EXPLORING THE ORIGIN AND DYNAMICS OF SOLAR MAGNETIC FIELDS Soumitra Hazra Department of Physical Sciences and Centre of Excellence in Space Sciences India Indian Institute of Science Education and Research Kolkata arXiv:1604.00563v1 [astro-ph.SR] 2 Apr 2016 This dissertation is submitted for the degree of Doctor of Philosophy in Science 2015 Dedicated to My Parents... Declaration This thesis is a presentation of my original research work. Wherever contributions of others are involved, every effort is made to indicate this clearly, with due reference to the literature and acknowledgments of collaborative research and discussions. The work has not been submitted earlier either in entirety or in parts for a degree or diploma at this or any other Institution or University. Some chapters of this thesis have either been published or are in the process of being published. This work was done under the guidance of Dr. Dibyendu Nandi, at the Indian Institute of Science Education and Research Kolkata (IISER Kolkata). Soumitra Hazra 2015 CERTIFICATE FROM THE SUPERVISOR This is to certify that this thesis entitled "Exploring the Origin and Dynamics of Solar Magnetic Fields" – which is being submitted by Soumitra Hazra (who registered on 11th August, 2009 for a PhD Degree with registration number 09RS028 at the Indian Institute of Science Education and Research Kolkata) – is based upon his own research work under my supervision and that neither this thesis nor any part of it has been submitted for any degree or any other academic award anywhere else. Dr. Dibyendu Nandi Associate Professor Department of Physical Sciences and Center of Excellence in Space Sciences India Indian Institute of Science Education and Research Kolkata West Bengal 741246 India Acknowledgements This is a special moment for me and I wish to express my sincere gratitude to my thesis supervisor Dibyendu Nandi, who introduced me to the exciting world of research in Astro- physics. This thesis work would never have been possible without his help and constant support during this period. He also taught me that one of the major components of scientific research is to be able to communicate your scientific ideas with others. I have learnt a lot of science as well as the methodolgy of tackling a difficult problem through discussions with him. I also thank him for his support and encouragement to attend different conferences which enabled me to interact with other scientists. I would like to thank B Ravindra for giving me the opportunity to visit his institute and work with him. His constant help, encouragement and discussion helped me grasp the skills of satelite data anyalisis quickly. I have completed an important project with him "The Re- lationship between Solar Coronal X-Ray Brightness and Active Region Magnetic Fields: A Study with High Resolution Hinode Observations". I am also extremly thankful to Aveek da, Andres, Piet, Dario, Bidya da, Dipankar da, Shravan Hanasoge, Paul Rajaguru, Durgesh Tripathi, Nandita Srivastava, Dhrubaditya Mitra and Prasad Subramanian for their helpful discussions and readiness to answer my numerious queries. I also want to thank Arnab Rai Choudhuri for his two books "Physics of Fluids and Plasma’ and "Astrophysics for Physi- cist" which I used as a text book during my Ph.D period. I am also greatful to all the faculty members and colleagues of the Department of Physi- cal Sciences, IISER Kolkata for their help and support. I want to thank Barun (nada), Dyuti, choto and baro Nandan (Das & Roy), Abhinav, Subhrajit (kaka), Gopal, Tanmoy, Sudipta, Rupak, Richarj, Sumi, Harkirat, Sanhita, Anirudha, Abhishek, Arghya da (mama), Basu da, Chandan da, Rabi da, Vivek da, Priyam da for making my initial life at IISER Kolkata fun and enjoyable. It gives me pleasure to thank my CESSI lab mates Mayukh, Prantika, Avyarthana, Rakesh, Sushant, Tamoghna, Athira, Sanchita, Prasenjit, Abhinna, Chandu da for their support. A special word of thanks to Mayukh and Prantika for their readiness to help me with MATLAB related issues. Mayukh has also collaborated with me in a paper. I x want to thank Sanjib Ghosh for his initial help in my first work. I also thank Madhusudan, Arun Babu, Wageesh, Sushant Bishoi, Grijesh Gupta, Krishna da, Vemareddy for discussion and help. It is also my pleasure to thank Ankan, Debmalya (motu), Chiranjeeb, Soumya (gambat), Diptesh, Deepak, Radhe, Soumen, Rafikul and all those who made my life mem- orable and enjoyable at IISER Kolkata. I also want to thank Prasanta da and Soma di for their help and support during my stay at Montana. It is also my pleasure to thank my masters and bachelors degree friends Monalisa, Arup, Amit, Amaresh, Arnab, Nikhil, Sarengi, Suman, Prithwish da, Asim da, Samaresh da and my childhood friends Palash, Dilip, Jagneswar, Gopi, Bubun, Bulbul da, Bappaditya, Sushanta, Arup Samanta, Dipak da, Abhi, Piu for their help and support. I also want to thank my maternal uncles