ASYMMETRY OF THE HELIOSPHERIC MAGNETIC

FIELD

ILPO VIRTANEN

Department of Physics University of Oulu Graduate School University of Oulu Finland

Academic Dissertation to be presented with the assent of the Doctoral Training Committee of Technology and Natural Sciences of the University of Oulu for public discussion in the Auditorium GO101, Linnanmaa, on 8th November, 2013, at 12 o'clock noon.

REPORT SERIES IN PHYSICAL SCIENCES Report No. 84

OULU 2013 UNIVERSITY OF OULU

Opponent Dr. Geza Erdös, Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary

Reviewers Prof. Rudolf von Steiger, University of Bern, Switzerland Dr. Andrey G. Tlatov, Kislovodsk Mountain Astronomical Station, Russia

Custos Prof. Kalevi Mursula, University of Oulu, Finland

ISBN 978-952-62-0255-6 ISBN 978-952-62-0256-3 (PDF) ISSN 1239-4327

Juvenes Print Oulu Oulu 2013

Virtanen, Ilpo,Asymmetry of the heliospheric magnetic field

Department of Physics, University of Oulu, FinlandReport No. 84 (2013)

Abstract

This thesis studies the structure and evolution of the large scale heliospheric magneticfield. The work covers the space age, the period when satellite measurements revolution-ized our knowledge about space. Now, this period is known to be the declining phase ofthe grand modern maximum of solar activity.

The thesis addresses how the hemispherical asymmetry of solar activity is seen inthe photospheric magnetic field and how it appears in the corona and in the heliosphereuntil the termination shock. According to geomagnetic and heliospheric observations,the heliospheric current sheet has been southward shifted around the solar minima since1930s. Using Ulysses probe observations, we derive an accurate estimate of 2 for thesouthward shift of the heliospheric current sheet during two very different solar minimumin the mid 1990s and 2000s. The overall structure of the heliospheric magnetic field haschanged significantly now when the grand modern maximum has come to an end. Duringthe present low solar activity the polar fields are weaker and the heliospheric current sheetcovered a wide latitudinal range during the previous minimum. When the heliosphericcurrent sheet is wide the asymmetry is less visible at the Earth’s orbit.

We extend our study to the outer heliosphere using measurements made by Voyagerand Pioneer probes and show that the hemispherical asymmetry in the coronal holeevolution, and the related southward shift of the heliospheric current sheet, are seenuntil the termination shock. In order to understand the origin of the hemisphericalasymmetry, we complete a multipole analysis of the solar magnetic field since 1976. Wefind that the minimum time southward shift of the heliospheric current sheet is due tothe quadrupole component of the coronal magnetic field. The quadrupole term existsbecause the generation and transport of the magnetic flux in the Sun tends to proceeddifferently in the northern and southern hemispheres.

During this and the following decade the Sun is most likely going to be less active thanit has been since 1920s. Therefore it is probable that the hemispherical asymmetry ofthe heliospheric magnetic field will be less visible in the ecliptic plane in the near future.Now, when the Sun seems to be at the maximum of cycle 24, we are looking forward tosee how the polar fields and the heliospheric magnetic field are formed when approachingthe following solar minimum. It is possible that, as the activity rises again after thepresent and future low cycles, the hemispherical asymmetry will be opposite to that ofthe 20th century and the minimum time heliospheric current sheet would be northwardshifted.

Keywords: Heliospheric magnetic field, Solar wind, Solar activity, Space climate

Preface

This work has been carried out at the Department of physics of the Universityof Oulu. I wish to express my gratitude to my supervisor Prof. Kalevi Mursulafor his extensive support during these years. He has always been very patientwhen considering my disordered ideas or informal literal documents. I sincerelyappreciate the freedom of research I have enjoyed in his group.

I am grateful for the financial support by the Finnish Graduate School in Astron-omy and Space Physics, European Commission’s Seventh Framework Programme(FP7), the Department of physics of the University of Oulu and the Academy ofFinland.

The Space Physics group has been a wonderful environment to carry out thework, even though our coffee is still rather bad.

I thank my parents and childhood family, who taught me that one should alwaysthink and question to find his own solution, in life and in science.

Finally, I am much obliged to my wife Satu and our sunshine Sanni for all thelove and support.

Oulu, October 15, 2013

Ilpo Virtanen

Original publications

This thesis consists of an introduction and 4 original papers.

I Virtanen, I. I., and K. Mursula (2010), Asymmetry of solar polar fields and thesouthward shift of HCS observed by Ulysses, J. Geophys. Res., 115, A09110,doi:10.1029/2010JA015275.

II Mursula, K., and I.I. Virtanen (2011), The last dance of the bashful ballerina?,Astronomy and Astrophysics , 525 , L12+., doi: 10.1051/0004-6361/200913975

III Mursula. K. and I.I Virtanen (2012), The wide skirt of the bashful ballerina:Hemispheric asymmetry of the heliospheric magnetic field in the inner andouter heliosphere, J. Geophys. Res., doi:10.1029/2011JA017197

IV Virtanen, I. I., and K. Mursula (2013), North-south asymmetric solar cycleevolution: signatures in the photosphere and consequences in the corona,Astrophysical Journal, submitted.

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

In all papers author had a major role in data analysis and in papers I and IVauthor was also the responsible writer.

Contents

AbstractPrefaceOriginal publicationsContents1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92. Solar cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1. Sunspot cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2. Solar magnetic cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3. Other solar activity parameters . . . . . . . . . . . . . . . . . . . . 142.4. Variable solar activity . . . . . . . . . . . . . . . . . . . . . . . . . 162.5. North-south asymmetry in sunspots . . . . . . . . . . . . . . . . . 162.6. Modern grand maximum . . . . . . . . . . . . . . . . . . . . . . . . 17

3. Solar Wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.1. Solar wind acceleration . . . . . . . . . . . . . . . . . . . . . . . . . 183.2. Coronal holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3. Solar wind properties . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4. Heliospheric magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . 244.1. Coronal magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . 244.2. Models of the coronal magnetic field . . . . . . . . . . . . . . . . . 264.3. Parker’s model of the heliospheric magnetic field . . . . . . . . . . 294.4. General properties of the HMF . . . . . . . . . . . . . . . . . . . . 294.5. Ulysses measurements . . . . . . . . . . . . . . . . . . . . . . . . . 304.6. Heliospheric magnetic flux . . . . . . . . . . . . . . . . . . . . . . . 314.7. Bashful Ballerina . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

1. Introduction

Sun is our nearest star and the main source of energy in the Earth. Sun alsomaintains life in the Earth. While learning more about the Sun, we have seen thatit also causes several significant long and short term changes in our environment.Besides the academic interest in understanding natural processes, solar researchhas also become important for technology development and especially for climatechange. With growing population and decreasing resources, it has become moreand more important to understand and possibly predict the mechanisms varyingthe environment. Heliosphere is the region of space surrounding the Sun, wherephysical processes are mainly controlled by solar activity, propagated by the so-lar wind (SW), the ionized gas emerging from Sun that carries the heliosphericmagnetic field (HMF). Space weather refers to the present conditions in the he-liosphere. Strong space weather events like flares and coronal mass ejections cancause dramatic economical losses since our technology is still vulnerable to thelargest burst of solar activity causing geomagnetic storms, solar energetic particleevents, radio blackout events etc. Space climate refers to heliospheric conditionsover longer periods of time. After more than 50 years of satellite era, we havelearned a lot about the long-term change in the Sun and heliosphere. At the sametime, we have learned to exploit old records, like sunspot images and geomagneticdata sets, in order to to extend space era beyond the satellite era. Comprehensiveanalysis of these various measurements shows that during most of the the 20thcentury Sun was very active, and thereby this era is now called the grand mod-ern maximum (GMM). Besides the high overall activity during the GMM, alsothe distribution of the activity was hemispherically and longitudinally asymmet-ric. This study is about the space climate, especially north-south asymmetries inheliosphere since 1960’s.

2. Solar cycle

2.1. Sunspot cycle

Sunspots are the most important indicator of solar activity, since black regionson the surface of the Sun can be observed even by human eye. Sunspots wereobserved by eye already in the prehistoric times, but the telescope improved so-lar measurements dramatically. A few decades after the start of telescope basedsunspot measurements the sunspots practically vanished. There was a period ofabout 70 years in 1645 - 1715 almost without sunspots. Ironically this time coin-cides with the reigning period of Louis XIV of France, the Sun King. This period,now called the Maunder minimum, was also very period in Europe [Eddy , 1976].

The nature of the sunspot cycle was found by Samuel Heinrich Schwabe in 19thcentury [Schwabe, 1844; Arlt , 2011]. Using yearly values Schwabe [1844] estimatedthe length of the cycle to be ten years. Fifteen years later, using more measurementand better time resolution, the length of the cycle was defined to be about 11 years[Wolf , 1859]. After almost 400 years of sunspot measurements is known that thelength of the cycle varies between 9 and 14 years. The typical time from sunspotminimum to sunspot maximum is 4.3 years, while from maximum to minimumtime it takes 6.6 years on an average [Hargreaves, 1992]. The connection betweensolar, auroral and geomagnetic activity dramatically evidenced for the first timeduring a massive flare in September 1859 which produced enormous geomagneticdisturbances [Carrington, 1859].

Wolf defined the sunspot number, a measure of sunspot activity to be

RZ = k(10g + s) (2.1)

where s is the number of individual sunspots, g is the number of sunspot groups,and k is an observer related normalization factor [Stix , 1989]. Besides the Wolf(Zurich) sunspot number RZ there are also other definitions for sunspot activity.The group sunspot number RG is defined as follows:

RG =12.08

NΣk′iGi, (2.2)

11

where Gi is the number of sunspot groups recorded by the ith observer, k′i is theith observers correction factor, N is the number of observers used to form the dailyvalue, and 12.08 is a normalization number chosen to make the mean RG identicalwith the mean RZ for the period 1874 – 1976 [Hoyt and Schatten, 1998]. TheRG is in general considered to be the most reliable quantity of sunspot activity.Sunspot number is a very useful indicator of solar activity cycle because of itslength [Hathaway , 2010]. However, sunspot number is not a perfect representativeof the solar magnetic field, especially during long spotless periods, when sunspotnumber is continuously zero, even though solar magnetic field is not stable. Thiswas particularly the situation during the extended solar minimum after peculiarsolar cycle 23 [SIDC-team, 2012].

Fig. 2.1. Sunspot numbers since 1610. a) Monthly (since 1749) and yearly (1700 –1749) Wolf sunspot number series. b) Monthly group sunspot number series. The greyline presents the 11-year running mean after the Maunder minimum. Standard (Zürich)cycle numbering as well as the Maunder minimum (MM) and Dalton minimum (DM) areshown in the lower panel [Usoskin, 2008] .

