Re: Faint (low volume) alarm under hood???
The knee-jerk reaction to every XF problem seems to be "replace the battery". I'm going to go out on a limb and disagree. My roadster is original battery, stored with a float charger the last 3 winters, and she runs great with no gremlins. My SRT6 appears to have a newer battery (I bought it used), but I have owned it three winters and store similarly. No problems. My A6, a 2003, is running the original battery after 182k miles.
That said, leaving the trunk slightly open will drain the battery. Been there, done that. However, a good battery should take and keep a full charge. So after it is fully re-charged via a trickle charger or driving, you need to find out if something is stuck on and draining the battery. A noise indicates something (alarm, pump, etc) is not shutting off and eventually will drain more juice than the little light in the trunk.
Last, if you have a concern about the health of your battery, take it to Autozone and have then test the alternator and battery. It is free, and I do this annually.