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Switching on the first light in the universe [Elektronische Ressource] / vorgelegt von Umberto Maio

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Ludwig-Maximilians-Universit¨atSigillum Universitatis Ludovici MaximilianiSwitching on the first lightin the UniverseDissertation der Fakult¨at fu¨r PhysikDissertation of the Faculty of Physics / Dissertazione della Facolta` di Fisicader Ludwig-Maximilians-Universit¨at Mu¨nchen`at the Ludwig Maximilian University of Munich / dell’Universita Ludwig Maximilian di Monacofu¨r den Grad desfor the degree of / per il titolo diDoctor rerum naturaliumvorgelegt von Umberto Maiopresented by / presentata daaus Montella, AV (Italy)from / daMu¨nchen, 10.10.2008Sigillum Universitatis Ludovici Maximiliani1. Gutachter: Prof. Dr. Simon D. M. Whitereferee: / relatore:2. Gutachter: Prof. Dr. Andreas M. Burkertreferee: / relatore:Tag der mu¨ndlichen Pru¨fung: 12.12.2008Date of the oral exam: / Data dell’esame orale:Curriculum vitæ et studiorumUmberto MaioPersonal dataFirst Name: UmbertoLast name: MaiondDate of birth: 22 March, 1981Place of birth: Avellino (Italy)Citizenship: ItalianHobbies: Literature, History, Philosophy, readingSports: swimming, playing footbal, cycling, runningLanguages: Italian, English, German, LatinContactsB Address: c/o Max-Planck-Institut fu¨r AstrophysikKarl-Schwarzschild-Straße, 1D-85748 Garching b. Mu¨nchen - M (Germany)orvia della Libera, 2583048 Montella, AV (Italy) Phone: +49 (0)89 30 000 2196, +39 (0)827 61275H Mobile: +49 (0)176 4714638, +39 (0)328 3826882@ E-mail: maio@mpa-garching.mpg.

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Published 01 January 2008
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Ludwig-Maximilians-Universit¨at
Sigillum Universitatis Ludovici Maximiliani
Switching on the first light
in the Universe
Dissertation der Fakult¨at fu¨r Physik
Dissertation of the Faculty of Physics / Dissertazione della Facolta` di Fisica
der Ludwig-Maximilians-Universit¨at Mu¨nchen
`at the Ludwig Maximilian University of Munich / dell’Universita Ludwig Maximilian di Monaco
fu¨r den Grad des
for the degree of / per il titolo di
Doctor rerum naturalium
vorgelegt von Umberto Maio
presented by / presentata da
aus Montella, AV (Italy)
from / da
Mu¨nchen, 10.10.2008Sigillum Universitatis Ludovici Maximiliani
1. Gutachter: Prof. Dr. Simon D. M. White
referee: / relatore:
2. Gutachter: Prof. Dr. Andreas M. Burkert
referee: / relatore:
Tag der mu¨ndlichen Pru¨fung: 12.12.2008
Date of the oral exam: / Data dell’esame orale:Curriculum vitæ et studiorum
Umberto Maio
Personal data
First Name: Umberto
Last name: Maio
ndDate of birth: 22 March, 1981
Place of birth: Avellino (Italy)
Citizenship: Italian
Hobbies: Literature, History, Philosophy, reading
Sports: swimming, playing footbal, cycling, running
