MHD numerical simulations in a cosmological context [Elektronische Ressource] / Federico Andrés Stasyszyn. Betreuer: Simon White

Federico Stasyszyn

Sujets

• Astronomie

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2011
• Nombre de lectures: 36
• Poids de l'ouvrage: 13 Mo

Extrait

Ludwig-Maximilians-Universit¨at
Sigillum Universitatis Ludovici Maximiliani
MHD numerical simulations
in a cosmological context
Dissertation der Fakult¨at fu¨r Physik
Dissertation of the Faculty of Physics
der Ludwig-Maximilians-Universit¨at Mu¨nchen
at the Ludwig Maximilian University of Munich
fu¨r den Grad des
for the degree of
Doctor rerum naturalium
vorgelegt von Federico Andr´es Stasyszyn
presented by
aus Co´rdoba, Argentina
from
Mu¨nchen, 15.03.2011Sigillum Universitatis Ludovici Maximiliani
1. Gutachter: Prof. Dr. Simon D. M. White
referee:
2. Gutachter: Prof. Dr. Harald Lesch
referee:
Tag der mu¨ndlichen Pru¨fung: 27.05.2011
Date of the oral exam:Contents
Contents I
Zusammenfassung VII
Abstract IX
I Introduction 1
1 Astrophysics and Magnetic Fields 3
1.1 Extragalactic physics basics . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Observation of Magnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.1 Synchrotron Emission . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Faraday rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3 Zeeman Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.4 Polarization of Optical Starlight . . . . . . . . . . . . . . . . . . . . 12
1.3 Magnetic field in galaxy clusters . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Large scale magnetic fields in the Universe . . . . . . . . . . . . . . . . . . 17
1.5 Numerical simulations of cluster formation . . . . . . . . . . . . . . . . . . 20
1.6 Open questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
II Numerical Methods 25
2 MHD - Smoothed Particle Hydrodynamics 27
2.1 Introduction to SPH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1.1 Interpolants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 Building our set of Equations . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.1 Co-moving variables and units system . . . . . . . . . . . . . . . . . 33
2.2.2 Magnetic signal velocity . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.3 Induction equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.4 Magnetic force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.3 Instability corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3.1 Improvements in the underlying SPH formalism . . . . . . . . . . . 36
2.3.2 Divergence force subtraction . . . . . . . . . . . . . . . . . . . . . . 36
2.3.3 Divergence Cleaning: Dedner Method . . . . . . . . . . . . . . . . . 37
2.3.4 Smoothing the magnetic field . . . . . . . . . . . . . . . . . . . . . 39
I2.3.5 Artificial magnetic dissipation . . . . . . . . . . . . . . . . . . . . . 39
2.3.6 Euler potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4 Test problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.4.1 Brio-Wu shock-tube . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.4.2 The effect of field regularization . . . . . . . . . . . . . . . . . . . . 45
2.4.3 Shock tube problems . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.4.4 Multi dimensional Tests - Planar Tests . . . . . . . . . . . . . . . . 50
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
III Applications 61
3 Galaxy cluster and magnetic fields 63
3.1 Galaxy cluster slices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.2 Magnetic field profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.3 Synthetic RM Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.4 Structure Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4 Large Scale cosmological magnetic fields 83
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 The Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2.1 The cosmological MHD simulations . . . . . . . . . . . . . . . . . . 84
4.2.2 Artificial MHD models . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2.3 Synthetic RM catalogs . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2.4 Magnetic depth of the universe . . . . . . . . . . . . . . . . . . . . 88
4.3 Evaluating the cosmological Cross-Correlation Signal . . . . . . . . . . . . 88
