SUDESHNA BORO SAIKIA MAGNETIC AND ACTIVITY CYCLES OF COOL STARS DISSERTATION Magnetic and activity cycles of cool stars Dissertation zur Erlangung des mathematisch-naturwissenschaftlichen Doktorgrades “Doctor rerum naturalium” der Georg-August-Universität Göttingen - im Promotionsprogramm PROPHYS der Georg-August University School of Science (GAUSS) vorgelegt von Sudeshna Boro Saikia aus Golaghat, Assam Göttingen, 2016 Betreuungsausschuss Dr. Sandra V. Jeffers, Institut für Astrophysik, Universität Göttingen Prof. Dr. Ansgar Reiners, Institut für Astrophysik, Universität Göttingen Mitglieder der Prüfungskommission Referent: Dr. Sandra V. Jeffers, Institut für Astrophysik, Universität Göttingen Korreferent: Prof. Dr. Stefan Dreizler, Institut für Astrophysik, Universität Göttingen 2. Korreferent: Prof. Dr. Jürgen Schmitt, Hamburger Sternwarte Weitere Mitglieder der Prüfungskommission: Prof. Dr. Ansgar Reiners, Institut für Astrophysik, Universität Göttingen Prof. Dr. Angela Rizzi, IV. Physikalisches Institut, Universität Göttingen Prof. Dr. Ariane Frey, II. Physikalisches Institut-Kern-und Teilchenphysik, Universität Göttingen Prof. Dr. Jens Niemeyer, Institut für Astrophysik, Universität Göttingen Tag der mündlichen Prüfung: 21.12.2016 Abstract Cool stars are known to exhibit weak to strong magnetic activity. Our nearest cool star, the Sun, is a middle aged and moderately active star with a cyclic generation of its magnetic field, which results in a 22 year magnetic cycle and a 11 year activity cycle. The physical process behind the solar cycles is called the dynamo. The aim of this thesis is to investigate the magnetic and activity cycles in cool stars over a range of stellar parameters, and to under- stand the dynamo mechanism and its dependence on basic stellar properties such as rotation and mass. The relationship between magnetic geometry and activity cycle was investigated. The large-scale magnetic field of three cool stars, HN Peg, 61 Cyg A and e Eridani is re- constructed using Zeeman Doppler imaging (ZDI). These stars vary in mass, rotation and age. The large-scale magnetic field of HN Peg is complex and highly variable, with a strong toroidal component, which is not seen in the Sun. The magnetic geometry of 61 Cyg A is strongly poloidal, which is a simple dipole during minimum activity and more complex dur- ing maximum activity, similar to the solar case. The large-scale field also flips polarity from one minimum to the next, indicating a solar-like magnetic cycle. This is the first detection of a solar-like magnetic cycle in any cool star other than the Sun. e Eridani shows a non ax- isymmetric complex magnetic field geometry during minimum chromospheric activity, with both poloidal and toroidal components. The toroidal percentage increases gradually in time, which is different from our Sun’s axisymmetric poloidal dipolar magnetic geometry at ac- tivity minimum. Magnetic proxies such as chromospheric activity were also used to provide information on the activity cycles in cool stars, although they do not provide information about the magnetic field geometry evolution or the magnetic cycle of the star. A cool star chromospheric activity catalogue of Ca II H and K activity was developed. For the entire cool star range, we use a recently developed calibration to obtain accurate log RHK0 measurements, the physical representation of chromospheric activity. For stars with long-term observations, the activity cycle periods were determined, using a period search algorithm, and their de- pendence on stellar rotation was investigated. For slowly rotating stars the chromospheric activity cycle periods show a possible dependence on rotation. This dependence has pre- viously been shown and called the ‘Inactive’ branch of stellar cycles. On the other hand, and in contrast to previous work, we show that rapidly rotating stars exhibit a more random distribution on the cycle period-rotation plane, indicating an ‘Active’ region rather than an ’Active’ branch. Furthermore, rapidly rotating stars also show the presence of multiple cy- cles. The multiple cycles might be caused by their complex magnetic field geometry, which can be completely different from the solar case. This thesis shows that cool stars exhibit a range of magnetic geometry variations during their activity cycle, which does not necessarily have to be solar-like. This result is important for understanding the dynamo processes acting in cool stars including our own Sun. v Contents 1. Introduction1 1.1. Cool stars...................................1 1.2. Our Sun....................................2 1.3. The 11 year solar cycle............................4 1.4. The 22 year solar magnetic cycle.......................5 1.5. The solar dynamo...............................5 1.6. Cool star magnetism.............................7 1.6.1. Stellar activity cycles.........................8 1.6.2. Stellar magnetic cycles........................ 