Figure 2.1 presents the Wolf sunspot number and the group sunspot numbersince their respective starting times. Figure shows that during most of the 20thcentury the Sun was very active and the highest sunspot maximum was reachedduring solar cycle 19 in late 1950s. This active Sun episode, which started in the1940s, can be regarded as the modern grand maximum (MGM) of solar activity[Usoskin, 2008]. Grand maxima and minima refer to periods of exceptionally high

12

1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010DATE

AVERAGE DAILY SUNSPOT AREA (% OF VISIBLE HEMISPHERE)

0.0

0.1

0.2

0.3

0.4

0.5

1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010DATE

SUNSPOT AREA IN EQUAL AREA LATITUDE STRIPS (% OF STRIP AREA) > 0.0% > 0.1% > 1.0%

90S

30S

EQ

30N

90N

12 13 14 15 16 17 18 19 20 21 22 23

http://solarscience.msfc.nasa.gov/images/BFLY.PDF HATHAWAY/NASA/MSFC 2012/08

DAILY SUNSPOT AREA AVERAGED OVER INDIVIDUAL SOLAR ROTATIONS

Fig. 2.2. Butterfly diagram of sunspots, daily sunspot area averaged over individual solarrotations [Hathaway , 2012] .

or low activity with the duration of several solar cycles. Contrary to 11-year solarcycle, the occurrence of grand minima and maxima is not driven by cyclic vari-ability, but by a stochastic or chaotic process [Usoskin et al., 2007].The magnetic nature of solar eruptions was suspected already during the 19th cen-tury, but this connection was questioned by several authors. Solar magnetism wasfound by Hale [1908], who discovered that the sunspot spectral lines are shifteddue to the strong magnetic fields, the Zeeman effect. After several years of contin-uous measurements it became clear that sunspots often appear in bipolar groupsand that the polarities of leading and trailing spots remain in the same order overone solar cycle. Anyhow, from cycle to another this orientation of polarities alter-nates, leading to the 22-years magnetic cycle, also called the Hale cycle [Hale et al.,1919]. Besides the magnetic properties of sunspots, it was found that while thecycle proceeds, the location of spots tends to move from higher to lower latitudes.Drawing sunspot locations in a time-latitude coordinate system produces a figure,which resembles the wings of a butterfly. This presentation of the sunspot cycle istherefore often called the butterfly diagram [Maunder , 1904]. The butterfly dia-gram of Figure 2.2 presents the latitudinal appearance of sunspots since 1870 andshows the cyclic variation of sunspots with some differences between the cycles.The butterfly diagram shows that cycles tend to overlap during solar minimumtimes. While the old cycle is passing away at low latitudes, the new cycle appearsat high latitudes.

2.2. Solar magnetic cycle

The first solar magnetograph was build by Babcock [1953] and it offered a pos-sibility to investigate the solar photospheric magnetic field also outside sunspots.Soon it was discovered that the magnetic field covers the whole solar surface, butthe field is significantly weaker than sunspot magnetic field. During solar minimaopposite magnetic polarities cover the northern and southern polar regions while

13

during solar maxima both poles alternate their polarities [Babcock , 1959]. Halespolarity laws established the existence of a well-organized toroidal magnetic fluxsystem, which was located somewhere in the solar interior and was the sourceof sunspots. In 1919, Larmor suggested the inductive action of fluid motion asone possible explanation for the origin of sunspot magnetic field [Larmor , 1919].Larmos’s theory was confounded by Cowling’s anti-dynamo theorem, which statedthat axisymmetric flows could not, in themselves, sustain an axisymmetric mag-netic field against Ohmic dissipation [Cowling , 1933]. It took a couple of decadesto discover that the Coriolis force could impart a systematic cyclonic twist to therising turbulent fluid elements in the solar convection, so breaking the axisymme-try and circumventing Cowlings theorem [Parker , 1955]. Parker’s dynamo theorybecame one of the corner stones in the modeling of solar magnetic fields. Duringthe following decades the αΩ dynamo model was developed. The fundamental ideaof the αΩ dynamo is the Ω effect which forms the toroidal field from a poloidalseed field, and the α effect which forms the poloidal field from toroidal. The Ωeffect is produced by differential rotation and the α effect arises from the Coriolisforce. It is also required that both diffusion and convection take place in solarplasma. Sunspots are related to the amount of toroidal magnetic field, with thetoroidal magnetic flux reaching its maximum around solar cycle maximum. Inthe declining phase of the cycle the α effect returns the toroidal field to poloidaland the polar fields reach their maximum at sunspot minimum (for a review, seee.g. Charbonneau [2005]). Mean field αΩ model is still widely used and acknowl-edged, but it neglects thermally-driven turbulent convection, which is crucial inthe outer layers of the Sun [Charbonneau, 2005]. Physically more reasonable, butalso much more challenging, is to solve the equations of magnetohydrodynamicsdirectly without resorting to ill-defined parametrizations for the small scales. Di-rect numerical simulations of the solar dynamo have improved significantly duringthe last few years, and recent studies have been able to produce solar-like activitycycles [Käpylä et al., 2012].

Photospheric magnetic field have been routinely monitored since 1960s but acontinuous calibrated data series start only in the 1970s. Snapshots of the mag-netic field intensity over the whole visible disk, magnetograms, show that thereare active regions with strong magnetic fields around sunspots. Moreover, outsidethese active regions the solar surface is covered by the quiet region magnetic net-work, formed by stronger magnetic fields around the convection cell boundaries.A common format to present the structure of the photospheric magnetic field isthe synoptic map, which shows the field over the whole (360) solar surface in alongitude-latitude chart. The photospheric magnetic field is so far measured onlyfrom the Earth’s vantage point. Therefore measurements during one full solarrotation are needed to collect one synoptic chart. However, during this periodmagnetic field may vary significantly, so that the synoptic chart does not give amomentary structure of the solar magnetic field at any moment of time.

Similarly to the sunspot butterfly diagram, the magnetic butterfly diagrampresents the longitudinal averages of the photospheric magnetic field for each rota-tion [Harvey , 1992]. Figure 2.3 presents the butterfly diagram of the photosphericmagnetic field. It looks quite similar to the sunspot butterfly diagram since active

14

Fig. 2.3. Butterfly diagram of the photospheric magnetic field [Hathaway , 2012] .

regions and sunspots are closely connected. Figure 2.3 shows that at the start of anew solar cycle the active regions are located at mid-latitudes, and while the cycleproceeds, active regions move to lower latitudes. The leading part of active regionapproaches the equator after the solar maximum. Since the polarity of the leadingpart in a northern and southern hemisphere is different, cancellation of the fluxover the equator increases while the cycle proceeds. Although sunspots occurrenceregions move practically only towards the equator, the magnetic butterfly diagramshows that some parts of active regions also travel towards the poles. Polewardtransport of the trailing part of the active regions is called the meridional circula-tion and it cancels the old polarity of the polar regions. Solar minimum is reachedwhen polar fields are oriented according to the polarity of the new cycle and equa-torial active regions have mainly disappeared [Leighton, 1964; Charbonneau, 2005].

2.3. Other solar activity parameters

Besides sunspots, there are several other parameters that have been measured overseveral decades and that describe solar activity. Figure 2.4 shows the daily valuesof sunspot number, F10.7 radio flux and total solar irradiance composition sincethe late 1970’s. The 10.7 cm (2800 MHz) solar radio wave emission, often calledthe F10.7 radio flux, has been measured since 1946 [Tapping , 1987]. Measurementsin radio waves are not affected by weather conditions and the data series is there-fore almost continuous. The F10.7 flux is related to the magnetic active regions,especially sunspots, but it also originates from the background magnetic network.This was explicitly shown during the extended solar minimum after solar cycle 23,when sunspots mainly disappeared, but the F10.7 flux remained at the level of

15

1980 1985 1990 1995 2000 2005 20100

100

200

300Daily sunspot number

1980 1985 1990 1995 2000 2005 2010

100

200

300

400F10.7 radio flux

1980 1985 1990 1995 2000 2005 20101362

1364

1366

1368

PMOD total solar irradiance composition

Fig. 2.4. Daily values of sunspot number, F10.7 radio flux and total solar irradiancecomposition.

about 30% of the maximum value. The F10.7 flux is often considered as a bestproxy for solar activity since it correlates very well with the sunspot number. How-ever, the relation between sunspot numbers and F10.7 changed around 2000/2001,when sunspot activity became smaller than F10.7 [Lukianova and Mursula, 2011],suggesting a fairly discontinuous change in solar behavior after the maximum ofcycle 23 [Tapping and Valdés, 2011]. Figure 2.4 shows also that daily variationsare smaller in the F10.7 flux than in sunspot number.

The solar activity parameter which is the most important for life on the Earth,the total solar irradiance (TSI), also correlating with the sunspot number [Fröhlichand Lean, 1998]. Besides the variations in TSI, there seems to be more significantsolar cycle variations in specific wavelengths, indicating that the shape of thesolar irradiance spectrum varies during the solar cycle [Ball et al., 2012]. Thismakes also the spectral solar irradiance (SSI) very important, especially sincesolar UV irradiance governs chemical and physical processes in the Earths upperatmosphere. Recent models of the TSI and SSI use sunspot records since 1610 andmeasured photospheric magnetic fields since 1974 as an input. Models are capableto reproduce measured TSI very reliably when using satellite magnetograms as

16

an input [Ball et al., 2011], but also ground-based measurements still give verygood agreement [Wenzler et al., 2006]. Models of the SSI are naturally much morecomplicated, but the recent advance with models connects photospheric magneticfield and spectral changes in irradiance [Krivova et al., 2007; Krivova et al., 2010;Ball et al., 2012].

2.4. Variable solar activity

The progress of the solar cycle is always basically similar, but there are also sig-nificant differences between cycles. During the last 250 years the highest monthlysunspot number reached during the cycle maximum has varied from 62 (cycle 5)to 254 (cycle 19). The shortest cycle lasted 9 years (cycle 2) and two longest ones(cycles 5 and 23) 12.6 years. Albeit cycle 4 is the longest cycle in Rz (based onproxy data), detailed analysis suggest that during this period in 1784 - 1799 therewere two cycles, the later one starting in 1793 [Usoskin et al., 2001, 2002, 2009].Solar cycle variability and especially sunspot cycle variability has been studiedfrom several aspects. One of the main goals of such studies is to predict future so-lar activity. Perhaps the most famous relationship is the Waldmeier effect in whichthe time of the rise of the sunspot number from minimum to maximum is inverselyproportional to the cycle amplitude [Waldmeier , 1939, 1955]. Even though thiseffect is widely cited, the correlation between the parameters seems to decreasesignificantly when using group sunspot number instead of the Wolf sunspot num-ber [Hathaway et al., 2002]. Dikpati et al. [2008] noted that Waldmeier effect isnot seen when considering sunspot areas. A better inverse correlation is foundbetween the cycle period and the amplitude of the following cycle [Solanki et al.,2002]. Although some solar cycle properties indicate periodicity and predictability,most of the predictions about the level of activity of cycle 24 were unsuccessful[Pesnell , 2008]. Key parameter here is the length of the solar dynamo memory,which may be less than one cycle, indicating that the amplitude of the forthcom-ing solar maximum cannot be predicted before the preceding minimum [Karak andNandy , 2012].

