Conversation so far:
Where did the Ashkenazi Jews migrate to?
By the 11th century Jewish settlers, moving from southern European and Middle Eastern centers, appear to have begun to settle in the north, especially along the Rhine
Was there any reason for Ashkenazi Jews moving from southern European and Middle Eastern centers to settle in the north, especially along the Rhine?
often in response to new economic opportunities and at the invitation of local Christian rulers

Question: Did they stay there or migrate more?
Self-contained rewrite: Did the Ashkenazi Jews stay in the nort, especially along the Rhine, or migrate more?