http://en.wikipedia.org/wiki/Khazar_the ... i_ancestry
These days, the Khazar conversion story is only told by anti-Semites and some Arab states. The DNA studies do not support it:
"According to Jon Entine, historians and scientists believe the Khazarian theory should more accurately be called a myth.[82] The theory, which claims that today's Ashkenazi Jews are descendants of Khazar converts to Judaism, is popular on Internet anti-Semitic websites.[83] A 2013 study of Ashkenazi mitochondrial DNA found no significant evidence of Khazar contribution to the Ashkenazi Jewish DNA, as would be predicted by the Khazar hypothesis[84] and although there is no historical or DNA evidence to support the Khazar idea, Alan Unterman maintains that it is still popular in some Arab states.[85]
The strong claim that Ashkenazis as a whole take their origin from Khazars has been widely criticized as there is no direct evidence to support it.[86][87] In addition, Ashkenazi Jews have been found to have a strong DNA connection to Israelites and the Middle East,[88] sharing many common genes with other Jews from some 3000 years ago.,[89][90] therefore it "does not support this [Khazar conversion] idea[91]
Using four Jewish groups, one being Ashkenazi, a Kopelman et al study found no direct evidence to the Khazar theory[92] while another research concluded that its findings "debunk one of the most questionable, but still tenacious, hypotheses: that most Ashkenazi Jews can trace their roots to the mysterious Khazar Kingdom that flourished during the ninth century in the region between the Byzantine Empire and the Persian Empire".[93] Some scientist believe that even if the theory were to be true, "only a small minority of the Khazars may have adopted Judaism."[94] and that "the questions of whether there was a Khazar contribution to the Ashkenazi Jews' lineage, or exactly what percentage of mitochondrial variants emanate from Europe, cannot be answered with certainty using present genetic and geographical data".[95]
Nadine Epstein, an editor and executive publisher of Moment magazine said "When I read Arthur Koestler's The Thirteenth Tribe, I bought his theory that Ashkenazim were descended from the Khazars ... But in 1997, Karl Skorecki in Haifa, Michael Hammer in Tucson and several London researchers surprised everyone by finding evidence of the Jewish priestly line of males, the Kohanim. Half of Ashkenazic men and slightly more than half of Sephardic men who claimed to be Kohanim were found to have a distinctive set of genetic markers on their Y chromosome, making it highly possible that they are descendants of a single male or group of related males who lived between 1180 and 650 B.C.E., about the time of Moses and Aaron.[95] In 2000, the analysis of a report by Nicholas Wade named Y Chromosome Bears Witness to Story of the Jewish Diaspora "provided genetic witness that these [Jewish] communities have, to a remarkable extent, retained their biological identity separate from their host populations, evidence of relatively little intermarriage or conversion into Judaism over the centuries.... The results accord with Jewish history and tradition and refute theories like those holding that Jewish communities consist mostly of converts from other faiths, or that they are descended from the Khazars, a medieval Turkish tribe that adopted Judaism."[95] In June 2014, Shaul Stampfer published a lengthy paper challenging the theory as ungrounded in sources contemporary with the Khazar period, stating: "Such a conversion, even though it’s a wonderful story, never happened".[96][97]"
Those who don't like Wiki should check the individual studies listed in the article....