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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 d...
#2: Post edited
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HDE 226868
·
2020-07-01T19:28:41Z (almost 4 years ago)
- <p>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.</p>
- <p>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.</p>
- <p>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?</p>
<p>As a start, I know that the collision rate for $N$ stars of mean velocity $v$, 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.
- <p>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.</p>
- <p>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.</p>
- <p>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?</p>
- <p>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.
#1: Post edited
by
HDE 226868
·
2020-07-01T19:28:16Z (almost 4 years ago)
<p><sup>Note: This sprung from <a href="http://meta.worldbuilding.stackexchange.com/questions/2211/a-hard-science-ultimatum">some annoyance</a> I've had with the <a href="/questions/tagged/hard-science" class="post-tag" title="show questions tagged 'hard-science'" rel="tag">hard-science</a> 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.</sup></p><p>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.</p><p>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.</p><p>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.</p><p>What stellar number density would both galaxies have to have?</p><p>Or, <a href="https://worldbuilding.stackexchange.com/questions/19044/what-stellar-number-density-would-two-galaxies-have-to-have-for-another-star-to#comment47280_19044">as Ayelis put it</a>,</p><blockquote><p>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?</p></blockquote><p>I am aware, by the way, of <a href="http://arxiv.org/pdf/0705.1170v2.pdf" rel="nofollow noreferrer">this paper</a> by Cox and Loeb.</p><p>Remember, this question has the <a href="/questions/tagged/hard-science" class="post-tag" title="show questions tagged 'hard-science'" rel="tag">hard-science</a> 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.</p><hr><p>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.</p>
- <p>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.</p>
- <p>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.</p>
- <p>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?</p>
- <p>As a start, I know that the collision rate for $N$ stars of mean velocity $v$, 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.