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Properties of the Solar Velocity Field Indicated by Motions of Sunspot Groups and Coronal Bright Points

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Properties of the Solar Velocity Field Indicated by Motions of Sunspot Groups and Coronal Bright Points DISSERTATION zur Erlangung des Doktorgrades an der Naturwissenschaflichen Fakultät der Karl-Franzens-Universität Graz Properties of the solar velocity field indicated by motions of sunspot groups and coronal bright points Ivana Poljančić Beljan begutachtet von Univ.-Prof. Dr. Arnold Hanslmeier Institut für Physik Karl-Franzens-Universität Graz und Dr. Roman Brajša, scientific advisor Hvar Observatory, Faculty of Geodesy University of Zagreb 2018 Thesis advisor: Univ.-Prof. Dr. Hanslmeier Arnold Ivana Poljančić Beljan Properties of the solar velocity field indicated by motions of sunspot groups and coronal bright points Abstract The solar dynamo is a consequence of the interaction of the solar magnetic field with the large scale plasma motions, namely differential rotation and meridional flows. The main aims of the dissertation are to present precise measurements of the solar differential rotation, to improve insights in the relationship between the solar rotation and activity, to clarify the cause of the existence of a whole range of different results obtained for meridional flows and to clarify that the observed transfer of the angular momentum to- wards the solar equator mainly depends on horizontal Reynolds stress. For each of the mentioned topics positions of sunspot groups and coronal bright points (CBPs) from five different sources have been used. Synodic angular rotation velocities have been calculated using the daily shift or linear least-square fit methods. After the conversion to sidereal values, differential rotation profiles have been calculated by the least-square fitting. Covariance of the calculated rotational and meridional velocities was used to de- rive the horizontal Reynolds stress. The analysis of the differential rotation in general has shown that Kanzelhöhe Observatory for Solar and Environmental research (KSO) provides a valuable data set with a satisfactory accuracy suitable for the investigation of differential rotation and similar studies. A significant correlation was found between the solar equatorial rotation speed and indices of the solar activity, for both tracers. Dif- ferent CBPs and sunspot groups results for the meridional flows are consistently inter- preted. The analysis of the horizontal Reynolds stress, by both tracers, showed transfer of angular momentum towards the solar equator, which is consistent with the observed solar differential rotation profile. The results presented in the thesis are original scien- tific contributions primarily fundamental in nature, but a part of the research also has possible applicative potential for the use of dynamo modelling. ii Thesis advisor: Univ.-Prof. Dr. Hanslmeier Arnold Ivana Poljančić Beljan Eigenschaften des solaren Geschwindigkeitsfeldes angegeben durch Sonnenfleckengruppen und koronale helle Punkte Abstract (German) Der Sonnendynamo ist eine Folge der Wechselwirkung des solaren Magnetfeldes mit großräumigen Plasmabewegungen, die sich durch differentielle Rotation und merid- ionale Bewegung zeigt. Daher ist das Ziel dieser Dissertation, präzise Messungen der differentiellen Rotation der Sonne zu präsentieren, die Abhängigkeit von Rotation und Aktivität besser zu verstehen, die Ursache für die Existenz verschiedener Resultate für meridionale Strömungen zu erklären und die Abhängigkeit der erwähnten Bewegung durch das Drehmoment und der Strömung in Richtung des Sonnenäquators mit der hor- izontalen Reynoldsspannung zu klären. Für jedes der genannten Themen wurden Posi- tionen von Sonnenfleckengruppen und hellen koronalen Punkten (CBPs) von fünf ver- schiedenen Quellen verwendet. Synodische Umlaufzeiten wurden nach der zweitägigen Abstand und der Methode der kleinsten Quadrate berechnet und ausgewertet. Nach Um- rechnung der synodischen Umlaufzeiten in die siderischen Umlaufzeiten, wurden dif- ferentielle Rotationsprofile unter Berücksichtigung der Methode der kleinsten Quadrate erstellt. Die Kovarianz der ermittelten Rotations- und Meridionalgeschwindigkeiten wurde verwendet, um die horizontale Reynoldsspannung zu berechnen. Die Unter- suchung der differentiellen Sonnenrotation hat gezeigt, dass der Datenbestand des KSO mit seiner zufriedenstellenden Genauigkeit für die Analyse der differentiellen Rotation und ähnlicher Studien durchaus geeignet ist. Es wurde eine statistisch bemerkenswerte Korrelation zwischen der Rotationsgeschwindigkeit am Äquator und dem Indikator der Sonnenaktivität für die beiden Tracer festgestellt. Die Analyse der horizontalen Reynoldsspannung beider Tracer zeigte auch eine Ablenkung des Drehimpulses in Richtung des Sonnenäquators. Die in dieser Dissertation dargestellten Ergebnisse sind ursprüngliche wissenschaftliche Beiträge mit fundamentalem Charakter, während ein Teil der Forschung das Potential besitzt, das Model des Dynamoprozesses besser zu beschreiben. iii Acknowledgements Special thanks go to my supervisor Univ.