The question is nearly a year old as I post this, but a new answer is needed to correct an inaccuracy shared in one way or another by no fewer than three earlier answers, regarding the word whence.
It is true that whence, like hence and thence, is an adverb. However, very occasionally but nonetheless entirely properly, whence unlike hence and thence is alternately used as a conjunction. For example,
Cats hunt mice, whence they derive their cruelty.
Of course, my own usage bears poor authority, but what of Milton's?
This you might have learned out of the Third Book of his Annals, whence you have all your regal right.
The word means "from which place" or "from which fact," but so used the preposition "from" is omitted, whence the only part of speech one can impute to the word, so used, is the conjunctive. (How's that for awkwardly pretentious writing on my part? At any rate, the usage of whence in the very paragraph you are reading may serve to make the point.)
Here is a real, past sentence of my own in which the conjunction whence is less pretentious:
This is not because swapping is wrong, but rather because the inner sum after the swap diverges, whence the outer sum after the swap has no concrete summand on which to work.
Could I not have used so there? Yes, I could, but so does not mean quite the same. The conjunction so in that place would tend to connote what Aristotle calls "efficient causality," whereas I had Aristotle's "final causality" in mind, as seemingly did Milton, as (if you will excuse the expression) did the cat.
The last of the three quotes happens to show one of only two such uses of whence the computer finds in a 600-page manuscript, so it is hardly asserted that whence the conjunction were common! It is not common. However, it is licit, old, established, nonarchaic, Saxon, occasionally indispensable, and always sanctioned by good writers' use.
But, still, admittedly, I do not think that it fits your particular sentence well.