Here is the letter. Two points of note.
First, the President makes clear that he is authorizing military force in Iraq “pursuant to my constitutional authority to conduct U.S. foreign relations and as Commander in Chief and Chief Executive.” This is a standard formulation in this context for inherent Article II power. The President is not relying on any congressional authorization.
Second, the President states that the military operations he authorized “will be limited in their scope and duration as necessary to protect American personnel in Iraq by stopping the current advance on Erbil by the terrorist group Islamic State of Iraq and the Levant and to help forces in Iraq as they fight to break the siege of Mount Sinjar and protect the civilians trapped there.”