SOLAR ACTIVE LONGITUDES AND THEIR ROTATION

LIYUN ZHANG

Department of Physics University of Oulu Finland

Academic dissertation to be presented, with the permission of the Faculty of Science of the University of Oulu, for public discussion in the Auditorium L6, Linnanmaa, on 30th November, 2012, at 12 o’clock noon.

REPORT SERIES IN PHYSICAL SCIENCES Report No. 78 OULU 2012 ● UNIVERSITY OF OULU

Supervisors Prof. Kalevi Mursula University of Oulu, Finland

Prof. Ilya Usoskin Sodankylä Geophysical Observatory, University of Oulu, Finland

Opponent Dr. Rainer Arlt Leibniz-Institut für Astrophysik Potsdam, Germany

Reviewers Prof. Roman Brajša Hvar Observatory, Faculty of Geodesy, University of Zagreb, Croatia

Assoc. Prof. Dmitri Ivanovitch Ponyavin St. Petersburg State University, St. Petergoff, Russia

Custos Prof. Kalevi Mursula University of Oulu, Finland

ISBN 978-952-62-0025-5 ISBN 978-952-62-0026-2 (PDF) ISSN 1239-4327

Oulu University Press Oulu 2012 Zhang, Liyun: Solar active longitudes and their rotation

Department of Physical Sciences, University of Oulu, Finland. Report No. 78 (2012)

Abstract

In this thesis solar active longitudes of X-ray flares and sunspots are studied. The fact that solar activity does not occur uniformly at all heliographic longitudes was noticed by Carrington as early as in 1843. The longitude ranges where solar activity occurs preferentially are called active longitudes. Active longitudes have been found in various manifestations of solar activity, such as sunspots, flares, radio emission bursts, surface and heliospheric magnetic fields, and coronal emissions. However, the active longitudes found when using different rigidly rotating reference frames differ significantly from each other. One reason is that the whole Sun does not rotate rigidly but differentially at different layers and different latitudes. The other reason is that the rotation of the Sun also varies with time. Earlier studies used a dynamic rotation frame for the differential rotation of the Sun and found two persistent active longitudes of sunspots in 1878-1996. However, the migra- tion of active longitudes with respect to the Carrington rotation was treated there rather coarsely. We improved the accuracy of migration to less than one hour. Accordingly, not only the rotation parameters for each class of solar flares and sunspots are found to agree well with each other, but also the non-axisymmetry of flares and sunspots is systematically increased. We also studied the long-term variation of solar surface rotation. Using the improved analysis, the spatial distribution of sunspots in 1876-2008 is analyzed. The statistical evidence for different rotation in the northern and southern hemispheres is greatly im- proved by the revised treatment. Moreover, we have given consistent evidence for the periodicity of about one century in the north-south difference.

Keywords: Solar activity, sunspots, X-ray flares, solar rotation, active longitudes.

This thesis is dedicated to my biological parents and my adoptive parents for all their love and support! They have been and will always be great sources of encouragement and inspiration throughout my life!

3

Acknowledgements

This work has been carried out in the Department of Physics at the University of Oulu, Finland. First, I would like to express my deepest gratitude to Prof. Ilya Usoskin. He very enthusiastically answered my questions at our first meet during the Beijing COSPAR 2006. He has been supporting me with my study and work ever since. He also guided me to write my first scientific paper in 2006. He encouraged me to come to Oulu to get valuable work experience under the guidance of Prof. Kalevi Mursula and himself. In the beginning of my first visit to Oulu, Ilya offered me plenty of help and guidance for managing the new daily life, including how to wait for a bus and how to use the knife and fork at lunch, too much to mention. Next, I wish to express my greatest gratitude to my principal supervisor, Prof. Kalevi Mursula who always has open mind and new ideas. He has always been giving me plenty of support and encouragement to deal with the problems I have had during doing the thesis. Accordingly, the scientific significance of the thesis has been greatly improved. I also sincerely appreciate his fatherly advices on my life. I would like to express my deepest gratitude to my Beijing chief Prof. Huaning Wang, a great scientist in solar physics and solar activity prediction. He has been guiding me through my science career since the very beginning and giving me continuous support. He always reminds me to find out what is the physics behind the phenomenon that I see. The other members of my Beijing group are also deeply acknowledged, especially Prof. Zhanle Du, Xin Huang, Jian Gao, Yanmei Cui and Rong Li, who greatly share my study, work and life. I am very grateful for the funding from the Department of Physics of the Uni- versity of Oulu, the Academy of Finland, the European Commission’s Seventh Framework Programme for eHeroes project, and the Key Laboratory of Solar Ac- tivity, National Astronomical Observatories, Chinese Academy of Sciences. I fully acknowledge the pre-examiners of my thesis Prof. Roman Brajˇsaand Assoc. Prof. Dimitri Ponyavin for their valuable comments and advice. I would

5 also like to express my sincere appreciation to Dr. Rainer Arlt who agreed to spare his time to be the opponent. I wish to express my warmest gratitude to all the other members in the Space Physics group for their friendship and help, Reijo Rasinkangas, Leena Kalliopuska, Olesya Yakovchouk, Alessandra Pacini, three Virtanen brothers, Timo Asikainen, Petri Kalliom¨aki,Tomi Karppinen, Lauri Holappa, Ville Maliniemi, Anita Aikio, Ritva Kuula, Tuomo Nygr´en,Kari Kalla, Timo Pitk¨anen,Lei Cai, Perttu Kantola and Raisa Leussu. Members of the Geophysics group are also acknowledged for their warm companionship during the coffee break. In the end I would like to thank my dear sister and brother for their constant support and love during my study and my life. I definitely must thank my beloved husband Ari Ronkainen for everything. He has been strongly supporting me for my work and for my hobbies. I would also like to thank my husband’s parents and relatives for their love and support.

Oulu, November 30, 2012

Liyun Zhang Original publications

This thesis consists of an introduction and four original papers.

I L. Zhang, K. Mursula, I. G. Usoskin, and H. N. Wang, Global analysis of active longitudes of solar X-ray flares, J. Atmos. Sol. Terr. Phys., 73, 258- 263, 2011. II L. Zhang, K. Mursula, I. G. Usoskin, and H. N. Wang, Global analysis of active longitudes of sunspots, Astron. Astrophys., 529, A23, 2011. III L. Zhang, K. Mursula, I. Usoskin, H. Wang, and Z. Du, Long-term variation of solar surface differential rotation, Bulletin of Astronomical Society of India, ASI Conference Series, 2, 175, 2011. IV L. Zhang, K. Mursula, and I. Usoskin, Consistent long-term variation in the hemispheric asymmetry of solar rotation, Astron. Astrophys., submitted.

In the text, original papers are referred to using roman numerals I-IV.

Contents

Abstract ...... 1 Acknowledgements ...... 5 Original publications ...... 7

1. Introduction ...... 11 2. Solar activity ...... 15 2.1. Sunspots ...... 15 2.1.1. Wolf sunspot numbers ...... 17 2.1.2. Group sunspot numbers ...... 19 2.1.3. Sunspot areas and positions ...... 20 2.1.4. Cyclicities in solar activity ...... 21 2.1.5. Grand minima and maxima ...... 25 2.2. Solar flares ...... 28 2.2.1. Classification of solar flares ...... 29 2.2.2. Phases of a typical flare ...... 31 2.2.3. Radio emissions during solar flares ...... 34 2.2.4. Flare models ...... 36 2.3. Coronal mass ejections ...... 39 2.4. Solar energetic particles acceleration ...... 41 3. Solar rotation ...... 43 3.1. Heliographic coordinates ...... 43 3.2. Surface rotation ...... 43 3.3. Internal rotation ...... 45 3.4. Torsional oscillation ...... 48 3.5. Meridional circulation ...... 51 4. Active latitudes ...... 55 5. Active longitudes ...... 58 5.1. History of active longitude research ...... 58 5.2. Flip-flop phenomenon ...... 69 5.3. Dynamo models ...... 70 5.4. North-South asymmetry ...... 74 5.4.1. N-S asymmetry in solar activity ...... 75 5.4.2. N-S asymmetry in solar rotation ...... 77 6. Summary ...... 82 1. Introduction

As is well known, the Sun is the source of energy that supports the existence of life on the Earth through radiation, which was originally recognized as visible sunlight, while solar electromagnetic radiation covers infrared, visible, and ultraviolet light. Most of the time the Sun appears as a quiet star to the naked-eye, but it is far more active when observed through telescopes, especially through the modern space-borne instruments with high temporal and spatial resolution. Even the quiet Sun appears very active in the observations of the newest space solar telescope - Solar Dynamics Observatory (SDO). Small scale tornadoes or cyclones are found to occur all over the quiet Sun with rotating magnetic fields [Zhang and Liu, 2011] (see the left panel of Fig. 1.1). Later phases of cyclones are observed to be associated with microflares. A huge tornado can be observed before a coronal mass ejection (CME) (see the right panel of Fig. 1.1). There are gradually changing activities and bursting activities on the Sun. The former refer to activities which vary gradually in size and energy and last a rel- atively long time. These include sunspots, plages, faculae, quiet filaments and prominences, coronal holes and streamers, solar wind, and the general radiation. The latter refer to explosive events with sudden and huge energy release. These events include, e.g., flares, CMEs, and explosive filaments and prominences. Solar activity affects the near-Earth space in many different ways. Variation in solar conditions at short time scales, e.g., from a few seconds to days is involved with space weather, while the long-term conditions, from several months to one solar cycle and longer, relate to space climate. Space weather effects are mainly caused by explosive transient solar events, i.e., flares and CMEs. The various types of radiation released in a flare can be absorbed in the Earth’s atmosphere. The heated atmosphere might drag a spacecraft to a lower orbit in altitude. Solar energetic particles (SEPs), which are accelerated up to relativistic velocities in a flare or by CME shock waves, can cause a disruption of technical systems and may threaten the life and health of astronauts working in the space outside the protection of the Earth’s magnetosphere. Gigantic clouds of ionized gas ejected in a CME can cause a series of geomagnetic effects when they reach and hit the Earth’s magnetosphere. These effects can cause malfunctions in satellite systems. They cause the ionosphere to more effectively absorb high frequency radio waves, 12

-580

Y (arcsec)

-600

-280 -260 X (arcsec)

Fig. 1.1. Tornadoes on the Sun observed with SDO/AIA 171A˚ EUV. Left panel: an example of small-scale tornadoes observed in the quiet Sun on 20 July 2010 [Zhang and Liu, 2011]. Right panel: A huge tornado observed before a CME with the width as large as five Earths on 25 September 2011. [Credit: NASA/SDO/AIA/Aberystwyth University/Li/Morgan/Leonard; http://users.aber.ac.uk/xxl/tornado.htm.]

thus affecting radio transmission or even making it impossible. The first solar induced technological damage was noticed in the telegraph transmission due to a white flare observed by Carrington and Hodgson in 1859. This event was widely spread through newspapers and articles, which caught much public attention and became the first famous space weather event. With more and more utilization of space and technical systems in our daily life, the economic and societal losses due to powerful solar explosive events have become more and more serious. In order to lessen this damage, sciences and techniques involved in these processes have to be improved. On one hand, we have to seek out signatures of indication of a powerful solar event and the connections of solar events and the space and near-Earth environment so that we can identify the geoeffective events from those which are not geoeffective. This study has developed into space weather and forecasting sciences. Although the Solar-terrestrial physics started long ago, a large amount of connections and physical mechanisms involved with solar activity and space effects are still open. The signatures of a geoeffective event have not been surely identified yet. On the other hand, we need to estimate how serious the effects from a solar event can be so that the corresponding protective measures for technical systems and humans can be found. Through observations of space-borne instruments, especially in the last decade, the appearance and evolution of solar activity and its effect on the solar-terrestrial environment has been roughly established. Space weather, nowadays, deals with activity conditions on the Sun and their effects on the near-Earth space, especially 13 what might be hazardous to the technological systems and endanger humans’ life and health both in the spacecraft and on the ground. At the present time the parameters of solar wind (the material in the interplan- etary space) can only be observed at the first Lagrangian point (L1 ∼1.5·106 km away to the Earth, 1/100 of the Sun-Earth distance). This leaves us only 30 to 60 minutes before the plasma reaches the Earth. ACE (Advanced Composition Explorer launched in 1997), SOHO (Solar and Heliospheric Observatory launched in 1995) and WIND (Global Geospace Science WIND moved to L1 in 2004) at the L1 point measure real time solar wind parameters, such as the magnetic field, the velocity density and temperature of electrons and protons. International Space Environment Service (ISES) consisting of 13 Regional War- ing Centers (RWCs) all over the world, and the European Space Agency (ESA) collect space-borne and ground-based space-weather related observations and fore- casts and provide the data to users. The Space Weather Prediction Center of NOAA (National Oceanic and Atmospheric Administration of USA) performs 3- day space weather forecasts and plots of the observational data (http://www.swpc. noaa.gov/today.html). The magnetic field in the interplanetary space has a spiral structure. This leads that only those charged particles accelerated in the flares occurring close to the western limb of the solar disc may hit the Earth. Magnetic clouds from CMEs with inclosed magnetic structure propagate radially from the Sun to the interplanetary space. Thus, CMEs may reach the near-Earth space when they appear close to the center of solar disc. Those events which occur on the back side of the Sun are not geo-effective. Therefore, the location of eruptions on the Sun is an important factor to space weather. It was noted long ago that solar activity does not occur uniformly at all longi- tudes on the Sun. Those longitude ranges where solar activity appear more often than elsewhere are called active longitudes. Active longitudes (ALs) were found in various manifestations of solar activity, such as sunspots, flares, surface mag- netic fields. However, the suggested ALs differ with each other significantly in rigidly rotating reference frame. This is because the Sun does not rotate rigidly but differentially with latitude and depth, showing the so-called surface and radial differential rotation. Accordingly, different types of solar activity appearing at different height in the solar atmosphere, e.g., sunspots at solar surface and CMEs in the high corona, rotate at different rates. And the rotation of one type of solar activity may change due to its latitudinal variation in a solar cycle. Taking solar surface differential rotation into account Usoskin et al. [2005] in- troduced a dynamic differentially rotating reference frame. In this frame, the shift of ALs due to the surface differential rotation was removed. Two persis- tent active longitudes of sunspots were found to last for 11 cycles. Using similar reference system two ALs of X-ray flares were found to exist for 3 cycles. The non-axisymmetry of solar flares is much higher than that of sunspots. Especially, the non-axisymmetry of X-class flares can reach 0.55, suggesting that 77.5% of powerful flares occur in the two active longitudes. This implies the importance of prediction of active longitudes of solar flares. However, the rotation parameters obtained for each class of solar flares differ with each other significantly. 14

In order to find out the source of the discrepancy among the rotation parameters for sunspots and each class of flares, the locations of sunspots and X-ray flares in last three solar cycles were reanalyzed in this thesis. Rotation rate of the Sun varies also with time. Increasing evidence [Howard and Harvey, 1970; Knaack et al., 2005; Balthasar, 2007] suggests that the rotation rate of solar surface changes from cycle to cycle, even within one cycle. The rotation rate in the northern hemisphere was found to vary differently with the southern hemisphere showing N-S asymmetry. The suggested faster rotating hemispheres in each solar cycle by different authors disagree with each other. The locations of sunspots in 1876-2008 are analyzed in this thesis in order to study the long-term variation in solar surface rotation. 2. Solar activity

