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Particularly when pondering or pensively coming to terms with something, one may give out an expulsion of air through the nose or mouth as an expression of mild perplexion or disbelief.
It's similar to a scoff, but with without any of the associated attitude or emotion (and definitely without eye-rolling); the facial expression is often blank and eyes often somewhat starry (as can happen when one thinks).
Does this expression have a name?
sigh (n.)
A slow breath out that makes a long soft sound, especially because you are disappointed, tired, annoyed, or relaxed
"I’ll wait,” he said with a sigh.
a sigh of exasperation/resignation/impatience/disappointment
His only reaction to the news was a sigh of disappointment.
She sat down beside him with a sigh of perplexity. Juliet Wilbor Tompkins; Open House (1909)
Her stepmother gave out a huge sigh. A sigh of disbelief! Judy Prescott; Finding Harry (2014)
You could call it an interjection. You might spell it onomatopoeically as hmm. And you would sound hmm with a little extra nasal puff:
hm(m)
interjection used in many ways, one of which is to indicate that one is thinking, feeling, introspecting
Source: Onomatopoeia List
It’s not a sigh (which indicates some level exasperation).
You might find Live Science’s article on hmm interesting:
Spoken with a rising intonation: “I didn’t understand — say again?”
Prolonged, with ample m’s: “I’m thinking deeply about what you said.”
High-pitched: “Yes, maybe — good idea!”
I would just add that hmm with a little puff means “I am thinking deeply about what you said, later.”
Consult your linguist if you’re looking for IPA squiggles or terms like labial nasal.