Languages: Italian, English, German, Latin
Contacts
B Address: c/o Max-Planck-Institut fu¨r Astrophysik
Karl-Schwarzschild-Straße, 1
D-85748 Garching b. Mu¨nchen - M (Germany)
or
via della Libera, 25
83048 Montella, AV (Italy)
Phone: +49 (0)89 30 000 2196, +39 (0)827 61275
H Mobile: +49 (0)176 4714638, +39 (0)328 3826882
@ E-mail: maio@mpa-garching.mpg.de, umbertomaio@hotmail.com
Education
th2008, 12 December: Ph. D. rer. nat. Ludwig-Maximilians-Universit¨at Mu¨nchen
Max-Planck-Institut fu¨r Astrophysik (Garching b. Mu¨nchen)
th2005, 14 July: Laurea in Astronomy,
University of Bologna Alma Mater Studiorum (Italy)
Faculty of Mathematical, Physical and Natural Sciences
Department of Astronomy
Thesis: Early structure formation in quintessence models
Supervisor: Prof. Dr. Lauro Moscardini
Final score: 110 / 110 cum laude
GPA: 29.5 (in 30 point system) and 11 laudes
st2000, 21 July: Diploma di Maturit`a Scientifica,
Liceo Scientifico R. d’Aquino, Montella - AV (Italy)
Final score: 100 / 100
1995 - 2000: Liceo Scientifico R. d’Aquino, Montella - AV (Italy)
1992 - 1995: Scuola Media G. Capone, Montella - AV (Italy)
1987 - 1992: Scuola Elementare G. Palatucci, Montella - AV (Italy)
Research
Subjects: cosmology, cosmic structure formation, gas physics, turbulence
Methods: analytical, numerical and statistical calculations (CFD simulations)Refereed publications
U. Maio, B. Ciardi, N. Yoshida, K. Dolag, L. Tornatore, The onset of star formation
in primordial haloes, submitted (2008).
U. Maio, Cloud fragmentation and initial mass function from turbulence modeling,
submitted (2008).
U.Maio,K.Dolag,B.Ciardi,L.Tornatore,Metalandmoleculecoolinginsimulations
of structure formation, Mon. Not. R. Astron. Soc., 379, 963-973 (2007).
U. Maio, K. Dolag, M. Meneghetti, L. Moscardini, N. Yoshida, C. Baccigalupi,
M. Bartelmann, F. Perrotta, Early structure formation in quintessence models and
its implications for cosmic reionization from first stars, Mon. Not. R. Astron. Soc.,
373, 869-878 (2006).
Non-refereed publications (proceedings and others)
U. Maio, B. Ciardi, K. Dolag, L. Tornatore, N. Yoshida, Early molecules, star
formation and metal pollution, in press, Paris (2008).
U.Maio, B. Ciardi, K.Dolag, L. Tornatore, N. Yoshida, Onset of star formation and
impact on the surroundings, IAU/CUP Symposium series, in press (2008).
U. Maio, B. Ciardi, K. Dolag, L. Tornatore, Cooling in primordial structure
formation, American Institute of Physics Conf. Proc. 990, 33 (2008).
Laurea/Master thesis
U. Maio, Formazione delle prime strutture in modelli cosmologici di quintessenza,
Tesi di Laurea, Alma Mater Studiorum Universit`a di Bologna (2005). Libro
moderno – Monografia – Tesi e dissertazioni – UBO2782561; [2005?]. - VII, 238 p. :
ill. ; 30 cm. Tesi ds. di laurea in Astronomia, Universit`a degli studi di Bologna,
Facolt`a di Scienze matematiche, fisiche e naturali, a.a. 2004/2005.