2.1. Sunspots

Sunspots appear visibly as dark spots compared to surrounding regions. Therefore, they can easily be observed even by naked-eye [Keller and Friedli, 1992], and are known as the one of several active solar phenomena which was observed earliest. For instance, several dark spots in one group (AR10930) can be seen in the solar disc observed on Dec 11, 2006 by SOHO (see Fig. 2.1 ). Although the details of sunspot generation are still a matter of research, sunspots are generally thought to be generated by toroidal magnetic fields lying below the photosphere and brought to the surface by buoyancy [Kivelson and Russell, 1995; Rigozo et al., 2001]. Registered sunspot observations have been dated at least back to the fourth century BC. Irregular naked-eye observations of sunspot activity can be found in Chinese dynastic chronicles since 28 BC [Ding, 1978; Polygiannakis et al., 1996; Mundt et al., 1991; Li et al., 2002] or even 165 BC [Wittmann and Xu, 1987]. These are Chinese oracle bones dating from before 1000 BC which record sunspots [Hs¨u,1972; Price et al., 1992]. It was shown that the oriental historic data really reflect some features of sunspot activity such as 11-year and century scale cycles, deep Maunder-type minima of solar activity [Ogurtsov et al., 2002]. However, these early records have some natural shortcomings: First, it is very likely that ancient astronomers often mixed real sunspots with other celestial or meteorologi- cal phenomena; Second, ancient sunspot observations were not systematic and, as a result, are non-uniform in time; Third, some climatic effects may be present in different ancient sunspot series [Willis et al., 1980]. Sunspots were first telescopically observed in 1610 by the English astronomer Thomas Harriot and the German (Frisian) father and son, David and Johannes Fabricius. David and Johannes Fabricius noted the rotation of sunspots and the Sun and published a description on the rotation in 1611. The rotation of the Sun and sunspots was independently discovered by Christoph Scheiner and Galileo Galilei as well in 1610 by observing sunspots continuously for a few days. They both published their observations in 1612. Using an improved telescope, Christoph Scheiner measured the rotation rate of sunspots near the equator in 1630. Unfor- tunately, not many sunspots were recorded in the following hundred years since 16

Fig. 2.1. Sunspots observed with SOHO/MDI continuum on 11 Dec 2006. [Credit: SOHO data archive].

the Sun happened to go through a long-term minimum period of activity during 1645-1715. Since the invention of telescope, daily sunspots have been observed for nearly four hundred years. Sunspot number series (see later) is the most used index of solar activity and probably the most analyzed time series in astrophysics [Usoskin and Mursula, 2003]. With the development of solar telescope, the structure of sunspots could be observed in detail. Most sunspots are observed to contain two parts known as the umbra and the penumbra. The umbra is at the center and the darkest part of a sunspot and has the strongest and vertical magnetic field of the sunspot, while the penumbra, surrounding the umbra, is a little lighter and its magnetic is weaker and nearly horizontal. Figure 2.2 depicts the detected structure of the sunspot group shown in Fig. 2.1 observed by Hinode Satellite. Accordingly, the areas of the umbra and penumbra can be obtained. The continuous measurement of sunspot areas began at Greenwich Observatory in 1874. 17

Fig. 2.2. The same sunspot group as shown in Fig. 2.1 observed with Hinode/SOT G-band. Credit: Hinode Science Center/NAOJ.

2.1.1. Wolf sunspot numbers

The most widely used index of solar activity is the Z¨urich or Wolf sunspot number (now continued by, and even referred to as the International sunspot number), often expressed by Rz, RW , RI , R, WSN, SSN or SN, which was introduced by Rudolf Wolf of Z¨urich Observatory in 1850s. Wolf started daily observations of sunspots in 1848 soon after Heinrich Shwabe discovered the sunspot activity cycle with a period of about 10 years in 1844 [Bray and Loughhead, 1964; Mundt et al., 1991]. Recognizing the difficulty in identifying individual spots and the importance of sunspot groups, Wolf in 1848 defined his “relative” sunspot number index as

Rz = k(10G + N), (2.1) where G is the number of sunspot groups, N the number of individual sunspots in all groups visible on the solar disc and k denotes the individual correction factor which compensates differences in observational techniques and instruments used by different observers, thus normalizing the different observations to each other [Wilson, 1992]. Rudolf Wolf worked at Z¨urich Observatory as the “primary” observer (judged as the most reliable observer during a given time) in 1848-1893. He extended the series back to 1749 by using the observations from the primary and secondary observers and filled in the gaps by using linear interpolation and geomagnetic dec- lination measurements as proxies. Therefore, Wolf sunspot numbers are a mixture of direct sunspot observations and calculated values [Hoyt and Schatten, 1998a]. The primary observers for the Rz series were Staudacher (1749-1787), Flaugergues (1788-1825), Schwabe (1826-1847), Wolf (1848-1893), Wolfer (1893-1928), Brunner (1929-1944), Waldmeier (1945-1980) (at the Swiss Federal Observatory, Z¨urich), 18 and Koeckelenbergh (since 1980, at the Royal Observatory of Belgium, Brussels). If the observations from the primary observer are not available for a certain day, then the observations from the secondary, tertiary observer, etc. are used. Us- ing the observations from a single observer aims to make Rz a homogeneous time series. The Rz index was provided and maintained by the Swiss Federal Observatory in Z¨urich, Switzerland through 1980. Since 1981 to the present the Rz index has been provided and maintained by the Sunspot Index Data Center in Brussels, Belgium [Hathaway et al., 2002]. The data process was changed in 1981 from using the observation of the primary observer to using a weighted average of observations by many observers when the Royal Observatory of Belgium took over the process of preparing the International sunspot numbers from the Z¨urich observatory. Yearly values of Rz series are available since 1700, monthly values start from 1749 and daily values from 1818 [Friedli, 2005]. However, the data is reliable only since Wolf’s time, i.e., 1848. The earlier data which was reconstructed by Wolf has pretty large uncertainties due to serious data gaps and the different calculation techniques used by observers. Data gaps of a few days in 1818-1848 are manageable. Data gaps of many months in 1749-1848 and of a few years in 1700-1749 were filled by Wolf. There are many filled values in 1700-1817 resulting in a rather poor sunspot index during this period. Moreover, Wolf obtained the daily values from his correspondents without checking the original observations himself. Thus significant uncertainties exist in the definition of G and N due to different observers. Vitinsky et al. [1986] estimated the systematic uncertainties to be about 25% in monthly sunspot numbers. The quality of the data is considered as ‘hardly reliable’ before 1749, ‘questionable’ during 1749-1817, ‘good’ during 1818- 1847, and ‘reliable’ from 1848 onwards [Eddy, 1976; McKinnon and Waldmeier, 1987; Kane, 1999]. The Rz index provided the longest continuous measure of solar activity [Waldmeier, 1961] until another sunspot index, Group sunspot number, was established in 1990s [Hoyt and Schatten, 1998a], which extends back to 1610. Usually, the daily values are averaged to monthly values in order to remove variations associated with the Sun’s 27-day synodic rotation period. The monthly values still have large oscillations and require additional averaging processes to produce a signal which varies smoothly from month to month. A commonly used averaging method is the 13-month running mean of the monthly values. If Rn is the monthly value for month n, then the 13-month running mean is given by

5 1 X R = (R + 2 R + R ), (2.2) n 24 n−6 n+i n+6 i=−5 simply called the smoothed sunspot number [Hathaway et al., 1999]. Solar cycle maxima and minima are usually determined by these smoothed monthly values. The period between two successive minima defines the solar cycle. Solar cycle 1 started in March 1755 and the present cycle 24 started in January 2009 [Hathaway, 2010]. Gleissberg filter/12221 filter is often used to smooth the values of solar cycle maxima in order to suppress the noise when studying long-term variations of solar 19

activity [Gleissberg, 1944; Soon et al., 1996; Mursula and Ulich, 1998]. The Gleiss- berg filtered solar maximum of cycle n [Gleissberg, 1944; Petrovay, 2010] has the form 1 (R )n = (Rn−2 + 2Rn−1 + 2Rn + 2Rn+1 + Rn+2 ). (2.3) max G 8 max max max max max

2.1.2. Group sunspot numbers

Noting that no error estimates are available in the Rz series and some early sunspot observations were not included in Wolf’s collection, Hoyt and Schatten [1998a;b] collected many more observations than Wolf did, and introduced the Group sunspot numbers since the observations from a few early observers have only the daily number of sunspot groups, but not the number of individual sunspots. The daily Group sunspot number RG is defined as 12.08 X R = k0G (2.4) G N i i i 0 where Gi is the number of sunspot groups recorded by the ith observer, ki is the ith observer’s individual correction factor, N is the number of observers used to form a daily value, and 12.08 is a normalization number scaling RG to Rz values in 1847-1976. The normalization number varies slightly due to the total number of observations used for different time period. The main importance of the RG series is in extending the sunspot number ob- servations back to the earliest telescopic observations in 1610. Hoyt and Schatten [1998b] compiled 455242 sunspot observations from 463 observers in 1610-1874. Only a few observers’ presentations are missing on Hoyt and Schatten [1998b] because their observations were burt or are missing. Much effort was taken to col- lect the observations before 1874, when the Royal Greenwich Observatory started recording detailed sunspot observations including their position and area. The database for RG has about 80% more daily observations than Rz for the period of 1610-1874. Therefore, the RG series is more reliable and homogeneous than the Rz series, especially before 1874. The two series agree closely with each other since 1950s [Hoyt and Schatten, 1998b; Letfus, 1999]. The main characteristics of solar cycles obtained from the two time series also agree with each other [Hathaway et al., 2002]. The RG series includes not only one primary observation but all available obser- vations. This approach allows to estimate systematic uncertainties of the resulting RG. The systematic uncertainties for the yearly RG values are caused by four aspects: missing observations; uncertainties in the values of k0; random errors in the daily values; and drifts in the k0 values. The final systematic error is about 10% before 1653, less than 5% in 1654-1727 and 1800-1849, 15-20% in 1728-1799, and about 1-2% in 1851-1995 with error rising mainly from missing observations [Hoyt and Schatten, 1998b]. The major result is that solar activity according to RG in 1700-1882 is 25-50% lower than that given by Wolf. Consequently RG sug- 20 gests that solar activity in the last few decades has been higher than it was during several earlier centuries. The RG series provides a pure sunspot series without filling in missing months or years. The number of days used to form the monthly mean values is also available for the series. This allows users to evaluate the data coverage for each period and to estimate related errors. The RG series has still some uncertainties and inhomogeneities [Letfus, 2000]. However, the great advantage of this series compared to Rz is that the uncertainties can be estimated and taken into account [Hoyt and Schatten, 1998b; Usoskin and Mursula, 2003]. Yearly RG values are available from 1610 to 1995. Within this 386-year inter- val there are 32 years when RG has an unreliable value (uncertainty greater than 25%) or is missing. The RG series has not been continued beyond 1995. There are minor problems in the work of Hoyt and Schatten [1998b]. E.g., the Julian calen- dar dates were taken to be Gregorian in some cases, and individual sunspots were occasionally defined as sunspot groups [Vaquero, 2007]. Also some published ob- servations were not covered in this work. Recently a great amount of old drawings of sunspot observations have been discovered and published [Vaquero, 2004; Arlt, 2008; 2009a;b; 2011]. Therefore, improvements on the work of Hoyt and Schatten [1998b] can be obtained. In addition to Rz and RG, there are some other sunspot numbers, such as the Boulder sunspot numbers and the American sunspot numbers. These additional numbers can be scaled to the International Sunspot Numbers by using appropriate correction factors [Hathaway, 2010].

2.1.3. Sunspot areas and positions

Another widely used solar activity index is the sunspot areas. In May, 1874 the Royal Greenwich Observatory (RGO) started compiling sunspot observations from a small network of observatories including Greenwich, England; Cape Town, South Africa; Kodaikanal, India; and Mauritius to produce daily sunspot positions and areas. Sunspot areas were measured in units of millionths of a solar hemisphere (µHem) by dividing the sunspot in photographs into small squares. Both umbral areas and whole spot areas were calculated. The measured areas were corrected for foreshortening on the visible disc. The accuracy of sunspot areas was determined up to 0.1 µHem. Sunspot positions were measured relative to the center of solar disc, i.e., latitude and central meridian distance. The accuracy of sunspot positions was determined to 0.1 degrees. The RGO stopped preparing its data in 1976 when the US Air Force (USAF) started compiling sunspot area and position data from its Solar Optical Observing Network (SOON) in 1977 with the help of the US National Oceanic and Atmospheric Administration (NOAA). The sunspot areas reported by USAF/NOAA are derived from sunspot drawings prepared at the SOON sites, which were initially measured by overlaying a grid and counting the number of cells that a sunspot covered and later (since late 1981) by employing an overlay with a number of circles and ellipses of different areas. 21

Sunspot positions are determined at the accuracy of 1 degree. Sunspot areas are determined by rounding to the nearest 10 µHem. The combined dataset of RGO and USAF/NOAA SOON, from May 1874 to the present, is available online at http://solarscience.msfc.nasa.gov/greenwch.shtml. The average daily sunspot area over each solar rotation is shown in the bottom panel of Fig. 4.1. Wilson and Hathaway [2006] have studied the measurements taken in RGO and SOON in detail. They also studied the relationship between sunspot area and sunspot number among RGO, SOON, Rome Observatory, Swiss Federal Observa- tory and Royal Observatory of Belgium. The relationship between total corrected sunspot area and sunspot number is not good for daily values, but becomes bet- ter when using monthly or yearly averages. However, the sunspot areas reported by USAF/NOAA are significantly smaller than those given by RGO [Fligge and Solanki, 1997; Baranyi et al., 2001; Hathaway et al., 2002]. Figure 2.3 obtained by Hathaway [2010] shows the relationship between sunspot area and sunspot number using 13-month running mean values. Top panel shows that the smoothed spot area reported by RGO and the smoothed International sunspot number have very high correlation (r = 0.994, r2 = 0.988). The best fit to the two quantities gives a slope of 16.7 and an offset of about 4. The zero point for the sunspot number is shifted slightly from zero because a single sunspot does not give a sunspot number of 1, but 11 (see E.q. 2.1) for a correction factor k = 1.0. Therefore, the rela- tionship between the RGO sunspot area ARGO and sunspot number Rz is roughly described as ARGO = 16.7Rz. (2.5) Bottom panel shows the relationship between the smoothed USAF/NOAA SOON sunspot areas and smoothed Rz.The slope of the fitting line is 11.32. Accordingly, we have ASOON = 11.32Rz. (2.6) To keep the later USAF/NOAA SOON sunspot areas consistent with the earlier RGO sunspot areas, the USAF/NOAA SOON sunspot areas should be multiplied by 16.7/11.32 ≈1.48. Digitizing the drawings of sunspot observations by Samuel Heinrich Schwabe, Arlt [2011] calculated sunspot positions and sizes in 1825-1867. Another large series of sunspot positions was obtained by Arlt [2008; 2009a] for the years 1749- 1796 from the drawings of Johann Staudacher. A number of positions of sunspots were determined by Arlt [2009b] from the observations at Armagh Observatory in 1795-1797.

