Assembly bias & redshift-space distortions: impact on cluster dynamics tests of general relativity

The redshift-space distortion (RSD) of galaxies surrounding massive clusters is emerging as a promising testbed for theories of modified gravity. Conventional applications of this method rely upon the assumption that the velocity field in the cluster environment is uniquely determined by the cluster mass profile. Yet, real dark matter haloes in N-body simulations are known to violate the assumption that virial mass determines the configuration space distribution, an effect known as assembly bias. In this Letter, I show that assembly bias in simulated dark matter haloes also manifests in velocity space. In the 1-10 Mpc environment surrounding a cluster, high-concentration 'tracer' haloes exhibit a 10-20 per cent larger pairwise-velocity dispersion profile relative to low-concentration tracer haloes of the same mass. This difference is comparable to the size of the RSD signal predicted by f(R) models designed to account for the cosmic acceleration. I use the age matching technique to study how colour-selection effects may influence the cluster RSD signal, finding a similar to 10 per cent effect due to redder satellites preferentially occupying higher mass haloes, and a similar to 5 per cent effect due to assembly-biased colours of centrals. In order to use cluster RSD measurements to robustly constrain modified gravity, we likely will need to develop empirical galaxy formation models more sophisticated than any in the current literature.