2.5. North-south asymmetry in sunspots

North-south asymmetry in sunspot evolution was found several decades ago [New-ton and Milsom, 1955] and has been investigated in detail by many authors ( seee.g. Temmer et al. [2006]; Zolotova and Ponyavin [2007]). The general patternsince solar cycle 19 has been the excess of sunspots in the northern hemisphereduring the rising phase of the cycle and in the southern hemisphere during thedeclining phase of the cycle [Temmer et al., 2006]. Analysis of measurementssince 1870s indicates that this asymmetry pattern experiences a phase shift everyfour cycles [Zolotova and Ponyavin, 2007]. However, before cycle 19 the asym-

17

metry was not clearly organized in different solar cycle phases and there weresignificant changes in shorter time scales. North-south asymmetries in the solarmagnetic field are naturally related to the asymmetric nature of solar dynamo.There are also clear evidences about the hemispheric asymmetry in rotation rates[Antonucci et al., 1990; Zhang et al., 2011, 2013] as well as in the meridional circu-lation [Hathaway and Rightmire, 2011], but the connection between these separatephenomenon is still mainly unknown.

2.6. Modern grand maximum

The Sun was very active over most of the 20th century. The highest activitytook place during the solar cycle 19 but the high activity period lasted from cycle15 until cycle 23. Investigation of the long-term solar activity during last 11,000years indicate that this active period was indeed exceptional and earns the namemodern grand maximum [Solanki et al., 2004; Usoskin, 2008]. The length of grandmaxima tend to be about 30 years, while the longest around 9000BC lasted about90 years. This indicated that the solar activity will most likely decrease duringthe 21st century [Solanki et al., 2004]. Solar cycle 23 started in May 1996. Thehighest monthly sunspot number was reached in March 2000 and cycle ended inDecember 2008 [SIDC-team, 2012]. Maximum of cycle 23 was reached in a typicaltime and the highest sunspot number of cycle 23 was still relatively large, followingthe trend of high solar activity during 21st century [Lockwood et al., 1999]. Thepeculiar nature of cycle 23 started to appear during the declining phase of thecycle, which was longer than for an average cycle in 20th century. Accordingto NOAA (American) sunspot records, during the minimum time after cycle 23there were 821 days when sunspots did not appear, while the number of spotlessdays during typical solar minima is about 486 days. After solar maximum in2000 sunspot magnetic field intensities become weaker and the smaller spots withshort lifetimes reduced by the factor of more than two during the declining phaseof cycle 23 [Lefèvre and Clette, 2011]. Besides these changes in sunspots, 35%decrease in the polar field strength between 1996 and 2009 was observed [Schrijverand Liu, 2008; Wang et al., 2009]. According to flux transport dynamo models,this decrease is related to 15% increase in the poleward flow speed [Wang et al.,2009]. Variations in the meridional flow speed during cycle 23 have been reported[Hathaway and Rightmire, 2011], as well as increase of the average flow speedfrom cycle 22 to cycle 23 [Ulrich, 2010]. However, especially since meridional flowspeed obtained by different instruments and methods do not agree [Ulrich, 2010],no reliable long-term statistics exist to allow an estimate of the specific nature ofmeridional flow during cycle 23.

3. Solar Wind

The solar wind is fully ionized plasma flowing outward from the solar corona to theheliosphere. Because of the extremely high conductivity of solar wind plasma, themagnetic field of solar corona is frozen in the motion of the plasma beyond the so-called source surface distance (about 2 – 5 Rs). This leads to the situation, wherethe outflowing plasma carries the solar magnetic field to the heliosphere. This isthe mechanism how the heliospheric magnetic field (HMF) is created. Because ofthis frozen-in condition, the dynamics of the heliospheric magnetic field follows thedynamics of the solar wind and there is always a close connection between HMFand solar wind.

Before the satellite era there was a hypothesis about material flowing occasion-ally outwards from the Sun. Chapman and Ferraro [1931] suggested that the Sunspits out material during solar flares. Biermann [1951] studied the behaviour ofcometary tails and found out that the shape of the tail is influenced by a particleflow from the Sun and that the flow is continuous. He concluded that the velocityof the solar wind is 500 - 1500 km/s and that during quiet times the hydrogendensity is around 100 cm−3 Biermann’s approximation for solar wind velocity waslater found to be quite reliable, and already before this hypothesis was tested, itgave many new aspects for theoretical work.

3.1. Solar wind acceleration

The first theoretical model about the expanding solar wind was published byParker [1958]. Parker’s model assumes constant solar wind temperature, onlytakes into account the effect of pressure gradient and gravitation, and neglects theelectromagnetic effects. The model includes the continuity (mass conservation)equation

∂ρ

∂t+∇ · ρu = 0, (3.1)

19

which connects the mass density ρ and the mass flux ρu, where u is the plasmavelocity. Another equation is the equation of momentum conservation

ρ∂u∂t

+ ρu · ∇u = −∇p+ ρgs. (3.2)

Assuming time independent radial flow with the same temperature for ions andelectrons the model leads to the equation(

u2 − 2kT

m

)1

u

du

dr=

4kT

mr− GMs

r2. (3.3)

Integration of 3.3 gives(u

uc

)2

− 2 ln

(u

uc

)= 4 ln

(r

rc

)+ 4

(rcr

)− 3, (3.4)

where

uc =

√2kT

m(3.5)

is the so called critical velocity and

rc =GMsm

4kT(3.6)

is the critical radius. Numerical solution of Equation 3.4 using parameter valuesapproximated for the Sun gives two physical solutions, an accelerating profile andso-called stellar-breeze. In both solutions critical velocity is reached at the criticalradius, but then plasma either accelerates or decelerates (stellar breeze). Measure-ments have shown that the temperature is around 6000 K in the solar photosphere,106 K in the corona and 105 K in 1 AU solar wind. Coronal temperature 106 K inEquations 3.4 – 3.6 gives a profile where the critical radius is 6Rs, the criticalvelocity 130 km/s and the solar wind velocity at 1 AU 480 km/s, which is a typicalmeasured value. Parker’s simplified model is still acknowledged and used in manystudies (like in Paper II). However, despite more than a half-century of study, thebasic physical processes that are responsible for heating the million-degree coronaand accelerating the supersonic solar wind are not well known [Cranmer , 2009].

3.2. Coronal holes

Coronal holes are areas, where solar coronal base density is smaller and emittedsolar wind is therefore less dense than on an average. In images of certain wave-lengths, like X-ray, UV and EUV coronal holes appear as darker regions, because ofthe lower coronal base temperature. The existence of coronal holes was discoveredfrom EUV maps in 1970s [Withbroe et al., 1971] and soon it become understood,that these are the low-density regions, where magnetic field diverges [Altschuleret al., 1972]. Measurements during Skylab mission during the declining phase of

20

Fig. 3.1. Solar corona on 3.6.2012. SDO AIA picuture at 19.3 nm wavelength, showing alarge equatorial coronal hole around central meridian.

the solar cycle 20 in 1973 – 1974 showed that solar poles are covered by coronalholes and that coronal holes are the source of fast solar wind [Zirker , 1977]. Laterstudies verified that fast solar wind originates from coronal holes where open mag-netic flux tubes expand strongly to the heliosphere [Wang and Sheeley , 1990]. Fastsolar wind sources at the coronal base in coronal holes are cooler than other solarwind sources, but after the acceleration process fast solar wind is hotter than slowsolar wind. After measurements over a full solar cycle, it was clear that duringminimum times there is mainly one large coronal hole in each polar region, butduring solar maximum coronal holes appear at any latitude and polar holes arenot developed [Hundhausen et al., 1981]. The evolution of solar wind structurerelated to the solar cycle development of the coronal holes was verified by theUlysses probe [McComas et al., 2008]. Polar coronal holes reach their maximumsize during the solar minima. Solar wind near the ecliptic plane is dominated bythe streams from polar holes during about half of the cycle. When flows frompolar coronal holes do not reach the ecliptic plane, there are flows from isolatedlow-latitude and mid-latitude coronal holes or polar coronal hole extensions whichhave a different flow character than flows from large polar holes [Luhmann et al.,2002].

The declining phase of the solar cycle 23 was exceptional also for coronal holes.The typical minimum time structure with large polar coronal holes was not reachedat the time when sunspot number was already very low. Equatorial coronal holeskept on occurring until the late declining phase of the cycle [Gibson et al., 2009].Also the size of polar coronal holes was smaller than normally. The area of thenorthern polar hole in 1996, at the beginning of solar cycle 23, was about 4.2%

21

of the total solar surface area but only about about 3.6% in 2007. The area ofthe southern polar hole was observed to be about 4.0% in 1996 and about 3.4% in2007 [Kirk et al., 2009]. The later existence of low latitude coronal holes and thesmaller polar coronal holes affected the heliospheric conditions significantly [Leeet al., 2009]. There was an exceptionally large number of high speed streams andrelated geomagnetic disturbances, as a consequence of the persistent equatorialcoronal holes [Gibson et al., 2009]. In the geomagnetic activity this was seenas a 9-day recurrence of the peak values in aa-index, which corresponds to thenonaxisymmetric structure of three high-speed streams during one 27-day solarrotation. Two of these streams come from polar coronal holes and the third onecomes from the long-lived equatorial coronal hole [Love et al., 2012].

3.3. Solar wind properties

The first in-situ solar wind measurements were made during the Soviet Luna 1mission in 1959 [Beatty , 2007], and during NASA Mariner II mission in 1962[Neugebauer and Snyder , 1962]. Solar wind has been monitored almost continu-ously since 1960s [OMNI database, 2012]. There have been several Earth-orbitingsatellites since the launch of IMP 1 satellite in 1963. The first probe located at L1point was ISEE 3 in 1978 - 1982, but continuous solar wind monitoring at L1 pointstarted in 1994 by Wind and in 1998 by ACE. Figure 3.2 shows the yearly runningmeans of solar wind velocity, proton temperature and proton density. Velocity andtemperature depict a clear solar cycle variation, but it is not straightforwardly con-nected to the sunspot cycle. The properties of solar wind plasma and magneticfield at the ecliptic plane are mainly related to the location and size of the coronalholes. Solar wind velocity at ecliptic plane typically reaches its maximum duringthe declining phase of the solar cycle, when polar coronal holes extend the lowlatitudes. Velocity reaches minimum during the ascending phase of cycle, whenpolar coronal holes are already vanishing and there is no significant amount ofequatorial coronal holes. Solar wind temperature correlates well with velocity, butplasma density is weakly anti-correlating with velocity and temperature.

Comparison between solar wind measurements and synoptic X-ray coronal mapsverified the relation between solar wind plasma properties and the location ofcoronal holes already in 1970’s [Krieger et al., 1973]. With that knowledge itwas possible to estimate solar wind properties at all latitudes. However only thein-situ measurements were able to reliably illustrate the overall structure of theheliosphere. Ulysses probe was launched in 1990, after a delay of four years dueto the disaster of space shuttle Challenger. During the mission Ulysses completedthree three polar orbits and made groundbreaking observations of the heliosphereoutside the ecliptic plane [Balogh et al., 2008]. Ulysses was set to the polar orbitusing the gravitation of Jupiter, which gave the probe the orbit with apogee at5.4AU and perigee at about 1.35 AU. During the first and the second orbit Ulyssesreached the maximum of heliographic latitude of ±80.2 during the polar passes.In the last orbit the maximum latitude was ±79.2.