2.1.4. Cyclicities in solar activity

The most prominent periodicity of sunspot activity is the 11-year cycle apart from the Sun’s 27-day rotation period. The 11-year cycle is also called the Schwabe cycle, discovered by Schwabe [1844] using a number of daily sunspot groups in 1826-1843. This cycle dominates the sunspot activity during almost the whole 22

Fig. 2.3. The relationship between sunspot area and sunspot number obtained by Hath- away [2010]. All the data used in this figure are 13-month running mean values. Top panel: RGO sunspot area vs. the International sunspot number in 1997 - 2010. The slope of the fit line is 16.7. Bottom panel: USAF/NOAA SOON sunspot area vs. the International sunspot number in 1977 - 2007. The slope of the fit line is 11.3. 23

observed time interval. However, this cycle varies in amplitude, length and shape [Usoskin and Mursula, 2003]. The idea of regular variations in sunspot numbers was suggested by the Danish astronomer Christian Horrebow in 1770s on the basis of his sunspot observations in 1761-1769 [Gleissberg, 1952; Vitinskii, 1965]. Unfortunately, his results were forgotten and the data lost. Later, in 1843, the amateur astronomer Heinrich Schwabe found that sunspot activity varies cyclically with the period of about 10 years [Schwabe, 1844]. This was the beginning of the continuing study of cyclic variations of solar activity [Usoskin and Mursula, 2003]. Figure 2.4 shows the Schwabe cycle in total monthly sunspot group numbers and in the standard smoothed sunspot numbers. The 11-year Schwabe cycle is the most prominent cycle in the sunspot series and in most other solar activity parameters. In addition, many other parameters including heliospheric, geomagnetic, space weather, and climate parameters also show the 11-yr periodicity. The background for the 11-year Schwabe cycle is the 22-year Hale magnetic polarity cycle, which is also known as Hale’s polarity law. Hale [1908] found that leading spots and trailing spots in a binary sunspot group have opposite magnetic polarity. And that leading spots in northern and southern hemispheres have also opposite magnetic polarity. Furthermore, the polarity of sunspot magnetic field changes in both hemispheres when a new 11-year cycle starts, see Fig. 2.5. This relates to the reversal of the global magnetic field of the Sun with the period of 22 years. It is often considered that the 11-year Schwabe cycle is the modulus of the sign-alternating Hale cycle [Sonett, 1983; Bracewell, 1986; Kurths and Ruzmaikin, 1990; de Meyer, 1998; Mininni et al., 2001]. Although the 22-year magnetic cycle is the basis for the 11-year Schwabe cycle, a 22-year cycle is not expected in the total (unsigned) SSN if the dynamo process is symmetric with respect to the changing polarity. Gnevyshev and Ohl [1948] studied the intensity (total number of sunspots over a cycle) of solar cycles and showed that solar cycles are coupled in pairs of a less intensive even-numbered cycle followed by a more intensive odd cycle. This is called the Gnevyshev-Ohl (G-O) rule or even-odd rule. Using Rz, the G-O rule works only since cycle 10 and fails for cycle pairs 4-5, 8-9 and 22-23 [Gnevyshev and Ohl, 1948; Storini and Sykora, 1997]. When using RG, the G-O rule is valid since the Dalton minimum and, in the reverse order, even before that [Mursula et al., 2001]. Silverman [1992] analyzed the power spectrum of monthly SSN for the period 1868 to 1990, and indicated the presence of a 33.3-yr peak. Attolini et al. [1990] carried out a careful power spectrum analysis of the historical aurora observed since circa 700 BC in the East (China, Japan, Korea) and in central Europe at latitudes between 30◦ and 45◦ and found a period of 66 years. The three-cycle quasi- periodicity also exists in a shallow water core taken from the Ionian Sea (Gallipoli Terrace) [Castagnoli et al., 1997]. Ahluwalia [1998] analyzed the Ap index and sunspot numbers in the last 6 decades, and pointed out that there is a three-cycle quasi-periodicity in both data. Ahluwalia [2000] further indicated the existence of three-cycle quasi-periodicity in the interplanetary magnetic field intensity, and the solar wind bulk velocity in 1963-1998. Currie [1973] found a period of 66.7-yr in monthly sunspot numbers in 1749-1957 by using the maximum entropy method. 24

Fig. 2.4. The 11-year Schwabe cycle seen in the monthly number of sunspot groups and the daily number of sunspots [Li, 2009a]. Top panel: monthly total number of sunspot groups in 1876 - 2009. Bottom panel: the monthly mean of daily sunspot numbers for the same time period. The thick lines show the corresponding 13-month running mean values.

Fig. 2.5. Hale’s polarity laws [Hathaway, 2010]. Left panel: A magnetogram from sunspot cycle 22 (2 August 1989). Yellow color denotes positive polarity and blue denotes negative polarity. Right panel: A corresponding magnetogram from sunspot cycle 23 (26 June 2000). 25

According to the relationship between SSN and Ap, he successfully predicted the size of cycle 23 (119). However, all these results are criticized by Wilson and Hathaway [1999], who claimed that they are mainly due to the short period and poor quality of data. The long-term variation of the amplitude of Schwabe cycles is known as the Gleissberg cycle [Gleissberg, 1944]. However, the Gleissberg cycle is not a cycle in a strict sense but rather a modulation of the cycle envelope with a varying time scale of 50-140 years [Gleissberg, 1971; Kuklin, 1976; Ogurtsov et al., 2002]. The period of about 200 (160-270) years is called Suess or de Vries cycle [Schove, 1983; Ogurtsov et al., 2002]. Suess [1980] found a significant 203 year variation in tree-ring radiocarbon records. Even longer (super-secular) cycles are found in cosmogenic isotope data. Most prominent cycles are the 600-700-yr cycle and the 2000-2400-yr cycle [Usoskin et al., 2004]. Gleissberg [1952] also suggested a 1000-yr variation.

2.1.5. Grand minima and maxima

The regular cyclicity of solar activity is sometimes intervened by periods of greatly depressed activity called grand minima. The last grand minimum and the only one covered by direct solar observations was the famous Maunder minimum during 1645-1715 [Eddy, 1976; 1983]. There are other grand minima found in the past from cosmogenic isotope data in terrestrial archives like 14C and 10Be, including Sp¨orerminimum (1420-1530), Wolf minimum (1280-1340), O¨ortminimum (1010- 1050), Dalton minimum (1790-1830) etc [Eddy, 1983; Kremliovsky, 1994; Komitov and Kaftan, 2004]. During the Dalton minimum, however, sunspot activity was not completely suppressed and still showed the Schwabe cyclicity. Sch¨ussler et al. [1997] suggested that this can be a separate, intermediate state of the dynamo between the grand minimum and normal activity. Grand minima and maxima are an enigma for the solar dynamo theory. It is intensely debated what is the mode of the solar dynamo during such periods and what causes such minima and maxima [Feynman and Gabriel, 1990; Sokoloff and Nesme-Ribes, 1994; Schmitt et al., 1996]. A large amount of work suggests that they are the result of random fluctuations of the dynamo governing parameters [Hoyng, 1993; Brandenburg and Sokoloff, 2002; Kowal et al., 2006; Moss et al., 2008; Usoskin et al., 2009]. Due to the recent development of precise technologies, such as the improvement in accelerator mass spectrometry, solar activity can be reconstructed over multiple millennia from concentrations of cosmogenic isotopes. Accordingly, several grand minima and maxima in the past were found from there, e.g., Eddy [1977a]; Voss et al. [1996]; Goslar [2003]; McCracken et al. [2004]; Usoskin et al. [2006]; Brajˇsa et al. [2009]; Hanslmeier and Brajˇsa[2010]. Stuiver and Braziunas [1989] studied the 14C record and suggested two types of grand minima: shorter Maunder-type and longer Sp¨orer-like minima [Stuiver et al., 1991]. The production of cosmogenic isotopes in the Earth’s atmosphere is not only defined by solar activity, but also 26

Table 2.1. Approximate years (in -BC/AD) of the centers and the durations of grand minima in the long sunspot number series [Usoskin et al., 2007a].

No. year duration comment of center (years) 1 1680 80 Maunder 2 1470 160 Sp¨orer 3 1305 70 Wolf 4 1040 60 a) 5 685 70 b) 6 -360 60 a, b, c) 7 -765 90 a, b, c) 8 -1390 40 b, e) 9 -2860 60 a, c) 10 -3335 70 a, b, c) 11 -3500 40 a, b, c) 12 -3625 50 a, b) 13 -3940 60 a, c) 14 -4225 30 c) 15 -4325 50 a, c) 16 -5260 140 a, b) 17 -5460 60 c) 18 -5620 40 - 19 -5710 20 c) 20 -5985 30 a, c) 21 -6215 30 c, d) 22 -6400 80 a, c, d) 23 -7035 50 a, c) 24 -7305 30 c) 25 -7515 150 a, c) 26 -8215 110 - 27 -9165 150 - a) Discussed in Stuiver (1980) and Suiver & Braziunas (1989). b) Discussed in Eddy (1977a, b). c) Shown in Goslar (2003). d) Exact duration is uncertain. e) Does not appear in the short sunspot number series. 27

Table 2.2. Approximate years (in -BC/AD) of the centers and the durations of grand maxima in the long sunspot number series [Usoskin et al., 2007a].

No. year duration comment of center (years) 1 1960 80 modern, b) 2 -445 40 - 3 -1790 20 a) 4 -2070 40 - 5 -2240 20 b) 6 -2520 20 a) 7 -3145 30 a) 8 -6125 20 - 9 -6530 20 - 10 -6740 100 - 11 -6865 50 - 12 -7215 30 - 13 -7660 80 - 14 -7780 20 - 15 -7850 20 - 16 -8030 50 - 17 -8350 70 - 18 -8915 190 - 19 -9375 130 - a) Discussed in Eddy (1977a, b). b) Center and duration of the modern maximum are preliminary since it is still ongoing. 28 modulated by the geomagnetic field. The earlier reconstruction of solar activity did not take the magnetic field into account. Recently, Beer et al [2003] and Solanki et al. [2004] developed a more appro- priate reconstruction model by taking both effects into account [see also Usoskin et al, 2003; Usoskin et al., 2004]. Using this new model, the solar activity can be quantitively reconstructed. Accordingly, the grand minimum can be quantitively defined [Usoskin et al., 2006; 2007a] . Usoskin et al. [2007a] defined the grand minimum as a period when the sunspot number (smoothed with the Gleissberg filter) is less than 15, while during grand maximum, it exceeds 50 during at least two consecutive decades. Tables 2.1 and 2.2 show the grand minima and maxima since 9500 BC found by Usoskin et al. [2007a]. The new definition leads to longer durations of grand minima. For example, the duration of Sp¨orerminimum in Table 2.1 is 50 years longer than that found by Eddy [1983]. Recent studies suggest that the Sun was more active in 1930s-2000 (cycles 17- 23) than in other times during last thousand years. Accordingly, this time period is called Modern Grand Maximum (MGM). However, more recent measurements have shown that sunspot levels in the declining phase of cycle 23 and in the start- ing phase of cycle 24 are far below average [Livingston et al., 2012; Penn and Livingston, 2011]. The last minimum before present sunspot cycle 24 lasted much longer than earlier minima showing the Sun’s unusual low activity [Li, 2009a]. The mutual relation between sunspots and solar radiation indices, such as UV/EUV indices, the 10.7cm flux, has dramatically changed at the end of 2001 after remain- ing stable for about 25 years until 2000 [Lukianova and Mursula, 2011; Tapping and Vald´es,2011]. In addition, the average magnetic field strength in sunspot umbra in 1998-2011 has been decreasing by 46 G per year [Livingston et al., 2012]. This implies that cycle 24 might mark the end of MGM.

2.2. Solar flares

A solar flare was first observed by Carrington and independently by Hodgson in 1859 in white (visible) light as a localized brightening of small areas within a complex sunspot group. It was also the first documented white light flare. A solar flare is observationally defined as a brightening of any emissions of the electromagnetic spectrum occurring at a time scale of minutes [Benz, 2008]. Solar flares are one of the two most important eruptive phenomena in the atmosphere of the Sun (the other are CMEs). They are the most efficient mechanism to release magnetic energy associated with active region filaments (prominences), sunspots or sunspot groups. The total energy released by a large flare can reach 4·1025 J, but the average energy of a solar flare is 1023−1024 J. The energy released in solar flares can be distributed in many forms: hard electromagnetic radiation (γ- and X-rays), energetic particles (protons and electrons), and mass flow. Small flares (microflares, nanoflares and X-ray bright points) can occur all over the Sun, in active regions and in the magnetic network of quiet corona [Parker, 1988; Benz and Krucker, 1998]. X-ray and EUV jets are frequently observed in 29 association with these small events [Shimojo et al., 1996]. The source regions of small flares can be diagnosed by EUV and X-ray images. Large (or regular) flares normally occur in active regions with complex magnetic structures observed in photospheric magnetograms. Flare prolific sites often show signatures of strongly twisted or sheared magnetic fields. Only regular flares are discussed in the following sections of this thesis.

2.2.1. Classification of solar flares

Fig. 2.6. Hα observation during a flare on 7 August 1972 by Big Bear Solar Observatory.

Before 1950s solar flares were mainly observed in Hα emission. Hα flares are also called optical flares. They are classified to five classes denoted by S, 1, 2, 3, and 4, based on the area of Hα emission. The maximum brightness of Hα emission is denoted by F, N, and B representing faint, normal, and bright. Accordingly, an SF flare belongs to the smallest class and has a faint brightness, while 4B denotes the largest class and is bright. Figure 2.6 presents the solar atmosphere at the flare site in the wavelength band of the Hα line emission observed on 7 August 1972 by Big Bear Solar Observatory. This particular flare, so-called seahorse flare, is an example of a two ribbon flare in which the flaring region appear as two bright lines threading through the area between two sunspots of a sunspot group. The 30

Fig. 2.7. GOES X-ray flux observed on 13-15 July 2000 during which an X-flare and several M and C flares occurred.

Class W/m2 Ergs/cm2/s A I < 10−7 I < 10−4 B 10−7 ≤ I < 10−6 10−4 ≤ I < 10−3 C 10−6 ≤ I < 10−5 10−3 ≤ I < 10−2 M 10−5 ≤ I < 10−4 10−2 ≤ I < 10−1 X 10−4 ≤ I 10−1 ≤ I

Table 2.3. X-ray flare classification and peak intensity. 31 two ribbons are also connected to each other through bright Hα loops. A hot 40-million-degree shell intersects the surface at the ribbons and condenses at the loop tops. Recently, solar flares are usually characterized and classified by their brightness in X-ray radiation since the continuous X-ray flux observations by Geostationary Operational Environmental Satellites (GOES) started in mid-1970s. The X-ray flux is measured in two bands, 0.5-4.0 A˚ and 1.0-8.0 A.˚ X-ray flares are classified to A, B, C, M, and X classes representing increasing powers of ten (see Table 2.3). A-class and B-class are defined according to the X-ray flux in 0.5-4.0 A˚ band, representing typical background levels around minimum and maximum of a solar cycle, respectively. C, M, and X classes are defined according to the X-ray flux in 1.0-8.0 A˚ band, indicating increasing levels of flaring activity. Accordingly, the biggest flares are called X-class flares. Within these main classes the flares are further divided into subclasses. For instance, a C5 flare has the measured peak intensity of 5.0×10−6 W/m2 and an X3 flare 3.0×10−4 W/m2 . Figure 2.7 gives an example of GOES X-ray flux observation in three days by GOES 8 and GOES 10. GOES 8 (1994-2004) and GOES 10 (1997-2009) both have 0.5-4.0 A˚ band and 1.0-8.0 A˚ band. In Fig. 2.7 the X-ray flux observed by GOES 10 is overlaid by GOES 8 with perfect matching each other. A large impulsive increase on 14 July 2000 was recorded in the 1.0-8.0 A˚ band (red) with the value of 5.7×10−4 W/m2. Accordingly, the flare level was classified as X5.7. A few M-flares and many C-flares were also observed in the three days. These C-, M- and X-flares caused also the increases in the 0.5-4.0 A˚ band (blue) but with lower intensity.

2.2.2. Phases of a typical flare

The flare process is mainly divided into four phases according to variation of electromagnetic radiation as presented in Fig. 2.8. At first, soft X-rays and EUV are observed to increase gradually due to the slow heating of coronal plasma in the flare region. This period is called the pre-flare phase followed by the impulsive phase, in which most of the energy is released and a large number of energetic particles (electrons and ions) is accelerated. An evident impulsive increase can be observed in hard X-rays, γ-rays, and microwaves (millimeter to centimeter radio waves), and a few impulses can be seen in decimetric and metric radio waves and EUV. A significant rapid increase is observed in soft X-rays. The fast increase in Hα intensity and line width terms the flash phase, which coincides partly with the impulsive phase. After the flash phase, plasma in the low corona (around the flare region) returns nearly to its original state, while the plasma ejections in the high corona, the magnetic reconfigurations, and shock waves keep accelerating particles continuously, causing metric radio bursts and interplanetary particle events. This period is named the decay phase. Noting that the fluxes of soft X-rays and Hα have different temporal evolution, flare phases in soft X-rays are characterized as early phase, impulsive phase, gradual phase and extended phase [Hudson, 2011]. In the past couple decades, many spacecraft (e.g., SMM, SOHO, TRACE, 32

time

Fig. 2.8. Phases of a typical flare (original figure by Benz [2008]).

