Venkateshwara (the Vishnu deity in Tirupati, AKA Balaji or Srinivasa). This excerpt describes how Brihaspati, guru of the gods, is called by Padmavathi's father Akasa Raja to fix a date for the marriage of Vishnu and Padmavathi:
Saying "So be it" the Lord of men called Brihaspati from the world of Suras asked him about (the hour) for the marriage of the girl and the bridegroom. The king asked: "The native star of the girl is Mrigashirsha; that of The Lord is Shravana. Let the conjunction of these two be considered." On hearing it [Brihaspati] said "The star Uttaraphalguni suits both of them for the increase of their happiness. It is declared so by the divine astrologers. Let their marriage be celebrated on the marriage be celebrated on the Uttaraphalguni day." He said, "Let it be celebrated duly in the month if Vaishakha."
My question is, why does Vishnu have Shravana as his Nakshatra or birth star? Vishnu's connection to Shravana Nakshatra isn't limited to Venkateshwara, by the way; this book says "Vishnu is the presiding deity over Shravana".
Now strictly speaking it's meaningless for Vishnu to have a "birth star". First of all, as Krishna says in the Bhagavad Gita, Vishnu is unborn, and second of all he's older than the stars! So I assume it's referring to the birth one of Vishnu's incarnations (avataras), because similar answers are given elsewhere in the story. As I discuss in this question, when Vishnu is asked by Padmavathi and her friends what dynasty he belongs to, he says he is a member of the solar dynasty, because Rama was a descendant of Surya the sun god. And when asked who his parents are, the answer given is Vasudeva and Devaki, the parents of Krishna. So presumably this too is a reference to one of Vishnu's incarnations
But which one? The Bala Kanda of the Ramayana says that Rama was born during Punarvasu Nakshatra, and the Srimad Bhagavatam says that Krishna was born during Rohini Nakshatra. So was someone else born during Shravana?
Do Hindu scriptures provide any explanation of why Shravana is considered the birth star of Vishnu?