Does Obama have authority to order military strikes in Yemen?

(A possibility that seems to be on the table.)  Recall our friend, the AUMF:

the President is authorized to use all necessary and appropriate force against those nations, organizations, or persons he determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons, in order to prevent any future acts of international terrorism against the United States by such nations, organizations or persons.

Al Qaeda is the relevant organization here, and so U.S. presidents can (indefinitely?) take military action against Al Qaeda, regardless of the country in which Al Qaeda members are located.  Note that a military strike against Al Qaeda in Yemen would be an act of war against Yemen unless Yemen consented to it (and it might), even though the government of Yemen itself does not support Al Qaeda (as far as anyone can tell) and indeed has been cooperating with the United States in the “war” (or “law enforcement action” or whatever it is) against Al Qaeda.  But Yemen, because of its own internal conflicts and the weakness of its government, may not be willing to take as aggressive action as the U.S. government wants it to—just like in Pakistan, where a similar war between the United States and Al Qaeda is taking place with only the quasi-consent of the Pakistani government.

But there is a further complication.  The relevant Al Qaeda in Yemen is called “Al Qaeda in the Arabian Peninsula.”  Is Al Qaeda in the Arabian Peninsula a branch of Al Qaeda, the organization that planned and executed the 9/11 attack and is therefore covered by the AUMF?  There are apparently contacts between the two Al Qaedas, but does that make them the same organization, or just two separate organizations that have—contacts?  What if the two Al Qaedas do not cooperate in any way; suppose that leaders of Al Qaeda in the Arabian Peninsula simply borrowed the name Al Qaeda, a kind of trademark violation intended to siphon off some of the reputational capital enjoyed by the original?  If so, the authority bestowed by the AUMF vanishes—poof!

All of this is moot if the U.S. government takes the precaution of blowing up its targets in Yemen rather than taking them prisoner.  As others on this blog have noted, the courts in their wisdom apply different standards in the two cases.  If Al Qaeda in the Arabian Peninsula is not a part of Al Qaeda, the president can draw on his constitutional authority for a military attack, as Reagan, Clinton, and other presidents have.  But if the U.S. military takes anyone prisoner, and the AUMF does not apply, then the outcome is anyone’s guess.  One suspects that for this reason any prisoners will be quietly turned over to the Yemenis, who would be happy to interrogate, intern, or dispatch a common enemy.