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INFERENCEFROMMODELLINGTHECHEMODYNAMICAL EVOLUTION OF THE MILKY WAY DISC jan rybizki Printed in October 2015 Cover picture: Several Circles, Wassily Kandinsky (1926) Dissertation submitted to the Combined Faculties of Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg, Germany for the degree of Doctor of Natural Sciences Put forward by Jan Rybizki born in: Rüdersdorf Oral examination: December 8th, 2015 INFERENCEFROMMODELLINGTHECHEMODYNAMICAL EVOLUTION OF THE MILKY WAY DISC Referees: Prof. Dr. Andreas Just Prof. Dr. Norbert Christlieb ZUSAMMENFASSUNG-RÜCKSCHLÜSSEAUSDER MODELLIERUNGDERCHEMODYNAMISCHEN ENTWICKLUNG DER MILCHSTRAßENSCHEIBE In der vorliegenden Arbeit werden die anfängliche Massenfunktion (IMF) von Feldster- nen und Parameter zur chemischen Anreicherung der Milchstraße, unter Verwendung von Bayesscher Statistik und Modellrechnungen, hergeleitet. Ausgehend von einem lokalen Milchstraßenmodell [Just and Jahreiss, 2010] werden, für verschiedene IMF-Parameter, Sterne synthetisiert, die dann mit den entsprechenden Hip- parcos [Perryman et al., 1997](Hipparcos) Beobachtungen verglichen werden. Die abgelei- tete IMF ist in dem Bereich von 0.5 bis 8 Sonnenmassen gegeben durch ein Potenzgesetz mit einer Steigung von -1.49 0.08 für Sterne mit einer geringeren Masse als 1.39 0.05 M ± ± und einer Steigung von -3.02 0.06 für Sterne mit Massen darüber. ± Im zweiten Teil dieser Arbeit wird die IMF für Sterne mit Massen schwerer als 6 M be- stimmt. Dazu wurde die Software Chempy entwickelt, mit der man die chemische Anrei- cherung der Galaktischen Scheibe simulieren und auch die Auswahl von beobachteten Ster- nen nach Ort und Sternenklasse reproduzieren kann. Unter Berücksichtigung des systema- tischen Eekts der unterschiedlichen in der Literatur verfügbaren stellaren Anreicherungs- tabellen ergibt sich eine IMF-Steigung von -2.28 0.09 für Sterne mit Massen über 6 M . ± Dies zeigt, dass die von der chemischen Entwicklung abgeleitete IMF, ähnlich wie die Ergebnissen aus hydrodynamischen Simulationen der Milchstraße, für hohe Massen der Salpeter[1955] IMF entspricht. Aufgrund der geringen Anzahldichte von massereichen Sternen kann dies durch Sternzählungen nur schwer nachgewiesen werden. ABSTRACT-INFERENCEFROMMODELLINGTHE CHEMODYNAMICALEVOLUTIONOFTHEMILKYWAYDISC In this thesis, the eld star Initial Mass Function (IMF) and chemical evolution parameters for the Milky Way (MW) are derived using a forward modelling technique in combination with Bayesian statistics. Starting from a local MW disc model [Just and Jahreiss, 2010], observations of stellar sam- ples in the Solar Neighbourhood are synthesised and compared to the corresponding volume- complete observational samples of Hipparcos [Perryman et al., 1997](Hipparcos) stars. The resulting IMF, derived from observations in the range from 0.5 to 8 M , is a two-slope bro- ken power law with powers of -1.49 0.08 and -3.02 0.06 for the low-mass slope and the ± ± high-mass slope, respectively, with a break at 1.39 0.05 M . ± In order to constrain the IMF for stars more massive than 8 M , a fast and exible chemical enrichment code, Chempy, was developed, which is also able to reproduce spatial and stel- lar population selections of observational samples. The inferred high-mass slope for stellar masses above 6 M is -2.28 0.09, accounting for the systematic eects of dierent yield ± sets from the literature. v This shows that constraints from chemical modelling, similarly to hydrodynamical simu- lations of the Galaxy, demand a Salpeter[1955] high-mass index. This is hard to recover from star count analysis given the rareness of high-mass stars. vi OVERVIEWANDPUBLICATIONS In this thesis, the mass distribution of stars and the evolution of elements in the Milky Way (MW) are investigated. For this, physically motivated models are constructed, their in- put parameters are changed, and the outcome is compared to observational data of discrim- inative power. This forward modelling approach is combined with the concept of Bayesian inference. Central to this technique is the construction of a likelihood function in order to sample the posterior probability distribution, which is performed by means of Markov Chain Monte Carlo (MCMC) methods. The thesis is organised in the following way. The rst chapter is an introduction to the evolution of the MW, with a focus on the processes governing the synthesis of the chemical elements. The statistical methodology will be introduced in chapter2. The rst example of Bayesian model inference, where the true distance of a star will be inferred from a parallax mea- surement, is taken in great detail from Bailer-Jones[2015]. This leads to the question of determining stellar number densities in a specic volume, which will be discussed in the second part of chapter2. The ideas presented in section 2.2.3 have been published in Just et al.