Note: This sprung from some annoyance I've had with the hard-science tag, and the goal of this question is to attract some really high-quality answers that any question using the tag deserves. An answer that meets the tough criteria of the tag will receive a bounty, and my gratitude.
The Milky Way and Andromeda will collide a few billion years in the future. Stellar collisions will be rare because - as Douglas Adams put it - "Space is big. Really, really big." In the galactic disk, the number density of stars is quite low. Chances are, the Solar System will not be ejected from the galaxy or collide with another star.
I'd like the star in my planetary system - similar to the Solar System, for all intents and purposes - in a spiral galaxy like the Milky Way to collide with another star in a spiral galaxy Andromeda, during the collision.
Obviously, there's no way for there to be a 100% chance of this happening. I'd settle for a 90% chance, give or take.
What stellar number density would both galaxies have to have?
Or, as Ayelis put it,
So basically, how many stars (of a typical stellar class distribution) would the Andromeda galaxy need to contain within its current bounds in order to pose a reasonable (90%+) threat of a stellar collision with our Sun when our galaxies collide?
I am aware, by the way, of this paper by Cox and Loeb.
Remember, this question has the hard-science tag. Make sure you understand what kind of answers are expected. I don't want to scare anyone off, but I really do want awesome answers here. Good work will absolutely be rewarded.
Note: Yes, I know that the resulting number will be quite large. However, it will be finite and calculable. Simply saying, "It's too large because [x,y,z reasons]" is not enough. The equations do not lie.