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Statistical Analyses of Massive Stars and Stellar Populations Dissertation zur Erlangung des Doktorgrades (Dr. rer. nat.) der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn vorgelegt von Fabian Schneider aus Duisburg Bonn 2014 Angefertigt mit Genehmigung der Mathematisch-Naturwissenschaftlichen Fakultät der Rheini- schen Friedrich-Wilhelms-Universität Bonn 1. Gutachter: Prof. Dr. Norbert Langer 2. Gutachter: Prof. Dr. Robert G. Izzard Tag der Promotion: Erscheinungsjahr: I, a universe of atoms, an atom in the universe. (Richard P. Feynman) Abstract Massive stars, i.e. stars more massive than about ten times that of the Sun, are key agents in the Universe. They synthesise many of the chemical elements that are so important for life on Earth, helped reionising the early Universe and end their lives in spectacular supernova explosions that are visible out to large distances. Because of their important role for much of astrophysics, accurate and reliable stellar evolution models are essential. However, recent developments regarding wind mass loss rates, internal mixing processes and duplicity seriously challenge our understanding of massive stars and stellar populations. It is now established that most, if not all, massive stars reside in binaries or higher order multiple systems such that more than two-thirds of all massive stars are expected to interact through mass transfer with a binary companion during their lives. We investigate the conse- quences of this finding for coeval stellar populations and show that the most massive stars in star clusters are likely all rejuvenated binary products that may seriously bias the determination of cluster ages. We further find that wind mass loss from stars and binary mass transfer leave their fingerprints in the high mass end of stellar mass functions. Using these fingerprints, we are able to age-date the young Arches and Quintuplet star clusters with far reaching consequences for the stellar upper mass limit that we revise to be in the range 200–500 M . Such an upper mass limit would allow for pair-instability supernovae in the local Universe. Large spectroscopic surveys such as the VLT-FLAMES Tarantula Survey (VFTS) deliver many atmospheric parameters of hundreds of massive stars that are ideal to probe and calibrate the physics used in stellar models. To make use of such data, we develop the Bayesian code Bonnsai and make it available through a web-interface. With Bonnsai we are able to match all available observables of stars including their uncertainties simultaneously to stellar models to determine fundamental stellar parameters like mass and age while taking prior knowledge such as initial mass functions into account. A key aspect of Bonnsai is that it allows us to identify stars that cannot be reproduced by stellar models. We use Bonnsai to test the Milky Way stellar models of Brott et al. (2011) with eclipsing binaries and find good agreement. We further use Bonnsai in combination with data from the VFTS to study the massive O and WNh stars in one of the largest starburst regions known to date, 30 Doradus. In particular we investigate their age distributions to learn about their formation history. The VFTS stars in our sample are mostly found outside clusters and associations and we do not find spatially coherent age patterns. The stars either formed continuously over the 30 Doradus field or in clusters and associations from where they were ejected to their current positions. The age distributions of our sample stars are consistent with the existence of at least two to four coeval stellar populations which would imply that most of the VFTS stars in our sample formed in clusters and associations. v Contents Contents ix 1 Introduction 1 1.1 Towards a modern picture of stellar evolution....................2 1.2 Modern massive star evolution............................6 1.2.1 Stellar wind mass loss.............................6 1.2.2 Interior mixing and rotation..........................8 1.2.3 Binary star evolution.............................. 10 1.3 This thesis........................................ 12 1.3.1 Role of binary star evolution in coeval stellar populations......... 13 1.3.2 The Bonnsai project............................. 14 2 Evolution of mass functions of coeval stars through wind mass loss and binary inter- actions 19 2.1 Introduction....................................... 20 2.2 Method......................................... 21 2.2.1 Rapid binary evolution code.......................... 21 2.2.2 Initial distribution functions.......................... 23 2.2.3 Binary parameter space............................ 24 2.2.4 Construction of mass functions........................ 29 2.3 Modulation of mass functions by stellar evolution.................. 