Help me out with grammar in this sentence

Hi English Forum

I was reading the Great Gatsby and stuck with this sentence having hard time understanding its grammatical structure: Something in his leisurely movements and the secure position of his feet upon the lawn suggested it was Mr Gatsby himself, come out to determine what share was his of our local heavens.

As for the end of the sentence starting with ",come out..", could anyone kindly explain how this sentence is structured? Specifically, I don't exactly see how the phrase of "come out.." connects with the prior fragment of the sentence, as I think it does not match tense nor fit any grammatical rules I'm aware of (like, participle construction or "it... that(who)" with a right form of tense "came" involved).

Thanks a lot in advance!