A new study done by Eran Israeli-Elhaik titled "The Missing Link of Jewish European Ancestry: Contrasting the Rhineland and the Khazarian Hypotheses" comes to some interesting conclusions:
However the author is careful to mention the weaknesses and limitations of his study. This is true of most genetics studies which rely on the samples available and the location of present dna rather than the dna testing of ancient remains. Nevertheless I think he convincingly demonstrates the important place that the Khazars play in the ancestry of the Eastern European Jews.
I believe that the Royal Khazars are those of R1a y-dna ancestry. The large amount of J y-dna and E y-dna comes from the Samaritan influx into Second Temple Judaism as well as the Samaritan diaspora that headed north to the Jewish Khazar Empire. Of course the J and E (with R1b ht35) is also found all populations of Jewish diaspora coming from the Second Temple Times. The ancient paternal line of Israel is R1b of which in Eastern European Jewry only has about 10-15 %, whereas the Netherlands-German-French Jewry have more like 30-40% R1b as do the Sephardi Jews. Iraqi and Syrian Jewry also has around 25% R1b. According to the famous Medieval Rabbis the descendants of the Lost Tribes of Israel were to be found among the Gentiles of France and the British Isles (Tzarefat and the Isles of Tzarefat).