Khazars

The idea that the Khazars converted by becoming Jews has been accepted by some. It follows that the Ashkenazi Jews are Khazars or not. Arthur Koestler, a Jew goes with the idea. Kevin MacDonald, a professor of psychology tells us that the science moves on. The current answer is messy. See what he has to say at Jewish Population, Genetics & Intelligence Revisited. Now David Duke has taken a position - see http://davidduke.com/rethinking-khazar-theory/

Khazars ex Wiki - https://en.wikipedia.org/wiki/Khazars
QUOTE
The Khazars ........ were a semi-nomadic Turkic people who created the most powerful Western steppe empire, Khazaria, between the late 7th and 10th centuries. Astride one of the major arteries of commerce between northern Europe and southwestern Asia, Khazaria became one of the foremost trading emporia of the medieval world, commanding the western marches of the Silk Road and played a key commercial role as a crossroad between China, the Middle East, and European Russia.[10][11] For some three centuries (c. 650–965) the Khazars dominated the vast area extending from the Volga-Don steppes to the eastern Crimea and the northern Caucasus[12]

Khazaria long served as a buffer state between the Byzantine empire and both the nomads of the northern steppes and the Umayyad empire, after serving as Byzantium's proxy against the Sassanid Persian empire. The alliance was dropped around 900 CE., as Byzantium began to encourage the Alans to attack Khazaria and weaken its hold on Crimea and the Caucasus, while seeking to obtain an entente with the rising Rus' power to Khazaria's north, which it aspired to convert to Christianity.[13] Between 965 and 969, the Kievan Rus ruler Sviatoslav I of Kiev conquered the capital Atil and destroyed the Khazar state.

Beginning in the 8th century, the Khazar royalty and notable segments of the aristocracy converted to Judaism; the populace appears to have been multi-confessional—a mosaic of pagan, Muslim, Jewish and Christian worshippers—and polyethnic.[14] A modern theory, that the core of Ashkenazi Jewry emerged from a hypothetical Khazarian Jewish diaspora, is generally treated with scepticism. This Khazarian hypothesis is sometimes associated with antisemitism and anti-Zionism.
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The jury is out on this one.