I think there's a comma that's used when you are omitting the subject and verb (perhaps to avoid a run-on sentence, which would be ungrammatical).
He felt good, like he was the king of the world.
(He felt good, he felt like he was the kind of the world.)
He said earnestly, with not the slightest hint of a smile.
(He said earnestly, he said with not the slightest hint of a smile.)
I have two questions:
- Is this the case? If not, what kind of comma is this?
- Are these sentences grammatically correct without the commas?