Yohkoh, RHESSI, SORCE, Hinode, SDO, STEREO) have observed solar flares in hard X-rays and γ-rays continuously with good spatial and temporal resolution. Many hard X-ray and γ-ray flares have been observed, even in weak flare classes. For example, 29 γ-ray flares were detected by RHESSI in 2002-2005, which cor- responded to GOES soft X-ray classes C9.6 to X17.0 [Ishikawa et al., 2011]. The space-based observations have provided many striking and excellent images. One important finding is that the coronal sources of hard X-rays and γ-rays are above the loop-top, showing systematically different signatures from the double footpoint sources. Krucker et al. [2008] present a good example of coronal hard X-ray source together with two footpoint X-ray sources as shown in the left panel in Fig. 2.9. This figure shows a TRACE 1600 A˚ image taken at 06:45:11 UTC, 20 January 2005, overplotted with 12-15 keV red contours (in the corona) and 250-500 keV blue contours at the two footpoints, implying that the coronal hard X-ray emissions are fainter than the emissions of the footpoint sources. This made it so hard to detect the coronal source earlier. The high coronal hard X-ray and γ-ray emissions show a fast rise and a slower constant exponential decay and the corresponding

33 Y (arcsecs) Y

X (arcsecs) 0020 0040

Fig. 2.9. Flare observations in hard X-ray and γ-rays. Left: two footpoint sources in γ- rays and one coronal source in hard X-rays observed during 06:43 - 06:46 UT, 20 January 2005 [Krucker et al., 2008]. Right: flare observation from soft X-rays (GOES) to γ-rays (RHESSI, in units of counts/s per detector) signifies three flare phases: the rise (or early) phase, impulsive phase, and decay (or late) phase [Lin et al., 2003]. 34 photon spectrum is harder (small value of power-law index) compared with the emissions from the footpoint sources. The right panel in Fig. 2.9 presents the RHESSI hard X-ray and γ-ray count rates for the 23 July 2002 flare together with GOES soft X-rays on the top [Lin et al., 2003]. The temporal evolution of hard X-rays and γ-rays determines three phases- rise phase, impulsive phase, and late phase. The impulsive phase overlap partly with the impulsive and gradual phases in soft X-rays. During the rise phase the hard X-ray emission comes from the coronal source appearing at the top of the flare loop. During the impulsive phase the emission mainly comes from footpoints, while an additional coronal source becomes visible in the late phase.

2.2.3. Radio emissions during solar flares

Among prominent characteristics of flares are the large number of line emissions and the consequences of the rapid energy release to particles. For example, 331 emission lines within the wavelength 3590-3990 A˚ were observed in the 3B flare of September 19, 1979 [Fang et al., 1991]. In a flare electrons and nuclei are accel- erated nearly to the speed of light. They can produce electromagnetic radiation throughout the spectrum from radio waves to X- and γ-rays, in which visible lines of Hα and Ca II H and K are among the most prominent emissions. Usually flares produce only emission lines, but large flares can produce continuum radiation (i.e., white light radiation). Energetic electrons emit radio emission in magnetized plasma. The radio bursts associated with solar flares are classified in five types according to their dynamical spectral features [Wild et al., 1963]. Type I bursts, the first observed radio bursts, are radio noise storms, composing of short-term (a few seconds) narrow band (a few MHz) bursts superposed on an increased continuum. This type of bursts can last for hours to days caused by supra thermal electrons being accelerated repeatedly in active regions. Radio noise storms can be observed in association with flares and CMEs. Top panel of Figure 2.10 shows a fraction of type I bursts [Payne-Scott, 1949]. Type II and Type III are frequency drifting bursts (see bottom panel of Fig. 2.10). Type II bursts drift significantly slower than type III and last for a longer time. The typical frequency drifts of Type II and Type III bursts are 0.25 and 20 MHz/s, respectively. In normal cases, bursts drift from high to low frequencies due to the upward motion of electrons along magnetic field lines. The accelerated electrons emit radio emissions at the local plasma frequency and its harmonic. Reverse drifting of type III bursts was also observed due to the downward flow of electrons. Accordingly such bursts are called reverse type III, including ‘U’ shape and ‘J’ shape [Pick and Vilmer, 2008]. Type II bursts occur a few minutes after the start of a flare, around the flash phase, and last for more than 10 min. Type III bursts start to be detectable already a few minutes before the flare impulsive phase. Type IV bursts are radio continua from millimeter to dekameter wavelength 35

Fig. 2.10. Flare-related radio emissions. Top: type I radio bursts (original figure from Payne-Scott [1949]). Bottom: idealized sketch of a complete radio event in the progress of a flare (original figure from Typical HiRAS Observations, http://sunbase.nict.go.jp/solar/denpa/hiras/types.html). 36 which can be observed after type II bursts in association with an intense flare. The associated flare is accordingly called type II+IV event. The probability of type IV bursts causing a sudden geomagnetic storm is a function of their radio importance (The radio importance of a flare is defined as the maximum flux density at 10 cm multiplied by the duration). Type V radio bursts are a broadband diffuse continuum with the highest fre- quencies at the start around 150 MHz. They last from tens of seconds to a few minutes. In general, type V bursts follow type III and were suggested to be caused by emissions of relatively low energetic electrons at the harmonic of local plasma in a open magnetic field. It should be noted that recent radio observations with high resolution show a few fine structures, e.g., the zebra pattern in type IV, spike bursts, and fiber bursts. Millisecond spikes were observed with the new solar broadband radio spectrom- eters of NAOC (National Astronomical Observatories, China). The brightness temperatures of spikes were suggested to be 1015 K and even higher. Moreover, submillimeter radio waves at a few hundred GHz caused by ultra relativistic elec- trons were also detected recently, together with hard X-rays and γ-rays [Raulin et al., 2004].

2.2.4. Flare models

A classical flare model is the ‘CSHKP’ (Carmichael-Sturrock-Hirayama-Kopp- Pneuman) model. In this model, a current sheet is produced above a closed magnetic loop before or after magnetic field line reconnection, forming a inverted Y type cusp-shaped magnetic field structure. Magnetic reconnection is the key- point in this model. Although this model has been extended by many authors, no substantial improvement on this model has been achieved so far. The magnetic reconnection model was even questioned by Akasofu [1995]. However, with the ad- vent of space-borne X-ray image telescopes, more and more evidence for magnetic reconnection have been obtained since 1990s. Using X-ray images observed by Yohkoh, Shibata [1999] developed a plasmoid- induced magnetic reconnection model, in which the plasmoid ejection triggers the impulsive phase. The sketch of this model presented by Shibata [1999] is shown in Fig. 2.11. The plasmoid (filament/prominence held by a twisted flux rope) is situated in the current sheet existing in the corona before a flare and prevents the magnetic field lines from reconnecting before a flare occurs. If the plasmoid starts to rise, the plasma surrounding the current sheet will fill in the region left behind the plasmoid, forming an inflow and driving the sheared or anti-parallel magnetic field lines to reconnect and release energy very fast. Magnetic reconnection further accelerates the plasmoid until the plasmoid is ejected away from the Sun. What drives the plasmoid to move originally is not clear. It seems that the structure of this process is beyond our observing ability at the moment [Hudson, 2011]. A large amount of plasma in the reconnection region is accelerated to ener- getic (non-thermal) particles, electrons and ions. The downward ejected energetic 37

Fig. 2.11. A sketch of the plasmoid-induced-reconnection flare model [Shibata, 1999].

Y(arcsecs) 140 180 220 180 140

900 940 980 X (arcsecs)

Fig. 2.12. HXR sources (left and middle panels are from Krucker et al. [2008]). Left: two footpoint sources and one coronal HXR source at the SXR loop top shown by 18-22 kev contours overlaid on SXR image observed with RHESSI during the 13 July 2005 flare [Battaglia and Benz, 2006]. Middle: two footpoint sources and one coronal HXR source above SXR loop top presented by 33-53 kev contours observed with Yohkoh during the 13 January 1992 flare [Masuda et al., 1994]. Right: cusp-shaped configuration observed with Yohkoh/SXT during the same flare as shown in the middle panel [Shibata, 1999]. 38 particles of the reconnection jet lose their energy through hard X-ray emission (bremsstrahlung) when they hit the top of the magnetic loop in the low corona, observed as the HXR loop top source in Fig. 2.11. The heated plasma at the loop top can be observed as downward flow in Hα in the transition region and chromo- sphere. The energetic particles continue propagating downward along the newly reconnected magnetic field lines, emitting HXR at the footpoints of coronal mag- netic loop in the chromosphere where density is high enough for the high-energy particles to have Coulomb collisions and slow down until reaching thermal speeds. In some cases, γ-rays and neutrons are observed resulting from the downward propagation of energetic ions from the accelerated site into the chromosphere. The heated plasma at the footpoints expands upwards along the magnetic field loop, filling up the existing coronal loop, observed as “evaporation” of chromo- spheric material in soft X-ray images. At the footpoints, enhanced Hα and EUV radiation is also observed. The two footpoints resulting from many reconnected magnetic lines form two bright ribbons. With the more and more magnetic fields reconnecting in the outer layers the two flare ribbons appear to move apart grad- ually. The energy deposited in the upper chromosphere is transported into the lower chromosphere and upper photosphere through thermal radiation and conduction. In some large flare cases, significant increase in white light continuum can be observed from chromosphere and photosphere during the impulsive phase, and is highly correlated with hard X-rays [Matthews et al., 2003]. It is pointed out that white light should be detected from all flares if the sensitivity of telescopes is high enough [Hudson et al., 2006]. The motion of the plasmoid may cause waves and fast shocks, which can further accelerate particles and cause solar energetic particle events (SEPs). The acceler- ation of SEPs is discussed more closely in section 2.4 since most SEP related flares have accompanying CMEs and large SEPs are considered more likely to be accel- erated by the CME shocks [Grayson et al., 2009; Cliver and Ling, 2009; Hudson, 2011]. It is generally accepted that flare energy is stored by sheared or anti-parallel magnetic fields and released by magnetic reconnection. The above discussed mag- netic reconnection model describes the observed features of flares very well. The upward streaming of energetic electrons is detected as Type III radio bursts drift- ing from high to low frequency due to the decreasing density of corona. Reverse Type III bursts from downward streaming of electrons are occasionally detected as well [Aschwanden et al., 1995]. The deduced acceleration sites of electrons lie above the X-ray loops. Hard X-ray sources at the footpoints and the loop top have been observed by RHESSI in several events (Battaglia and Benz [2006]; see the left panel of Fig. 2.12). A coronal hard X-ray source above the loop top before the impulsive phase has been observed by Yohkoh hard X-ray images (Masuda et al. [1994]; middle panel of Fig. 2.12). A cusp-shaped configuration is well observed with Yohkoh/SXT (Shibata [1999]; Tsuneta et al. [1992]; right panel of Fig. 2.12). An increasing number of radio, EUV and X-ray observations support the magnetic reconnection model and the cusp geometry of flares. However, to the date, most flare processes before the impulsive phase still re- 39 main unobservable. Some basic major questions have not been solved. A flare is generally considered as a coronal phenomenon with many chromospheric fea- tures observed when the energy is transported into the dense chromosphere. But where the energy comes from and what triggers the magnetic reconnection is not very clear yet. Observations of photospheric magnetic fields show that large-scale sheared magnetic fields are often detected in an active region before a flare, and an increase in the field strength is observed during some flare cases [Wang et al., 2004], suggesting a trigger mechanism due to the emergence of new magnetic flux from below.

2.3. Coronal mass ejections

Fig. 2.13. A jet-like CME and a loop-like CME observed with SOHO/LASCO [Chen, 2011].

Coronal mass ejections are mass (plasma) and magnetic field eruptions with a large amount of plasma and magnetic fields expanding from the low corona and ejected into the interplanetary space. They are the largest-scale eruptive phenomenon in the Sun. It is generally believed that the energy released in a CME originates from the free magnetic energy stored in the corona, i.e., non- potential magnetic energy in access of potential magnetic energy. This energy is released during magnetic reconnection into several energy forms, such as plasma heating, particle acceleration, waves and kinetic energy of the ejecta. CMEs are morphologically divided into two classes, narrow CMEs and normal CMEs, due to their angular width less or greater than ∼10◦. When a CME with an angular width of tens of degrees propagates from the Sun to the interplanetary 40

Fig. 2.14. Jet-like CME model [left panel; Chen, 2011] and loop-like CME model [right panel; Forbes, 2000].

space along or close to the Sun-Earth line, it is observed to surround the whole solar disc, i.e., the projection angle in the plane of sky recorded in a 2D image is ∼360◦. This kind of CME is called the halo CME. CMEs were grouped into impulsive and gradual types in 1980s-1990s according to the observed speed of evolution. It was suggested that impulsive CMEs concur with solar flares, and gradual CMEs are correlated with eruptive filaments. Later observations show that CMEs, flares and eruptive filaments do occur together in many cases, but no clear correlations are found. Therefore, CMEs can not be simply classified as impulsive or gradual and this classification of CMEs is no longer in use. With modern soft X-ray and EUV observations, structures of CMEs can be observed in more detail, although many processes still remain unknown. Accord- ingly, CMEs are nowadays classified into jet-like and loop-like classes according to the structure of magnetic fields (open or connected to solar surface as a loop). It is generally agreed that a jet-like CME (see the left panel of Fig. 2.13) is caused by the magnetic reconnection within an emerging flux or between a coronal loop and the open magnetic fields of a coronal hole, resulting in a compact flare (see the left panel of Fig. 2.14). This reconnection model is similar to the model of X-ray jets produced during microflares [Shimojo et al., 1996]. Most of narrow flares show jet-like eruption. Loop-like CMEs normally consist of three parts, a closed frontal loop followed by a dark cavity and a bright core (see the right panel of Fig. 2.13). A sketch of the corresponding model is presented in the right panel of Fig. 2.14 [Forbes, 2000]. Statistics show that very powerful flares above class X2.0 have a one-to-one 41 association with CMEs [Hudson, 2011; Yashiro et al., 2006]. Based on the above discussed model of solar flares, the present CME model has been developed (see Fig. 2.14), involving flaring X-ray loops, eruptive filament/prominence forming the bright core in the cavity, and frontal loop. The global picture of a loop-like CME is as follows. A twisted or sheared coronal magnetic flux rope (similar to but normally larger than the flux rope in Fig. 2.11), perhaps holding a prominence, rises for some reason, driving the magnetic field lines under it to reconnect. The fast magnetic reconnection causes a flare in the low corona close to solar surface. Meanwhile, the field lines tying to solar surface and keeping the flux rope from flowing away from the Sun are cut off during the reconnection. When the flux rope moves outwards very fast, it stretches the magnetic field lines lying above it to form the frontal loop and causes a shock wave as well, which can further accelerate particles in the interplanetary space. The stretching or expanding frontal loop leads to low plasma density behind it which is seen as a dark cavity in white-light. Unlike flares, the magnetic reconnection is not always necessary in the eruption of flux rope during a CME. Many other processes can trigger the flux rope to erupt, such as loss of equilibrium and MHD instability [Vrˇsnaket al., 1991; Vrˇsnak,2008].

