The Distribution of Dark Matter and Stellar Orbits in Nine Coma Early-Type Galaxies Derived from Their Stellar Kinematics Jens Thomas
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The distribution of dark matter and stellar orbits in nine Coma early-type galaxies derived from their stellar kinematics Jens Thomas M¨unchen 2006 The distribution of dark matter and stellar orbits in nine Coma early-type galaxies derived from their stellar kinematics Jens Thomas Dissertation an der Fakult¨at f¨ur Physik der Ludwig–Maximilians–Universit¨at M¨unchen vorgelegt von Jens Thomas aus Essen M¨unchen, den 05.04.2006 Erstgutachter: Prof. Dr. Ralf Bender Zweitgutachter: Prof. Dr. Ortwin Gerhard Tag der m¨undlichen Pr¨ufung: 27.10.2006 Contents Zusammenfassung xv 1 Introduction 1 1.1 General motivation .......................... 1 1.2 Dynamical modelling of early-type galaxies ............ 4 1.3 The orbit superposition technique .................. 7 1.4 State of affairs ............................ 9 1.5 Aims and structure of the thesis .................. 12 2 Mapping distribution functions by orbit superpositions 15 2.1 Introduction .............................. 15 2.2 The orbit library ........................... 17 2.2.1 Spatial and velocity binning ................. 18 2.2.2 Orbital properties ...................... 18 2.2.3 Choice of orbits ........................ 19 2.2.4 Use of the library ....................... 22 2.3 Orbital weights and phase-space densities ............. 22 2.3.1 Phase-space densities of orbits ............... 23 2.3.2 Orbital weights from DFs .................. 23 2.4 Orbital phase volumes ........................ 24 2.5 Mapping distribution functions onto the library .......... 28 2.5.1 Spherical γ-models ...................... 29 2.5.2 Flattened Plummer model .................. 32 2.5.3 Changing the spatial coverage of the library ........ 34 2.5.4 Changing the number of orbits in the library ....... 36 2.6 Fitting the library .......................... 36 2.6.1 Maximum entropy technique ................ 36 2.6.2 The smoothing parameter α ................. 38 2.7 Reconstructing distribution functions from fitted libraries .... 38 2.7.1 Hernquist model ....................... 39 2.7.2 Flattened Plummer model .................. 42 2.8 Summary ............................... 44 vi CONTENTS 3 Regularisation and orbit models for NGC 4807 47 3.1 Introduction .............................. 47 3.2 NGC 4807: model input ....................... 49 3.2.1 Photometric data ....................... 49 3.2.2 Deprojection ......................... 49 3.2.3 Kinematic data ........................ 51 3.3 Orbit superposition models ..................... 53 3.3.1 Basic grids .......................... 53 3.3.2 Luminous and dark mass distributions ........... 53 3.3.3 Orbit collection ........................ 55 3.3.4 Orbit superposition ..................... 55 3.3.5 Comparing model with data kinematics .......... 56 3.4 Regularisation ............................. 57 3.4.1 Motivation .......................... 57 3.4.2 Regularisation from isotropic rotator models ....... 58 3.5 Recovering isotropic rotator models ................. 64 3.5.1 Mass-to-light ratio Υ and inclination i ........... 64 3.5.2 Internal kinematics ...................... 65 3.5.3 Mass distribution ....................... 66 3.6 Dark matter in NGC 4807 ...................... 70 3.7 Stellar motions in NGC 4807 .................... 75 3.8 Phase-space structure of NGC 4807 ................. 76 3.9 Summary and Discussion ...................... 83 3.9.1 Regularised orbit models .................. 83 3.9.2 Luminous and dark matter in NGC 4807 ......... 84 2 2 3.9.3 Comparing the kinematics: χGH versus χLOSVD ...... 85 3.9.4 The outer parts of NGC 4807 ................ 88 3.9.5 Internal stellar kinematics of NGC 4807 .......... 91 4 The coma sample and its modelling: general survey 93 4.1 Summary of observations ...................... 93 4.2 Modelling setup and regularisation ................. 95 4.3 Notes on individual galaxies ..................... 96 4.4 Confidence levels ...........................108 5 Mass composition of Coma ellipticals 111 5.1 Outline ................................111 5.2 Evidence against constant mass-to-light ratios ...........111 5.3 Crosscheck with stellar populations .................113 5.3.1 Independent stellar mass-to-light ratios .......... 114 5.3.2 Stellar population gradients .................115 5.3.3 Projection effects .......................118 5.3.4 Discussion ...........................120 5.3.5 Conclusions ..........................125 5.4 Spatial distribution of luminous and dark matter ......... 127 5.4.1 Circular velocity curves ...................127 CONTENTS vii 5.4.2 Mass-density profiles .....................128 5.4.3 Dark matter fractions ....................131 5.5 Uncertainties in the mass decomposition ..............132 5.5.1 Central dark matter .....................132 5.5.2 Radially increasing stellar mass-to-light ratios ....... 