When I suggested that autoclose could be an option, I was more thinking of that you want the results now, but Shanky's response makes me think that you may want to monitor the server for a while.
Autoclose can still be an option for this, but in such case, you need to turn off all maintenance jobs, backups etc, so that the database is not opened for that reason. But there could be an application server that polls something every once in a while on its own initiative.
Shanky's idea has the problem that it may not capture occasional queries. That is, it could be that this is a legacy database that someone has reason to peek into, once or twice per week. And the peeking application server is a problem here too.
In that light, a trace which captures login, RPC:Starting and SQL:Starting will give you more information, as you can analyse the submitted queries to see if there is a real user behind them.
Or just take the brutal approach: put the database(s) offline and wait for a support ticket to come in...