And there was light : Voronoi-Delaunay radiative transfer and cosmic reionisation
Paardekooper, J.P.
Citation
Paardekooper, J. P. (2010, December 16). And there was light : Voronoi-Delaunay radiative transfer and cosmic reionisation. Retrieved from https://hdl.handle.net/1887/16247
Version: Corrected Publisher’s Version
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And there was light
Voronoi-Delaunay radiative transfer and cosmic reionisation
Voronoi-Delaunay radiative transfer and cosmic reionisation
Proefschrift
ter verkrijging van
de graad van Doctor aan de Universiteit Leiden,
op gezag van de Rector Magnificus prof. mr. P.F. van der Heijden, volgens besluit van het College voor Promoties
te verdedigen op donderdag 16 december 2010 te klokke 10:00 uur
door
Jan-Pieter Paardekooper
geboren te Alphen aan den Rijn in 1982
Promotiecommissie
Promotor: Prof. dr. V. Icke
Referent: Prof. dr. G. Mellema (Stockholm University) Overige leden: Dr. A. Ferrara (SISSA, Trieste)
Prof. dr. K. Kuijken
Prof. dr. S. Portegies Zwart Dr. J. Schaye
Prof. dr. P. Shapiro (University of Texas at Austin) Dr. E. Tolstoy (Universiteit Groningen) Prof. dr. R. van de Weygaert (Universiteit Groningen)
Earth and moon and sun and stars Planets and comets with tails blazing All are there forever falling Falling lovely and amazing Nick Cave
Omslagontwerp door IlonaH
Contents
1 Introduction 1
1.1 The formation of galaxies . . . 1
1.1.1 The Hot Big Bang model . . . 1
1.1.2 Structure formation . . . 2
1.2 The physics of cosmic reionisation . . . 4
1.3 Observational constraints on cosmic reionisation . . . 5
1.4 Simulations of cosmic reionisation . . . 6
1.4.1 Computational requirements . . . 6
1.4.2 Radiative transfer . . . 7
1.5 This thesis . . . 8
Part I: Numerical Method 13
2 SimpleX2: Radiative transfer on an unstructured, dynamic grid 15 2.1 Introduction . . . 162.2 The SimpleX method . . . 17
2.2.1 Grid calculation . . . 17
2.2.2 Radiation Transport . . . 23
2.3 Parallellisation strategy . . . 26
2.3.1 Domain decomposition . . . 27
2.3.2 Parallel radiative transfer . . . 27
2.3.3 Scaling tests . . . 28
2.4 Radiative transfer of ionising radiation . . . 30
2.4.1 Cosmological radiative transfer equation . . . 31
2.4.2 Ionisation processes . . . 31
2.4.3 Assigning sources . . . 32
2.4.4 Interaction . . . 34
2.4.5 Solving the photoionisation rate equation . . . 35
2.4.6 Time stepping . . . 35
2.4.7 Solving for the temperature state of the gas . . . 36
2.5 Summary . . . 38
viii And there was light
3 Creating the SimpleX grid 41
3.1 Introduction . . . 42
3.2 Sampling the density distribution . . . 43
3.2.1 The sampling function . . . 43
3.2.2 Sampling a cosmological density field . . . 45
3.2.3 The result of undersampling . . . 45
3.3 Creating the point distribution . . . 48
3.3.1 Regular input grid . . . 48
3.3.2 Particle-based input . . . 51
3.4 Assigning density values . . . 53
3.4.1 Mesh-based interpolation . . . 54
3.4.2 Particle-based interpolation . . . 55
3.4.3 Tesselation-based interpolation . . . 55
3.5 Summary . . . 56
4 Towards radiation hydrodynamics with SimpleX 59 4.1 Introduction . . . 60
4.2 Updating the Delaunay triangulation . . . 60
4.2.1 QHull . . . 60
4.2.2 A parallel dynamic and kinetic Delaunay triangulation algorithm . . . . 62
