2.5.1 Stellar Mass

The Structure of Elliptical Galaxies and Galaxy Clusters by David Augustin Buote Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 1995 ( Massachusetts Institute of Technology 1995. All rights reserved. (Z>- "IV k Author ......... v . w. .. .. ......... Department of Physics May 5, 1995 n / / ? _ Certified by ...... ..............I 'J%v - Claude R. Canizares Professor Thesis Supervisor Accepted by .............................. ....................... George F. Koster Chairman, Departmental Graduate Committee MASSACHUSETTSINSTITUTE nF rrrH"NOLOGY JUN 2 61995 LIBRARIES 6Cepnr, The Structure of Elliptical Galaxies and Galaxy Clusters by David Augustin Buote Submitted to the Department of Physics on May 5, 1995, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract I have analyzed the X-ray-emitting gas in elliptical galaxies and galaxy clusters to probe their structure and dynamics. In addition to extending previous studies of detailed hydrostatic modeling of these systems, I have developed a new method to test for the existence of dark matter that is free from uncertainties in the tempera- ture gradients and (in principle) does not require any model fitting. Applying these techniques to ROSAT PSPC data of the E4 galaxy NGC 720 I concluded that the dark matter distribution is highly elongated with ellipticity, c S, 0.5 - 0.7; similar, but weaker, constraints are obtained for the E7/S0 galaxy NGC 1332. These results provide the first strong evidence for flattened halos in normal (i.e. no polar rings) ellipticals. I have also demonstrated that X-ray analysis of the aggregate shape of a galaxy cluster on scales of r 1-2 Mpc is insensitive to subclustering on small scales (S few hundred kpc). From analysis of ROSAT PSPC data of the aggregate shapes of five Abell clusters I concluded that they are quite elongated ( 0.40 - 0.55) and are consistent with the shapes traced by the galaxy isopleths. Finally, I have devised a method to quantitatively relate the morphologiesof clusters to their dynamical states. Applying this method to ROSAT PSPC images of 55 clusters I find that the statistics of this method, power ratios, suggest an evolutionary track for the clusters; i.e. the location of a cluster along the track indicates the dynamical state of the cluster and the distribution of clusters along this track measures the formation and evolution of clusters in our sample. In principle power ratios can be used to address any problem where cluster evolution is an issue. Thesis Supervisor: Claude R. Canizares Title: Professor On Dark Matter by Augustin LaTorre What wasn't thought was there Is now assuming status Whirling globes acting strange As on an unknown lattice. By scratching head & with computer And using higher math We found out the reason why The globes had such a path. And the reason for it all After computing all the data Was something unknown hitherto It is called Dark Matter. And matter it must be Though unseen in inky dark Like the me-ow without the cat The trill without the lark. It all seems to reason well Else Newton's Laws in traction If a force that was applied Did not produce reaction. Acknowledgments My transformation from a callow acolyte to an adept, at least within a very specialized sphere (or, shall I say, ellipsoid?), has been a journey at times rewarding, often arduous, but never dull. The journey never could have been completed without the advice, encouragement, and support of many professors, fellow graduate students, and especially my family and friends. Since it is impossible to acknowledge everyone, I extend a universal thanks!" to those special people who, for lack of space (or my memory!), I fail to explicitly recognize. I must first express warm thanks to my thesis supervisor, Claude Canizares, for suggesting such an interesting research topic and also allowing me the freedom to explore other avenues of my choice. I have greatly appreciated Claude's easy-going style and willingness to send me to relevant conferences and provide the necessary computing resources. Thanks are also due to the other astrophysics professors on my thesis committee: Ed Bertschinger and John Tonry. Ed's cosmology class was proba- bly the most influential course I took at MIT, and I especially value the discussions we had during his office hours. I also thank Ed for welcoming me to his cosmology group meetings which have allowed me to keep abreast of the current trends in theoretical cosmology. I thank John for asking me to investigate his clever geometrical exposi- tion of elementary gravitational-lens theory. The hours I spent with John fleshing out these ideas were certainly some of the most intellectually stimulating of my graduate career. What can I say about John Tsai? If it were not for John it is unlikely I would have tackled the issue of substructure in clusters and a very