-Prof. Dr. Arnold Hanslmeier and my mentor Dr. Roman Brajša. You were always there, opened for conversation and giving answers, encouraging me to go constantly forward. I am deeply grateful to Univ.-Prof. Dr. Rajka Jurdana-Šepić for being there in every moment, for responding to my e-mails, always in an amazingly short time, for all the sleepless working nights with thousands of e-mails. I would like to thank Dr. Werner Pötzi from the Kanzelhöhe Observatory for So- lar and Environmental Research for the hospitality during my stay at Kanzelhöhe, for patience and understanding during our long conversations, for giving answers to many questions concerning the topics connected with the Kanzelhöhe sunspot drawings and full disc white light CCD images. I also thank to Assoc. Univ.-Prof. Dr. Astrid Veronig for discussions during my attendance on the PhD seminars, which prompted me to deepen and broaden the analysis of the Kanzelhöhe data. I am deeply grateful to Mag. Is- abell Piantschitsch for being my guide in solving the whole variety of paperwork during my doctoral studies and for being so kind and friendly. Without most of the people from Hvar Observatory this thesis would not have be- come what it is. I thank Dr. Bojan Vršnak. Special thanks goes to Dr. Davor Sudar and Dr. Domagoj Ruždjak for the fruitful discussions and plenty of suggestions. Dr. Ivica Skokić helped me immensely, by giving plenty of advice concerning the programming in Python. I thank M.Sc.M.E. Damir Hržina from Zagreb Observatory for his assistance during the work on KSO paper in upgrading the program ”Sungrabber” according to my requirements, whenever I needed. This thesis was financially supported in part by Croatian Science Foundation under the project 6212 “Solar and Stellar Variability” and in part by the University of Rijeka under the project number 13.12.1.3.03. Without these financial supports my travels to Graz would be quite difficult. There are no words that can describe my gratitude to my husband, his parents and my parents, especially to my mother. Thank you mom for suporting me in all aspects, espe- cially by looking after my son whenever I needed. I still feel your support, somewhere from above. iv Contents 1 Introduction 1 1.1 List of publications ............................. 6 2 Observations of the solar differential rotation 8 2.1 Sunspots and sunspot groups as tracers ................... 10 2.1.1 Magnetic properties of sunspots ................... 10 2.1.2 The evolution of a sunspot ...................... 12 2.2 Coronal bright points as tracers ....................... 14 2.3 Surface rotation ............................... 15 2.4 Internal rotation ............................... 17 2.5 Meridional motions ............................. 19 2.6 Horizontal Reynolds stress ......................... 21 2.7 Relationship between the solar rotation and activity . 23 3 Theory of the solar differential rotation 26 3.1 Angular momentum transport and magnetic braking . 26 3.2 Axisymmetric and non-axisymmetric convective motions . 27 3.3 The Λ-effect and eddy viscosity ...................... 28 3.4 Angular momentum transport ....................... 31 3.5 Models of the differential rotation ..................... 32 3.5.1 Mean-field models .......................... 33 3.5.2 Global (explicit) models ....................... 34 4 Peer-reviewed publications 36 4.1 Paper I: Solar differential rotation in the period 1964 - 2016 determined by the Kanzelhöhe data set ......................... 36 4.2 Paper II: A relationship between the solar rotation and activity in the pe- riod 1998–2006 analysed by tracing small bright coronal structures in SOHO-EIT images ............................. 48 4.3 Paper III: A Relationship between the Solar Rotation and Activity Anal- ysed by Tracing Sunspot Groups ...................... 55 4.4 Paper IV: Meridional motions and Reynolds stress from SDO/AIA coro- nal bright points data ............................ 67 v 4.5 Paper V: Meridional Motion and Reynolds Stress from Debrecen Photo- heliographic Data .............................. 74 5 Conclusion 88 References 96 vi 1 Introduction Solar activity manifests itself in many diverse phenomena (sunspots, flares, coronal mass ejections, etc.) that vary on several distinct timescales. The most prominent manifestation of solar activity is the 11-year Schwabe cycle. Extensive reviews on the long-term behaviour of the solar activity and the Schwabe cycle are given by Hathaway (2010) and Usoskin (2017). It is generally accepted that the solar cycle is magnetic in nature and generated by dynamo processes within the Sun. The Sun’s magnetic field is maintained
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