Was Jesus actually born at midnight?

In Luke 2, we get a narration of events surrounding the birth of Jesus. The angels announce the Nativity to the shepherds who are watching over the sheep in fields, mentioning the Town of David as the location and the time of the Nativity as ' today '( Lk 2:11) In Biblical times when the concept of 24-hours' day was not in vogue, day and night were separately counted (Mtt 12:40). The shepherds go to Bethlehem to see the Child (Lk 2:15 ) and return after spreading the news (Lk 2:17-2O) implying that they stayed put in Bethlehem much through the day. It is therefore, possible that Jesus was born in day- time, the news was disclosed to the shepherds after sundown, they set out to Bethlehem early next morning and retuned during the day. But then, Christmas is celebrated in Vigil Service between 24 th and 25 th December, implying that Jesus was born at midnight. The practice perhaps owes its origin more to tradition than to scriptural narratives. My question, therefore , is : Was Jesus actually born at midnight ? Inputs from scholars of any denomination are welcome.