The Phase-Space Distribution of Galaxy Clusters

Abstract

We provide the modeling framework to enable a proposed new measurement of the Hubble constant, using the radial extent of galaxy clusters as a standard ruler. Observationally, we plan to measure the angular extent of the cluster and the velocity of galaxies around the cluster. More massive clusters have galaxies that orbit faster, so we can use the velocity of galaxies within clusters to estimate an effective cluster mass. To enable this, we have calibrated the relation between line-of-sight galaxy velocity and cluster mass using cosmological simulations. With an estimate of halo mass now in hand, we can infer the radius of the dark matter halo containing it. To enable this, we have also calibrated the relationship between halo mass and radius with simulations. We find that a halo whose mass is $1\times10^{14}$ $M_\odot/h$ has a physical radius of $596\pm3$ kPc/h, better than $1\%$ precision. Comparing the halo radius inferred from galaxies' velocities to their angular extent allows us to estimate the distance to the cluster, which in turn can be used to assemble a Hubble diagram for galaxy clusters. The high level of precision in the halo radius needed to establish this measurement is founded on a recent insight in halo modeling: galaxies in halos can be split into two populations: those orbiting their host dark matter halo, and those falling into the host for the first time. Here, we present an algorithm that uses the galaxies' accretion history to distinguish between them. We use our split catalog to generate fits for the orbiting and infalling galaxy phase space densities. Importantly, each can be described as depending on a single fundamental scale, the halo radius $r_h$. Both the orbiting and density profiles can be described with 5$\%$ accuracy using $r_h$ as the length scale. In velocity space, we show that the infalling velocity distribution has a bimodal appearance due to the impact of the Hubble flow on galaxy velocities. Our model of the distribution of galaxy line-of-sight velocities is also 5\% accurate. Finally, to prepare the calibration for application to galaxy clusters, we characterize the impact of cluster selection effects the phase space distribution of galaxies. To do so, we select clusters based on the galaxy counts in cylinders of height $\pm$20 h$^{-1}$~Mpc and $\pm$60 h$^{-1}$~Mpc along the line of sight. The distributions of line-of-sight velocities for both orbiting and infalling galaxies are robust to cluster selection; so is the projected orbiting surface density. The projected surface density of the infalling population, however, exhibits a strong scale-dependent bias, where the scale is set by the aperture used in the process of cluster selection. Finally, we suggest the next steps needed to characterize the dependence of the halo radius on the assumed cosmology, as well as the possible influence of baryonic processes on it. As a coda, we also include work on the broadband emission of galaxy clusters, and examine the possible detection of extra-solar neutrinos (via the ICECUBE and Auger experiments) from the Coma cluster of galaxies, as well as for $\gamma$-ray-bright clusters.