2.4. Solar energetic particles acceleration

Solar energetic particles (SEPs), mainly protons, and a smaller amount of electrons and heavy ions, were first noted by Forbush as three unusual cosmic ray increases [Forbush, 1946]. Later they were detected by ground neutron monitors and diag- nosed as ground level events (GLEs; also called ground level enhancements). Only extreme high-energy particles (∼1GeV) from powerful solar eruptions can cause a GLE. Statistics show that SEPs occur every four days on an average, while GLEs occur only once a year [Duggal and Pomerantz, 1971]. GLEs are suggested to be associated with the impulsive phase of flares [Aschwanden, 2012], while large SEPs are proposed to be mainly accelerated by CME shocks [Cliver and Ling, 2009]. After a few decades of observations and studies, the SEP events were divided into two types, impulsive events and gradual (long-duration) events according to the duration of soft X-rays [Cane et al., 1986; Reames, 1999]. The impulsive SEPs were thought to relate with flare acceleration processes and have accompanying Type III radio emissions, high ratio of Fe/O, enhanced 3He and high charge state of Fe. The impulsive SEPs probably result from wave-particle interaction caused by magnetic reconnection during a flare, as mentioned in Sect. 2.2.4. The gradual SEPs were associcated with CMEs and Type II radio burst events, being acceler- ated by coronal and interplanetary shocks driven by CMEs. Gradual events have a lower Fe/O ratio and a lower Fe charge state than impulsive events [Cliver, 2009]. However, recent observations show that ‘impulsive’ characteristics are some- times observed also during gradual events [Cane et al., 2006]. Considering the newly observed signatures of SEPs and the suggested acceleration models, Cliver [2009] presented a sketch of a new SEP acceleration model (see Fig. 2.15) and 42

Fig. 2.15. A sketch of a new SEPs acceleration model [Cliver, 2009].

suggested a revised classification of SEP events [see Table 2 of Cliver, 2009, for details]. According to this scheme, SEP events are classified into flare and shock SEP classes instead of impulsive and gradual classes. Shock class has two sub- classes, quasi-perpendicular shocks and quasi-parallel shocks (denoted by Q-perp and Q-par, respectively in Fig. 2.15). Large (gradual) SEP events with impulsive characteristics are considered to result from quasi-perpendicular shock accelerated supra-thermal particles originating from flares. While large SEP events without impulsive characteristics are quasi-parallel shock accelerated supra-thermal parti- cles originating from CMEs and solar winds [Cliver and Ling, 2009]. 3. Solar rotation

3.1. Heliographic coordinates

In order to determine a position on the Sun or in the heliosphere we have to employ a coordinate reference frame. For this purpose we first need to know the rotation axis of the Sun. The direction of the rotation axis of the Sun is given by two rotation elements or angles. One is the angle of inclination i between the ecliptic plane and the solar equatorial plane. The other is the ecliptic longitude of the ascending node of the Sun’s equator determined by the angle, in the ecliptic plane, between the vernal equinox direction and the ascending node, where the Sun moves to celestial north through the ecliptic plane. Once the axis of solar rotation is known, the solar latitude ψ, also called the heliographic latitude, is easily defined as the angular distance from the equator. Frequently used is also the polar angle (angular distance to the North Pole), or the so called co-latitude θ=π/2-ψ. However, there are no fixed points on solar surface to define the solar longitude. Defining the longitude is even more difficult for a differentially rotating surface like the Sun. Carrington introduced in 1850s a rigidly rotating (14.1844 deg/day, sidereal) longitudinal frame by observing low latitudinal sunspots. This is the rotating rate of sunspots close to the latitude of 17◦-20◦. The sidereal rotating pe- riod of this longitudinal coordinate frame is 25.3800 days and its synodic period is 27.2753 days, which is the so-called Carrington rotation (CR) period. CR number 1 was defined to begin at 21:38:44 UT on 9 November 1853 with longitude 0◦ at the central meridian of solar disc and increasing westwards to 360◦. CR number 2105 started on the Christmas Eve in 2010. At the start of each new rotation the longitude value of φ =0 is given to the center of the solar disc.

3.2. Surface rotation

The Sun’s surface rotation was noted by Harriot, Fabricius, Galileo, and Scheiner in the early decades of the 17th century, soon after the invention of telescope by ob- 44 serving the sunspots across the solar disc. Harriot did not publish his observations of sunspots although he shared them with a group of correspondents in England [The Galileo Project: Thomas Harriot 1560-1621]. Johannes Fabricius published a book in 1611 named ‘Narration on spots observed on the Sun and their appar- ent rotation with the Sun’. Unfortunately, the existence of the book cannot be firmly verified up to the time. Scheiner and Galileo independently published their observations in 1612. Galileo gave a rotation period of 29.5 days. With improve- ment of the telescope, Scheiner obtained a rotation period of 27 to 28 days from the observations in 1609-1625 [Scheiner, 1630]. Scheiner also noted the differential rotation on the solar surface. His book ‘Rosa Ursina’, published in 1630 presented evidence that the pass of sunspots across the solar disc took a slightly longer time at high latitudes than near the equator. However, the heliographic latitude and longitude reference frame was not established until 1863 by Carrington. It took 250 years until Carington established, by tracking sunspots, that the surface solar rotation rate decreases with increasing heliospheric latitude, implying that the Sun’s outer layers are in a state of differential rotation. He determined the (sidereal) surface rotation rate (in degrees per day) as a function of heliographic latitude to be as follows

Ω(ψ) = 14.25 − 2.75sin7/4ψ. (3.1) However, for practical purposes the power 7/4 is quite awkward. A more modern approach is to expand the rotation rate as

Ω(ψ) = A + Bsin2ψ + Csin4ψ, (3.2) where A is the equatorial rotation rate. A, B, and C need to be determined from observation. In addition to sunspots, many other tracers, e.g., photospheric plasma (Dopp- lergrams), coronal holes (EUV intensity maps) and surface magnetic fields (mag- netograms) have been used to determine the rotation rate of solar surface. Some examples of values for A, B and C determined from different tracers are shown in table 3.1. From table 3.1 one can see that: (1) the rotation parameters obtained for different tracers are not necessarily in agreement with each other; (2) the two sets of parameters determined by all sunspots are close to each other and so are the groups and recurrent spots; (3) the sunspot groups and recurrent spots have a lower value of A than sunspots on an average, indicating that these have been braked by the slower rotation of the solar plasma; (4) the value of B is exception- ally small for coronal holes, which implies that coronal holes rotate quite rigidly. (More recent results on solar surface differential rotation will be discussed in Sect. 5.4.2) 45

authors tracers A B C Howard et al. [1984] Mt. Wilson; all spots 14.522 -2.840 1921-1984 Balthasar et al. [1986] Greenwich; all spots 14.551 -2.870 1874-1976 14.545 -2.720 -0.580 Howard et al. [1984] Mt. Wilson; sunspot groups 14.393 -2.946 1921-1984 Newton and Nunn [1951] Greenwich; recurrent spots 14.368 -2.690 1878-1944 Scherrer et al. [1980] Wilcox; photospheric plasma 14.440 -1.980 -1.980 1976-1979 Snodgrass [1983] Mt. Wilson; surface magnetic 14.366 -2.297 -1.624 fields 1967-1982 Wagner [1975] OSO-7; coronal holes 14.296 -0.510 May 1972-Oct. 1973

Table 3.1. Coefficients of Eq. 3.2 describing the differential rotation of the Sun’s surface (in deg/day) measured from different tracers.

3.3. Internal rotation

Helioseismology has revolutionized the study of differential rotation since we can now empirically determine the rotation even inside the Sun. By using helioseismol- ogy inversion of 5-min oscillation data, GONG (The Global Oscillation Network Group) found out that the rotation velocity at the poles is 3/4 of that at the equator (see Fig. 3.1). Differential rotation continues throughout the convection zone. However, near the base of convection zone, rotation changes its character and becomes solid-body rotation, which continues in the radiative interior. This region of sudden change in the rotation rate is the so-called “tachocline” [Basu and Antia, 2003]. Basu and Antia [2003] have drawn a contour diagram of solar rotation as a function of depth (see Fig. 3.2) by using solar oscillation data of GONG. From Figs. 3.1 and 3.2 one can see that angular velocity does not change with latitude or depth in the underlying radiative core, where the radius is less than 0.68R . This region rotates almost rigidly and the rate is close to the rate of the convection zone at 30◦ latitude. The rotation rate of convection zone at some latitudes, such as at 15◦ and 60◦, does not change with depth, i.e., ∂Ω/∂r ≈ 0. There are two shears in the rotation rate profile (Fig. 3.1), where the rotation rate increases rapidly with the decreasing radius, i.e., ∂Ω/∂r < 0. One is close to the solar surface, from ◦ the surface to around 0.95R . The other appears at high latitude (above 30 ) around 0.8-0.7R , close to the tachocline. The shear close to the tachocline region is generally believed to be responsible for driving the solar dynamo. The rotation rate decreases with decreasing radius at latitudes below 30◦. According to the helioseismic solution of Charbonneau et al. [1999], Dikpati and 46

r R / ⊙

Fig. 3.1. The solar internal rotation law (picture is taken from Elstner and Korhonen [2005]).

Charbonneau [1999] suggested the following expression for the differential rotation Ω(r, ψ): 1 r − r Ω(r, ψ) = Ω + [1 + erf(2 c )]{Ω(ψ) − Ω }, (3.3) c 2 d c where Ω(ψ) = A + Bsin2ψ + Csin4ψ (Eq. 3.2) is the surface latitudinal differential rotation and erf(x) is the error function. The best fit values of parameters are set as Ωc/2π = 432.8 nHz (Ωc ' 13.46 deg/day), A/2π = 460.7 nHz (A ' 14.33 deg/day), B/2π = -62.69 nHz (B ' -1.95 deg/day), C/2π = -67.13 nHz (C ' -2.088 deg/day), rc = 0.71R , d = 0.05R . The parameter rc denotes the radius of the tachocline center and d refers to the thickness of the tachocline. This definition characterized the differential rotation profile of solar-like stars by purely latitudinal differential rotation Ω(ψ) with equa- torial acceleration, smoothly matching across a tachocline to a rigidly rotating “core” at a rate Ωc. This profile has been widely used in solar dynamo models. 47

r / R ⊙

r / R ⊙

Fig. 3.2. A contour diagram of solar rotation as a function of equatorial (horizontal) and polar (vertical) depth. The contours are drawn at intervals of 5 nHz. The thick contour around the equator and close to the surface denotes Ω = 460 nHz [Basu and Antia, 2003]. 48

Fig. 3.3. Residuals of the rotation rates of zonal flows at a few typical depths, obtained using 2D regularized least-squares inversion of GONG data during 1995-2005 [Antia, 2006].

3.4. Torsional oscillation

Torsional oscillation is called the pattern of alternating bands (or zones) of faster (slower) than average rotation moving from mid-latitudes during cycle minimum towards the equator (poles, respectively). During cycle maximum faster (slower) bands exist on the equatorial (poleward) side of mean latitude of activity. It is believed that this pattern extends throughout most of the convection zone. The migrating zonal flow pattern was first detected by Howard and Labonte [1980] in Doppler measurements (digital full-disk velocity data from the 5250 A˚ line of Fe I) at the solar surface carried out at Mt. Wilson Observatory in 1968- 1979. They found belts of faster than average rotation that migrate from mid- latitudes to the equator. The migration of the zonal flow bands during the solar cycle is closely connected to the migration of the magnetic activity belt. The flow pattern was first detected helioseismically by Kosovichev and Schou [1997] in early f-mode data from the MDI (Michelson Doppler Imager) aboard the SOHO 49

Fig. 3.4. Residuals of the rotation rates of zonal flows shown as a function of latitude at the depth of r = 0.98R at a few selected times in 1995 - 2000. The thin solid line is for GONG 1-3 months centered around June 1995; the light-dotted line is for June 1996; the short-dashed line is for 1997 June; the long-dashed line is for June 1998; the thick solid line is for June 1999; and the thick-dotted line is for June 2000 [Antia and Basu, 2000]. 50

(Solar and Heliospheric Observatory) spacecraft, and was seen to migrate [Schou, 1999]. Antia and Basu [2000] found that in addition to the pattern of converging to equator with increasing time, there is another system of zonal flow bands at high latitudes (>45◦) that migrate towards the poles as the solar cycle progresses. Figure 3.3 [Antia, 2006] shows the velocity residuals of zonal flows at a few repre- sentative depths and latitudes obtained using a two-dimensional (2D) regularized least-squares helioseismic inversion of GONG data in 1995-2005. Moreover, the amplitudes of the zonal flows at a certain depth change with latitude. Figure 3.4 [Antia and Basu, 2000] presents residuals of the rotation rates of zonal flows shown as a function of latitude at the depth of r = 0.98R at a few selected times. Considering the length of a solar cycle as 11 years [Vorontsov et al., 2002], the time-varying rotation profile of zonal flows can be described as

Ω(r, θ, t) = Ω0(r, θ)+A1(r, θ)cos2πνt+A2(r, θ)sin2πνt ≡ Ω0(r, θ)+Asin(2πνt+φ), (3.4) where Ω0 is the time-invariant part of the profile, t is time in years, with ν fixed at 1/11 cycles per year, and φ is phase (0≤ φ ≤2π). Early results have shown that the zonal flow pattern can only be found from the surface [Howard and Labonte, 1980; Ulrich et al., 1988; Schou, 1999] to around 0.9R [Howe et al., 2000a; Antia and Basu, 2000], not continuous to the base of convection zone or tachocline. With accumulation of more seismic data it has now become clear that the zonal flow pattern penetrates though most of the convection zone [Vorontsov et al., 2002; Basu and Antia, 2003; Howe et al., 2005; Antia et al., 2008]. Recently, Howe et al. [2009] made the first study of the differences in the zonal-flow pattern between the cycle 22/23 minimum and the cycle 23/24 minimum. They suggested that the extended cycle 23/24 minimum during the last few years is probably due to the fact that the flow bands were moving more slowly towards the equator. Antia and Basu [2010] confirmed this difference of zonal-flow pattern between the two minima [Nandy et al., 2011]. They also found that the low-latitude prograde band that bifurcated in 2005 merged well before the cycle 23/24 minimum, which is in contrast to this band’s behavior during the cycle 22/23 minimum where the merging happened during the minimum. The length of solar cycle 23 in zonal pattern determined to be 11.7 years by correlating zonal-flow pattern with itself, i.e., shorter than the length derived from sunspot numbers (about 12.6 years; Hathaway [2010]). Howe et al. [2000b; 2007] reported a 1.3-yr oscillation in the equatorial region around r = 0.72R during the rising phase of the solar cycle, but that has not been confirmed by other studies. The origin of torsional oscillations or alternating zonal flows is not fully under- stood, but since the zonal flow banded structure and the magnetic activity pattern seem to be closely related [Howe et al., 2000a; Antia et al., 2008; Sivaraman et al., 2008], it is generally believed that zonal flows arise from a nonlinear interaction between magnetic fields and differential rotation [K¨uker et al., 1996; Covas et al., 2000; 2004]. 51 3.5. Meridional circulation

Meridional circulation means a circular flow throughout the meridional plane in- cluding longitudinally averaged north-south and radial velocity components. Un- like differential rotation, meridional circulation is not yet fully constrained by observation, but a poleward surface flow with the velocity of 10-20 m/s has been detected by various techniques, such as Doppler measurements [Duvall, 1979; Hath- away, 1996], magnetic tracers [Komm et al., 1993; Hathaway and Rightmire, 2010], and helioseismic analysis [Giles et al., 1997; Braun and Fan, 1998]. The equator- ward return flow below the solar surface has not been observed yet. But it must exist, since mass does not pile up at the solar poles [Dikpati et al., 2004].