22

350400450500550

Solar wind velocity, proton temperature and proton density, yearly running means.

V sw [k

m/s

]

0,5

1

1,5

T p [105 K]

1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 20152468

n p [cm

- 3 ]

Fig. 3.2. Yearly running means of solar wind velocity, proton temperature and protondensity.

Figure 3.3 shows the solar wind speed during the three Ulysses orbits as apolar plot. The first and third orbits are close to solar minima and the secondorbit around solar maximum. Ulysses measurements verify that during the solarminimum the solar wind velocity is continuously high at high latitudes, where solarwind is from polar coronal holes. At solar maximum the coronal holes can appearat any latitude and the solar wind velocity varies at all latitudes [McComas et al.,2002].

Solar wind can be characterized in two main categories, the slow wind and thefast wind [Rosenbauer et al., 1977]. Ulysses measurements verify that there aretwo separate populations of solar wind and the velocity distribution function hasa minimum at around 600km/s. When considering measurements over the wholemission in 1990 – 2008 the distribution maxima for slow and fast wind are about430km/s and 760km/s. The fast solar wind population is significantly larger duringthe solar minimum and the slow solar wind population during solar maximum,which is a direct consequence of the solar cycle evolution of polar coronal holes.At the ecliptic plane, where practically all the other probes have been located, thedistribution looks way different, since the pure fast solar wind mainly appears athigher heliographic latitudes. At low latitudes the distribution maximum followsthe maximum of slow solar wind and there is no clearly separated fast solar windpopulation [Erdös and Balogh, 2012].

If the Sun is quiet the fast solar wind origins from coronal holes, but in thecoronal mass ejections (CME) plasma velocity reaches high values and the plasmais not from coronal hole. Separation between coronal hole and CME plasma can

23

Fig. 3.3. a-c) Polar plots of the solar wind speed for Ulysses three polar orbits. Redand blue colored to indicate measured magnetic polarity. In each plot, the earliest timesare on the left (nine o’clock position) and progress around counterclockwise. From thecenter out, blended images from the Solar and Heliospheric Observatory (SOHO) Ex-treme ultraviolet Imaging Telescope (Fe XII at 1950 nm), the Mauna Loa K coronameter(700-950 nm), and the SOHO C2 white light coronagraph [McComas et al., 2008].

be done according to charge states:

O7+

O6+· C

6+

C5+

< 0.01 → coronal hole plasma

> 0.01 → plasma from other source

(3.7)

which less prone to statistical errors than other methods [von Steiger et al., 2010].Charge states remain unchanged in the solar wind plasma and thereby are relatedto the temperatures in the coronal base. Equation 3.7 actually separates the solarwind populations according to temperature of the source region. Source regiontemperature is lower and related charge state ratio is smaller in the coronal holeplasma than in the plasma from the other regions.

4. Heliospheric magnetic field

Solar magnetic field is formed in the convection layer and transported to the solarphotosphere, forming a complicated structure of magnetic network. At small spec-tral scales, this magnetic field experiences rapid chances that are still unattainableeven by the latest instrumentation.

4.1. Coronal magnetic field

Because of the extremely high conductivity, the plasma and magnetic field in theSun and heliosphere are frozen-in to each other [Alfvén, 1943]. The ratio betweenkinetic and magnetic pressures in plasma, the β∗-parameter is defined as follows

β∗ =ρv2 + nkT

B2/2µ0, (4.1)

where ρ is the plasma mass density, v is the velocity, n is the number density, Tis the temperature and B is the magnetic flux density.

The β∗-paramete defines whether the magnetic field follows the plasma motion(β∗ >> 1) or whether the plasma follows the magnetic field (β∗ < 1). In thephotosphere β∗ varies significantly depending on the strength of the magneticfield. In the chromosphere and lower corona β∗ << 1 in general and the plasmafollows the magnetic field. The height where β∗ = 1, called the Alfvén layer, variesaccording to the local magnetic field strength. For quiet regions it can be less than1.5 solar radius, but above sunspots it can reach one more than ten times higheraltitudes [Gary , 2001]. The sphere where solar wind starts to expand radially,called source surface, is roughly at the same radial distance as the average Alfvénlayer. However, source surface radius is defined semi-empirically to fit the coronalmodels with measurements. In the Alfvén layer β∗ = 1, but in the source surfacefield should expand radially, which refers the the condition, where the plasmamotion controls the magnetic field and β∗ > 1. Definition of the source surfaceis very important, since when the magnetic field starts to follow plasma motion,

25

Fig. 4.1. The solar corona in white light during the total solar eclipse of 2008 August 1[Habbal et al., 2010].

solar wind expands mainly radially and structures are mapped radially outwardsin the heliosphere.

The basic minimum time coronal magnetic configuration where closed loopsof the magnetic field appear at lower altitudes and the coronal magnetic fieldat higher altitudes expands radially was seen in early solar eclipse photographs[Pneuman and Kopp, 1971]. Figure 4.1 presents a white light image of the solareclipse in August 1, 2008, showing that the magnetic field forms closed loops untilabout one solar radius. Around the poles the field opens roughly radially overthe whole visible range. These are the polar coronal holes. The structure of thelower coronal magnetic field is complicated and the formation of the heliosphericmagnetic field in the upper solar corona is not known in detail. Between thephotosphere and the source surface the field experiences dramatic changes andthe fields of opposite polarity partly cancel each other. As a result, the magneticfield in the heliosphere, outside the source surface is roughly a "stretched dipole",especially during the solar minima. In this configuration both polarities coverroughly half of the sphere and the layer between the opposite polarities forms theheliospheric current sheet. Figure 4.1 presents the magnetic field configurationduring the negative solar minimum after the solar cycle 23, when the magneticfield points towards the Sun in the northern hemisphere (T-sector) and away fromthe Sun in the southern hemisphere (A-sector). The orientation of the dipole axis

26

was opposite in the previous solar minimum. The successive activity cycles form a22-year magnetic solar cycle. However, the dipole axis and the solar rotation axisare not exactly aligned even during solar minimum. The angle between these twoaxes, called the solar dipole tilt, varies over the solar cycle, reaching a maximumduring sunspot maximum and minimum during sunspot minimum.

4.2. Models of the coronal magnetic field

The structure of the coronal magnetic field can be seen in the solar eclipse pho-tographs or in the coronagraph images, but the field components or the line-of-sightfield intensity cannot be measured. Since the coronal magnetic field is very impor-tant for heliospheric research, including space weather forecasting, several methodshave been developed in order to to extrapolate the photospheric magnetic field tocorona. The most traditional and well-known model is the potential field sourcesurface model (PFSS) [Altschuler and Newkirk , 1969; Schatten et al., 1969]. Thismodel assumes that the field between photosphere and source surface is a potentialfield, meaning that there are no currents included. If the current density j = 0,Ampere’s law gives

∇× B = 0. (4.2)

Since the magnetic field is always sourceless,

∇ · B = 0 (4.3)

these two equations lead to the Laplace equation

∇2φ = 0, (4.4)

where φ refers to the scalar potential of the magnetic field. The PFSS model re-quires two boundary conditions, the measured photospheric magnetic field and theassumption that field at the source surface (typically at 2.5 solar radius) is purelyradial. Traditional magnetographs can only measure the line-of-sight componentof the photospheric magnetic field. Since information of the field direction is nat-urally required, it is most often assumed in the PFSS model that the photosphericmagnetic field is radial [Wang and Sheeley , 1992]. With these boundary conditionsthe Laplace equation has a well known solution in terms of spherical harmonics[Wilcox Solar Observatory , 2009]:

Br(r, θ, φ) =

∞∑n=1

n∑m=0

Pmn (cos θ)(gmn cosmφ+ hm

n sinmφ)C(r, n), (4.5)

Bθ(r, θ, φ) = −∞∑

n=1

n∑m=0

∂Pmn

∂θ(cos θ)(gmn cosmφ+ hm

n sinmφ)D(r, n), (4.6)

27

Bφ(r, θ, φ) =

∞∑n=1

n∑m=0

Pmn (sin θ)(gmn cosmφ− hm

n cosmφ)D(r, n), (4.7)

where Pmn (cos θ) are the associated Legendre functions and r is the radial distance

and

C(r, n) =

(Rs

r

)n+2

n+ 1 + n(

rrss

)2n+1

n+ 1 + n(

Rs

rss

)2n+1

, (4.8)

D(r, n) =

(Rs

r

)n+2

1−(

rrss

)2n+1

n+ 1 + n(

Rs

rss

)2n+1

. (4.9)

Radial functions C(r, n) and D(r, n), where Rs is the solar radius and rss is thesource surface radius (2.5 Rs), fulfill the condition of purely radial magnetic fieldat r = rss.

Harmonic coefficients gmn and hmn are solved as follows:

gmnhmn

=

2n+ 1

X · Y

X∑i=1

Y∑j=1

Bphotj,i

sin θiPmn (cos θi)

cos(mφj)sin(mφj)

(4.10)

where Bphotj,i refers to the measured photospheric line-of-sight value at bin (i,j),

and sin(θi)−1 term comes from the assumption of the radial magnetic field in the

photosphere. Denominator X · Y counts the number of surface elements in thesynoptic map, which has X data bins in sine latitude and Y in longitude. One freeparameter for model solution is n, the highest order of the multipole expansion 4.5- 4.7. In WSO model n = 9, but for example Wang and Sheeley [1992] truncatethe multipole at n = 17. Figure 4.2 shows the synoptic map of the photosphericline-of-sight field and the PFSS model at 2.5 RS for Carrington rotation 2000.

The reliability of the PFSS model has been widely criticized since the modelneglects the effect of currents and includes only low orders of the magnetic fieldstructure. Moreover the magnetograph data sets suffer from a well-known satura-tion effect and from the por visibility of the opposite magnetic hemisphere of theSun, the so-called vantage point effect [Svalgaard et al., 1978; Ulrich et al., 2002;Sun et al., 2011]. Anyhow, despite the known weaknesses of the model, PFSS isstill a fair tool in predicting the polarity of the large scale coronal and heliosphericmagnetic field [Paper II], especially when comparing the quality of the model withthe simplicity of the model or the time needed for calculations [Riley et al., 2006].

