# Timing and Lensing of the Colliding Bullet Clusters: barely enough time and gravity to accelerate the bullet

## TL;DR

This paper constrains dark matter in colliding galaxy clusters using timing arguments and lensing data, finding that standard CDM models are barely consistent with observed high velocities without requiring unrealistically large dark matter masses.

## Contribution

It provides semi-analytical constraints on dark matter content in merging clusters using classical timing arguments and lensing data, exploring both Newtonian and MONDian models.

## Key findings

- CDM models with ~10^{15} Msun are marginally consistent with observed velocities.
- Higher gas speeds (~5000-5400 km/s) challenge the gravitational binding in standard models.
- Relativistic MONDian models can reproduce high velocities with less dark matter.

## Abstract

We present semi-analytical constraint on the amount of dark matter in the merging bullet galaxy cluster using the classical Local Group timing arguments. We consider particle orbits in potential models which fit the lensing data. {\it Marginally consistent} CDM models in Newtonian gravity are found with a total mass M_{CDM} = 1 x 10^{15}Msun of Cold DM: the bullet subhalo can move with V_{DM}=3000km/s, and the "bullet" X-ray gas can move with V_{gas}=4200km/s. These are nearly the {\it maximum speeds} that are accelerable by the gravity of two truncated CDM halos in a Hubble time even without the ram pressure. Consistency breaks down if one adopts higher end of the error bars for the bullet gas speed (5000-5400km/s), and the bullet gas would not be bound by the sub-cluster halo for the Hubble time. Models with V_{DM}~ 4500km/s ~ V_{gas} would invoke unrealistic large amount M_{CDM}=7x 10^{15}Msun of CDM for a cluster containing only ~ 10^{14}Msun of gas. Our results are generalisable beyond General Relativity, e.g., a speed of $4500\kms$ is easily obtained in the relativistic MONDian lensing model of Angus et al. (2007). However, MONDian model with little hot dark matter $M_{HDM} \le 0.6\times 10^{15}\msun$ and CDM model with a small halo mass $\le 1\times 10^{15}\msun$ are barely consistent with lensing and velocity data.