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Globular Clusters and Galactic Nuclei

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Globular Clusters and Galactic Nuclei Scuola di Dottorato “Vito Volterra” Dottorato di Ricerca in Astronomia– XXIV ciclo Globular Clusters and Galactic Nuclei Thesis submitted to obtain the degree of Doctor of Philosophy (“Dottore di Ricerca”) in Astronomy by Alessandra Mastrobuono Battisti Program Coordinator Thesis Advisor Prof. Roberto Capuzzo Dolcetta Prof. Roberto Capuzzo Dolcetta Anno Accademico 2010-2011 ii Abstract Dynamical evolution plays a key role in shaping the current properties of star clus- ters and star cluster systems. We present the study of stellar dynamics both from a theoretical and numerical point of view. In particular we investigate this topic on different astrophysical scales, from the study of the orbital evolution and the mutual interaction of GCs in the Galactic central region to the evolution of GCs in the larger scale galactic potential. Globular Clusters (GCs), very old and massive star clusters, are ideal objects to explore many aspects of stellar dynamics and to investigate the dynamical and evolutionary mechanisms of their host galaxy. Almost every surveyed galaxy of sufficiently large mass has an associated group of GCs, i.e. a Globular Cluster System (GCS). The first part of this Thesis is devoted to the study of the evolution of GCSs in elliptical galaxies. Basing on the hypothesis that the GCS and stellar halo in a galaxy were born at the same time and, so, with the same density distribution, a logical consequence is that the presently observed difference may be due to evolution of the GCS. Actually, in this scenario, GCSs evolve due to various mechanisms, among which dynamical friction and tidal interaction with the galactic field are the most important. On the other side, the collisionless stellar halo component stands unchanged, thus the difference between the two profiles may correspond to mass lost by the GCS to the galactic center. There the GCs merge and they contribute to the formation/accretion of a luminous and compact central Nuclear Star Cluster (NSC). This is known as the “merger model” for the formation of NSCs, observed at the center of many galaxies and also in the Milky Way (MW) center. In the second part of this work a new high performance code, NBSymple, is presented. NBSymple is an efficient N-body integrator implemented on a hybrid CPU+GPU platform, exploiting a double-parallelization on CPUs and on the hosted Graphic Processing Units (GPUs). The precision is guaranteed by direct summa- tion for force evaluation, and on the use of high order, symplectic time integration methods. The code allows the choice between two different symplectic integrators: a second-order algorithm (commonly known as leapfrog) and a much more accurate (but also time consuming) sixth-order method. The effect of the external galactic field is represented as an analytical approximation of its gravitational potential. The code has been widely tested and benchmarked. Moreover, it has been used for various applications (globular clusters quasi-radial orbit through a galactic massive central object, primordial evolution of young stellar clusters, etc.). NBSymple and another, publicly available, direct summation code, φGRAPE, have been used to explore the the previously described merger mode for the Galactic NSC formation. In particular, we used self consistent N-body simulations where the Galaxy was modeled using observational data about the Milky Way, and including the presence of the Galactic central supermassive black hole. We let decay 12 GCs iii initially located on different circular orbits at the same galactocentric distance. The merging of clusters in the central zone of the Galaxy and its following evolution due to two-body relaxation generates a NSC that actually resembles the one observed at the center of the MW. By mean of numerical simulations carried on with NBSymple, we investigated more in detail the dynamical evolution of GCs in the MW potential with particular attention to the formation of clumpy structures in the tidal tails that arise around the orbiting cluster. Although various hypothesis have been proposed, the formation process of these clumps is not yet clearly understood. Through a statistical analysis of the orbital properties of the stars that “escape” from the cluster we aimed to a better understanding of the on going process. Studying and comparing such simulations with observational data we could gain to a deeper knowledge of the shape Galactic potential and, more generally, of the Galactic dynamics. iv Contents Introduzione 1 Introduction 5 1 A brief introduction to Stellar Systems 13 1.1 Associations and stellar streams . 13 1.2 Openclusters ............................... 14 1.3 GlobularClusters............................. 