Standard US ROE: You take out a Carrier, we nuke you.
I THINK the decision rests with the Fleet Admiral.
All sorts of twists and turns though. Even if under attack by Israel, the Iranians would likely try to get some variety of “plausible deniability”, such as blaming it on al-Qaeda. They might use naval mines, or a nuclear fire ship directed at a port, or just a smuggled steel shipping container.
They are far more interested in the final goal of the US leaving the area. And if this involves not firing a shot, they would be happy with that.
Unlike a buffoon like Saddam, the Iranians tend to think things through.
With Obama as President, do you think the Fleet Admiral has this discretion? I doubt it.