### What are the chances of a star colliding with another during a galactic collision?

• HotSaucey

5 years ago

My specific example for the question is the future collision of the galaxies Milky Way (our own galaxy) and Andromeda in a couple billion years. The star in question is obviously the sun in this case. I want to know the chances of a collision with another star and if it's significant or not. The sun might be dead by the time that happens so the specific part of that question might not be relevant. But the density of stars in a galaxy is not high in the arms where the the sun is but higher in the galactic core. The stars like the sun will very likely not collide with anything because the volume that the star actually occupy is much smaller than the space between stars in both galaxies. @A.C.A.C. Why do you say might? Which bit is sufficiently uncertain to attract a qualifying word? I say the Sun will be alive when the collision takes place. There is a whole subsection on this question on the relevant Wikipedia page. https://en.m.wikipedia.org/wiki/Andromeda–Milky_Way_collision I think the chance of our sun being involved in a collision is extreemly low. That a star will hit another star during the collision, I've heard people say that won't happen, but I find it hard to believe. But stars are spread out enough that collisions will be quite rare. (I don't want to answer as I'm not 100% sure). If stellar collisions are observed within galaxies, I would think they would happen, at least a few times, in a galactic merger. https://en.wikipedia.org/wiki/Stellar_collision  @RobJeffries Wikipedia says the collision with Andromeda will happen in 4.5b years and I could have sworn that the sun was expected to be a red giant by then but it now that I read up on it it seems like the sun is expected to last >5.5b years. Originally I thought the 2 events would be sufficiently close enough that there is a high chance that the sun will be a white dwarf by then. 5.5 billion years would be to reach the end of the main sequence. More like 7.7 billion to become a white dwarf. e.g https://arxiv.org/abs/0801.4031 @A.C.A.C.

• 5 years ago

Let's see what we get from some back-of-the-envelope estimates.

Imagine throwing one star (e.g., the Sun) at the other galaxy. How likely is it we'll hit a star in the other galaxy? Well, it's basically proportional to how big a target each star in the other galaxy is (its cross-sectional area) compared to the size of the whole galaxy, multiplied by the total number of stars in the target galaxy.

Let's assume it's the Milky Way-Andromeda scenario, so each galaxy has about 100 billion stars, and each star is roughly the same size as the Sun (some are much larger, most are smaller). The actual target area for an individual star is a circle with twice the star's radius (we're counting one star just grazing the other as a collision). Let's also assume the stars are more or less evenly distributed in a circular disk. Since "100,000 light years" is a common (and not completely crazy) estimate of the Milky Way's size, that's a circle of radius = 50,000 light years (about $$10^{16}$$ meters).

So: 100 billion stars in the target galaxy, each with target radius $$\sim 2 R_{\odot}$$, gives us a total target area of $$10^{11} \times \pi (2 R_{\odot})^{2} \approx 10^{30}$$ m$$^{2}$$.

The area of the target galaxy is $$\pi R_{gal}^{2} \approx 10^{42}$$ m$$^{2}$$. So the chance of our Sun hitting a star in the other galaxy is $$\approx 10^{30} / 10^{42} = 10^{-12}$$ -- or about one in a trillion.

The odds of any star from our galaxy not hitting a star in the other galaxy would be $$(1 - 10^{-12})^{10^{11}} \approx 0.90$$.

So there's only about a 10% chance of one (or more) of the galaxy's 100 billion
stars hitting a star in the other galaxy. And the chances of any one particular star (like our Sun) hitting a star in the other galaxy is about one in a trillion. Factoring in Roche limit breakups (leading to partial collisions?) and the denser center parts of the two galaxies colliding, which is expected to happen I would think the odds of collision goes up, but running the math on that gets a bit problematic for me. Still, props on doing the math. Well, the original question was about "collisions", so I went with that. I also neglected gravitational focussing, which increases the effective impact parameter and thus the odds of collisions. But that's still not going to get you more than one or two orders of magnitude, which means the chances go from 1 in a trillion to, say, one in 10 or 100 billion. Still utterly insignificant. Increased central density doesn't change the base chance for a random individual star (like the Sun) to collide: sure, more stars per square meter in one part of the target galaxy, but they're in a smaller area now, so it's harder to hit the region with those stars. (The math cancels out.) It *is* true that the dense centers of the two galaxies will, if you let the whole merger play out (beyond the first collision) spiral into the common center via dynamical friction and merge, so the odds that *some* stars will collide will be higher.