In practical use, models of the coronal magnetic field are particularly importantfor the heliospheric models and space weather forecasts. Heliospheric magneticfield structure and solar wind composition and velocity are mainly radially mappedstructures of the coronal magnetic field. Space weather models typically combinea coronal model and a model for the heliospheric propagation of solar wind and

28

50 100 150 200 250 300 350

−50

0

50

Measured line−of−sight magnetic field in the photosphere

Latit

ude

−500

0

500

50 100 150 200 250 300 350

−50

0

50

Potential field extrapolation at 2.5 Rs

Carrington longitude

Latit

ude

−10

0

10

Fig. 4.2. Upper panel: Synoptic map of the line-of-sight component of the photosphericmagnetic field measured at WSO during Carrington rotation 2000. Lower panel: Radialcomponent of the PFSS model at the source surface (2.5Rs).

related magnetic field. A simple method to approximate the solar wind velocityat the source surface is to calculate the so-called flux tube expansion factor, whichrefers to the ratio between the radial magnetic field strength in the photosphereand in the corona [Wang and Sheeley , 1990]. Since coronal holes are regions ofthe open (roughly radial) magnetic field configuration and sources of the fast solarwind, there is an inverse correlation between the expansion factor and the solarwind velocity. Methods to derive the solar wind speed at the source surface and thesolar wind propagation in the heliosphere are typically semi-empirical [Arge andPizzo, 2000]. Data assimilation methods are often used since physical processes inthe corona are still not known in detail [Arge et al., 2010].

Physical processes in the corona are complicated and not known in detail, butoutside the source surface the plasma motion starts dominating the structure ofthe magnetic field and the radial evolution is more easily predicted [Zhao et al.,2005]. In the literature the heliospheric magnetic field (HMF) is still often calledthe interplanetary magnetic field (IMF). Term IMF dates back to time, when itwas not known, how far away from the Sun the solar wind carries the magneticfield. Anyhow, Voyager 1 and 2 missions have expanded our knowledge about theHMF and it is now known, that the heliospheric termination shock where solarwind starts to decelerate is located at about 100 AU , depending on the solarcycle phase, heliographic latitude and longitude [Stone et al., 2005, 2008]. Theoutermost layer of the heliosphere was found in August 25th 2012, when Voyager1 may have left the helioshpere at 121.7 AU [Webber and McDonald , 2013].

29

4.3. Parker’s model of the heliospheric magnetic field

The basic theory of the HMF was published by Parker [1958]. In this famouspublication Parker first presents the mechanism of the solar wind acceleration andthen derives the related HMF configuration, assuming infinite plasma conductivityand related frozen-in condition between the plasma and the magnetic field. Theseassumptions and the measured solar rotation lead to the spiral structured wherefield behaves like

B = Bss

(rssr

)2(r +

vφ − rΩ

vrcosλφ

)(4.11)

where Bss is the magnetic field at source surface rss, vr and vφ are radial andtangential components of the solar wind velocity, Ω is the angular velocity of theSun and λ is the latitude. At large distances, where vφ << rΩ the angle betweenB and r, called spiral angle δ, gets the form

tan δ =rΩ

vr. (4.12)

At the source surface the field is mainly radial, but already at 1 AU at the equatorthe δ is about 45 and, while the distance from the Sun increases, HMF becomesmore and more tangential. Tangential component is largest at the equator anddecreases according to cos θ-term when moving to higher latitudes. According toParker’s model the HMF is purely radial over the poles and the polar componentis zero in general.

4.4. General properties of the HMF

The first satellite missions reaching te heliosphere showed that at the ecliptic planethe HMF consists of sectors of both polarities, the magnetic field pointing towardsthe Sun (T-sector) and away from the Sun (A-sector) [Wilcox and Ness, 1965].The polarity pattern was found to repeat with solar rotation period, which verifiedthe solar origin of the heliospheric magnetic field [Ness and Wilcox , 1964]. Aftermultiple satellite measurements in 1962 – 1969 Rosenberg and Coleman [1969] con-cluded, that both sectors (polarities) appear during each solar rotation. However,during the spring (fall) time, when Earth is in the heliographic south (north), thepolarity that is dominating the south (north) pole in the photosphere appears moreoften in the heliosphere as well. This regulation, now called called the Rosenberg-Coleman rule, is valid around solar minima, when the heliospheric magnetic fieldhas the stretched dipole type structure. Satellite measurements in 1960s verifiedthat during solar minimum one polarity mainly covers the northern hemisphere inthe heliosphere and another polarity covers the southern hemisphere. The layerbetween polarities, the heliospheric current sheet (HCS), is the continuation of thecoronal magnetic equator to the heliosphere. Since both polarities appear oftenseveral times during each solar rotation although Rosenberg-Coleman rule holds,

30

it is so that the HCS is located around the heliographic equator but is not flat. Be-cause of its wavy structure, HCS is often called the ballerina skirt. Probes flying inthe outer heliosphere have verified that the structure of the HMF at low latitudesis mainly following Parker’s model. From the source surface until the terminationshock, and even beyond, the large scale HMF structure is mainly mapped radiallyoutwards [Burlaga et al., 1984, 2002]. The same observation was also concludedin Paper III.

4.5. Ulysses measurements

The first out-of-ecliptic measurements of the HMF were made by Ulysses [Baloghet al., 2008]. After Jupiter flyby in 1992 the probe attained a polar orbit aroundthe Sun. Ulysses observed a typical HMF sector structure at low latitudes, butin June 1993 the probe moved for the first time in to the unipolar region at 30southern latitude [Smith et al., 1993]. This disappearance of the sector structurewas due to the increasing latitude of the probe and the decreasing HCS tilt dueto declining solar activity. The probe completed the first pole-to-pole fast latitudescan in 1994 – 1995, measuring the HMF from −80.2 to 80.2 latitude in 322 days.Measurements during the first fast latitude scan showed that the radial componentof the HMF is practically independent of latitude [Smith and Balogh, 1995]. Atfirst large scales the Ulysses measurements agree with the predictions by Parker’smodel, but at small scales strongly deviates from Parker’s spiral [Smith et al.,2000a; Schwadron, 2002]. Also the large scale field does not exactly follow Parker’sprediction. High latitude measurements showed some deviation from the expectedvalues and a small as north-south asymmetry in both spiral and meridional angleof the HMF was noted [Forsyth et al., 1996]. During the first orbit of the probe in1992 – 1998 the spiral angle tended to be larger than expected at high southernhigh and the meridional angle distribution showed an unexpected double peakstructure at high northern latitudes [Forsyth et al., 2002]. These deviations aremost likely due to large scale Alfvén waves or HMF foot point motion acrosscoronal hole boundaries [Forsyth et al., 2002; Schwadron and McComas, 2005].

In Paper I we calculate the cumulative flux density for each Ulysses fast latitudescan. These results give a clear picture about the large scale structure of HMF in1994 – 1995, 2000 – 2001 and 2007. The first fast latitude scan took place dur-ing the solar minimum and Ulysses mainly observed the T-sector in the southernhemisphere and the A-sector in the northern hemisphere. HCS was found to berelatively flat, with both polarities appearing roughly between -15 and +18 lati-tude. During the next fast latitude scan in 2000 – 2001 the HMF had a maximumtype structure and both polarities appeared at any latitude. Both sectors appearedmainly once during each solar rotation, which indicated tilted dipole type HMFstructure for maximum time as well [Smith et al., 2001]. The last scan took placein 2007 during the late declining phase of solar cycle 23. The large scale field wasreversed to the previous minimum, with T-sector dominating in the north andA-sector in the south. The HCS region was found to be much wider than during

31

the previous minimum, both polarities appearing between -28 and +24 latitude.Ulysses measurements and previous studies with IMP 8 and Voyager data showedthat the width of the HCS varies from minimum to another. During the solarminimum in 1980’s HCS was found to be thinner than during the minimum in1970s or 1990s [Richardson and Paularena, 1997]. In Paper III we noted that theouter heliosphere probes measured more variability in sector occurrences duringthe solar minimum in the 1990s than during the two previous minima. These ob-servations are related to the weakening of the polar fields and the related weakerdevelopment of polar coronal holes during the last few decades.

4.6. Heliospheric magnetic flux

Magnetic field is sourceless according to Maxwell’s laws. Therefore, the totalsigned magnetic flux over any closed volume is zero. To estimate the magneticenergy in the heliosphere we calculate the total (unsigned) flux, i.e. the integral ofthe absolute value of HMF Br over a closed sphere. Solar cycle also modulates thetotal heliospheric magnetic flux. Total magnetic flux in the photosphere correlatesstrongly with the sunspot number, but the HMF flux has a much smaller relativevariation over the solar cycle than sunspots. The magnetic flux through the sourcesurface is easily derived from the coronal magnetic field data obtained using PFSSmodel. If we use the original measured photospheric magnetic field and the PFSSmodel as described in Equations 4.5 - 4.10, the total flux through the source surfaceis only about 1/4 of the total flux derived from HMF measurements.

This discrepancy relates to the saturation of the measured spectral lines, whichleads to underestimated values for the photospheric magnetic field. Saturatedvalues cannot be corrected individually, but by comparing measurements usingmultiple spectral lines saturating at different magnitudes, it is possible to define theaverage reduction factor for each latitude [Ulrich, 1992]. One of the most commonlatitudinal correction factors is 4.5 − 2.5 sin2 λ [Wang and Sheeley , 1995; Ulrich,1992]. After applying the latitudinal correction to the measured photosphericmagnetic field, the total flux determined with the PFSS model matches well withthe measured heliospheric flux [Wang et al., 2000].

Both coronal and HMF fluxes are mainly related to the strength of the dipolecomponent of the solar magnetic field, which also determines the area of polarcoronal holes. As shown by Ulysses observations, the HMF flux is independent oflatitude and longitude [Balogh et al., 1995]. Therefore the total flux of the HMFcan be reliably determined using the measurements of one satellite only [Owenset al., 2008]. Some time ago Lockwood et al. [2009a] suggested that, unexpectedly,the total flux in Voyager, Pioneer and Ulysses increases with r. They explainedthis excess by the kinematic effect of solar wind speed variations on the frozen-inheliospheric field [Lockwood et al., 2009b]. However, Smith [2011] used Ulyssesdata and a mathematical simulation to show that the cause of the flux excessis the replacement of Br by its modulus |Br| when calculating the total flux.The modulus rectifies some of the large amplitude magnetic field variations and

32

increases the total HMF flux in calculations. Also, the variance of the magneticfluctuations decreases less rapidly with distance than Br, which intensifies theeffect when r increases [Smith, 2011]. It has also been shown that the fluctuationsare distributed symmetrically perpendicular to the average HMF field line direction[Erdös and Balogh, 2012]. This gives a possibility to reduce the effect of thefluctuations on the measured flux density.

4.7. Bashful Ballerina

Heliospheric current sheet is the layer between the two HMF polarities. HCS isoften called the ballerina skirt, since it has typically a wavy structure, not followingthe heliographic equator. Local deflections of the HCS to higher latitudes definethe HMF sector structure measured, e.g., at 1AU. During the declining phaseand solar minima the most common HCS configuration is flat and tilted (withrespect to the heliographic equator). Since the tilt angle is typically larger thanthe maximum latitude of the Earth’s the vantage poin of about 7.2, both sectorsappear normally during each rotation. Typically even the minimum time HCSstructure is more complicated and both sectors may appear more than once duringrotation [Hoeksema et al., 1983]. HCS structure is even more complicated aroundsolar maxima. Because several coronal holes there may even be several currentsheets.

