On the Distribution of Dark Matter in Clusters of Galaxies

Abstract

The goal of this thesis is to provide constraints on the dark matter density profile in galaxy clusters by developing and combining different techniques. The work is motivated by the fact that a precise measurement of the logarithmic slope of the dark matter on small scales provides a powerful test of the Cold Dark Matter paradigm for structure formation, where numerical simulations suggest a density profile $\rho_{DM} propto r^{-1}$ or steeper in the innermost regions. We have obtained deep spectroscopy of gravitational arcs and the dominant brightest cluster galaxy in six carefully chosen galaxy clusters. Three of the clusters have both radial and tangential gravitational arcs while the other three display only tangential arcs. We analyze the stellar velocity dispersion for the brightest cluster galaxies in conjunction with axially symmetric lens models to jointly constrain the dark and baryonic mass profiles jointly. For the radial arc systems we find the inner dark matter density profile is consistent with $\rho_{DM}propto r^{-\beta}$, with $langle\beta\rangle=0.52^{+0.05}_{-0.05}$ (68\% CL). Likewise, an upper limit on $\beta$ for the tangential arc sample is found to be $\beta<$0.57 (99\% CL). We study a variety of possible systematic uncertainties, including the consequences of our one-dimensional mass model, fixed dark matter scale radius, and simple velocity dispersion analysis, and conclude that at most these systematics each contribute a $Delta \beta sim 0.2$ systematic into our final conclusions. These results suggest the relationship between dark and baryonic matter in cluster cores is more complex than anticipated from dark matter only simulations. Recognizing the power of our technique, we have performed a systematic search of the Hubble Space Telescope Wide Field and Planetary Camera 2 data archive for further examples of systems containing tangential and radial gravitational arcs. We carefully examined 128 galaxy cluster cores and found 104 tangential arcs and 12 candidate radial arcs, each of whose length to width ratio exceeds 7. Twenty-four additional radial arc candidates were identified with smaller length to width ratios. In order to confirm the nature of these radial arc candidates, we obtained Keck spectroscopy of 17 candidate radial arcs, suggesting that the contamination rate from non-lensed objects is $sim$30-50\%. With this catalog of gravitational arcs, we use the number ratio of radial to tangential arcs as a statistical measure of the inner logarithmic dark matter slope, $\beta$, in galaxy cluster cores. This abundance ratio is fairly constant across various cluster subsamples partitioned according to X-ray luminosity and optical survey depth. Using two-component mass models for cluster cores, we show that the arc statistics in our survey are consistent with $\beta lesssim 1.6$, depending on various assumptions, the most important of which is the stellar mass associated with the brightest cluster galaxy. Finally, in order to refine and confirm the analysis technique presented for the six galaxy clusters with gravitational arcs and brightest cluster galaxy dynamics, and to address several comments on our earlier work, we present a more elaborate two dimensional lens model of the cluster MS2137 using a newly upgraded gravitational lensing code. We combine these two-dimensional lens model constraints with the velocity dispersion data of the brightest cluster galaxy to constrain the dark and baryonic mass profiles jointly. We find the inner dark matter density profile to be consistent with a distribution with logarithmic inner slope $langle\beta\rangle=0.25^{+0.35}_{-0.12}$ (68\% CL) in agreement with the axially symmetric model presented earlier for MS2137 ($langle\beta\rangle=0.57^{+0.11}_{-0.08}$) with simpler assumptions. However, we do find a significant degeneracy remains between the scale radius, $r_{sc}$, and inner logarithmic slope, $\beta$, which might be resolved with further lensing data at larger radii. Notwithstanding this limitation, we conclude that our technique of combining gravitational lensing with stellar dynamics offers a reliable probe of the dark matter distribution in clusters and that, most likely, a discrepancy remains between numerical predictions in the CDM paradigm and our observations.