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 good that the Solar System will not be ejected from the galaxy or collide with another star.

I'd like the Sun-like star in my planetary system in the Milky Way to collide with another star in Andromeda during the interaction between the two galaxies. 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 for there to be a ~90% chance of a collision? In other words, how many stars would the two galaxies have to have for a collision to be this probable?

As a start, I know that the collision rate for $N$ stars of mean velocity $v$ and gravitational cross-section $\sigma$ in a volume $V$ is $$\Gamma=\frac{N\sigma v}{V}$$ and so if the collision takes a time $\tau$, then the total fraction of stars that collide is $$f\approx\frac{2\Gamma\tau}{N}=\frac{2\sigma v\tau}{V}$$ However, this assumes that the stars are all essentially identical, with random motions in a uniform, unchanging space. During a galactic collision, however, the kinematics of the stars should change drastically throughout the interaction, so I'm not sure if the above approach is valid.

posted over 9 years ago

4y ago

HDE 226868‭

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