THESIS FOR THE DEGREE OF LICENTIATE OF PHILOSOPHY A quantum-chemical study to the magnetic characteristics of methanol and its applications in astronomy BOY LANKHAAR DEPARTMENT OF SPACE,EARTH AND ENVIRONMENT CHALMERS UNIVERSITY OF TECHNOLOGY GOTHENBURG,SWEDEN 2018 A quantum-chemical study to the magnetic characteristics of methanol and its applications in astronomy BOY LANKHAAR © Boy Lankhaar, 2018 Division of Astronomy & Plasma Physics Department of Space, Earth and Environment Chalmers University of Technology SE–412 96 Gothenburg, Sweden Phone: +46 (0)31–772 10 00 Contact information: Boy Lankhaar Chalmers University of Technology Onsala Space Observatory SE–439 92 Råö, Sweden Phone: +46 (0)31–772 55 42 Email: [email protected] Printed by Chalmers Reproservice Chalmers University of Technology Gothenburg, Sweden 2018 iii A quantum-chemical study to the magnetic character- istics of methanol and its applications in astronomy BOY LANKHAAR Department of Space, Earth and Environment Chalmers University of Technology ABSTRACT Magnetic fields play an important role during star formation. Direct magnetic field strength observations have proven specifically challenging in the dynamic protostellar phase. Because of their occurrence in the densest parts of star forming regions, masers, through polarization observations, are the main source of magnetic field strength and morphology measurements around protostars. Of all maser species, methanol is one of the strongest and most abundant tracers of gas around high-mass protostellar disks and in outflows. However, because experimental determination of the magnetic character- istics of methanol has remained unsuccessful, a magnetic field strength analysis of these regions could hitherto not be performed. In this thesis, we present quantum-chemical calculations of the magnetic characteristics of methanol. We present the parameters characterizing the internal magnetic interactions: the hyperfine structure, as well as the parameters characterizing the interaction of methanol with an external magnetic field. We use these parameters in re-analyzing methanol maser polarization observa- tions. With these calculations, we can confirm the presence of dynamically important magnetic fields around protostars. Keywords: magnetic field - stars: formation - stars: massive - masers - polarization iv v RESEARCH CONTRIBUTIONS This thesis is based on the work comprised of the following contributions: I Lankhaar, B., Groenenboom, G.C., van der Avoird, 2016. Hyperfine interactions and internal rotation in methanol. Journal of Chemical Physics 145, 244301, 2016. doi: 10.1063/1.4972004 II Lankhaar, B., Vlemmings, W.H.T., Surcis, G., van Langevelde, H.J., Groenenboom, G.C., van der Avoid, A., 2018. Characterization of methanol as a magnetic field tracer in star-forming regions. Nature Astronomy 2, 145–150. https://doi.org/10.1038/s41550- 017-0341-8 The author contributed also to the following publications (not appended): I. Dall’Olio, D., Vlemmings, W.H.T., Surcis, G., Beuther, H., Lankhaar, B., Persson, M.V., Richards, A.M.S., Varenius, E., 2017. Methanol masers reveal the magnetic field of the high-mass protostar IRAS 18089-1732. Astronomy and Astrophysics 607, A111. doi: 10.1051/0004-6361/201731297 II. Vlemmings, W.H.T., Khouri, T., O’Gorman, E., de Beck, E., Humphreys, E., Lankhaar, B., Maercker, M., Olofsson, H., Ramstedt, S., Tafoya, D., Takigawa, A., 2017. The shock-heated atmosphere of an asymptotic giant branch star resolved by ALMA. Nature Astronomy 1, 848-853. doi: 10.1038/s41550-017-0288-9 vi vii ACKNOWLEDGMENTS This thesis is the summary of two years of work in science. In this time, I have and have had a lot to be thankful for. First of all, I should thank my supervisor, Wouter Vlemmings, for giving me the oppor- tunity to work in the amazing field of astronomy. I guess it has been a leap of faith to employ and supervise somebody with a scientific background so different from your own. But our discussions and collaboration have sure been educational and fruitful to me. I have a great respect for your strong grip on astrophysics and your ability to recognize the physicality behind complex mathematical equations. Besides my current supervisor, I am still endebted a lot to my previous supervisors, Ad van der Avoird and Gerrit Groenenboom. When I was still a master-student, you have shown and taught me how to be critical in ways I couldn’t have conceived myself. Our continuing collab- oration is of great value to me. I would also like to thank all the people working at the Onsala Space Observatory that make it the great place it is to work at. An honourable mention here for the PhD students; togheter, we lighten the burden put on anyone moving to a strange and new country. Then, I would like to thank my friends and family, that provide and participate in a range of brilliantly entertaining activities that have nothing to do with the content of this thesis, and, more importantly, give copious support when needed, which has been very relevant to the content of this thesis. Finally, my thanks and love to Yasmin, who is always there for me and puts up with my moodyness that once in a while finds its roots in this work. CONTENTS 1 INTRODUCTION 1 1.1 Maser . .3 1.2 High-mass star forming regions . .6 2 MOLECULAR PHYSICS OF METHANOL 11 2.1 The energy-spectrum of methanol . 