# Doubts about the formation of the bullet cluster

The bullet cluster is formed by the collision of two clusters of galaxies. After the collision, the stars and galaxies in those two clusters passed through each other. But the intergalactic gas clouds got slowed down during the collision and got stuck in between. Why didn't the stars and galaxies suffer collision? Is it that the probability that two galaxies will collide head-on is very small?

• Is it easier to dodge all the snow falling (gas), or a snowball (star)? – Jon Custer Jan 15 '19 at 13:32

Your guess is basically correct: the probability of any two galaxies in the clusters colliding directly is not all that large. Even if two galaxies collide head on, the number of direct stellar collisions is still likely to be $$0$$. This is because, by volume, galaxies are mostly "empty" space (actually, mostly low-density gas & dust).
The calculation is fairly straightforward. To simplify a lot but still show the difference, let's assume that the interacting cluster has a size of $$\sim 1\,{\rm Mpc}^3$$, the size of a star is $$\sim 1\,{\rm R}_\odot$$, the size of a gas particle is about the Bohr radius, and that the interacting cluster contains an even mix of stars and gas by mass, each of about $$10^{13}\,{\rm M}_\odot$$, with typical stars of $$\sim 1\,{\rm M_\odot}$$ and typical gas particles with the mass of a proton. I also assume that each component is uniformly distributed through the volume. Each of these numbers and assumptions is "wrong" by up to a couple of orders of magnitude, but that's ok. The number density of stars is then about $$n_\star\sim 10^{13}\,{\rm Mpc}^{-3}$$, while for the gas it's about $$n_{\rm gas}\sim 10^{70}\,{\rm Mpc}^{-3}$$. Taking the collisional cross sections to be about the size of the corresponding particles, I get very rough estimates for the mean free paths ($$l=(\sigma n)^{-1}$$, where $$\sigma$$ is the cross section) of stars and gas of: $$l_\star\sim10^{14}\,{\rm Mpc}$$ $$l_{\rm gas}\sim10^{-5}\,{\rm Mpc}$$ In other words, a star is expected to travel a distance many (many, many, many!) times the size of the interacting clusters before a collision, while a gas particle will typically collide before it's made it one one-hundred-thousandth of the way across the system.