Fig. 3.5. Solar meridional flow model. Left: Streamlines for the meridional circulation denoted as small and big dots plotted at 1-yr time intervals. The meridional flow follows along the streamlines. The flow is counterclockwise when observed near the surface. The

base of the meridional flow is theoretically constructed at r = 0.71R according to mass conservation, right above the center of the tacholine ∼0.70R . Right: Typical meridional flow pattern in the two hemispheres with streamlines denoted as arrows. [Dikpati et al., 2004] 52

Meridional flows were initially found at the solar surface in 1970s [Duvall, 1979; Howard, 1979; Topka and Moore, 1982]. Howard et al. [1980] showed that the large-scale velocity patterns on the Sun include not only solar rotation but also another component. This velocity field which they called the “ears” was found to be symmetric about the central meridian. Beckers [1978] pointed out that the ears have a similar form to that expected from a meridional flow velocity. Subsequent work [Labonte and Howard, 1982; W¨ohland Brajˇsa,2001] confirmed the merid- ional flows and found radial flows as well. van Ballegooijen and Choudhuri [1988] studied a model of meridional circulation and suggested a meridional circular flow velocity form

R 1 c c u (r, θ) = u ( )2(− + 1 ξn− 2 ξn+k)ξsinmθ[(m+2)cos2θ−sin2θ], r 0 r n + 1 2n + 1 2n + k + 1 (3.5) R u (r, θ) = u ( )3(−1 + c ξn − c ξn+k)sinm+1θcosθ, (3.6) θ 0 r 1 2

R where ξ(r) = ( r ) − 1, u0 is a measure of the velocity amplitude, and k and m are two free parameters which describe the radial and latitudinal dependence of the velocity, respectively (k > 0 and m ≥ 0). The constants c1 and c2 are chosen so that ur and uθ vanish at the base of the convection zone: (2n + 1)(n + k) c = ξ−n, (3.7) 1 (n + 1)k 0 (2n + k + 1)n c = ξ−(n+k), (3.8) 2 (n + 1)k 0

R where ξ0 = ( )−1. Applying this mathematical form to a flux transport dynamo r0 model Dikpati et al. [2004] obtained the typical meridional circulation flow pattern depicted in Fig. 3.5. The obtained maximum speed of the meridional flow close to the surface is around 15 m/s. However, because the meridional-flow speed is more than an order of magnitude smaller than other flows at the solar surface, it is difficult to be measured accu- rately. Only local helioseismic techniques, e.g., the time-distance technique [Hill, 1988] and ring-diagram technique [Duvall et al., 1993] can be used for such an analysis. With improved observational techniques, the meridional flow has been reliably measured at the solar surface using both magnetic elements as tracers [Komm et al., 1993; Hathaway and Rightmire, 2010] and Doppler velocities [Hath- away, 1996]. These observations show a general flow towards the poles in both hemispheres that is roughly antisymmetric about the equator. The amplitude of this flow shows a variation over the solar cycle with fast flows (11.5 m/s) at mini- mum and slow flows (8.5 m/s) at maximum of cycle 23 [Hathaway and Rightmire, 2010]. Recent results [Beck et al, 2002; Gonz´alezHern´andez et al, 2008; 2010; Basu and Antia, 2010] imply that the pattern of the meridional flow also shows bands of fast and slow flows, very similar to those of the zonal flows and to the butterfly diagram, 53

Fig. 3.6. Antisymmetric pattern of meridional flows in northern and southern hemispheres plotted as a function of time and latitude at the depth of r = 0.998R . Top: the speed of meridional flows is overplotted with the position of sunspots. Bottom: the flow speed is overplotted with zonal flow speed contours obtained by Antia et al. [2008]. To make the plot symmetric about the equator, the sign of the flow has been reversed in the southern hemisphere. Accordingly, positive values represent the flow towards the poles in both hemispheres. The contours are spaced at intervals of 1 m/s with solid representing prograde speeds and dashed representing retrograde [Basu and Antia, 2010]. 54

as can be seen in Fig. 3.6. There is a good match between the positions of the sunspots and the region of low-speed meridional flows and between the migrating pattern of the meridional flow with that of the zonal flow. Basu and Antia [2010] found that the meridional flows not only vary with depth, and latitude, but that the time dependence of the variation is a function of both depth and latitude. Therefore, the flow form can be simply expressed as

u(r, θ, t) = u0(r, θ) + u1(r, θ)sin(ωt) + u2(r, θ)cos(ωt), (3.9) where ω = 2π/T is the frequency of the solar cycle. Meridional flows play a key role in the operation of solar dynamo. They are believed to be responsible for transporting magnetic elements towards the poles on the solar surface [Wang et al., 1989] and towards the equator near the base of the convective zone [Choudhuri et al., 1995; Dikpati and Charbonneau, 1999]. They also play a role in the generation of differential rotation and its temporal variation [Glatzmaier and Gilman, 1982; Spruit, 2003] and in the spatiotemporal distribu- tion of sunspots and the solar cycle period [Choudhuri et al., 2007; Nandy and Choudhuri, 2002; Hathaway et al., 2003]. Variations in the equatorward merid- ional flow during a solar cycle have been suggested to be able to cause a deep solar minimum [Nandy et al., 2011]. In the surface flux transport dynamos, the prolonged cycle 23/24 minimum can be explained by faster meridional flow and the observed weaker polar fields compared to cycle 22/23 minimum [Schrijver and Liu, 2008; Wang et al., 2005; 2009], but the prolonged minimum conflicts with the flux transport dynamos which produce stronger polar fields and a short cycle with fast meridional flow [Dikpati et al., 2006; Choudhuri et al., 2007]. A fast meridional flow in the surface flux models can slow down the process of opposite polarities canceling each other across the equator. Therefore, the flow carries ex- cess of elements of both polarities to the poles with a only slight excess of elements with the polarity of the polarward side of the sunspot latitudes. This requires a longer time to reverse the old polar fields and builds up weaker polar fields of the opposite polarity. 4. Active latitudes

Sunspots are known to appear preferably in a narrow high latitude belt at the beginning of a solar cycle and approach the equator as the solar cycle progresses. Individual sunspot cycles can be separated near the time of minimum by the lat- itude of the emerging sunspots and, more recently, by the magnetic polarity of sunspots as well. Sunspots of the old cycle and the new cycle coexist during a few years around solar minima. The latitude migration and the partial overlap of the successive sunspot cycles leads to the famous pattern of sunspots called Sp¨orer’slaw of zones by Maunder [1903] and was illustrated by his famous but- terfly diagram [Maunder, 1904]. NASA’s Marshall Space Flight Center updates their butterfly diagram together with average daily sunspot area every month at http://solarscience.msfc.nasa.gov/SunspotCycle.shtml, which shows the latitudi- nal positions of sunspots for each rotation since 1874. Figure 4.1 shows an example of their butterfly diagram for the years 1874-2011 and the corresponding sunspot areas for the same time interval. Hathaway et al. [2003] investigated the latitude positions of sunspot areas as function of time relative to the time of minimum.The centroid positions of sunspot areas in each hemisphere are calculated for each solar rotation. They also studied the area weighted averages of these positions in 6-month intervals and found that all cycles start with sunspot zones centered at about 25◦ from the equator. The equatorward drift is more rapid early in the cycle, slows down later in the cycle and eventually stops at about 7◦ from the equator [Hathaway, 2010]. Sunspots appear very often in pairs. The trailing sunspot of the pair tends to appear further out from the equator than the leading spot. Thus the line connecting the trailing sunspot with the leading one is not parallel to the equator. Normally, the higher the sunspot latitude is, the greater is the inclination of the connecting line to the equator. This pattern of sunspot emergence is called Joy’s law. While sunspots drift slowly to the equator, the magnetic fields at higher latitude (related to trailing sunspot polarities according to Joy’s law) are transported to- wards the poles where they eventually reverse the polar field at the time of sunspot cycle maximum. The radial magnetic field averaged over longitude for each solar rotation is shown in Fig 4.2 [Hathaway, 2010]. This magnetic butterfly diagram 56

Fig. 4.1. Top: A butterfly diagram of the latitude of sunspot occurrence versus time. Bottom: average daily sunspot areas of each Carrington rotation in units of hundredths of a solar hemisphere (10µHem). [Courtesy of Hathaway/NASA/MSFC.]

Fig. 4.2. Magnetic butterfly diagram constructed from the average radial magnetic field of each Carrington rotation using the synoptic magnetic maps observed by Kitt Peak and SOHO [Hathaway, 2010]. 57 exhibits Hale’s law, Joy’s law, the polar field reversals as well as the transport of higher latitude magnetic field elements towards the poles. 5. Active longitudes

5.1. History of active longitude research

Solar activity occurs preferentially at some longitude ranges rather than uniformly at all heliographic longitudes. These longitude ranges are called active longitudes. It has been found that various manifestations of solar activity, such as sunspots [Vitinskij, 1969; Bumba and Howard, 1969; Balthasar and Sch¨ussler,1983; 1984; Berdyugina and Usoskin, 2003; Juckett, 2006], radio emission bursts [Haurwitz, 1968], faculae and plages [Maunder, 1920; Mikhailutsa and Makarova, 1994], flares [Jetsu et al., 1997; Bai, 1987a;b; 1988; 1994; 2003a; Temmer et al., 2004; 2006a], prominences [Fenyi, 1923], coronal emission [Benevolenskaya, 2002; Badalyan et al., 2004; Sattarov et al., 2005], surface magnetic fields [Benevolenskaya et al., 1999; Bumba et al., 2000], heliographic magnetic field [Ruzmaikin et al., 2001; Takalo and Mursula, 2002; Mursula and Hiltula, 2004], total solar irradiance [Mordvi- nov and Willson, 2003], EUV radiation [Benevolenskaya et al., 2002], and sur- face helicity [Bao and Zhang, 1998; Pevtsov and Canfield, 1999; Kuzanyan et al., 2000] are non-axisymmetric and mainly occur in preferred longitude bands. These preferred active longitudes were given different names when they were found in different indices, e.g., active sources [Bumba and Howard, 1969], Bartels active longitudes [Bumba and Obridko, 1969], streets of activity [Stanek, 1972], sunspot nests [Casenmiller et al., 1986], hot spots [Bai, 1990], helicity nests [Pevtsov and Canfield, 1999], and complexes of activity [Benevolenskaya et al., 1999]. Even in the very early days of solar physics Carrington [1863] suspected that sunspots do not form randomly over solar longitude but appear in certain longi- tudinal zones of enhanced solar activity. However, studies on this topic have been carried out since 1930s [Chidambara Aiyar, 1932; Losh, 1939; Lopez Arroyo, 1961; Bumba and Howard, 1965; Warwick, 1954; 1965; Balthasar and Sch¨ussler,1984; Wilkinson, 1991]. As a result, the tendency for active regions to cluster in pre- ferred heliographic longitudes on time scales of days, months or even longer were recognized long. The longitudinal distribution of sunspots and flares was initially studied in so- lar disc [Chidambara Aiyar, 1932; Evans et al., 1951; Behr and Siedentopf, 1952; 59

Fig. 5.1. Longitudes of two-day sunspots observed at first and last appearances [Chi- dambara Aiyar, 1932] in solar disc reference frame. The thick (thin) solid line denotes the first (last) appearance of Greenwich data and the dotted line denotes the first ap- pearance of Kodaikanal data. 60

Fig. 5.2. Longitudinal distribution of total daily sunspot numbers summed over each 1 solar rotation in 27 3 day frame in 1903-1937 [Losh, 1939]. The horizontal axis denotes the day of synodic solar rotation and the vertical axis is Wolf number. 61

Fig. 5.3. Longitudinal distribution of total daily sunspot numbers of each solar rotation, using the same data as Losh [1939], in 27.2753 day frame for each solar cycle in 1903-1937 [Warwick, 1965]. 62

Fig. 5.4. Active region chart [Dodson and Hedeman, 1975] shown by longitudes of large plages with area of at least 1000 µHem in Carrington frame in 1970-1974. Time runs from left to right. Vertical axis denotes Carrington rotation number, from top to bottom. The ‘antecedents’ (‘descendents’) of each region are denoted by leftwards (rightwards) and downwards shifted connecting lines. The size of the circle reflects the size of the plage. Heavy dark circles denote flare-rich plages. A dark square outline represents a region associated with proton events. Data are repeated for half a rotation on the right. 63

Dodson and Hedeman, 1964], and later in some rigidly rotating coordinate refer- ence frames, e.g., in Carrington frame [Warwick, 1965; Vitinskij, 1969; Trotter and Billings, 1962], in Bartels frame (with synodic rotation period of exactly 27 days) [Bumba and Howard, 1969; Balthasar and Sch¨ussler, 1983; Bai, 1990], or in other 1 rotation frame (e.g., 27 3 days in Losh [1939]). Accordingly, active longitudes were found to appear at different longitudinal positions in different reference frames. Figure 5.1 shows the longitudinal distribution of first (thick-line) and last (thin- line) appearances of two-day spots in solar disc in 1874-1930 [Chidambara Aiyar, 1932]. The frequency of their occurrence suggests a minimum between longitudes 30◦ and 50◦ on either side of the Sun’s central meridian. The maximum frequency of sunspot occurrence is found to be at different longitudes in reference frames with different rotation period. Figures 5.2 and 5.3 show the longitudinal distri- 1 bution of sunspot (Wolf) number in 1903-1937 in 27 3 -rotation-day frame [Losh, 1939] and in 27.2753-day Carrington frame [Warwick, 1965], respectively. The active longitudes of sunspot activity were found more consistent in 27.2753-day 1 (Carrington) frame than in 27 3 -rotation-day frame. Warwick [1965] also noticed that proton flares leading to polar-cap absorption occurred mainly in two active longitudes separated by around 180◦. However, Wilcox and Schatten [1967] pointed out that the Carrington rotation period is not the rotation period of the Sun, and therefore one should take the rotation period as a free parameter of the analysis, which needs to be determined by observations. They reanalyzed the longitude of proton flare data used by Warwick [1965] and found that the active longitudes are more evident by using 28.0, 28.8, 30.8, 31.9, and 32.9 days as the rotation period than using Carrington period. Following this idea by Wilcox and Schatten [1967], a number of other periodicities were found as well, such as, 12, 13.6, 31.63, 51, 73, 77, 103, 129, and 154 days [Knight et al., 1979; Bogart, 1982; Fung et al., 1971; Rieger et al., 1984; Bai, 2003b; Bogart and Bai, 1985; Bai and Cliver, 1990; Bai and Sturrock, 1991; 1993; Bai, 1987b; 1992a;b; Ozg¨u¸cand¨ Atac, 1994]. So-called evolutionary charts of active regions and active-region family trees are also popular methods to study the longitude of long-lived and complex large active regions, in which solar flares occur quite often. Dodson and Hedeman [1968] noticed a band of active longitudes, whose Carrington longitude values increased in time, suggesting a corresponding rotation period of 27d or slightly less. They also noticed that strong solar activity occurs in areas separated by 180◦ in longitude. Studying the evolutionary charts in 1970-1974, Dodson and Hedeman [1975] confirmed that active longitudes rotate faster than Carrington frame and found two active longitude bands centered around 90◦ and 270◦ in 1970-1971, but only one active longitude band centered around 180◦ in 1973-1974 (see Fig. 5.4). Recently, long-lived active longitudes of sunspots with the non-axisymmetry about 0.1 were suggested by Berdyugina and Usoskin [2003] and the migration of active longitudes was found to be in agreement with solar differential rotation. Although this result was criticized by Pelt et al. [2005] who claimed that the active longitude pattern found by Berdyugina and Usoskin [2003] is an artefact of the used method. In the subsequent work Usoskin et al. [2005] analyzed the effects of theirs method by using randomly generated data as the longitudes of sunspots. 64

Fig. 5.5. Longitudinal distribution of first appearance of (area weighted) sunspots in the northern hemisphere in 1878-1996. a) Sunspots in the Carrington frame. Distribution is nearly uniform. b) Sunspots in the dynamic reference frame. Non-axisymmetry is Γ = 0.11. c) Only one dominant spot of each Carrington rotation is considered, whence Γ = 0.19. d) The same as panel c) but averaged over half year in each of the two determined active longitude bands, whence Γ = 0.43. The solid line in each panel represents the best fit of double Gaussian [Usoskin et al., 2005]. 65

Fig. 5.6. Active longitudes of X-class flares [Zhang et al., 2007a]. The longitudinal distribution of X-flares in the dynamic reference frame for the time period of 1975-2005. The horizontal axis denotes the longitude and the vertical the number of flares. The solid line depicts the best fit of double Gaussian with two peaks at 90◦ and 270◦. 66