and aunts (mama and mamima), paternal uncles and aunts for their encouragement and support. Finally, I would like to thank my parents and sister for their constant patience and sup- port. They have always shared my joys and sorrows and have given their unconditional love. Thanks to all of my family members and friends for their understanding and supporting me. Abstract The Sun is a magnetically active star and is the source of the solar wind, electromagnetic ra- diation and energetic particles which affect the heliosphere and the Earth’s atmosphere. The magnetic field of the Sun is responsible for most of the dynamic activity of the Sun. This thesis research seeks to understand solar magnetic field generation and the role that mag- netic fields play in the dynamics of the solar atmosphere. Specifically, this thesis focuses on two themes: in the first part, we study the origin and behaviour of solar magnetic fields us- ing magnetohydrodynamic dynamo theory and modelling, and in the second part, utilizing observations and data analysis we study two major problems in solar physics, namely, the coronal heating problem and initiation mechanisms of solar flares. The magnetic field of the Sun, whose evolution is evident in the 11 year cycle of sunspots, is created within the Sun through complex interactions between internal plasma flows and fields. It is widely believed that magnetic fields of not just the Sun, but all as- tronomical bodies are produced by this hydromagnetic dynamo process. To explain the origin of the solar cycle, Eugene Parker first proposed the idea of flux recycling between the toroidal (which is in the azimuthal i.e., φ-direction) and poloidal (which is in r-θ plane) field components . Currently, flux transport dynamo models based on the Babcock-Leighton mechanism for poloidal field generation appears as a promising candidate for explaining dif- ferent aspects of the solar cycle. In this scenario, the toroidal field is produced within the convection zone due to stretching of the poloidal component by strong differential rotation while the poloidal field is produced at the solar surface due to decay and dispersal of tilted bipolar sunspot pairs. Flux transport mechanisms such as diffusion, meridional flow and tur- bulent pumping shares the role of communicator between these two largely separated source layers. In chapter 1, we describe observations of solar magnetic fields and development of solar dynamo theory to motivate our work. An outstanding issue related to the solar cycle is extreme fluctuations, specifically the occurrence of extended periods of reduced or no activity, known as grand minima episodes. The origin of such episodes have eluded a consistent theory. The Maunder minima was xii such an episode during 1645-1715 AD when there was almost no sunspots observed on the Sun. There is also observational evidence of many such episodes in the past. The crucial fact is that the solar cycle has recovered from these episodes every time and regained nor- mal activity levels. It is expected that during grand minima phases, the Babcock-Leighton mechanism would not be able to produce poloidal field as this mechanism relies on the presence of sunspots on the solar surface. This leads to the following fundamental ques- tion: How does the solar cycle recover every time from these episodes? We address this question through diverse means. In chapter 2 of this thesis, we develop a mathematical, low order time delay dynamo model (based on delay differential equations) removing all spatial dependence terms from the magnetic induction equation and mimic flux transport through the introduction of finite time delays in the system. By introducing fluctuations in the Babcock-Leighton source term of this low order dynamo model, we, for the first time explicitly demonstrate that a solar cycle model based on the Babcock-Leighton mechanism alone can not recover from a grand minima. We find that an additional poloidal field gener- ation mechanism effective on weak magnetic field is necessary for recovery of the sunspot cycle from grand minima like episodes. Modeling the Babcock-Leighton mechanism in a correct way to capture the observed surface dynamics is a challenging task. Two different approaches, mainly near-surface alpha-coefficient formulation and the double ring formalism has been followed to model the Babcock-Leighton mechanism for poloidal field generation. Earlier it has been shown that the second approach, i.e., the double ring formalism is more successful in explaining observational results compared to the near-surface alpha-coefficient formulation. Inspired by this, we develop a 2.5D kinematic solar dynamo model where we simulate the Babcock- Leighton mechanism via the double ring algorithm. In chapter 3 of this thesis, we utilize this state-of-the spatially extended model in a solar like geometry to validate our findings on entry and exit from Maunder minima like episodes.