What were the roots of Arab Jews?

Answer 1

It depends on how the term "Arab Jew" is meant.

If the term "Arab Jew" to refer to "Jews from the Arab World" it is worth noting that they identify themselves either as "Mizrahim" (Jews of the East) or "Jews from the Arab World". The term Arab Jew is seen by both Arabs and Jews to be quite problematic, but can be used as it makes "Arab" the physical descriptor of the type of Jew. The reverse (Jewish Arab) is not even historically acceptable for describing these types of people, whereas this type of identification is how Muslims and Christians identify (Muslim Arabs and Christian Arabs) because their religion describes what type of Arab they are.

The Mizrahim trace their origins back to the countries that came under Arab Islamic control prior to the arrival of the Muslims. The communities in Northern Africa were populated by Jews during the Roman Diaspora period. The communities in Iraq were the remnants of those Jews deported by the Babylonians who never returned to the Land of Israel, and so on.

If the question is referring to the Arab Tribes in the Pre-Islamic Period that embraced Judaism, it is unclear whether these were Arabs who converted to Judaism or they were Jews who migrated to Arabia and took on Arabic language and customs. Those Jewish Arab Tribes disappeared during the 600s CE because of the conflicts between them and nascent Islam and because of Caliph Omar's edict that all Jews had to leave Arabia or convert to Islam. As a result, none of these Jewish Arab Tribes have modern descendants who see themselves as Jews.