I'd say since functions as an adverb, modifying long, in your sentence.
Here is what the American Heritage Dictionary says:
1. From then until now or between then and now: They left town and haven't been here since.
2. Before now; ago: a name long since forgotten.
3. After some point in the past; at a subsequent time: My friend has since married and moved to California.
PS: this is not the full listing of definition.