Umberto MaioLearn all the rules and
then break some of them
Nepalese tantraContents
Contents 3
Zusammenfassung 13
Abstract 15
Riassunto 17
Introduction 19
Conventions and abbreviations 23
I General overview 25
1 Mathematical description of the Universe 27
1.1 The approach of General Relativity . . . . . . . . . . . . . . . . . . . . . . . 27
1.1.1 The field equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.1.2 The geodesics equations . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.2 Relativistic cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1.2.1 The metric of the Universe from the cosmological principle . . . . . . 32
1.2.2 The Friedmann equations . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.2.3 Equation of state, density evolution and temperature evolution . . . . 35
1.3 Frequently used cosmological quantities . . . . . . . . . . . . . . . . . . . . 37
1.3.1 Redshift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
1.3.2 Density parameters and Friedmann equations . . . . . . . . . . . . . . 39
1.3.3 Time-redshift relation . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.3.4 Distances and expansion of the Universe . . . . . . . . . . . . . . . . 42
32 Mathematical description of cosmic structure formation 47
2.1 The global scenario: hot big bang . . . . . . . . . . . . . . . . . . . . . . . . 47
2.2 From primordial fluctuations to structure formation . . . . . . . . . . . . . . 49
2.2.1 Linear evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.2.2 Non-linear evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.3 Statistics of structure formation . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.4 Dark matter haloes and baryonic structure formation . . . . . . . . . . . . . 61
2.4.1 Gas and halo properties . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.4.2 Protogalaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3 Star formation, initial mass function and feedback 69
3.1 First stars and subsequent generations . . . . . . . . . . . . . . . . . . . . . 69
3.2 Stellar system properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3 Features of primordial stars . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.4 Feedback processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.4.1 Mechanical feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.4.2 Radiative feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.4.3 Chemical feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.5 Final remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
II Cosmological simulations 81
4 Numerical simulations of early structure formation 83
4.1 Numerical techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.1.1 Treatment of gravitation . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.1.2 Treatment of fluido-dynamics . . . . . . . . . . . . . . . . . . . . . . . 86
4.2 The code Gadget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.2 Star formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.2.3 Metal enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3 Implementation of molecule and metal chemistry . . . . . . . . . . . . . . . 92
4.3.1 Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.3.2 Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.3.3 Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5 Tests for star formation, molecule and metal chemistry 105
5.1 Star formation and wind feedback. . . . . . . . . . . . . . . . . . . . . . . . 105
5.2 Redshift evolution of primordial chemical species . . . . . . . . . . . . . . . 112
5.3 Cosmic structure formation from homogeneous initial conditions . . . . . . . 114
5.4 Formation and evolution of a cluster . . . . . . . . . . . . . . . . . . . . . . 117
5.4.1 Metal fine-structure cooling . . . . . . . . . . . . . . . . . . . . . . . . 118
5.4.2 Adding molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.4.3 Star formation and metal pollution history . . . . . . . . . . . . . . . 124
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6 On the onset of star formation 129
6.1 On the onset of star formation events . . . . . . . . . . . . . . . . . . . . . . 129
6.2 Threshold for star formation. . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.3 Simulation set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.4.1 Mean-region simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.4.2 High-density region simulation . . . . . . . . . . . . . . . . . . . . . . 141
6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7 Early structure formation and critical metallicity 151
7.1 Simulation set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.2 Effects of Z on SFR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154crit
7.3 Filling factor and Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159crit
7.4 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
8 A model for the IMF 163
8.1 Properties of the star forming regions . . . . . . . . . . . . . . . . . . . . . . 164
8.2 Turbulence and fragmentation processes . . . . . . . . . . . . . . . . . . . . 167
8.3 Turbulence and IMF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1688.3.1 Treatment of turbulence . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.3.2 Connection to the IMF . . . . . . . . . . . . . . . . . . . . . . . . . . 174
8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
8.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
9 Conclusions 183
III Appendices 187
A Cooling function 189
A.1 Definition of cooling function . . . . . . . . . . . . . . . . . . . . . . . . . . 189
A.2 Statistical equilibrium of atoms and molecules . . . . . . . . . . . . . . . . . 189
A.2.1 Collisional rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
A.2.2 Radiative rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
A.2.3 General expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
B Star formation rate indicators 197
B.1 Stellar luminosities and star formation . . . . . . . . . . . . . . . . . . . . . 197
B.2 Schmidt law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
C Molecular and atomic data 201
C.1 Molecular rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
C.2 Metal atomic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
D Entropy 209
E Gravitational instability and viscous dissipation 211
E.1 Perturbative treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
E.2 Time-scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
IV Bibliography 215