[2015] with a contribution from the author. In chapter3, the Initial Mass Function ( IMF) parameters are inferred from Solar Neighbour- hood stars, using a local MW disk model. Most of this chapter has been published in Rybizki and Just[2015]. In chapter4, a chemical evolution model of the local MW disc is presented and impor- tant model parameters, constraining the high-mass IMF, the infall and the SuperNova of type Ia (SN Ia), are inferred from abundances of Solar Neighbourhood stars. Section 4.3 of this chapter contains results, which are submitted as conference proceedings [Just and Ry- bizki, 2015]. The thesis will be concluded with a summary and a concise outlook. vii ACKNOWLEDGEMENTS First and foremost I would like to thank Prof. Andreas Just for his condence in my work and his guidance. The generous nancial support and the freedom to ponder ideas are very much appreciated as well as his positive supervision style. I am much obliged to PD Coryn Bailer-Jones and Dr. Ewan Cameron for their help with statistical questions, which I came across frequently, and for nurturing my fascination of Bayesian statistics. For most enjoyable lunch breaks and for partaking in my science and non-science related challenges I wish to express my deep gratitude to Dr. Robert Schmidt. His presence made the Astronomisches Rechen-Institut (ARI) feel more like a home for me. I am very grateful to Prof. Norbert Christlieb for readily agreeing to referee this thesis. Fur- thermore I wish to thank Prof. Eva Grebel and Prof. Luca Amendola for willingly joining my examination committee. I also want to mention the highly valued advice and helpful strategic planning from my thesis committee consisting of Prof. Eva Grebel, Dr. Glenn van de Ven and Prof. Andreas Just. Special thanks go to PD Christian Fendt who coordinated the International Max Planck Research School (IMPRS) activities that formed a sociable community out of our IMPRS generation. At ARI, I would like to thank Hendrik Heinl for caring about the social activities and for his support especially towards the end of my thesis writing. For numerous entertaining lunch breaks I want to thank Dr. Markus Demleitner and Aksel Alpay who also helped me to master the computationally expensive MCMC simulations. In the same respect Dr. Peter Schwekendiek and Sven Weimann always provided me with helpful computing advice and maintained the excellent Perseus machine. I want to thank the whole ARI administration, especially mentioning Martina Buchhaupt for thoroughly taking care of my administrative issues and Stefan Leitner for mocking me for my poor hand crafting skills. I enjoyed the scientic and non-scientic exchange with Dr. Corrado Boeche with whom I could lament about the intriguing complexity of selection functions. Last but not least I would like to thank Alex Hygate, Carolin Wittmann, Clio Bertelli, PD Coryn Bailer-Jones, Dr. Corrado Boeche, Daniel Haydon, Dr. Frederik Schönebeck, Dr. Ger- not Burkhardt, Hendrik Heinl, Peter Zeidler, Reza Moetazedian, Dr. Robert Schmidt, Timo Hirscher and Tina Gier for proof reading this thesis and for making the ARI a sociable workspace. My PhD project was funded by SFB 881 The Milky Way System. I would also like to acknowledge nancial support from the Heidelberg Graduate School of Fundamental Physics and the IMPRS which allowed me to participate in several interesting summer schools and useful workshops giving me the opportunity to learn from the best in the eld and be an active part of the international community. ix CONTENTS i introduction 1 1 the milky way galaxy 3 1.1 Etymology . .3 1.2 History . .3 1.3 Cosmology . .4 1.4 Elemental synthesis and stellar evolution . .7 1.4.1 Primordial nucleosynthesis . .7 1.4.2 First stars . .7 1.4.3 Reionization . .8 1.4.4 Low-mass stars . .9 1.4.5 Intermediate-mass stars . .9 1.4.6 High-mass stars . 12 1.4.7 Chemical enrichment - a simple model . 12 1.5 Structure of the Milky Way . 14 1.5.1 Halo . 14 1.5.2 Barred bulge . 15 1.5.3 Disc(s) . 16 1.5.4 Formation scenarios . 18 1.6 Deciphering the Milky Way evolution . 18 1.6.1 Extragalactic observations . 18 1.6.2 Simulations . 18 1.6.3 Analytical models . 19 1.6.4 Milky Way observation . 19 2 statistical inference with astronomical data 21 2.1 Bayesian inference . 21 2.1.1 Conditional probability . 21 2.1.2 Parameter estimation using Bayes’ theorem . 22 2.1.3 An example - Inferring distances from parallaxes . 23 2.1.4 Sampling the parameter space . 28 2.1.5 Model comparison . 30 2.2 Stellar number densities from star counts . 31 2.2.1 Magnitude and distance cuts . 32 2.2.2 Binary splitting and analytic extinction correction . 33 2.2.3 Probabilistic distances . 35 2.2.4 Using inhomogeneous extinction data . 36 2.2.5 Probabilistic binary correction . 37 2.2.6 Relaxing completeness . 37 2.2.7 Modelling a magnitude limited sample . 38 ii milky way disc model inference 39 3 the local initial mass function, as derived from star counts 41 3.1 Introduction .
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