Figure 4.3 shows the polarity of the HMF from 2000 on in 2-year steps, eachsynoptic map being the first completely measured rotation of the year. Whiteindicates the polarity away from the Sun and black toward the Sun, the colorchanges at the magnetic equator, which refers to the HCS at the corona. Duringsolar maximum in 2000 and 2002 there are multiple current sheets, but while thesolar minimum approaches, HCS became less and less tilted. Tilt angle reachesthe minimum value during the solar minimum in 2008. The latitudinal extent ofthe HCS starts growing again from its minimum state as activity starts increasing(see plot for 2010).

A southward or northward shift of the HCS refers to the situation when thelongitudinally averaged latitude of HCS deviates from zero. The first evidenceof the momentary southward shift of the heliospheric current sheet (HCS) wasfound using Ulysses cosmic ray measurements during the first fast-latitude scanin mid-1990s [Simpson et al., 1996]. Cosmic ray flux in a certain energy rangeis smaller in the vicinity of the heliospheric current sheet and the latitude of shecosmic ray flux minimum marks the location of HCS. However, this pioneeringresult in the study of hemispherical asymmetry was based only on one south-northorbit of Ulysses lasting only a couple of solar rotations. Like Figure 4.3 shows, theHCS latitude is highly dependent on longitude. The momentary HCS latitude isnot representative of the longitudinally averaged HCS latitude. This problem wasquantified and discussed for the Ulysses HMF measurements in Paper I.

Crooker et al. [1997] studied the HCS location using HCS crossings measured byUlysses and Wind in March 1995 to construct a rotational map of the HCS latitude.

33

Fig. 4.3. Synoptic maps of the HMF polarity at 2.5 solar radius, according to PFSSextrapolation of the WSO data. First full Carrington rotation of each year. Whiteindicates polarity away from the Sun and black toward the Sun.

They concluded that the HCS latitude varies from +17 to -20, indicating arotation averaged southward shift of about few degrees. Surprisingly, they alsofound that at the same time coronal streamer belt was located from +13 to -4latitude, indicating an average northward shift. In order to remove the effectof temporal HMF variations in Ulysses, Smith et al. [2000b] investigated Windmeasurements at L1 point. They concluded that a smaller HMF magnitude inthe northern hemisphere indicates a roughly 10 southward shift of the HCS, inagreement with Simpson’s result. Figure 4.4 shows a rough sketch of the idea thatthe magnetic polarity dominating in the northern hemisphere is weaker and coversa larger area.

Reanalysis of HMF observations at 1 AU since 1960s showed that during solarminimum times the field with polarity from the northern heliographic hemisphereappears more often than the polarity from the southern hemisphere [Mursula andHiltula, 2003]. This proves that such a southward shift is a general long-term pat-tern, now called the bashful ballerina. Moreover, HMF sector polarities extractedfrom ground-based geomagnetic field observations showed that the HCS was shiftedsouthward even during earlier cycles, at least since solar cycle 16 [Hiltula and Mur-sula, 2006]. In paper II we show that when the Sun is more active and has strongpolar fields during minimum times and polar coronal holes with unipolar fieldsextending closer to the equator, their asymmetry can better be viewed at lowlatitudes. This analysis, based on comparison between the HMF measurementsat 1 AU and the coronal magnetic field at source surface clarified the question of

34

1088 SMITH ET AL. Vol. 533

FIG. 6.ÈSchematic of an asymmetric current sheet. This two-dimensional diagram represents conditions near the Sun where the e†ect of rotation can beneglected. Radial solar wind Ñow, which is established a few radii outside the solar corona, assures that the radial Ðeld and current sheet separatingoppositely directed Ðelds are also radial. The current sheet takes the shape of a cone or skirt rather than a plane. It divides space into two unequal volumes,unequal areas on a sphere enclosing the Sun, or unequal solid angles measured at the SunÏs center. Since the positive and negative magnetic Ñuxes mustbalance, average (south) exceeds (north) as indicated. The solar rotation axis can be considered to be inclined relative to the current sheet normal asB

RB

Rusual so that the HCS wobbles up and down, with both sectors being typically observed at low latitudes.

reported many years ago (Wilcox 1972), but the conse-quences, especially for cosmic rays, was not appreciated,nor did these ““ anomalous ÏÏ observations attract muchattention in other respects.

It is easily calculated that a deÑection of 10¡ toward thesouth will lead to a ratio, which is consistent withB

RN/B

RS,

the W ind measurements in the two sectors. The solid anglesnorth and south for a given latitude angle, d, are

)N

\ 2n(1[ sin d), )S\ 2n(1] sin d) . (1)

Hence, for an o†set angle of d \ [10¡,

BN/B

S\ (1] sin [10¡)/(1 [ sin [10¡) \ 0.70 . (2)

Figure 3 shows that averages of 2.5/3.5 \ 0.71 are in rea-sonable agreement with this ratio.

The existence of an ““ o†set ÏÏ in the solar magnetic Ðeldcan be justiÐed physically in a number of ways. One simpleexplanation is that the solar magnetic dipole is o†settoward the south pole, or equivalently a quadrupole havingthe proper sign is present in addition to the dipole. Such asituation would lead to a weaker polar cap Ðeld in the norththan in the south ; however, if the dipole Ðeld lines open intothe solar wind the magnetic Ñux issuing from the two poleswould be the same (except for sign). SuperÐcially, this con-dition would lead to weaker magnetic pressure over thenorth pole and a displacement of the neutral line andcurrent sheet northward rather than southward. However,near the Sun other considerations enter because of possibleaccompanying asymmetries in the areas of the two polarcoronal holes, the speeds of the solar wind from the poleswhich inÑuences the ram pressures, etc. In fact, one of thescientiÐc beneÐts in recognizing that north-south asym-metries can be present is the consideration of consequences

for the Sun and the global heliosphere which may result inimproved theoretical models of the di†erent regions.

The consequences of a displacement or deÑection of theHCS and of a basic north-south asymmetry in the globalheliosphere need to be assessed. Theoretical e†orts are nowunder way to incorporate an asymmetry into cosmic-raymodels. Such revisions will be simpler if the asymmetry is oflong duration, for example, longer than the time it takes thesolar wind to reach the outer boundaries of the heliosphere,so that steady state solutions are relevant. Such consider-ations also make it imperative that the presence or absenceof an asymmetry be investigated in magnetic Ðeld obser-vations and source surface calculations for intervals predat-ing the Ulysses epoch.

Preliminary simulations, based on the University ofArizona two-dimensional steady state modulation model,show that the di†erence of B between the north and southas observed by Ulysses produces a north-south asymmetryin Galactic cosmic rays of the same magnitude and natureas that observed by the cosmic-ray experiments. Thephysical cause of the e†ect is that an increase (decrease)of the magnetic Ðeld magnitude decreases (increases) thecosmic-ray transport coefficients, including both the driftvelocity and the di†usion coefficients. Hence, the hemi-sphere with the increased magnetic Ðeld (south) has areduced cosmic-ray intensity because of the reduced particletransport. A paper reporting these results in more detail isin preparation.

Joyce Wolf of JPL supported the data analysis and pre-pared the Ðgures in this report. The continuing interest ofJohn Simpson and helpful discussions with him, MingZhang, and Bruce McKibben are greatly appreciated. Dis-cussions with Andre Balogh of Imperial College are also

Fig. 4.4. Schematic of southward shifted HCS. HMF is weaker in the northern hemisphereand according to conservation of the flux, this leads to a larger area covered by thenorthern polarity and to a southward shifted HCS [Smith et al., 2000b].

small asymmetry seen in OMNI data during the declining phase of solar cycle 23when the polar fields were exceptionally weak [Wang et al., 2009]. These papersproved very reliably that the southward shift of HCS is a long-term pattern, butthe magnitude of the shift was not very well quantified.

In paper I we first scaled Ulysses HMF flux measurements to 1 AU and thencalculated the cumulative flux density for the three pole-to-pole fast latitude scans.The slope of the cumulative flux density curve gives the average value of Br in therespective hemisphere. Cumulative flux densities for minimum time fast latitudescans in 1994 – 1995 and 2007 show that the magnitude of Br in one hemispherehas very little variation from pole to mid latitudes. Moreover, during both mini-mum time fast scans, Br is weaker in the northern hemisphere. The rule of fluxconservation and a simple integration over the whole sphere show that, despite thevery different polar field magnitudes during two fast scans, the average latitudeof HCS is shifted about 2 southward from the heliographic equator during thesetwo minima. Roughly the same HCS shift of about 2 was found by Erdös andBalogh [2010] using the same data, but slightly different method.

The coronal magnetic field solved using WSO measurements of the photosphericmagnetic field and the PFSS model allows to calculate the occurrence of sector po-larities over the whole sphere. The analysis of sector occurrence indicates that thenorthern polarity dominates at the source surface and HCS was typically south-

35668 ULRICH Vol. 725

Cycle 23 average

–80 –60 –40 –20Latitude

0 20 40 60 80–20

–10

Vm

erid

(m

/s)

0

10

20

Hathaway et al. (2010)

MWO, Magnetic Corrected, Hi ResErrors - 3 × error of the mean.

Figure 10. Comparison between the Doppler-shift velocity of the gas determinedin this study with magnetic feature tracking velocities determined by Hathaway& Rightmire (2010). The MWO curve is the same as shown in Figure 7.

(A color version of this figure is available in the online journal.)

Figure 11. Comparison of the meridional circulation derived from magneticpattern tracking by Komm et al. (1993) to the more recent result presented byHathaway & Rightmire (2010) using the same technique.

(A color version of this figure is available in the online journal.)

magnetic feature rate. It is too low to be the plasma rate and doesnot have the functional shape to be the magnetic feature rate.The paper by Gizon et al. (2003) discussed the close connectionbetween the supergranulation and magnetic features so it maynot be surprising to find that this result occupies an intermediatestate between the plasma flow and the magnetic feature motions.

7. DISCUSSION AND CONCLUSIONS

This report is an extension of the work by Ulrich & Boyden(2005) which included this velocity component along with thesectoral velocities (torsional oscillations) and two componentsof the magnetic field. That work used summary data in theform of 34 × 34 point arrays and did not include the effectsof magnetic fields on the apparent velocity. The present studyutilizes 256 × 256 point arrays from a new reduction whichprovide much more detail in the meridional circulation velocity.

2 0 0 2

–20

0

20

2 0 0 1

1 9 9 8

2 0 0 0

1 9 9 9

1 9 9 7

1996

–80 – 60 –40 – 20 0 20 40 60 80

Latitude (degrees)

Vm

erid

(m

/s)

Figure 12. Meridional circulation velocity derived by Gizon & Rempel (2008)based on feature tracking of the surface supergranulation pattern plotted as bluedashed lines. The comparison lines with error bars are extracted from Figure 6above. The supergranulation feature tracking lines are derived from the periodswhen the MDI spacecraft carries out its dynamics campaign and involve onlyabout one month per year. The comparison lines from this study are yearlyaverages so the sampled times are not identical.

(A color version of this figure is available in the online journal.)

