Dynamical Analysis of Clusters


One of the key tools we have in our armory for analysing the clusters themeselves or their member galaxies is the caustic diagram. This is simply a plot of redshift versus projected cluster-centric radius for those galaxies in our spectroscopic survey.

The sphere of influence of a cluster extends well beyond the virial radius within which galaxies lie within its dark matter halo and are encountering the hot plasma which forms the intra-cluster medium (ICM). Clusters lie at nodes of the filamentary structure forming the large-scale structure of the Universe. Their gravitational pull extends well beyond the virial radius drawing those galaxies in the connecting filaments to detach from the overall Hubble expansion of the Universe, and slowly fall towards the cluster, forming a coherent infall pattern extending out to 10-20 Mpc from the cluster. As they fall inwards they are accelerated by the gravitional potential of the cluster, reaching a maximal velocity as they pass through the cluster for the first time. They then ultimately become virialized members, orbiting on bound orbits around the cluster. This behaviour produces the characteristic "trumpet"-shaped caustic profile of galaxies infalling and orbiting around a massive cluster.

By identifying and mapping this caustic profile, we can identify all those galaxies within the sphere of influence of the cluster (including those beyond the virial radius) as those lying within the caustic itself.

The width of the caustic profile itself as a function of cluster-centric radius can be used to measure the mass profile of the cluster, not just within the virial radius, but beyond. The width of the profile at a given radius can be associated to the escape velocity a galaxy would have at that distance from the cluster. This caustic method for mass estimation has the key advantage that it does not depend on the (hydro)dynamical state of the cluster (e.g. relaxed or merging) in the same way masses derived from X-ray emission or the SZ-effect may be.

FIGURE 1: Stacked caustic profile of the 30 most massive clusters in the Millennium cosmological simulation as they would be observed at z=0.21. Each point indicates a galaxy from the Bower et al. (2006) semi-analytic model catalog, colored according to when it was accreted into the cluster, those being accreted earliest being indicated by red symbols. Here accretion epoch is defined as the redshift when the galaxy passes within r500 for the first time. Galaxies yet to pass through r500 by z=0.21 are indicated in blue and dominate at large cluster-centric radii and along the caustics. Taken from Haines et al. (2012)


The location of a galaxy within the caustic profile has been shown to be strongly linked to when it was accreted into the cluster. Galaxies currently falling into the cluster for the first time tend to lie along the caustics themselves, while those galaxies accreted earliest, when the cluster core was still forming and gaining mass, will tend to have the lowest cluster-centric radii and line-of-sight velocities. We can analyse the locations of sub-populations of galaxies in the caustic diagrams of individual clusters, or stack over the many clusters in our sample by scaling each cluster's caustic profile by its velocity dispersion and r_500 radius.

We have used this method to show that the cluster galaxies detected by Herschel due to their ongoing obscured star formation are most likely infalling into the clusters for the first time, as are the X-ray AGN detected as point sources in our Chandra X-ray data. This confirms dynamically that both star formation and nuclear activity are strongly suppressed once a galaxy falls into the cluster. We aim to use this method to quantify the time-scales over which star formation is shut down in galaxies when they are accreted within the clusters.

FIGURE 2: Stacked observed caustic diagram of galaxies from the 26 LoCuSS clusters for which Chandra X-ray data exist. Each gray point indicates a spectroscopic cluster member. The red curves indicate the 1-sigma velocity dispersion profile as a function of radius. X-ray AGN identified as point-sources in the Chandra data are indicated by larger magenta (black) symbols according to whether they are detected (not-detected) with Spitzer at 24um. Blue symbols indicate broad-line QSOs. The X-ray AGN can be seen to lie predominately along the caustics, indicative of an infalling population. The open magenta symbols and error bars indicate the velocity dispersion of the cluster X-ray AGN, which is 1.51x that of inactive cluster galaxies. This kinematic segregation is significant at the 4.66-sigma level. Taken from Haines et al. (2012)



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