A large number of statistical tests showed that the average non-axisymmetry of randomly generated sunspots is 0.02 and the probability to obtain the 0.1 non- axisymmetry is less than 10−6. This implies that the persistent active longitudes were not an artifact of method. If we correct the observed Carrington longitudes of sunspots according to the expected migration, the active longitudes should be consistent in the new frame. Taking this concept into account Usoskin et al. [2005] found that two persistent active longitudes of sunspots separated by 180◦ have existed during 11 cycles (1878-1996) with the level of non-axisymmetry about 0.1 in a dynamic reference frame (see Fig. 5.5). If only the position of one dominant spot for each Carrington rotation is considered the non-axisymmetry increases to 0.19. This explains why the previously found active longitudes are not stable in any rigidly rotating reference frame. However, a systematic drift of active longitudes for sunspot numbers was not found by Balthasar [2007], probably because the sunspot numbers do not carry good longitudinal information, being an index covering the whole visible solar disc. A similar method to Usoskin et al. [2005] was employed by Zhang et al. [2007a;b] in the analysis of the longitudinal distribution of solar X-ray flares. They found that two active longitudes of X-ray flares have existed during three solar cycles since GOES started X-ray observations in 1975. They also noted that the level of non-axisymmetry increases with the X-ray intensity. The non-axisymmetry for all three classes of X-ray flares was found to be significantly larger than that for sunspots. The non-axisymmetry for powerful X-ray flares can reach up to 0.55 (0.49) in northern (southern) hemisphere, implying that more than 70% of strong X-ray flares occurred in the two preferred active longitudes. Based on the active longitudes and their migration with time in Carrington frame Zhang et al. [2008] developed a simple prediction of solar active longitudes. However, the differential rotation parameters obtained for different solar tracers were found to be quite different; even the parameters obtained for one class of X-ray flares were different from those obtained for another class [Zhang et al., 2007b]. Note that in earlier studies [Usoskin et al., 2005; Zhang et al., 2007b], the time resolution for the calculation of the shift of ALs was one Carrington rotation period. The migration M of ALs with respect to the Carrington reference frame was given by N Xi M = Tc (Ωj − Ωc), (5.1)

j=N0 where N0 and Ni denote the Carrington rotation numbers of the first and the (i)th rotation of the data set, Tc = 27.2753 days is the synodic Carrington rotation period, Ωj is the rotation rate of ALs, and Ωc is the angular velocity of Carrington frame (in sidereal frame 14.1844 deg/day and in synodic frame 13.199 deg/day). The same value of M was used as the migration of ALs from the beginning to the end of the (i)th Carrington rotation. However, even small difference between the values of Ωj and Ωc (e.g., 0.2 deg/day) can cause a difference of up to a few degrees (5.5 deg) between the beginning and the end of a Carrington rotation. Thus, taking the same value of M in the beginning and the end of a Carrington rotation could significantly lower the accuracy of the best fit rotation parameters. 67

In Paper I, we change the time resolution of M from one Carrington rotation to less than one hour. The time of M is taken the observation time of a flare or sunspot group transformed to a fractional day k of the Carrington rotation. Accordingly, the improved version of M has the form

Ni−1 X M = Tc (Ωj − Ωc) + k(ΩNi − Ωc) , (5.2)

j=N0 where Ni−1 denotes the (i-1)th Carrington rotation number. Using this improved method, we reanalyzed in Paper I the GOES X-ray flare data. The differential rotation parameters for the three classes of flares were found to agree with each other and the non-axisymmetry for the longitudinal distribution of flares was sys- tematically improved as well, which gives strong support for the success of the improved method and the extracted parameter values. The non-axisymmetry of X-class flares in the last three solar cycles can reach 0.59, suggesting that 79.5% of powerful flares occur in the two active longitudes. We also noticed that the northern and southern hemispheres rotate at significantly different average angu- lar frequencies during last three solar cycles. In Paper II, using the improved method we studied the long-term variation of the differential rotation parameters of active longitudes of sunspots in 1874-2009, separately in the northern and southern hemispheres. The obtained rotation pa- rameters in the two hemispheres suggest a long-term period of variation of roughly one century. The difference between the average rotating rates of the northern and southern hemispheres is in agreement with earlier studies [Bai, 2003a; Hoeksema and Scherrer, 1987; Brajˇsaet al., 1997; 2000], but does not support the result of Gigolashvili et al. [2005] who claimed that the northern hemisphere rotates faster during the even cycles (20 and 22) while the rotation of southern hemisphere dom- inates in odd ones (cycles 19 and 21). (See Sect. 5.4.2 and Table 5.2 for more detailed discussion about results on hemispheric difference found in Papers II, III and IV.) Active longitudes have also been found in stellar activity of starspots, such as, spots on FK Com-type stars [Jetsu et al., 1991; 1993; 1999; Korhonen et al., 2002], on very active young solar analogues [Berdyugina et al., 2002; J¨arvinenet al., 2005a;b; Berdyugina and J¨arvinen,2005], and on RS CVn stars [Berdyugina and Tuominen, 1998; Lanza et al., 1998; Rodon`oet al., 2000]. Two permanent active longitudes 180◦ apart seem to be a conspicuous pattern of stellar activity but can continuously migrate in the orbital reference frame. The nonlinear migration of active longitudes is a typical behaviour for single stars, young solar type dwarfs, and FK Com-type giants, which suggests the presence of differential rotation and similar changes in mean spot latitudes as on the Sun. 68

Fig. 5.7. Migration and flip-flop of active longitudes of sunspots [Berdyugina and Usoskin, 2003]. Semi-annual phases of the two active longitudes of sunspots in solar cycles 12-22 in the northern hemisphere are plotted. Filled circles stand for the phases of the dominant active longitude during the corresponding half year, and open circles stand for the less active longitude. Curves depict the phase migration lagging behind the Carrington frame. Vertical lines denote solar cycle minima. For better visibility, the migration restarts from zero every second cycle. 69

Fig. 5.8. Longitudinal distribution of X-class flares in 1975-1985 in the dynamic reference frame mentioned in Sect. 5.1. Two active longitudes are centered around 90◦ and 270◦, 180◦ apart. Six gathering areas of flares are denoted by numbers [Zhang et al., 2007a].

5.2. Flip-flop phenomenon

Periodic switching of the dominant activity from one active longitude to the other is the so-called flip-flop phenomenon, which was first observed on the single, rapidly rotating giant FK Comae [Jetsu et al., 1991]. Doppler images show that the active regions evolve in size and indicate possible cyclic variations. While one active longitude reduces its activity level, the other increases. When the active longitudes have roughly the same activity level, a switch of the dominant activity from one longitude to the opposite one occurs [Berdyugina et al., 1998; 1999; Korhonen et al., 2009]. Long time series of photometric data imply that flip-flops are regularly repeated on FK Comae, RS CVn stars, and young solar analogues, indicating a flip-flop cycle [Jetsu, 1996; Jetsu et al., 1999; J¨arvinenet al., 2005b; Berdyugina and J¨arvinen,2005]. A list of stars exhibiting a flip-flop phenomenon was recently reconstructed [Berdyugina, 2005]. The solar active longitudes also exhibit a flip-flop cycle. An analysis of 120 years of sunspot data [Berdyugina and Usoskin, 2003] suggests that on the Sun the alternation of the dominant spot activity between the two opposite longitudes occurs periodically, at about 1.8-1.9-yr period on average, indicating 3.8-yr and 3.65-yr flip-flop cycles in the northern and southern hemispheres, respectively. Transforming the Carrington longitudes (0◦-360◦) into phases (0-1), they calcu- lated the average phase every half a year, separately for the northern and southern hemispheres. Accordingly, a phase lag diagram of the two active longitudes with respect to Carrington reference frame was obtained (see Fig. 5.7. for the phase for 70

the northern hemisphere). The migration continues over all 11 cycle and the active longitude delay for about 2.5 rotations per cycle. Filled circles denote the phases of the active longitude, which is dominant during the corresponding 6 months, and open circles denote the less active longitude. Curves depict the migration of the phase lag, resulting from the change of the mean latitude of sunspots and differen- tial rotation. The active longitudes separated by 0.5 (180◦) in phase are persistent in both hemispheres for at least 120 years. The migration continues throughout the entire period and results in a phase lag of about 28 rotations for 120 years. One longitude dominates the activity typically for 1-2 years. Then a switch of dominance to the other active longitude occurs rather rapidly. On an average, six switches of the activity occur during the 11-yr sunspot cycle and, thus, results in the 3.7-yr flip-flop cycle, about 1/3 of sunspot cycle. Similar flip-flop period was also found in heliospheric magnetic field [Takalo and Mursula, 2002; Mursula and Hiltula, 2004] and solar X-ray flares [Zhang et al., 2007a;b]. Removing the migration of active longitudes due to differential rotation, the recovered longitude distribution of X-class flares (see Fig. 5.8) suggests that there are two persistent active longitudes centered around 90◦ and 270◦. There are six groups of flare occurrence in Fig. 5.8 arranged around the two active longitudes. They demonstrate the periodical alternation of the dominance of active longitudes in cycle 21. This implies that a flip-flop cycle of flares is 1/3 of sunspot cycle period as well. A similar 1:3 relation between flip-flop and main activity cycle was found also in other stars [Berdyugina and J¨arvinen,2005].

5.3. Dynamo models

We are interested in the recent studies of the dynamo models for explaining the active longitudes and flip-flops observed on the Sun and solar-like stars rather than the conventional solar dynamo theory for explaining the sunspot cycle and the butterfly diagram. The typical astrophysical dynamo is modeled by an electrically conducting ro- tating sphere, whose internal structure and motions are symmetric with respect both to the rotation axis and to the equatorial plane. A model of this kind ex- cites different dynamo modes that have different symmetries and stabilities in the kinematic case. The excited magnetic fields can be decomposed into two parts that are sym- m m metric (BS ) and antisymmetric (BA ) about the equatorial plane and have the following form

m m BA,S = Re[CA,Sexp(imφ)], (5.3) m m where CA and CS denote the antisymmetric and symmetric complex vector fields with respect to the equatorial plane. Both are symmetric about the rotation axis. m is a non-negative integer denoting the Fourier component with respect to the azimuthal coordinate φ (longitude) [Brandenburg et al., 1989; R¨adleret al., 1990]. The total energy E of the B-field can be expressed as 71

Fig. 5.9. The solar dipole (A0 and S1) and quadrupole (A1 and S0) dynamo modes (pic- ture taken from Fluri and Berdyugina [2004]). The four modes depict the distribution of the poloidal magnetic field on the solar surface. The gray scale indicates the relative strength of the magnetic field with white and black depicting opposite polarities. Assum- ing the rotation axis in vertical direction, the A0 and S0 modes depict two axisymmetric modes while A1 and S1 depict non-axisymmetric modes about the axis. 72

1 Z E = B2 × dV, (5.4) 2µ where the integral is taken over the fluid body and outer space. A measure P of the degree of symmetry or antisymmetry of a B-field about the equatorial plane and a measure M for the deviation of a B-field from the symmetry about the axis of rotation can be defined by E − E P = S A (5.5) ES + EA and

M = 1 − E0/E, (5.6)

respectively, where ES and EA are the total symmetric and antisymmetric parts of E from Eqs. 5.3 and 5.4, E0 is the energy in the axisymmetric part (M = 0) of the field. The evolution of solutions of the solar dynamo can be followed in a (P , M) diagram with the four ‘corner solutions’ of (P , M) = (1,0),(-1,0),(1,+1),(-1,1), which are associated with the nonlinear continuation of the linear S0, A0, S1, and A1 modes, respectively [R¨adleret al., 1990; Moss, 2005]. The surface magnetic fields of the S0, A0, S1, and A1 modes are displayed in Fig. 5.9. In slowly rotating stars, like the Sun, axisymmetric modes (A0 and S0) are preferably excited. In more rapidly rotating stars the non-axisymmetric modes (e.g., A1 and S1) get excited [Moss et al., 1995; Moss, 2005]. Besides the symmetry of the modes, their oscillatory properties are important. The mean-field dynamo theory favours oscillating axisymmetric modes with a clear cyclic behaviour and sign changes as in the sunspot cycle, while non-axisymmetric modes appear to be rather steady. For explaining the flip-flop phenomenon, where we see both active longitudes and oscillations, an oscillating axisymmetric dynamo mode needs to co-exist with the non-axisymmetric mode. The possibility of such a mechanism was first demonstrated by Moss [2004] who obtained a stable solution with an oscillating axisymmetric mode and a steady, mixed-polarity non-axisymmetric mode. Moss [2005] studied the non- axisymmetric magnetic field generation in rapidly rotating late-type stars and proposed that a combination of S0 and S1 can produce the flip-flop. The super- imposed magnetic field structure of S1 and S0 is presented in Fig. 5.10. In this model if the non-axisymmetric field S1 remains constant and the axisymmetric component S0 changes its sign and oscillates regularly every half cycle, the two active longitudes will switch by 180◦ at the same frequency of the S0 field. The flip-flops occurring at the frequency of the sign changes of the axisymmetric mode have been observed in some RS CVn stars. More frequent flip-flops, as observed in single stars and the Sun, suggest a more complex field configuration. Fluri and Berdyugina [2005] suggested that a combination of one axisymmetric dynamo mode (A0) and two non-axisymmetric modes (S1 and Y22 with m = 1 and m = 2, respectively) might explain the two solar active longitudes and the flip-flops. Fluri and Berdyugina [2004] showed that flip-flops could also occur due to alternation of relative strength of two non-axisymmetric (S1 and A1) modes, even without 73

Fig. 5.10. Superimposed magnetic field structure of S0 and S1. Solid lines depict the S0 mode (quardrupole, axisymmetric) and dashed lines depict the S1 mode (dipole, non- axisymmetric ) [Moss, 2005]. With the fields directed as indicated, the latitudinally averaged field has a maximum at longitude 0◦ (on the left). If the direction of the S0 field is reversed, the maximum will appear at longitude 180◦ (on the right). 74 the sign change of any of the modes involved. Jiang and Wang [2007] studied the condition for the excitation of the dominant axisymmetric mode and the condition that favours the non-axisymmetric mode and developed a coexistence of A0 mode and S1 mode which results in the flip-flop phenomenon. They pointed out that the axisymmetric magnetic field is mainly concentrated near the high latitude of ◦ approximately 55 at about 0.7R , where the radial shear of differential rotation is strong, while the non-axisymmetric field occur near the intermediate latitude of 35◦ at the bottom of the tachocline, where the differential rotation is weak and the diffusivity is low. The solar dynamo could in principle generate non-axisymmetric magnetic con- figurations. However, a non-axisymmetric kinematic dynamo mode, even if prefer- ably excited, must rotate rigidly without exhibiting any effect of phase mix- ing, which results from the effect of the high differential rotation on the non- axisymmetric field. For a high differential rotation star as the Sun, the relative rotation between two nearby latitude belts stretches the non-axisymmetric field and leads to a differential rotation of the non-axisymmetric configuration. This is known as phase mixing [Bassom et al., 2005; Berdyugina et al., 2006; Usoskin et al., 2007b]. Phase mixing enhances the losses caused by turbulent diffusion. Therefore, the non-axisymmetric magnetic structures excited by various dynamos are expected to rotate rigidly. A seeming interpretation for the rigidly rotating non-axisymmetric magnetic field and the differential rotation of active longitudes observed from sunspots was proposed by Berdyugina et al. [2006] (described in Usoskin et al. [2007b]) in terms of the so-called the stroboscopic effect. The stroboscopic effect means that the non-axisymmetric magnetic structure underlying the active longitudes is strongly affected by differential rotation, while the rotation law for the magnetic structure is still quasi-solid body. It gives the impression of a differential rotation of active longitudes.

