Is Newt Gingrich Living in Sin?

He is currently divorced from his second wife, who is still alive, and married to his third. He also a Catholic convert. The Catholic church, as I understand its doctrine, does not accept divorce. Unless he somehow obtained an annulment, doesn't that make his current marriage adultery?
It's one thing to have committed a sin, repented, and reformed. But it looks as though he continues to commit mortal sin on a regular basis. Am I missing something?