The impact of the magnetically induced, apparent velocity shiftis incorporated into the analysis. A new velocity zero point hasbeen determined from the minimum of a fit of the line-of-sightcomponent of the meridional circulation on the solar centralmeridian to a quadratic function of b − b0. This new zero pointhas increased the derived meridional circulation velocities byabout 2 m s−1 and removes an annual effect previously found.

The primary results are given in Figure 6. The time depen-dence seen in this figure confirms similar variations found byvarious methods. The meridional circulation changes sign athigh latitude for several of the years with this pattern beingpresent for a longer period following the sunspot minimum be-tween cycles 21 and 22 than for a similar period between cycles22 and 23. The average of the circulation velocity over eachcycle confirms the pattern used by Dikpati et al. (2010a) in amodel for the greater length of cycle 23 compared to cycle 22.This reversed cell may be an effect from the polar magneticfield which reach maximum strength at sunspot minimum. Ifthe reversed cell is a rebound effect, the weaker polar fields

Fig. 4.5. Comparison between the Doppler-shift velocity of the gas [Ulrich, 2010] withmagnetic feature tracking velocities [Hathaway and Rightmire, 2010].

wards shifted by a few degrees in mid-1980s and mid-1990. The largest momentary(rotational) shifts were up to 10 [Zhao et al., 2005]. In Paper IV we analyze themultipole components of the coronal magnetic field using WSO measurementsand the PFSS model. We first derive the rotationally averaged HCS latitude us-ing coronal field based on all photospheric data and then repeat the calculation ofHCS latitude using a different coronal magnetic field data, where we have removedthe g02 quadrupole component of the coronal magnetic field. Comparing these twocalculations shows clearly that the g02-term is the cause of the time southward shiftof the HCS in minimum times. After finding the multipole component behind theasymmetry, the next question is what are the sources of the coronal quadrupolecomponent in the photosphere? This can be easily answered by studying how thephotospheric field at different latitudes contributes to the g02-term. Our resultsclearly show that the g02-term is mainly related to the difference between north-ern and southern polar field intensities in the photosphere. In fact, the g02-termis mainly due to the differences between the highest northern and southern databins of WSO data. In paper IV we also discuss the formation of the asymmetry inthe photosphere’s polar fields. The magnetic butterfly diagram, and especially thesum of northern and southern fields (Figure 4 of paper IV), show that flux is trans-ported asymmetrically from active regions towards the poles. It seems that bothflux generation and transport are typically north-south asymmetric. Wang andRobbrecht [2011] suggested that north-south asymmetric production of magneticflux, which is also seen in sunspot asymmetry, leads to the polar field asymme-try. However, observations of the heliospheric magnetic field and coronal modelssuggest a slightly more complicated view to the asymmetry [Paper IV]. The essen-tial element is the north-south asymmetry in poleward flux transport. Since the

36

flux is transported polewards by the meridional flow, it is most likely that besidesthe north-south asymmetric production of the magnetic flux, also the asymmetrictransportation may significantly contribute to the observed asymmetry of polarfield intensities.

Investigation of meridional flows is rather complicated in general [Hathaway ,1996]. Three methods used are the tracking the motion of magnetic elements[Hathaway and Rightmire, 2010], investigation of the Doppler shift of spectrallines [Ulrich, 2010] and helioseismology [Gizon and Rempel , 2008]. Figure 4.5shows that the different methods seem to yield quite different results, which are notnecessary due to errors but methodological differences. Tracking the motion of themagnetic elements Hathaway and Rightmire [2011] consider single pixel elementswith absolute field strength less than 100G. Doppler method [Ulrich, 2010] ignoresall pixels with magnetic field intensity more than 20G, describing the velocity ofgas flow rather than the motion of magnetic elements. Results obtained by Dopplermethod cannot explain the polar field development, but meridional flow profilesobtained by magnetic element tracking seem to be in agreement with measuredpolar field intensities [Janardhan et al., 2010]. Moreover, the model which takesinto account meridional flows and the hemispherical asymmetry in flux generationin the active regions seems to be in agreement with the asymmetries betweennorthern and southern polar field magnitudes [Kosak et al., 2012; Rightmire-Uptonet al., 2012]. However, further studies are still needed in order to explain thedifferences between the results obtained by different methods.

5. Summary

This thesis presents a study of the structure and long-term evolution of the helio-spheric magnetic field (HMF). The most important subject studied is the north-south asymmetry of the solar magnetic field and the related southward shift of theheliospheric current sheet. In order to obtain a global picture about the asymmet-ric nature of the Sun and heliosphere, we have used measurements of the magneticfield in the photosphere and the PFSS model and satellite measurements fromseveral locations in the heliosphere. We extended our study to polar latitudes andouter heliosphere using data from the Pioneer, Voyager and Ulysses probes.

Paper I deals with Ulysses measurements of the HMF. We scaled the magneticfield radial component to 1 AU and investigated the north-south asymmetry inmagnetic flux. Results show that during the fast latitude scans in 1994 - 1995and 2006 the radial component is weaker in the northern hemisphere leading to anaverage 2 southward shift of the heliospheric current sheet. The constant valueof the shift is significant especially since these two minima have very differentintensities of polar fields. Moreover, we also studied in Paper I how the north-southasymmetry appears in Ulysses data during the HCS crossings and showed thatUlysses measurements around the current sheet are only able to determine theHCS latitude in that specific longitude where the probe crosses the HCS. Theoverall shift of the HCS cannot be reliably determined from measurements withinthe current sheet because the the probe’s high latitudinal speed at the perigee.

In paper II we used hourly HMF values of the OMNI data base since 1964and the coronal field based on the PFSS model and Wilcox solar observatorymeasurements of the photospheric magnetic field since 1976. We investigated theradial development of the HMF radial component and developed the so-calledn-value, which describes how the radial component decreases with radial distance.During the period when HCS is shifted southwards, the n-value was found to besignificantly different for the two HMF sectors. In paper II we also noted that themeasurements at the ecliptic plane depict the asymmetry less systematically forcycle 23 than for cycle 22 because the weaker polar fields in solar cycle 23 producea wider HCS region and mask the asymmetry to be clearly seen at low latitudes.

In paper III we reanalyzed the observations of the HMF made by the Pioneer10 and 11 and Voyager 1 and 2 heliospheric probes since 1972. Observations at the

38

distant probes and at 1 AU showed a very consistent picture of the HMF sectorstructure in the entire heliosphere, and even beyond the termination shock. HMFobservations by the probes also supported the southward shift of the heliosphericcurrent sheet. Pioneer 11 and Voyager 1 showed that the development of northernpolar coronal holes was very systematic and active during all the four solar minimasince mid-1970s, while Voyager 2 observations showed a less systematic and delayeddevelopment of southern coronal holes in 1980s, 1990s and 2000s. This delay inthe evolution of southern coronal holes with respect to the rapid and systematicevolution of northern coronal holes leads to a larger extent of northern coronalholes and the southward shift of the HCS for a few years in the late decliningphase of each solar cycle.

In paper IV we studied the hemispherical asymmetry in the photospheric andcoronal magnetic fields using Wilcox Solar Observatory measurements of the pho-tospheric magnetic field since 1976 and the PFSS model. Multipole analysis ofthe photospheric magnetic field shows that during the late declining phase of so-lar cycles since 1970s, the bashful ballerina phenomenon is a consequence of theg02 quadrupole term, signed oppositely to the dipole moment. Surges of new fluxtransport magnetic field from low latitudes to the poles, thus leading to a system-atically varying contribution to the g02-term from different latitudes. In the case ofa north-south asymmetric flux production this is seen as a quadrupole contribu-tion traveling towards higher latitudes. When the quadrupole term is largest, themain contribution comes from the polar latitudes. At least during the four recentsolar cycles the g02-term arises because the magnitude of the southern polar fieldis larger than in the north in the late declining to minimum phase of the cycle.

The study presented in this thesis covers several aspects about the structureand evolution of the large scale HMF since 1960s. This period, the declining phaseof the grand modern maximum, also happens to coincide with the time knownas space age, when satellite measurements revolutionized our knowledge aboutspace. Quite recently we have seen that many paradigms based on measurementsduring the active Sun are not necessary valid when the Sun is quiet. This thesisgives a clear picture of how the hemispherical asymmetry of solar activity is seenin the photospheric magnetic field and how it appears in the corona and in theheliosphere until the termination shock. Besides the hemispherical asymmetries,we also showed that the overall structure of the HMF has changed significantlywhen the grand modern maximum seems to end in 2000s. When solar activitydecreases, the polar fields become weaker and the HCS covers a wider latitudinalrange. Stronger polar fields and the thinner HCS also impact the Earth signifi-cantly. According to geomagnetic observations, the north-south asymmetry of theHMF and the southward shift of the HCS has been the persistent condition duringsolar minima since 1930s. In the following decades the Sun is most likely goingto be less active than it has been since 1920s. Then the asymmetry of the HMFwill be less visible in the satellite measurements at 1AU and in geomagnetic fields.More work is needed to understand how the north-south asymmetry is formed inthe photospheric magnetic field. The north-south asymmetry in sunspot recordsis well known, but it seems that the asymmetry in large scale photospheric mag-netic field is more complicated than in sunspots. It has been recently suggested

39

that the variations in the meridional flow speed explain variability in polar fields.Consequently, hemispherical asymmetry in meridional flow would contribute topolar field asymmetry. Now, when the Sun seems to be at the maximum phase ofthe cycle 24, we look forward to observing how the polar fields and the HMF areformed when approaching the following solar minimum. It is also possible that,after the present (and possible next) weak cycle, the more active cycles woulddepict an opposite asymmetry and a northward shifted HCS [Mursula and Zieger,2001; Paper II ].

References

Alfvén, H., On the existence of electromagnetic-hydrodynamic waves, Ark. Mat. Astron.Fys., 29 , 1–7, 1943.

Altschuler, M. D., and G. Newkirk, Magnetic Fields and the Structure of the SolarCorona. I: Methods of Calculating Coronal Fields, Solar Physics, 9 , 131–149, 1969.

Altschuler, M. D., D. E. Trotter, and F. Q. Orrall, Coronal Holes, Solar Physics, 26 ,354–365, 1972.

Antonucci, E., J. T. Hoeksema, and P. H. Scherrer, Rotation of the photospheric magneticfields - A north-south asymmetry, Astrophysical Journal , 360 , 296–304, 1990.

Arge, C. N., and V. J. Pizzo, Improvement in the prediction of solar wind conditionsusing near-real time solar magnetic field updates, Journal of Geophysical Research,105 , 10,465–10,480, 2000.

Arge, C. N., C. J. Henney, J. Koller, C. R. Compeau, S. Young, D. MacKenzie, A. Fay,and J. W. Harvey, Air Force Data Assimilative Photospheric Flux Transport (ADAPT)Model, Twelfth International Solar Wind Conference, 1216 , 343–346, 2010.

Arlt, R., The sunspot observations by Samuel Heinrich Schwabe, AstronomischeNachrichten, 332 , 805, 2011.

Babcock, H. D., The Sun’s Polar Magnetic Field., Astrophysical Journal , 130 , 364, 1959.