5.4. North-South asymmetry

Comparisons of activity in the two solar hemispheres show significant differences, which is called the north-south (N-S) asymmetry. The hemisphere with a higher solar activity is also called the active or preferred hemisphere [Hathaway, 2010]. Besides the N-S asymmetry in solar activity level, N-S asymmetry is also found to exist in solar rotation. The variations in solar rotation are suggested to be most likely related to variations in solar activity [Javaraiah, 2003b; Javaraiah et al., 2005]. Recently, Javaraiah [2010] proposed that the mean meridional motion of the sunspot groups exhibits north-south difference as well. We give a brief review on the N-S asymmetry of solar activity and solar surface differential rotation in Sect. 5.4.1 and in Sect. 5.4.2, respectively. 75 5.4.1. N-S asymmetry in solar activity

As early as in 1890s Sp¨orer[1889; 1890] and Maunder [1904] noted that there were often long periods of time when most sunspots were found preferentially in one hemisphere. Significant N-S asymmetry was found in a large amount of solar activity indices, such as the sunspot number and areas [Newton and Milsom, 1955; Waldmeier, 1971; Roy, 1977; Vizoso and Ballester, 1990; Carbonell et al., 1993; Li et al., 2000; 2002; Temmer et al., 2002; Vernova et al., 2002; Krivova and Solanki, 2002; Knaack et al., 2004; Temmer et al., 2006b], the number of flares [Garcia, 1990; Verma, 1987; 1992; Li et al., 1998; Temmer et al., 2001; Joshi and Pant, 2005; Joshi et al., 2006; 2007], the flare index [Ata¸cand Ozg¨u¸c,1996;¨ Joshi and Joshi, 2004], prominences/filaments [Hansen and Hansen, 1975; Vizoso and Ballester, 1987; Joshi, 1995; Verma, 2000; Gigolashvili et al., 2005], photospheric magnetic fields [Howard, 1974; Rabin et al., 1991; Song et al., 2005], coronal EUV bright points [Brajˇsaet al., 2005], coronal green line intensity [Ozg¨u¸cand¨ Ucer,¨ 1987; Storini and Sykora, 1995; Sykora and Ryb´ak,2005], and the heliospheric magnetic fields [Mursula and Hiltula, 2003; 2004; Virtanen and Mursula, 2010]. Thus, the northern and southern hemispheres should always be considered separately when studying solar activity. Some results on the preferred hemisphere in cycles 8-23 are displayed in Table 5.1. However, quantifying the asymmetry itself is problematic. Taking the absolute asymmetry index produces a strong signal around the solar maximum times, while taking the relative asymmetry index produces a strong signal around the minimum times. The absolute asymmetry ∆ and relative (or normalized) asymmetry δ can be expressed as follows

∆ = An − As, (5.7)

A − A δ = n s , (5.8) An + As where An and As denote the activity index in northern and southern hemispheres, respectively. The high relative asymmetry found during solar minima is due to only a few sunspot groups appearing on the Sun. If all of them are in the same hemisphere, the momentary absolute value of the relative asymmetry approaches to 1 [Swinson et al., 1986; Vizoso and Ballester, 1990]. Table 5.1 shows that during cycle 10, the N-S asymmetry shifts from northern dominance to the southern dominance and remains there until cycle 13. The N-S asymmetry shifts back to the northern dominance in cycle 14 and continues to favor the northern hemisphere until cycle 20. Southern dominance is restored in cycle 21 and persist until recently. This implies that the N-S asymmetry of solar activity has a long-term characteristic time scale of about 110 yr [Verma, 1993]. Long-term trend in the N-S asymmetry has also been proposed [Newton and Milsom, 1955; Waldmeier, 1957; Bell, 1962; Vizoso and Ballester, 1990; Carbonell et al., 1993; Duchlev, 2001]. Besides the long-term periodicity of N-S asymmetry of solar activity, variations at other periods of about 1 to 4 cycles [Vizoso and Ballester, 1987; 1989; Ozg¨u¸cand¨ 76

authors tracer solar more active cycle hemisphere Bell [1962] sunspot groups 8-9 North ... sunspot groups 10-13 South Li et al. [2002] sunspot groups 12-13 South ... sunspot areas 12-13 South ... sunspot numbers 12-13 South Bell [1962] sunspot groups 14-18 North Temmer et al. [2006b] sunspot numbers 18-20 North Li et al. [2002] sunspot groups 19-20 North ... sunspot numbers 19-20 North ... sunspot areas 19-20 North ... flare index 19-20 North ... sudden disappearances 19-20 North ... of prominences ...... Verma [1987] major flares 19-20 North ... radio bursts 19-20 North ... white light flares 21 South ... radio bursts 21 South ... HXR bursts, CMEs 21 South Temmer et al. [2006b] sunspot numbers 21-23 South Goel and Choudhuri [2009] polar faculae numbers 21-23 South

Table 5.1. Preferred hemispheres in cycles 8-23. 77

Ucer,¨ 1987; Verma, 1993; Carbonell et al., 1993; Duchlev and Dermendjiev, 1996; Knaack et al., 2004; Javaraiah, 2008] and short-term periods of 1 to 5 yr [Ozg¨u¸c¨ and Ucer,¨ 1987; Vizoso and Ballester, 1989; 1990; Verma, 1993; Knaack et al., 2004] were also found. Swinson et al. [1986] and White and Trotter [1977] claimed that there is a 22-yr period in the N-S asymmetry of solar activity. However, Carbonell et al. [1993] argued that the 22-yr period in the sunspot N-S asymmetry is not statistically significant. The N-S asymmetry of solar activity within a solar cycle is related to the phase difference between the northern and southern hemispheres, i.e., solar activity does not synchronously reach its maximum in the two hemispheres [Waldmeier, 1971; Temmer et al., 2006b; Li, 2008; 2009b; Li et al., 2010]. Carbonell et al. [2007] studied the N-S asymmetry in daily hemispheric sunspot number, X-ray flares, solar flare index, the yearly hemispheric number of active prominences, the monthly hemispheric sunspot area, the hemispheric averaged photospheric magnetic flux density and the total hemispheric magnetic flux in each Carrington rotation. They found that many effects influence the statistical significance of the N-S asymmetry, e.g., the type of data and data binning. They proposed different statistical tests for integer, dimensionless data (e.g., the daily international sunspot numbers, or the daily X-ray flare numbers), non-integer, dimensionless data (e.g., the hemispheric sunspot numbers), and non-integer and dimensional data (e.g., flare index, magnetic flux in density). Appropriate data binning should be considered for different types of activity parameters. It is believed [Goel and Choudhuri, 2009] that the Babcock-Leighton process of poloidal field generation is the source of randomness in the solar dynamo and that the randomness of the Babcock-Leighton process may give rise to a stronger poloidal field in one hemisphere compared to the other. Feeding the actual value of the observed polar field at solar minima to a theoretical model based on mean field equations, Goel and Choudhuri [2009] developed a numerical dynamo model to explain the N-S asymmetry. They suggested that the asymmetry of the poloidal field produced at the end of a sunspot cycle is the major factor determining the asymmetry of the next cycle.

5.4.2. N-S asymmetry in solar rotation

The N-S asymmetry in solar differential rotation has been reported by many au- thors [Gilman and Howard, 1984; Howard et al., 1984; Balthasar et al., 1986; Hoeksema and Scherrer, 1987; Antonucci et al., 1990; Japaridze and Gigolashvili, 1992; Brajˇsa et al., 1997; 2000; Georgieva and Kirov, 2003; Georgieva et al., 2003; 2005; Mursula and Hiltula, 2004; Javaraiah, 2003a; Nesme-Ribes et al., 1997; Gigo- lashvili et al., 2003; 2005; 2007; W¨ohlet al., 2010]. The measured rotation velocities differ from each other not only for different types of solar activity formations, but they differ even for the same types as ob- tained by different authors. The discrepancy of the obtained velocities for different tracers of solar activity can be explained by their different heights in the solar at- mosphere, where the radial differential rotation causes differences. Discrepancies 78

authors tracer solar faster cycle hemisphere Javaraiah [2003a] sunspot groups 12 South ... sunspot groups 13 North ... sunspot groups 14-20 South Gigolashvili et al. [2003] Hα filaments 20, 22 North ... Hα filaments 19, 21 South Scherrer et al. [1987] PMF 20-21 North Hoeksema and Scherrer [1987] coronal magnetic field 21 North Antonucci et al. [1990] PMF 21 North Brajˇsaet al. [1997] Hα filaments 21-22 North ... LBT regions 21-22 North Brajˇsaet al. [2000] LBT regions 21-22 North Knaack et al. [2005] PMF 21, 23 North ... PMF 22 South Bai [2003a] major flares 19-23 North W¨ohlet al. [2010] SBCS 23 South Paper II sunspot groups 12 North ... sunspot groups 13-16 South ... sunspot groups 17-23 North Paper III sunspot groups 13-16 South ... sunspot groups 17-22 North

Table 5.2. Faster rotating hemisphere in cycles 12-23. LBT denotes low-brightness- temperature, PMF photospheric magnetic fields, and SBCS small bright magnetic structures.

among the same types of tracers may be due to different time binning of data. Increasing evidence [Balthasar et al., 1986; Bai, 2003a; Knaack and Stenflo, 2005; Knaack et al., 2005; Balthasar, 2007; Heristchi and Mouradian, 2009] suggests that the solar differential rotation changes from cycle to cycle and even within one cycle. Bouwer [1992] claimed that precise periods between 27 and 28 days persist only for a short time, sometimes only for a few solar rotations. Howard and Harvey [1970] found that the differential rotation even varies day by day. Therefore, both the depth of the phenomenon in the solar atmosphere and the time of occurrence should always be taken into account when studying solar differential rotation and its variation. Balthasar et al. [1986] and Balthasar [2007] studied the long-term variation of solar differential rotation using sunspot groups and sunspot numbers as tracers. However, they did not separate northern and southern hemispheres. The long-term variation of differential rotation from cycle to cycle, separated for the northern and southern hemispheres, has not been widely studied yet. The obtained results so far are listed in Table 5.2. The results obtained by different authors significantly contradict each other. 79

In Paper II, we studied the long-term variation of the solar surface rotation using the improved analysis mentioned in Sect. 5.1 and sunspot observation in 1874-2009. This paper confirms the result [Bai, 2003a; Hoeksema and Scherrer, 1987; Brajˇsaet al., 1997; 2000] that the northern hemisphere rotates faster than the south in the last five solar cycles and suggests that the long-term period of N-S asymmetry of solar rotation is around 11 cycles. Heristchi and Mouradian [2009] and Plyusnina [2010] analyzed the variation of solar differential rotation in northern and southern hemispheres with time, but found no N-S asymmetry in cycles 19-23. This is probably due to the tracers they used. Heristchi and Mouradian [2009] used the daily sunspot numbers, which do not carry sufficient longitude information since they are smoothed over the whole solar disc. Similarly, Plyusnina [2010] used the daily values of sunspot group areas summed over the whole disc and also over each hemisphere. The data was smoothed in large longitude windows from 30◦ to 90◦. Javaraiah [2003a] found that the variation of A (equator rotation angular ve- locity, see Eq. 3.2) has a 90-yr periodicity and B (latitude gradient) has a 100-yr periodicity in the northern and southern hemispheres, respectively. Such long- term periodicity of the differential rotation parameters was also found in in the combination of sunspots in the two hemispheres [Javaraiah et al., 2005]. This sug- gests a long period of N-S asymmetry of solar rotation in time scale of a hundred years. The long-term periodicity of the variation of solar surface rotation is gener- ally thought to be related to the long-term trend of solar cycle (i.e., the Gleissberg cycle), which may result from the coupling of the Sun’s spin and orbital motions with respect to the center of mass of the solar system. Shorter periods (17-yr, 22 yr, 47-yr, etc.) of N-S asymmetry of solar rotation have also been proposed [Javaraiah, 2003a;b; Georgieva and Kirov, 2003; Gigo- lashvili et al., 2005]. Gigolashvili et al. [2005] found that the northern hemisphere rotates faster during even cycles (20 and 22) while the rotation of southern hemi- sphere dominates in odd ones (cycles 19 and 21). Changes in the northern and southern hemispheres could be interpreted as an oscillation with a 22-yr period. However, most other results listed in Table 5.2 do not support their observations. In Paper II, we noticed that the best fit rotation parameters obtained for longer fit intervals, e.g., 3-cycle and 6-cycle intervals, have less uncertainties and more consistent variation than the parameters obtained for shorter interval such as 1- cycle interval (see Table 5 and Fig. 5 in Paper II). The rotation parameters obtained for sunspots in last three cycles in each hemisphere in Paper II agree well with those obtained for X-ray flares for the same time period in Paper I. This gives further support to the improved method. In Paper III, we reanalyzed the sunspot data in 1874-2009 using 3-cycle running fit intervals. The results show that the average rotation rates in each hemisphere vary quite similarly during the whole time period as when using 1-cycle intervals. In earlier studies, the weight of sunspot area was used in the merit function to search for the best fit rotation parameters, giving more weight to large spots. Accordingly, the rotation parameters obtained , e.g., in Paper II are closer to the rotation of large sunspots. To study the effect of large spots, the weight in the merit function was removed in Paper III. We found that there was little difference 80 between the values of rotation parameters obtained in Paper II with weight and in Paper III without weight, and that the long-term variation of rotation in the two hemispheres agrees well with each other. The faster rotating hemispheres remain the same in the two papers during the whole time period (see Table 5.2).

◦ Fig. 5.11. The yearly rotation rates Ω17 at the average latitude of 17 . in the northern (filled circles) and southern (open circles) hemispheres obtained for 3yr-running fit inter- vals and no weighting, and smoothed over 11 points (a solar cycle). The horizontal line denotes the mean value of Ω17 over the whole time period.

In Paper II, we also found that the non-axisymmetry of sunspots decreases with increasing fit interval. This decrease most likely results from the long-term variation in solar rotation. In Paper IV, we studied the long-term variation in solar rotation using short fit intervals such as 1-yr, 3-yr and 5-yr. The long-term variation in rotation parameters obtained for 1-yr, 3-yr and 5-yr intervals also show the same pattern presented in Fig. 5.11. Figure 5.11 shows the yearly rotation rate at the average latitude of sunspots of 17◦ in each hemisphere obtained using 3-yr running fit intervals. The rotation parameters obtained for each 3-yr period are used for the middle year. The yearly parameters are smoothed over a solar cycle to show the variation pattern more clearly. The long-term evolution of the rotation in the two hemispheres obtained using such short fit intervals also show an anti-correlation. Comparing Fig. 5.11 with the right-hand side panels of Figure 5 in Paper II, one can notice that the only disagreement between the rotation parameters obtained for 3-yr intervals and those obtained for 3-cycle intervals exists in the first 3-cycle period (1890-1910). This is probably related to the extremely weak and long solar minima, during which the short interval fits may easily lose the continuous evolution of phase. During cycles 15-22, the rotation of the northern hemisphere keeps increasing while the southern hemisphere keeps decreasing. The results for this period agrees well between short and long fit intervals. 81

Fig. 5.12. North-south asymmetry (N-S)/(N+S) in Ω17 obtained from Fig. 5.11.

The difference between the rotation rates of northern and southern hemispheres obtained for 3-yr fit intervals is shown in Fig. 5.12. The two peaks of the difference in the rotation of the two hemispheres at about 1900 and 1990 suggest a long-term periodicity in N-S asymmetry of about 90 years. This supports the results of Javaraiah [2003a] who also found a 90-yr periodicity in the differential rotation parameters. 6. Summary

In this thesis we studied solar active longitudes of X-ray flares and sunspots. We noted that in earlier work the migration of active longitudes with respect to the Carrington rotation was based on rather coarse treatment. We improved the ac- curacy to less than one hour. Accordingly, not only the rotation parameters for each class of solar flares and sunspots are found to agree well with each other, but also the non-axisymmetry of flares and sunspots is found to be systematically enhanced. The non-axisymmetry of X-class flares in the last three solar cycles can reach 0.59, suggesting that 79.5% of powerful flares occur in the two active longitudes. This hightlights the importance of prediction of active longitudes of solar flares. Using the improved analysis, the spatial distribution of sunspots in 1876-2008 is studied. The non-axisymmetry of sunspots is found to be slightly improved. The statistical evidence for different rotation in the northern and southern hemispheres is greatly improved by the revised treatment. Moreover, we have given consistent evidence for the periodicity of about one century in the north-south difference. We found that the active longitudes of sunspots are well determined by short time intervals due to the variation of solar rotation. The non-axisymmetry of active longitudes determined by 3-yr fit intervals is significantly larger than obtained by 11-cycle interval. In the future work, we will study the correlation between the active longitudes of sunspots and the active longitudes of flares at short time scales, and we reexamine the flip-flop phenomenon using the improved analysis. References

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