11 2.1.1 Torsion-rotation structure . 11 2.1.2 Hyperfine structure . 13 2.1.3 Methanol in a magnetic field . 15 2.2 Molecular physics behind the methanol maser . 16 3 MASER POLARIZATION THEORY 21 3.1 Maser polarization by magnetic fields . 21 3.1.1 Evolution of the density operator . 21 3.1.2 Evolution of the radiation field . 25 3.2 Alternative polarization mechanisms . 28 3.2.1 Co-propagating maser-rays . 28 3.2.2 Anisotropic pumping . 28 3.2.3 Dichroic unsaturated masers . 29 3.2.4 Anisotropic resonant scattering . 29 3.3 Alternative maser polarization and methanol . 30 4 METHANOL MASER OBSERVATIONS 33 5 OUTLOOK 37 5.1 Hyperfine-resolved pumping . 37 5.2 SiO maser observations in AGB stars . 38 6 INTRODUCTION TO PAPERS 41 BIBLIOGRAPHY 43 ix x CONTENTS PAPER I 53 PAPER II 69 Chapter 1 INTRODUCTION In this thesis, we will examine the polarization of masers, and in particular, methanol masers. We will discuss a number of subjects, from the molecular scale to the scale of star-formation. This thesis is divided in two parts. The first part consists of six introductory chapters, that will include all of the necessary knowledge to appreciate the appended papers, which form the second part. The introductory chapters are organized as follows. We will start off with an introductory note to the maser-device and its develop- ment, to afterwards move on to the astrophysical maser. We will give a small introduction to the underlying physics of the polarization of the maser, which is tightly bound to spectral splitting due to the Zeeman effect. The polarization of methanol masers can prove a valuable tool in mapping magnetic fields around high-mass star forming regions. It is therefore that the introduction continues with a brief summary of high-mass star formation, its challanges, and the con- flicting theories within this subject, as well as the role methanol maser polariza- tion observations can play in formulating constraints for the theory of massive star formation. The underlying molecular physics is paramount into explaining not only methanol masers’ polarization (Zeeman effect), but also the mechanism behind the mas- ing of different specific transitions. In Chapter 2, we will discuss the molecu- lar physics of methanol. We will start the discussion with methanols torsion- rotation structure. We will introduce a formalism that describes the motion of the constituents (electrons and nucleii) of a rotor with one site of internal ro- tation, like methanol. The kinetic energy of the torsion-rotation motions and their movement through the torsional potential will yield the torsion-rotation Hamiltonian. In the section that follows, we will use the derived expressions for the (charged) particles motions into deriving their resulting magnetic mo- ments. The interaction of these magnetic moments with the nuclear spins of methanols protons, together with the mutual interactions of the nuclear spins 1 2 INTRODUCTION of the protons, will consitute the hyperfine structure. The magnetic moments interaction with an external magnetic field are the Zeeman effects, which will be discussed in the third section of this chapter. We finish the chapter with a short section on the molecular physics behind the methanol masers. We will give some intuitive arguments, based on methanols collisional and radiative rates, as to why we observe some transitions as masers. It is important to note that for methanol, generally, a distinction is made between two classes of masers that have a different excitation mechanism. We will discuss these two classes of masers individually. When we have introduced the molecular physics of methanol, we are ready to set up the theory of maser polarization by a magnetic field. We introduce a ra- diation field that couples two states in an ensemble and a phenomenological ex- pression for the maser pumping, to the earlier found expressions for methanols energy structure. We show how the state-populations evolve in time in this system. This evolution will be synchronous with the evolution of the radiation field, due to its interaction with the molecular ensemble. The state-population evolution and the radiation evolution will constitute the maser equations. We will show how the evolution of polarized radiation naturally arises in a molec- ular ensemble that is permeated by a magnetic field. We continue this chapter with a discussion of mechanisms that will polarize state-populations partially. Such introduced polarization in the state-populations will greatly enhance the polarization of the maser-radiation.