4.3.1 Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.3.2 Evaluating uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3.3 Magnetic depths . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3.4 Magnetic field models . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.4 Simulating the observational process . . . . . . . . . . . . . . . . . . . . . 92
4.4.1 Foreground removal procedure . . . . . . . . . . . . . . . . . . . . . 92
4.4.2 Adding observational noise . . . . . . . . . . . . . . . . . . . . . . . 92
4.4.3 Adding Galactic foreground . . . . . . . . . . . . . . . . . . . . . . 93
4.5 The simulated observational cross-correlations: an example . . . . . . . . . 96
4.5.1 Signal pile-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.5.2 Differentiating cosmic magnetization . . . . . . . . . . . . . . . . . 97
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
IV Conclusions 101
5 Summary and outlook 103V Appendices 109
A Magnetohydrodynamics and Plasma Physics 111
B Finding optimal numerical parameters 115
B.1 Divergence threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
B.2 Regularization by smoothing the magnetic field . . . . . . . . . . . . . . . 116
B.3 Artificial dissipation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
B.3.1 Time dependent artificial dissipation . . . . . . . . . . . . . . . . . 117
B.4 Dedner Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
C Resolution convergence tests 121
D ∇·B distribution analysis 123
VI Acknowledgments 127
VII Bibliography 131List of Figures
List of Figures V
1.1 Cluster images: Abell 1689 . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Radio Image of Coma cluster . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3 Rotation measurement as function of cooling rate. . . . . . . . . . . . . . . 16
1.4 Intergalactic contribution to the RM as a function of redshift z . . . . . . 19ig s
2.1 Test 5A without any correction. . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2 Test 5A with the standard implementation. . . . . . . . . . . . . . . . . . . 44
2.3 Test 5A with Dedner cleaning scheme. . . . . . . . . . . . . . . . . . . . . 45
2.4 Test 5A smoothing the magentic field. . . . . . . . . . . . . . . . . . . . . 46
2.5 Test 5A including artificial dissipation. . . . . . . . . . . . . . . . . . . . . 48
2.6 Test 5A including time dependent artificial dissipation. . . . . . . . . . . . 49
2.7 Representative plot of eight shock tube problems. . . . . . . . . . . . . . . 50
2.8 Magnetic modulus in Fast Rotor test. . . . . . . . . . . . . . . . . . . . . . 52
2.9 Density cut of the Fast Rotor test.. . . . . . . . . . . . . . . . . . . . . . . 53
2.10 Density in Strong Blast test. . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.11 Density cut of the Strong Blast test. . . . . . . . . . . . . . . . . . . . . . . 55
2.12 Magnetic energy results for the Orszang-Tang Vortex. . . . . . . . . . . . . 56
2.13 Pressure cut of the Orszang-Tang Vortex. . . . . . . . . . . . . . . . . . . . 57
2.14 ∇·B error comparison in the Orszang-Tang Vortex . . . . . . . . . . . . . 58
2.15 Comparison plot between all the implementation in tests. . . . . . . . . . . 59
3.1 Zoom into the simulated cluster . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 Density slice cut trough the galaxy cluster . . . . . . . . . . . . . . . . . . 66
3.3 Cluster slice of the magnetic energy . . . . . . . . . . . . . . . . . . . . . . 67
3.4 cluster slice in the∇·B errors. . . . . . . . . . . . . . . . . . . . . . . . . 68
3.5 Resolution comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.6 Magnetic field profile for different methods. . . . . . . . . . . . . . . . . . . 71
3.7 Profiles comparing different parameters. . . . . . . . . . . . . . . . . . . . 72
3.8 Magnetic field profiles for different resolutions. . . . . . . . . . . . . . . . . 72
3.9 Synthetic RM maps for different schemes . . . . . . . . . . . . . . . . . . . 73
3.10 Synthetic RM maps for different resolutions . . . . . . . . . . . . . . . . . 74
3.11 Comparison maps between simulations and observations. . . . . . . . . . . 75
3.12 Structure functions comparing between theory and observations . . . . . . 77
3.13 Structure and correlation function in different schemes . . . . . . . . . . . 78
3.14 Structure and correlation function in different resolution. . . . . . . . . . . 79
V4.1 Mean cosmic magnetic field as a function of density. . . . . . . . . . . . . . 85
4.2 Full sky maps of the local universe. . . . . . . . . . . . . . . . . . . . . . . 86
4.3 Cross-correlation functions of different estimators . . . .