I agree that authenticity is hard to define and I agree with the part I bolded. I'm not sure the fact that there are lots of influences (hunger, etc.) on our emotions means that expressing the emotions (whatever the emotions are at the moment) means they aren't authentic. Even if you want to say a feeling is not authentic if you know that it was influenced by hunger or whatever, we don't ALWAYS give an emotion "more importance than its due" or "an intensity that it doesn't deserve," ... oh wait a minute, you kind of already wrote some of this stuff in your last paragraph

"So, what is authenticity? Is it reflected by that particular emotion that appeared at that time"

I guess I was saying I think it's the emotion felt/appeared at that moment. If you intellectually realize later that there was another hidden emotion behind it, then the hidden one could become authentic if you start to feel the hidden one. Does that make sense?

"or is it the emotion felt but not expressed"

I think it's the emotion felt whether it's expressed or not.

"or is it the ability to restrain ourselves when emotions feel too strong"

I don't think that has to do with authenticity.

Also, irrelevant to defining authenticity, I didn't mean to suggest you should restrain yourself when emotions feel too strong, I meant to find a way to express them and still be respectful of the other person. I don't really think you should worry too much about being respectful of your therapist because the whole point of therapy is that it's okay to make mistakes and your difficulty seems like it's a lot more about expressing your emotions at all than about being disrespectful by over-expressing them. (me too.) I just meant I don't think you were wrong for also later going back and questioning whether you were sarcastic to your t. I think it would be good to talk to her about that too. (I have no clue whether you were actually sarcastic to her or not. I guess if you were it was probably really subtle and she wouldn't be upset about it. But whatever the case was, I think we can learn from t's how to more frequently express strong emotions respectfully. I think Sunrise has a post on this thread where she gave some example of doing that.) Anyway, even if I'm making sense, and t's can teach us how to express more strong emotions more respectfully and consideratley, I'm not sure it's ALWAYS possible to get that right. Maybe learning how to do it more often is the best one can do. What do you think?

or is it allowing ourselves to emote no matter what the consequences?

I don't think people should always show all their emotions. That might be authentic, but I think being authentic ALL the time probably isn't a good idea. But for people like me and you, I think expressing them a lot more could be good. My t says I don't express emotions much. Maybe my post before sounded like I thought being authentic is always the way to go, but I didn't mean to sound like that.