I am trying to understand how the Jews who returned to Jerusalem after the Babylonian exile worshipped in the rebuilt Temple. Since they did not have the Ark of the Covenant, what would have been found in the Holy of Holies, and what did the High Priest do on the Day of Atonement? I guess this question would also be extended to the Temple as it was in Jesus’ time. When the Veil was rent at his death, what would have been seen beyond the veil? I have read in your Yom Kippur publication what modern day Jews do for Day of Atonement observance. Does this apply in any way to pre-70 A.D. worship in the Second Temple?
Your observation is correct: there was no Ark of the Covenant to be put in the Holy of Holies when the Temple was rebuilt and reinaugurated in 515 B.C. What they did is get a hold of a stone that remained from the Solmonic Temple and put that stone within the Holy of Holies and on the Day of Atonement they would sprinkle the stone with the Day of Atonement blood. Thus when the veil of the Temple was torn, what was seen would have just been the large foundation stone.
For more details as to what was conducted in the second Temple period, I highly recommend a book by Alfred Edersheim entitled The Temple and its Ministry in the Time of Christ. I think you will find a lot of the details there that you may be looking for.