Is there a way to realize that, at a given moment, how many users are (MO) on line? Thank you
As far as I know, there is no such thing. See also this post on Mathematics Meta. Number of people online. On main meta you can find some feature requests such as View approximate number of users online or How many SO users are online?.
Depending on what purpose you want this for, perhaps some other measures might be useful for you.
On Math.SE you can see patterns of chat messages posted per day/per week in the main chatroom - which might correlate with users online. This will not work on MathOverflow, since chat here is rather inactive, but somebody with sufficient knowledge of SQL should be able to make a SEDE query showing number of posts in various time slots - which also seems a reasonable approximation. Maybe you can use query from answer to this question on meta.SE: What is the best time to ask questions? (Do not forget to switch site to MathOverflow, when you try the query.)
You can also find some already existing queries (and try them also for MathOverflow) in these posts from Mathematics Meta: Best time to ask a question, Depending on the tag is there a possibility to know on which days and hours are there more answers?, When is peak time for this website?.
Users with 25k+ rep have access to site analytics. Here you can learn a bit about traffic on site, but AFAIK you do not see there breakdown by the time of day/day of week.