Is there an English word for a wifeless man who has a concubine? [duplicate]

Not a husband - as he does not have a wife before the concubine.

Is there a single word for this or is there a lexical gap in the English language?

Sample sentence:

The concubines fell at the feet of [their men]

"Their men" obviously referring to the specific word I'm looking for, but may not exist in the English language.

Solution 1:

The dark history of concubines suggest that the women were purchased in the market place or kidnapped during battle against their wish or they can be a wilful​ second wife or sexual partner without marriage. So, the male who purchase or keep such female should be her master or concubinator. Yes, concubinator is a rare word but you can find it in few online books. Example

The Oxford Encyclopedia of Women in World History, Volume 1 by Oxford University Press uses the word: Concubinator.

Types of Concubinage. Most commonly, a concubine is a womn who provides sexual and/or reproductive services to a man of higher social standing in whose household she resides. In some cases, concubinage is monogamous; that is, concubine and concubinator live together in a quasi-marriage that is the locus of emotional and......

Other sources on google books.