15 1.3.1 Color-Magnitude diagram . 17 1.3.2 Dynamical and structural properties . 18 1.3.2.1 Surface brightness profile . 18 1.3.2.2 Dynamical properties . 20 1.4 NuclearStarClusters .......................... 21 1.4.1 Nuclear star clusters along the Hubble sequence . 21 2 Globular cluster system erosion in elliptical galaxies 25 2.1 The formation and the evolutionary mechanisms of GCSs . 26 2.1.1 Scenario 1: different formation ages . 26 2.1.2 Scenario 2: The coeval birth hypothesis . 27 2.2 Previousresults.............................. 29 2.2.1 The Milky Way, M 31 and M 87 . 31 2.2.2 Other 11 elliptical galaxies . 33 2.2.3 The Fornax cluster: NGC 1379, NGC 1399, NGC 1404 . 33 2.3 Method for Scenario 2: improvements and new results . 34 2.3.1 NGC1400............................. 36 2.3.2 NGC1407............................. 37 2.3.3 NGC3258............................. 38 2.3.4 NGC3268............................. 40 2.3.5 NGC4374(M84) ........................ 40 2.3.6 NGC 4406 (VCC 881) . 41 2.3.7 NGC4472(M49) ........................ 43 2.3.8 NGC4636............................. 44 2.4 A new result: the correlation between Ml, MV and Mbh ....... 45 v 2.5 Summary ................................. 47 3 The N-body problem and the dynamical evolution of stellar sys- tems 49 3.1 The N-bodyproblem........................... 49 3.1.1 The integrals of motion . 51 3.1.2 TheVirialTheorem . .. .. .. .. .. .. 53 3.1.3 Stability and some consequences of the virial theorem . 55 3.2 Time scales in N-bodysystems ..................... 56 3.3 Thenumericalapproach . 58 3.3.1 Computational issues and possible solutions . 59 3.4 Numericalmethods............................ 61 3.4.1 Treemethods........................... 61 3.4.2 Fast Multipole methods . 62 3.4.3 Particle-mesh methods . 62 3.4.4 Adaptive Mesh Refinement method . 63 3.4.5 Self consistent field methods . 63 3.4.6 P3MandPM-Treemethods. 63 3.4.6.1 Direct N-body calculations and time integration . 64 3.4.7 From Hamiltonian dynamics to symplectic integrators . 64 3.5 Hardware solutions for the direct summation method . ..... 67 4 NBSymple, a double parallel, symplectic N-body code running on Graphic Processing Units 71 4.1 The N-bodycode............................. 72 4.2 Implementationofthecode . 73 4.2.1 Hardwareandsoftware. 73 4.2.2 Thecodestructure.. .. .. .. .. .. .. 76 4.3 Results................................... 79 4.3.1 Performances and accuracy of the codes . 79 4.3.2 Hardware and software double precision arithmetics . 84 4.3.3 Codetimeprofiling.. .. .. .. .. .. .. 86 4.4 Somesimulationtests .......................... 87 4.4.1 Quasi circular cluster orbits in the Milky Way . 87 4.4.2 Quasi radial cluster-massive black hole collisions . ...... 89 4.5 FERMI architecture: benchmarks and comparisons . 90 4.6 MPI implementation and benchmarks . 95 4.7 Anewcode,benchmarksandtests . 96 4.7.1 Sometestsofthecode . 97 4.8 Young clusters primordial evolution with NBSymple . ..... 98 4.8.1 Themodel ............................ 101 4.9 TidaltailsaroundPalomar14. 104 4.10Summary ................................. 106 vi 5 Dissipationless Formation and Evolution of the Milky Way Nuclear Star Cluster 109 5.1 NSCsformationmodels . 110 5.2 Generaltests ............................... 111 5.2.1 Thecode ............................. 112 5.2.2 Themodels ............................ 112 5.2.3 GC on a circular orbit . 113 5.2.4 GConaradialorbit . 115 5.3 TheMilkyWayNSC........................... 116 5.4 The Milky Way case: Initial conditions . 117 5.4.1 The Galactic Model . 117 5.4.2 The Globular Cluster Model . 119 5.5 N-bodysimulations ........................... 122 5.5.1 Results: densityprofiles . 123 5.5.2 Results: morphology of the NSC . 127 5.5.3 Results:kinematics . 130 5.6 Collisional evolution of the Nuclear Star Cluster . 132 5.7 Discussion................................. 135 5.7.1 Massive Globular Cluster Orbital Decay in the Milky Way . 135 5.7.2 Star Formation History of the Milky Way Nuclear Cluster . 137 5.7.3 Mass-radius relation . 139 5.8 Summary ................................. 141 6 Tidal tails and clumpy structures around Globular Clusters 143 6.1 Searching for tidal tails in the sky and in simulations: a brief review 144 6.2 Modelsandmethods ........................... 146 6.2.1 Numericalmethods. 146 6.2.2 TheGalacticmodel . 147 6.2.3 Globular cluster model . 148 6.3 Results................................... 150 Conclusions 151 Conclusioni 156 A The formal error on the estimates of number of lost Globular Clus- ters 161 B A simplified derivation of the relaxation time 167 C The distribution of the Globular Clusters orbits 171 Bibliography 173 vii Introduzione Nel 1971 l’astronomo francese Charles Messier pubblicò un catalogo di oggetti celesti nebulosi brillanti. Il primo oggetto del catalogo, M1, era la Nebulosa del Granchio; il secondo,
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