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Switching on the First Light in the Universe

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Switching on the First Light in the Universe Ludwig-Maximilians-Universit¨at Sigillum Universitatis Ludovici Maximiliani Switching on the first light in the Universe Dissertation der Fakult¨at f¨ur Physik Dissertation of the Faculty of Physics / Dissertazione della Facolta` di Fisica der Ludwig-Maximilians-Universit¨at M¨unchen at the Ludwig Maximilian University of Munich / dell’Universita` Ludwig Maximilian di Monaco f¨ur 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 M¨unchen, 10.10.2008 Sigillum Universitatis Ludovici Maximiliani 1. Gutachter: Prof. Dr. Simon D. M. White referee: / relatore: 2. Gutachter: Prof. Dr. Andreas M. Burkert referee: / relatore: Tag der m¨undlichen Pr¨ufung: 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 Date of birth: 22nd 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 f¨ur Astrophysik Karl-Schwarzschild-Straße, 1 D-85748 Garching b. M¨unchen - 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: [email protected], [email protected] Education 2008, 12th December: Ph. D. rer. nat. Ludwig-Maximilians-Universit¨at M¨unchen Max-Planck-Institut f¨ur Astrophysik (Garching b. M¨unchen) 2005, 14th 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 2000, 21st July: Diploma di Maturit`aScientifica, 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, Metal and molecule cooling in simulations 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`adi Bologna (2005). Libro · moderno – Monografia – Tesi e dissertazioni – UBO2782561; [2005?]. - VII, 238 p. : ill. ; 30 cm. Tesi ds. di laurea in Astronomia, Universit`adegli studi di Bologna, Facolt`adi Scienze matematiche, fisiche e naturali, a.a. 2004/2005. Umberto Maio Learn all the rules and then break some of them Nepalese tantra Contents 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 TheapproachofGeneralRelativity . ..... 27 1.1.1 Thefieldequations ............................ 28 1.1.2 Thegeodesicsequations. 30 1.2 Relativisticcosmology . ... 31 1.2.1 The metric of the Universe from the cosmological principle ...... 32 1.2.2 TheFriedmannequations. 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-redshiftrelation . .. 41 1.3.4 Distances and expansion of the Universe . .... 42 3 2 Mathematical description of cosmic structure formation 47 2.1 Theglobalscenario: hotbigbang. .... 47 2.2 From primordial fluctuations to structure formation . ........... 49 2.2.1 Linearevolution .............................. 50 2.2.2 Non-linearevolution. 55 2.3 Statisticsofstructureformation. ....... 57 2.4 Dark matter haloes and baryonic structure formation . .......... 61 2.4.1 Gasandhaloproperties. 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 Stellarsystemproperties. .... 71 3.3 Featuresofprimordialstars . .... 73 3.4 Feedbackprocesses ............................... 75 3.4.1 Mechanicalfeedback. 75 3.4.2 Radiativefeedback ............................ 77 3.4.3 Chemicalfeedback............................. 77 3.5 Finalremark ................................... 79 II Cosmological simulations 81 4 Numerical simulations of early structure formation 83 4.1 Numericaltechniques. .. 84 4.1.1 Treatmentofgravitation . 84 4.1.2 Treatment of fluido-dynamics . .. 86 4.2 ThecodeGadget................................. 88 4.2.1 Overview.................................. 89 4.2.2 Starformation............................... 90 4.2.3 Metalenrichment ............................. 92 4.3 Implementation of molecule and metal chemistry . ........ 92 4.3.1 Molecules.................................. 94 4.3.2 Metals ................................... 97 4.3.3 Cooling................................... 99 4.4 Summary .....................................104 5 Tests for star formation, molecule and metal chemistry 105 5.1 Starformationandwindfeedback. .105 5.2 Redshift evolution of primordial chemical species . ...........112 5.3 Cosmic structure formation from homogeneous initial conditions. 114 5.4 Formationandevolutionofacluster . .117 5.4.1 Metalfine-structurecooling. 118 5.4.2 Addingmolecules .............................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 Ontheonsetofstarformationevents. .129 6.2 Thresholdforstarformation. .131 6.3 Simulationset-up................................ 132 6.4 Results ......................................135 6.4.1 Mean-regionsimulation . 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 Simulationset-up................................ 151 7.2 Effects of Zcrit onSFR..............................154 7.3 Filling factor and Zcrit ..............................159 7.4 Remarks......................................159 7.5 Summary .....................................160 8 A model for the IMF 163 8.1 Propertiesofthestarformingregions. .......164 8.2 Turbulence and fragmentation processes . .......167 8.3 TurbulenceandIMF ...............................168 8.3.1 Treatmentofturbulence . 170 8.3.2 ConnectiontotheIMF . .174 8.4 Discussion.....................................178 8.5 Summary .....................................180 9 Conclusions 183 III Appendices 187 A Cooling function 189 A.1Definitionofcoolingfunction . .189 A.2 Statistical equilibrium of atoms and molecules . ..........189 A.2.1Collisionalrates . .. .. 190 A.2.2Radiativerates...............................193 A.2.3Generalexpressions . 194 B Star formation rate indicators 197 B.1 Stellar luminosities and star formation . ........197 B.2Schmidtlaw....................................198 C Molecular and atomic data 201 C.1Molecularrates.................................. 201 C.2Metalatomicdata ................................204 D Entropy 209 E Gravitational instability and viscous dissipation 211 E.1 Perturbativetreatment. 211 E.2Time-scales ....................................214 IV Bibliography 215 List of Figures 1 Introduction: evolution of cosmological systems . ......... 20 1.1 Density parameter evolution (closed, flat, open models) ............ 40 1.2 Density parameter evolution (matter-radiation-Λ model) ........... 41 1.3 AgeoftheUniverse ............................... 43 1.4 Measurements of the cosmic expansion rate . ...... 45 1.5 Distances ..................................... 46 2.1 Cosmic microwave background fluctuation map . ...... 50 2.2 Densitycontrast(ΛCDMmodel) . .. 54 2.3 Spherical“top-hat”model . ... 56 2.4 Matterpowerspectrum(ΛCDMmodel) . .. 58 2.5 Mass variance and non-linear scale . ..... 59 2.6 Massfunctions .................................. 61 2.7 HandHecooling................................. 63 2.8 Primordial
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