10 1.7. Motivation................................... 11 2. Methods of field detection 13 2.1. Mechanisms for magnetic field detection................... 14 2.1.1. Zeeman effect............................. 14 2.1.2. Polarisation of light and the Stokes parameters........... 16 2.2. Instrumentation and data reduction...................... 19 2.2.1. An astronomical spectrograph.................... 19 2.2.2. Instrumentation to detect polarisation................ 21 2.2.3. Least square deconvolution...................... 23 2.3. Magnetic field measurements using Stokes V and I ............. 25 2.3.1. Longitudinal magnetic field measurement.............. 25 2.3.2. Zeeman Doppler imaging (ZDI)................... 26 2.4. Indirect proxies of magnetic activity..................... 31 2.4.1. Chromospheric activity........................ 31 2.4.2. Coronal activity............................ 34 2.5. Summary................................... 35 3. Variable magnetic field geometry of the young Sun HN Pegasi (HD 206860) 37 3.1. Abstract.................................... 38 3.2. Introduction.................................. 38 3.3. HN Peg.................................... 39 3.4. Observations................................. 40 3.5. Mean longitudinal magnetic field (Bl).................... 41 3.6. Chromospheric activity indicators...................... 42 3.7. Large-scale magnetic field topology..................... 48 3.7.1. Radial velocity............................ 49 3.7.2. Inclination angle........................... 49 3.7.3. Differential rotation......................... 49 vii 3.7.4. Magnetic topology.......................... 50 3.8. Discussion................................... 55 3.8.1. Long-term magnetic variability................... 55 3.8.2. Large scale magnetic topology.................... 57 3.8.3. Differential rotation......................... 59 3.9. Summary................................... 59 4. A solar-like magnetic cycle on the mature K-dwarf 61 Cygni A (HD 201091) 61 4.1. Abstract.................................... 62 4.2. Introduction.................................. 62 4.3. Physical properties of 61 Cyg A....................... 64 4.4. Instrumental setup and data reduction.................... 66 4.4.1. Optical data.............................. 66 4.4.2. X-ray data............................... 67 4.5. Magnetic field detection: direct and indirect approach............ 67 4.5.1. Mean longitudinal magnetic field.................. 67 4.5.2. Chromospheric activity as a proxy of magnetic activity....... 68 4.6. Large-scale magnetic field geometry..................... 74 4.6.1. Vector magnetic field......................... 74 4.6.2. Evolution of the different multipolar modes over the magnetic cycle 80 4.6.3. Differential rotation......................... 82 4.7. Long-term evolution of the magnetic and activity cycle........... 82 4.8. Discussion................................... 84 4.8.1. Large-scale magnetic field...................... 84 4.8.2. Chromospheric activity........................ 86 4.9. Summary................................... 87 5. Göttingen chromospheric activity catalogue: questioning the Active branch of stellar activity cycles 89 5.1. Abstract.................................... 89 5.2. Introduction.................................. 90 5.3. Data analysis................................. 92 5.4. Chromospheric activity............................ 94 5.4.1. S-index................................ 94 5.4.2. Chromospheric Ca II H and K.................... 96 5.4.3. Vaughan-Preston gap......................... 97 5.5. Long-term evolution of chromopsheric activity vs rotation......... 98 5.6. Conclusions.................................. 104 6. The relation between stellar magnetic field geometry and chromospheric activity cycles: the complex field of e Eridani at activity minimum 105 6.1. Abstract.................................... 105 6.2. Introduction.................................. 106 6.3. Observations and Data Analysis....................... 106 6.3.1. Least Squares Deconvolution..................... 107 viii 6.3.2. Chromospheric emission - Ca II H&K................ 107 6.4. Large-scale magnetic field geometry..................... 107 6.4.1. Magnetic maps............................ 108 6.4.2. Magnetic energy........................... 109 6.5. Discussion................................... 110 6.6. Conclusions.................................. 113 7. Summary and conclusions 115 7.0.1. Variable magnetic geometry of the young sun HN Pegasi (HD206860) 116 7.0.2. A solar-like magnetic cycle on the mature K dwarf 61 Cygni