29 2.3.1 Single star populations............................. 29 2.3.2 Binary star populations............................ 33 2.3.3 Stellar populations with varying binary fractions.............. 36 2.3.4 Quantification of evolutionary effects on the PDMF............ 37 2.4 Blue straggler stars................................... 40 2.4.1 Expected and observed blue straggler star frequencies........... 40 2.4.2 Binary fraction of blue straggler stars.................... 43 2.4.3 Apparent ages of blue straggler stars..................... 45 2.5 Determination of star cluster ages.......................... 46 2.6 Conclusions....................................... 47 2.7 Supplementary material................................ 49 2.7.1 Binary parameter space continued...................... 49 2.7.2 Uncertainties in the models.......................... 56 2.7.3 Unresolved binary stars............................ 57 2.7.4 Stochastic sampling.............................. 58 vii 3 Ages of young star clusters, massive blue stragglers and the upper mass limit of stars 61 3.1 Introduction....................................... 62 3.2 Methods and observational data........................... 63 3.2.1 Rapid binary evolution code.......................... 63 3.2.2 Initial distribution functions for stellar masses and orbital periods.... 64 3.2.3 Monte Carlo experiments........................... 64 3.2.4 Observations.................................. 65 3.2.5 Binning procedure of mass functions..................... 66 3.3 Analyses of the Arches and Quintuplet clusters................... 66 3.3.1 The Arches and Quintuplet mass functions................. 66 3.3.2 The ages of Arches and Quintuplet...................... 69 3.4 Stochastic sampling of binary populations...................... 70 3.5 The stellar upper mass limit.............................. 73 3.6 Uncertainties...................................... 75 3.6.1 Modelling uncertainties............................ 75 3.6.2 Observational uncertainties.......................... 78 3.6.3 Dynamical interactions in star clusters.................... 80 3.6.4 Star formation histories............................ 80 3.7 Conclusions....................................... 81 3.8 Supplementary material................................ 83 3.8.1 Star formation histories cont.......................... 86 4 BONNSAI: a Bayesian tool for comparing stars with stellar evolution models 89 4.1 Introduction....................................... 90 4.2 Method......................................... 91 4.2.1 Bayes’ theorem................................. 91 4.2.2 Bayesian stellar parameter determination.................. 92 4.2.3 Likelihood function............................... 93 4.2.4 Prior functions................................. 93 4.2.5 Stellar model grids............................... 95 4.2.6 Goodness-of-fit................................. 95 4.2.7 Our new approach in practice......................... 98 4.3 Testing Bonnsai with mock stars........................... 99 4.3.1 Mock Star A.................................. 99 4.3.2 Mock Star B.................................. 102 4.4 Testing stellar evolution models with eclipsing binaries............... 104 4.4.1 Description of our test............................. 108 4.4.2 The role of rotation in Milky Way binaries................. 109 4.4.3 The ages of primary and secondary stars................... 110 4.4.4 Effective temperatures and bolometric luminosities............. 115 4.5 Conclusions....................................... 117 5 The age distribution of massive O and WN stars in 30 Doradus 119 5.1 Introduction....................................... 120 5.2 Method......................................... 121 5.2.1 Atmosphere modelling............................. 121 viii 5.2.2 BONNSAI.................................... 123 5.2.3 Sample selection................................ 124 5.2.4 Incompleteness correction........................... 125 5.3 Our sample of massive VFTS stars.......................... 126 5.3.1 Hertzsprung–Russell diagram......................... 127 5.4 The ages of the massive VFTS stars......................... 129 5.4.1 The whole 30 Dor region............................ 129 5.4.2 The R136 region................................ 132 5.4.3 The NGC 2060 region............................. 136 5.4.4 Stars outside R136 and NGC 2060...................... 138 5.4.5 The age of the central R136 cluster...................... 138 5.4.6 The overall star formation process...................... 140 5.5 Discussion........................................ 143 5.5.1 The ages of our sample stars in context of previous investigations..... 143 5.5.2 Massive star formation in isolation.....................
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