On the Distribution of Dark Matter in Clusters of Galaxies Thesis by David J. Sand In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2005 (Defended September 6, 2005) ii iii c 2005 David J. Sand All rights Reserved iv v Acknowledgements There are many, many people to thank for this thesis and without them it would not have been possible. I have been lucky to have a great advisor in Richard Ellis. During my first year when I was looking for a research group, he was the only one eager to talk with me and to offer me a position. Richard was always there to give praise and sage advice at the right times. He always has the big picture in mind, something that is easy to miss when you’re buried in data. And he is always out advertising your work to others. He would also light a fire under my ass when necessary. One of my greatest mentors here at Caltech has been Tommaso Treu. His importance can not be overstated. From my first moments joining Richard Ellis’ group until the day before my thesis defense, Tommaso has been there to hear my concerns, to focus my thoughts, and to calm me down. He has taught me nearly everything I know about doing science and astronomy. More than that, he has been a great friend. He and his wife, Stefania Tutino, have always provided wonderful food and conversation. Thank you so much Tommaso and Stefania. I hope we stay close. A separate mention is due to my office mates Kevin Bundy and Stanimir Metchev, along with my pseudo-office mate Josh Eisner. Thank you for the good times and the friendship these last several years. I am confident that I have made life-long friends. I would like to deeply and dearly thank Vivian Castro for her love during my first year of graduate school and her support ever since. I wish great things for her. Russel White always gave me the call, with an occasional chili burger and many, many drinks behind us. I wish to thank Alice Shapley for always being available to talk, gossip and give advice, even many years after she left Caltech. I would like to thank Mike Santos and Alison Farmer for many nights of hours-long conversation. Farmer John, you weren’t a bad roomate either. It was excellent grabbing coffee and having scientific discussions with Graham Smith. Thanks to Jean-Paul Kneib for his hospitality in Marseilles so that Chapter 5 of vi this thesis could happen. Little Dan and Brian are always up for a chat or some lunch or even a 40 oz. Good luck, don’t work too hard. Melissa Enoch has always been a good friend to me, despite the hard time that I give her. Pizza and a movie was always so great or even a quick run to In n’ Out. We have had our ups and downs, but hopefully we will continue to be friends. Thanks go to my thesis committee: Andrew Blain, John Mulchaey and Marc Kamionkowski. John was always supportive and allowed me to come up to Carnegie whenever for a quick chat. Marc was the one who encouraged me to switch to an observational cosmology group and to work with Richard Ellis in particular. Thanks Marc, I owe you one. Keep listening to hip-hop. This acknowledgement section would not be complete if I did not thank Ernie and Ernesto’s lunch truck, who kept my belly happy with good food and were always friendly. The lunch trucks in Tucson will pale in comparison. My family deserves particular thanks. My parents have been incredibly sup- portive all these years. Even though I don’t call enough or let them visit enough, my love is strong. The free meals were always appreciated as well as the advice you gave on life in general. Thank you for encouraging me to go to grad school, for whatever reasons I had. Finally, I am deeply grateful to my sunshine, Eva Rose Murdock. Thank you so much for popping into my life out of no where. You have supported and loved me beyond all expectations and I will never forget it. Bring on the adventures. vii On the Distribution of Dark Matter in Clusters of Galaxies by David J. Sand In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 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 ρ r−1 or steeper in the innermost regions. DM ∝ 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 ρ r−β, with β = 0.52+0.05 DM ∝ h i −0.05 (68% CL). Likewise, an upper limit on β for the tangential arc sample is found to be β <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 ∆β 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. viii 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 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, β, 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 β < 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 gravita- tional 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 β = 0.25+0.35 (68% h i −0.12 CL) in agreement with the axially symmetric model presented earlier for MS2137 ( β = 0.57+0.11) with simpler assumptions. However, we do find a significant h i −0.08 degeneracy remains between the scale radius, rsc, and inner logarithmic slope, β, 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 clus- ix ters and that, most likely, a discrepancy remains between numerical predictions in the CDM paradigm and our observations. x xi Contents 1 Introduction 1 1.1 Observational Evidence for Dark Matter . 2 1.2 Predictions from Simulations of Structure Formation . ...... 6 1.3 The Dark Matter Density Profile on the Dwarf and Normal Galaxy Scale................................... 10 1.4 Measuring the Dark Matter Density Profile in Clusters . 13 1.4.1 Gravitational Lensing . 14 1.4.2 X-ray measurements of the ICM . 18 1.4.3 Dynamics ............................ 22 1.5 Goals of this Thesis & Thesis Overview . 24 2 The Dark Matter Density Profile of the Lensing Cluster MS2137- 23: A Test of the Cold Dark Matter Paradigm∗ 29 2.1 Introduction............................... 30 2.2 Observations .............................. 31 2.2.1 KeckSpectroscopy .. .. .. .. .. .. .. 31 2.2.2 Hubble Space Telescope Imaging . 33 2.3 Luminous and Dark Matter Distribution . 33 2.3.1 MassModel........................... 33 2.3.2 Gravitational Lensing . 36 2.3.3 Lensing+Dynamics . .. .. .. .. .. .. 37 2.4 SummaryandDiscussion . 40 xii 3 The Dark Matter Distribution in the Central Regions of Galaxy Clusters: Implications for CDM 43 3.1 Introduction............................... 44 3.2 SampleSelection ............................ 48 3.3 ImagingDataandAnalysis .