Depending on who you ask, the Bullet Cluster is evidence for and against dark matter. While I think that the Bullet Cluster is evidence for dark matter, this is not my field and my knowledge might not be up to date. Nevertheless, here are my arguments written in the style of St. Aquinas.
Is the Bullet Cluster evidence for dark matter?
Objection 1: The reason the Bullet Cluster is thought to be evidence of dark matter is because of gravitational lensing detection of unseen mass at the sides of the colliding clusters. This is thought to only be explainable by dark matter theories. However, relativistic extensions of MOND is capable of reproducing the gravitational lensing detection.
Objection 2 (Sabine’s objection): Different theories predicts clusters with different velocities. Numerical simulations using dark matter theories (Lambda-CDM) shows that it is extremely unlikely for two clusters to collide with such high relative velocities as is seen in the Bullet Cluster.
On the contrary:
The Bullet Cluster provides good evidence for dark matter because the existence of dark matter explains the behavior of the different components of the Bullet Cluster well.
I answer that:
The main reason the Bullet Cluster provides good evidence for dark matter is not because of the existence of the “unseen mass”, but due to its behavior. In the dark matter picture, the original two clusters in the collision posses two main components: gas and dark matter. When it collides, the dark matter components pass through each other, forming the “wings” of the cluster. The gaseous components cannot pass through each other and got stuck in the middle.
Reply to Objection 1:
While it is true that relativistic extensions of MOND can produce the gravitational lensing signatures, it is not good enough for two reasons: first, relativistic MOND still require ~100% the mass of the cluster to be “unseen”. While this is less than the ~1000% that naive MOND requires, it is still substantial. Further, as was mentioned previously, this “unseen” matter cannot be mundane gas that is too dim to see, because they have to pass through each other.
Reply to Objection 2:
This claim depends on the various inputs of the numerical simulations, all of which are less than certain. Most numerical cosmological simulations rely on ad-hoc prescriptions to model processes that are beyond the computational resolution. The robustness of this claim is therefore still suspect. Further, to my knowledge there is no cosmological simulations using MOND-type theories that can produce these high velocity cluster collisions (although there is some theoretical evidence showing that this is possible in MOND-type theories).