important part of my thesis would never have come about. John, many thanks for convincing me that I should think seriously about finding a way to quantify substructure. Working with John has been my first collaboration outside MIT, and I think my independence and confidence have grown as a result. I look forward to continuing our collaboration on the power ratios! Many graduate students, some graduated, some still here, have either taken the time to listen to my ramblings about my research, have engaged me in general stimulating scientific discussions, have commiserated with me about all the various in- dignities that graduate students must inevitably suffer, and have even played some very good games of volleyball of which I had the pleasure of participating. I first thank Eric Gaidos, comrade-in-Canizares, for being an effective "sounding board" by being diligent to always remind me that other viewpoints exist, especially from those who live outside 0.1 - 10 keV. I also want to thank Chris Becker, John Blakeslee, Jim Frederick, Lam Hui, Una Hwang, C.-P. Ma, gene Magnier, Bob Rutledge, Uros Seljak, and Jon Woo for scientific chats over these years. All the current denizens of room 616 - Eric, Bob, Derek, Jeff, and Patrick - I thank you for making this small room always a pleasant environment for work or just shooting-the-breeze. I hope I have not been too insufferable these last few months as my thesis has neared completion and the job situation has become increasingly more depressing. I know you guys won't say anything but I will: Thanks for putting up with me. My work was made easier by a few scientists who were considerate enough to share their computing resources with me. In particular, I thank Mark Bautz, Dan Dewey, George Ricker, and Mike Wise for kindly allowing me use of their computers. In this limited space I cannot possibly express all the gratitude I owe to my family and friends, but that does not mean I will not try! Mom and Dad, thanks for your constant encouragement and support, both emotionally and financially, whenever I have needed it - the care packages" have also been much appreciated! Paul, my bro, same goes to you! I would like to specially thank Nana and Papa for just being so wonderful over these many years. To my buddies Fran and Paul (i.e. Riches): thanks for being there all these years - has it really been that long? Through it all these past five years, the good times, the bad times, the ups and downs, there has been a constant in my life, my best friend, Hweilee. Without her kindness and reassuring warmth I could not have accomplished this thesis while maintaining my sanity. Thanks, Hwei, for everything: it would not have been the same without you! Finally, I thank my grandfather for his unique interpretation of dark matter. Contents 1 Introduction 12 1.1 Theoretical Motivation . ................ 12 1.1.1 Dark Matter . ................ 12 1.1.2 Substructure in Galaxy Clusters . ............... 14 1.2 Status of the X-ray Observations .... ................ 15 1.3 Goals of this Thesis ............ ................ 17 2 Geometrical Evidence for Dark Matter: X-ray Constrail nts on the Mass of the Elliptical Galaxy NGC 7201 21 2.1 Introduction. ......................... 22 2.2 Observations and Data Analysis .............. 24 . 2.2.1 Spatial Analysis ................... 25 2.2.2 Spectral Analysis ................... 36 2.3 Geometrical Evidence for the Existence of Dark Matter 39 2.3.1 Physical Interpretation of the X-ray Isophote Shapes 39 2.3.2 Geometric Implications ... ...... ..... ... 43 2.3.3 Implications for Alternative Theories of Gravitation 47 2.4 Total Gravitating Matter Distribution ........... ... 50 2.4.1 Model ......................... ... 50 2.4.2 Shape of the Total Matter .............. ... 54 2.4.3 Estimate of the Total Matter ............ 56 2.5 Dark Matter Distribution .................. ... 58 2.5.1 Stellar Mass ... 59 6 2.5.2 X-ray Gas Mass ......... 61 .. 2.5.3 Results . .. .. .. 62 2.6 Discussion . .......... 65 2.7 Conclusion . 68 A. Analytical Calculation of AcM and AOM 71 B. Projections of Non-Similar Spheroids 73 3 X-ray Constraints on the Intrinsic Shape of the Lenticular Galaxy NGC 1332 100 3.1 Introduction .................... 101 ........... 3.2 Spatial Analysis of the X-ray data ......... ... **....** 104 3.2.1 Image Reduction . .. *....... 104 3.2.2 Radial Profile . ........... 106 3.2.3 Ellipticity of the X-ray Surface Brightness .......... 108 3.3 Spatial Analysis of the Optical data ....... 112 .... ,...., 3.4 Spectral Analysis of the X-ray data ........ 114 3.5 Geometric Test for Dark Matter: Clarification and Applications. 118 .... ,,..... 118 3.5.1 Theory ................... ......... 3.5.2 Application ................. 121 3.6 Composite Gravitating Matter Distribution . 126 .........

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