4.2.3 Performance . . . 63
4.3 Radiation hydrodynamics with SimpleX . . . 66
4.3.1 SimpleX and Eulerian hydrodynamics . . . 67
4.3.2 SimpleX and smoothed particle hydrodynamics . . . 67
4.3.3 Hydrodynamics on the Voronoi grid . . . 68
4.4 SimpleX in AMUSE . . . 68
4.5 Summary . . . 69
Part II: Application to the Epoch of Reionisation 71
5 SimpleX2: Cosmological tests 73 5.1 Introduction . . . 745.2 Basic physics . . . 74
5.3 Test 1: Isothermal H ii region expansion . . . 75
5.3.1 Ballistic transport . . . 76
5.3.2 Direction conserving transport . . . 78
5.3.3 Combined transport . . . 79
5.4 Test 2: H ii region expansion, the temperature state . . . 81
5.4.1 Ballistic transport . . . 81
5.4.2 Combined transport . . . 83
5.5 Test 3: Shadowing behind a dense cloud . . . 87
5.5.1 Ballistic transport . . . 87
5.5.2 Combined transport . . . 88
5.6 Test 4: Multiple sources in a cosmological density field . . . 91
Contents ix
5.6.1 Constant temperature . . . 92
5.6.2 The temperature state . . . 96
5.6.3 Comparison to other codes . . . 101
5.7 Summary . . . 105
6 The escape of ionising radiation from high-redshift dwarf galaxies 109 6.1 Introduction . . . 110
6.2 Method . . . 114
6.2.1 Initial conditions . . . 114
6.2.2 The two-phase nature of the ISM . . . 116
6.2.3 Star formation and feedback . . . 117
6.2.4 Radiative transfer . . . 118
6.2.5 Dust . . . 118
6.2.6 Calculation of the escape fraction . . . 120
6.3 Results . . . 120
6.3.1 Galaxy morphologies . . . 120
6.3.2 Star formation rates . . . 125
6.3.3 Escape fractions . . . 131
6.3.4 Observational consequences . . . 135
6.4 Numerical constraints . . . 135
6.4.1 Escape of radiation from massive sources only . . . 136
6.4.2 Resolution study . . . 139
6.4.3 Local gas clearing . . . 140
6.5 Implications for reionisation models . . . 142
6.6 Discussion . . . 144
6.6.1 Resolution . . . 144
6.6.2 The interplay of radiation and gas . . . 144
6.6.3 Physical processes . . . 145
6.6.4 Galaxy morphologies . . . 146
6.7 Conclusions . . . 147
7 Recombination photons in the Epoch of Reionisation 153 7.1 Introduction . . . 154
7.2 The photoionisation of a pure hydrogen gas . . . 155
7.3 The OTS approximation in numerical methods . . . 157
7.4 Recombination radiation in the SimpleX method . . . 159
7.5 H ii region around a Lyman limit source . . . 160
7.5.1 The contribution of diffuse photons to total radiation field . . . 160
7.5.2 The OTS approximation and the evolution of the H ii region . . . 162
7.6 The effect of the density profile . . . 163
7.6.1 The contribution of diffuse photons to total radiation field . . . 164
7.6.2 The OTS approximation and the evolution of the H ii region . . . 165
7.7 The effect of the source spectrum . . . 167
7.7.1 The contribution of diffuse photons to total radiation field . . . 167
7.7.2 The OTS approximation and the evolution of the H ii region . . . 167
x And there was light
7.8 Shadowing effects . . . 170
7.9 The OTS approximation in reionisation simulations . . . 172
7.9.1 Density field . . . 172
7.9.2 The OTS approximation and reionisation on large scales . . . 173
7.9.3 The OTS approximation and reionisation on smaller scales . . . 175
7.10 Conclusions . . . 176
Nederlandse Samenvatting 178
Curriculum Vitae 187
Nawoord 189