132 5.6 Regularisation .............................135 5.7 Dark matter distribution functions .................136 5.8 Summary ...............................140 6 Dynamical structure of Coma ellipticals 143 6.1 Outline ................................143 6.2 Flattening and anisotropy ......................143 6.2.1 Galaxy fits ..........................144 6.2.2 Maximum entropy models ..................146 6.3 Local dynamical structure around the poles ............147 6.3.1 Velocity anisotropies .....................147 6.3.2 Anisotropy and H4 ......................149 6.3.3 The local distribution function ...............150 6.4 The bulk of stars at intermediate latitudes .............153 6.5 Local dynamical structure around the equatorial plane ...... 154 6.5.1 Velocity anisotropy ......................154 6.5.2 The local distribution function ...............155 6.5.3 The vertical structure ....................159 6.6 Discussion of the dynamical structure ...............165 6.7 Regularisation .............................169 6.8 Summary ...............................170 7 Scaling relations 177 7.1 Outline ................................177 7.2 Stellar mass-to-light ratios ......................177 7.3 Orbital anisotropy ..........................180 7.4 Fundamental plane ..........................183 7.5 Tully-Fisher relation of ellipticals ..................187 7.6 Centre-halo relation .........................189 7.7 Dark matter scaling relations ....................190 7.7.1 Halo scaling relations ....................191 7.7.2 Central dark matter .....................196 7.8 Summary ...............................198 8 Summary and conclusions 201 A The sensitivity of Υdyn on the central photometric resolution 207 B The centre of GMP0144/NGC4957 209 C Orbital shape parameters 213 viii Contents D The average local distribution function 217 E The triple nucleus of M31 219 Danksagung 249 List of Figures 2.1 Surface of Section in a flattened Hernquist potential ....... 20 2.2 Example of a Voronoi tessellated surface of section ........ 26 2.3 Distribution of orbital energies and angular momenta in a library 28 2.4 Isotropic Hernquist model mapped by an orbit superposition .. 30 2.5 Anisotropic Hernquist model mapped by an orbit superposition . 31 2.6 Plummer model mapped by an orbit superposition ........ 33 2.7 DF-mapping with orbit libraries of different spatial extension .. 35 2.8 DF-mapping with different number of orbits ............ 37 2.9 Isotropic Hernquist model fitted by an orbit library ........ 40 2.10 Reconstructed DF of isotropic Hernquist model .......... 41 2.11 Accuracy of the reconstructed isotropic Hernquist DF ...... 42 2.12 Anisotropic Hernquist model fitted by an orbit library ...... 43 2.13 Plummer model fitted by an orbit library ............. 45 2.14 Accuracy of the reconstructed Plummer DF ............ 46 3.1 Photometric data and deprojections of NGC 4807 ......... 50 3.2 Deprojections of NGC 4807, viewed edge-on ............ 52 3.3 Smooth reconstruction of an isotropic rotator model ....... 59 3.4 Overfitted reconstruction of an isotropic rotator model ...... 60 3.5 Model-kinematics along not observed position angles ....... 61 3.6 Accuracy of reconstructed velocity moments ............ 63 3.7 Reconstruction of mass-to-light ratio and inclination ....... 65 3.8 Reconstruction of internal velocity moments ............ 67 3.9 Recovery of the mass decomposition of a test model ....... 68 3.10 Recovery of dark halo parameters of a test model ......... 69 3.11 The stellar mass-to-light ratio Υ of NGC 4807 ........... 71 3.12 Projected kinematics of edge-on models of NGC 4807 ...... 72 3.13 The mass structure of NGC 4807 .................. 73 3.14 The dark halo parameters of NGC 4807 .............. 74 3.15 Luminous and dark matter profiles in models of NGC 4807 ... 76 3.16 Projected kinematics of an i = 50◦ model of NGC 4807 ..... 77 3.17 Internal velocity moments in the best-fitting model of NGC 4807 78 3.18 Confidence intervals for the velocity moments of NGC 4807 ... 79 3.19 Internal kinematics of the i = 50◦ model of NGC 4807 ...... 80 x LIST OF FIGURES 3.20 Phase-density versus energy in the bestfit model of NGC 4807 .. 81 3.21 Phase-density versus ϑmax and Lz/Lz,circ for NGC 4807 ..... 82 3.22 Stellar populations versus dynamical models for NGC 4807 ... 86 2 3.23 Reconstruction of a test model from min(ˆχLOSVD) ........ 87 2 3.24 Halo structure of NGC 4807 from min(ˆχLOSVD) .......... 89 3.25 The keel in the DF of NGC4807 and its projected kinematics .. 90 4.1 Photometry and kinematics of NGC 4827 against models .... 99 4.2 Photometry and kinematics of NGC 4860 against models . 100 4.3 Photometry and kinematics of NGC 4952 against models .