I have become aware of a kingdom in Eurasia that was one of very few in history to have converted to Judaism. I am aware of theories that put the origin of the previously large number of Jews in Eastern Europe on the Khazar kingdom rather than the diaspora theory, as well as those against it. However, I wanted to find a more in depth side to the discussion from some reputable historians. Links for reference: http://www.jewishvirtuallibrary.org/jsource/Judaism/khazars.html http://failedmessiah.typepad.com/failed_messiahcom/2013/01/new-genetic-study-reportedly-proves-khazar-ancestry-for-ashkenazi-jews-567.html http://rationalwiki.org/wiki/Khazar_myth http://www.yivoencyclopedia.org/article.aspx/Khazaria
Not very. First off, the only serious evidence for it is the genetic study you referenced. It only indicates that there'd be some Khazar origin among Ashkenazi Jews; that they're a mix. And it disagrees with numerous other studies and has some issues, notably the fact that Armenians were selected as the "Khazar control", even though the Khazars were a Turkic group and Armenians aren't.
But besides that, there's a lot against it. Most damning is Yiddish. Despite occasional speculation to the contrary (which is similarly flawed), Yiddish is a Germanic language, which shows a dialect continuum moving from Central to Eastern Europe. You really couldn't get that if Ashkenazi Jews were primarily Khazars.
Simply put, there's just not much evidence for it, and there is a bunch against it. To quote the last link you posted:
The role of the Khazars in the shaping of East European Ashkenazic Jewry is periodically the subject of speculation. Judaized Khazars may have been one of the components of what became the largest Jewish community in the modern era, but it is very unlikely that they were a determinative element.