<p>Suppose the sun moves through a column of Andromeda stars <span class="math-container">$L$</span> parsecs long with density <span class="math-container">$\rho$</span> and random positions. The probability of encountering at least one star within <span class="math-container">$r$</span> of the sun along this column would be <span class="math-container">$$F(r)=1-e^{-\pi r^2 L \rho}$$</span> (basically, what is the probability of no "success" when doing a Poisson sample of the column volume times density). </p>

<p>Setting <span class="math-container">$F(r_{1/2})=1/2$</span> to find the distance where we should expect a 50% chance of a star more nearby we get <span class="math-container">$r_{1/2}=\sqrt{\ln(2)/\pi L \rho}$</span>. If we plug in <span class="math-container">$\rho=0.14 $</span> per cubic parsec and <span class="math-container">$L=1000$</span> parsec (assuming a flat disk-disk collision) I get <span class="math-container">$r_{1/2}=0.02$</span> parsec. That is 4125.296 AU, reassuringly far.</p>

<p>To get the mean distance we can use <a href="https://stats.stackexchange.com/questions/10159/find-expected-value-using-cdf">the not very well known but useful formula</a> <span class="math-container">$E[r]=\int_0^\infty (1-F(r)) dr =\int_0^\infty e^{-\pi r^2 L \rho} dr = 1/2\sqrt{L \rho}\approx 0.042$</span> parsec.</p>

<p>Depending on your views of disk thickness and angle on merger <span class="math-container">$L$</span> and <span class="math-container">$\rho$</span> may vary a fair bit. A sideways collision might have <span class="math-container">$L=67$</span> kpc reducing the distances by a factor of 8.1. Direct collisions still remain very unlikely, but messed up Oort clouds seem very likely. </p>

CC BY-SA 4.0
2019-05-18T18:11:41.820Z
Thank you. That's further than I expected (8000 AU). As you say Oort cloud disruption, but probably nothing to the planets.
Steve Linton
CC BY-SA 4.0
2019-05-18T18:07:03.297Z
2019-05-18T18:07:03.297Z
Anders Sandberg
<p>This is closely related, but distinct question to <a href="https://astronomy.stackexchange.com/questions/22545/what-are-the-chances-of-a-star-colliding-with-another-during-a-galactic-collision">What are the chances of a star colliding with another during a galactic collision?</a>.</p>

<p>The accepted answer to that question places the odds of the Sun colliding with another star at about <span class="math-container">$10^{-12}$</span>, what I want to ask is how near a near-miss is expected? In other words, what is the expected closest encounter between the Sun and another star during the collision? A more sophisticated answer would give the expected distribution of close encounters by distance.  </p>

<p>A more general version of the question is -- what disruptive events would a typical star such as the Sun expect to experience during the merger?</p>

CC BY-SA 4.0
2019-05-17T07:55:03.670Z
Given we do not even know how many stars are in each galaxy (including our own) except to an order or magnitude, it's pretty optimistic expecting someone to calculate a near-miss distance for encounters that's much better than a random guess.
StephenG - Help Ukraine
<galaxy><milky-way>
What is the likely closest encounter for a typical star during the Milky Way Andromeda Merger?
Steve Linton
# What is the likely closest encounter for a typical star during the Milky Way Andromeda Merger?

(Asked by: username_0 on 2019-05-16)

This is closely related, but distinct question to [What are the chances of a star colliding with another during a galactic collision?](https://astronomy.stackexchange.com/questions/22545/what-are-the-chances-of-a-star-colliding-with-another-during-a-galactic-collision).

The accepted answer to that question places the odds of the Sun colliding with another star at about $10^{-12}$, what I want to ask is how near a near-miss is expected? In other words, what is the expected closest encounter between the Sun and another star during the collision? A more sophisticated answer would give the expected distribution of close encounters by distance.

A more general version of the question is -- what disruptive events would a typical star such as the Sun expect to experience during the merger?

**Tags:** galaxy, milky-way
> **Comments:**
> **username_1**: Given we do not even know how many stars are in each galaxy (including our own) except to an order or magnitude, it's pretty optimistic expecting someone to calculate a near-miss distance for encounters that's much better than a random guess.  

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## 1 answers

### Answer by username_2 on 2019-05-18. Score: 2 | Accepted answer

Suppose the sun moves through a column of Andromeda stars $L$ parsecs long with density $\rho$ and random positions. The probability of encountering at least one star within $r$ of the sun along this column would be $$F(r)=1-e^{-\pi r^2 L \rho}$$ (basically, what is the probability of no "success" when doing a Poisson sample of the column volume times density).

Setting $F(r\_{1/2})=1/2$ to find the distance where we should expect a 50% chance of a star more nearby we get $r\_{1/2}=\sqrt{\ln(2)/\pi L \rho}$. If we plug in $\rho=0.14 $ per cubic parsec and $L=1000$ parsec (assuming a flat disk-disk collision) I get $r\_{1/2}=0.02$ parsec. That is 4125.296 AU, reassuringly far.

To get the mean distance we can use [the not very well known but useful formula](https://stats.stackexchange.com/questions/10159/find-expected-value-using-cdf) $E[r]=\int\_0^\infty (1-F(r)) dr =\int\_0^\infty e^{-\pi r^2 L \rho} dr = 1/2\sqrt{L \rho}\approx 0.042$ parsec.

Depending on your views of disk thickness and angle on merger $L$ and $\rho$ may vary a fair bit. A sideways collision might have $L=67$ kpc reducing the distances by a factor of 8.1. Direct collisions still remain very unlikely, but messed up Oort clouds seem very likely.

> **Comments:**
> **username_0**: Thank you. That's further than I expected (8000 AU). As you say Oort cloud disruption, but probably nothing to the planets.  

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