Babcock, H. W., The Solar Magnetograph., Astrophysical Journal , 118 , 387, 1953.

Ball, W. T., Y. C. Unruh, N. A. Krivova, S. Solanki, and J. W. Harder, Solar irradi-ance variability: a six-year comparison between SORCE observations and the SATIREmodel, Astronomy and Astrophysics, 530 , A71, 2011.

Ball, W. T., Y. C. Unruh, N. A. Krivova, S. Solanki, T. Wenzler, D. J. Mortlock, and A. H.Jaffe, Reconstruction of total solar irradiance 1974-2009, Astronomy and Astrophysics,541 , A27, 2012.

Balogh, A., E. J. Smith, B. T. Tsurutani, D. J. Southwood, R. J. Forsyth, and T. S.Horbury, The Heliospheric Magnetic Field Over the South Polar Region of the Sun,Science, 268 , 1007–1010, 1995.

Balogh, A., L. J. Lanzerotti, and S. T. Suess, The Heliosphere through the Solar ActivityCycle, Springer-Praxis Books and Springer Science+Business Media, 2008.

41

Beatty, J. K., Book Review: Russian Planetary Exploration : History, Development,Legacy, and Prospects / Springer/Praxis, 2007, Sky and Telescope, 113 , 060,000, 2007.

Biermann, L., Kometenschweife und solare korpuskularstrahlung., Zeitschrift für Astro-physics, 29 , 274–286, 1951.

Burlaga, L. F., R. P. Lepping, K. W. Behannon, and L. W. Klein, Large-scale interplane-tary magnetic fields - Voyager 1 and 2 observations between 1 AU and 9.5 AU, Journalof Geophysical Research, 89 , 10,659–10,668, 1984.

Burlaga, L. F., N. F. Ness, Y. Wang, and N. R. Sheeley, Heliospheric magnetic fieldstrength and polarity from 1 to 81 AU during the ascending phase of solar cycle 23,Journal of Geophysical Research (Space Physics), 107 , 1410–+, 2002.

Carrington, R. C., Description of a Singular Appearance seen in the Sun on September1, 1859, Monthly Notices of the Royal Astronomical Society , 20 , 13–15, 1859.

Chapman, S., and V. C. A. Ferraro, A new theory of magnetic storms, part 1, the initialphase, Journal of Geophysical Research, 36 , 171–186, 1931.

Charbonneau, P., Dynamo Models of the Solar Cycle, Living Reviews in Solar Physics,2 , 2, 2005.

Cowling, T. G., The magnetic field of sunspots, Monthly Notices of the Royal Astronom-ical Society , 94 , 39–48, 1933.

Cranmer, S. R., Coronal Holes, Living Reviews in Solar Physics, 6 , 3, 2009.

Crooker, N. U., A. J. Lazarus, J. L. Phillips, J. T. Steinberg, A. Szabo, R. P. Lepping,and E. J. Smith, Coronal streamer belt asymmetries and seasonal solar wind varia-tions deduced from Wind and Ulysses data, Journal of Geophysical Research, 102 ,4673–4680, 1997.

Dikpati, M., P. A. Gilman, and G. de Toma, The Waldmeier Effect: An Artifact of theDefinition of Wolf Sunspot Number?, Astrophysical Journal , 673 , L99–L101, 2008.

Eddy, J. A., The Maunder Minimum, Science, 192 , 1189–1202, 1976.

Erdös, G., and A. Balogh, North-south asymmetry of the location of the heliosphericcurrent sheet revisited, Journal of Geophysical Research (Space Physics), 115 , 1105,2010.

Erdös, G., and A. Balogh, Magnetic Flux Density Measured in Fast and Slow Solar WindStreams, The Astrophysical Journal , 753 , 130, 2012.

Forsyth, R. J., A. Balogh, E. J. Smith, G. Erdös, and D. J. McComas, The underlyingParker spiral structure in the Ulysses magnetic field observations, 1990-1994, Journalof Geophysical Research (Space Physics), 101 , 395–404, 1996.

Forsyth, R. J., A. Balogh, and E. J. Smith, The underlying direction of the heliosphericmagnetic field through the Ulysses first orbit, Journal of Geophysical Research (SpacePhysics), 107 , 1405, 2002.

Fröhlich, C., and J. Lean, The sun’s total irradiance: Cycles, trends and related climatechange uncertainties since 1976, Geophysical Research Letters, 25 , 4377–4380, 1998.

Gary, G. A., Plasma Beta above a Solar Active Region: Rethinking the Paradigm, Solarphysics, 203 , 71–86, 2001.

42

Gibson, S. E., J. U. Kozyra, G. de Toma, B. A. Emery, T. Onsager, and B. J. Thompson,If the Sun is so quiet, why is the Earth ringing? A comparison of two solar minimumintervals, Journal of Geophysical Research (Space Physics), 114 , A09,105, 2009.

Gizon, L., and M. Rempel, Observation and Modeling of the Solar-Cycle Variation of theMeridional Flow, Solar Physics, 251 , 241–250, 2008.

Habbal, S. R., M. Druckmüller, H. Morgan, I. Scholl, V. Rušin, A. Daw, J. Johnson, andM. Arndt, Total Solar Eclipse Observations of Hot Prominence Shrouds, AstrophysicalJournal , 719 , 1362–1369, 2010.

Hale, G. E., On the probable existence of a magnetic field in sun-spots, AstrophysicalJournal , 28 , 315–343, 1908.

Hale, G. E., F. Ellerman, S. B. Nicholson, and A. H. Joy, The Magnetic Polarity ofSun-Spots, Astrophysical Journal , 49 , 153, 1919.

Hargreaves, J. K., The solar-terrestrial environment. an introduction to geospace - thescience of the terrestrial upper atmosphere, ionosphere and magnetosphere, CambridgeUniversity Press, |c1992, 1992.

Harvey, K. L., The Cyclic Behavior of Solar Activity, in The Solar Cycle, edited by K. L.Harvey, vol. 27 of Astronomical Society of the Pacific Conference Series, p. 335, 1992.

Hathaway, Nasa Marshall Space Flight Center, http://solar-science.msfc.nasa.gov/SunspotCycle.shtml , 2012.

Hathaway, D. H., Doppler Measurements of the Sun’s Meridional Flow, AstrophysicalJournal , 460 , 1027, 1996.

Hathaway, D. H., The Solar Cycle, Living Reviews in Solar Physics, 7 , 1, 2010.

Hathaway, D. H., and L. Rightmire, Variations in the Sun’s Meridional Flow over a SolarCycle, Science, 327 , 1350–, 2010.

Hathaway, D. H., and L. Rightmire, Variations in the Axisymmetric Transport of Mag-netic Elements on the Sun: 1996-2010, The Astrophysical Journal , 729 , 80, 2011.

Hathaway, D. H., R. M. Wilson, and E. J. Reichmann, Group Sunspot Numbers: SunspotCycle Characteristics, Solar Physics, 211 , 357–370, 2002.

Hiltula, T., and K. Mursula, Long dance of the bashful ballerina, Geophysical ResearchLetters, 33 , L03,105, 2006.

Hoeksema, J. T., J. M. Wilcox, and P. H. Scherrer, The structure of the heliosphericcurrent sheet - 1978-1982, Journal of Geophysical Research, 88 , 9910–9918, 1983.

Hoyt, D. V., and K. H. Schatten, Group Sunspot Numbers: A New Solar Activity Re-construction, Solar Physics, 179 , 189–219, 1998.

Hundhausen, A. J., R. T. Hansen, and S. F. Hansen, Coronal evolution during the sunspotcycle - Coronal holes observed with the Mauna Loa K-coronameters, Journal of Geo-physical Research, 86 , 2079–2094, 1981.

Janardhan, P., S. K. Bisoi, and S. Gosain, Solar Polar Fields During Cycles 21 - 23:Correlation with Meridional Flows, Solar Physics, 267 , 267–277, 2010.

Käpylä, P. J., M. J. Mantere, and A. Brandenburg, Cyclic Magnetic Activity due toTurbulent Convection in Spherical Wedge Geometry, Astrophysical Journal Letters,755 , L22, 2012.

43

Karak, B. B., and D. Nandy, Turbulent Pumping of Magnetic Flux Reduces Solar CycleMemory and thus Impacts Predictability of the Sun’s Activity, Astrophysical JournalLetters, 761 , L13, 2012.

Kirk, M. S., W. D. Pesnell, C. A. Young, and S. A. Hess Webber, Automated detectionof EUV Polar Coronal Holes during Solar Cycle 23, Solar physics, 257 , 99–112, 2009.

Kosak, M., L. Upton, and D. Hathaway, High Latitude Meridional Flow on the Sun MayExplain North-South Polar Field Asymmetry, AGU Fall Meeting Abstracts, p. C1,2012.

Krieger, A. S., A. F. Timothy, and E. C. Roelof, A Coronal Hole and Its Identification asthe Source of a High Velocity Solar Wind Stream, Solar physics, 29 , 505–525, 1973.

Krivova, N. A., L. Balmaceda, and S. K. Solanki, Reconstruction of solar total irradiancesince 1700 from the surface magnetic flux, Astronomy and Astrophysics, 467 , 335–346,2007.

Krivova, N. A., L. E. A. Vieira, and S. K. Solanki, Reconstruction of solar spectral irra-diance since the maunder minimum, Journal of Geophysical Research: Space Physics,115 , n/a–n/a, 2010.

Larmor, J., How could a rotating body such as the Sun become a magnet?, Reports ofthe British Association, 87 , 159160, 1919.

Lee, C. O., J. G. Luhmann, X. P. Zhao, Y. Liu, P. Riley, C. N. Arge, C. T. Russell, andI. de Pater, Effects of the Weak Polar Fields of Solar Cycle 23: Investigation UsingOMNI for the STEREO Mission Period, Solar physics, 256 , 345–363, 2009.

Lefèvre, L., and F. Clette, A global small sunspot deficit at the base of the index anomaliesof solar cycle 23, Astronomy and Astrophysics, 536 , L11, 2011.

Leighton, R. B., Transport of Magnetic Fields on the Sun., Astrophysical Journal , 140 ,1547, 1964.

Lockwood, M., R. Stamper, and M. N. Wild, A doubling of the Sun’s coronal magneticfield during the past 100 years, Nature, 399 , 437–439, 1999.

Lockwood, M., M. Owens, and A. P. Rouillard, Excess open solar magnetic flux fromsatellite data: 1. Analysis of the third perihelion Ulysses pass, Journal of GeophysicalResearch, 114 , 11,103–+, 2009a.

Lockwood, M., M. Owens, and A. P. Rouillard, Excess open solar magnetic flux fromsatellite data: 2. A survey of kinematic effects, Journal of Geophysical Research, 114 ,11,104–+, 2009b.

Love, J. J., E. Joshua Rigler, and S. E. Gibson, Geomagnetic detection of the secto-rial solar magnetic field and the historical peculiarity of minimum 23-24, GeophysicalResearch Letters, 39 , 4102, 2012.

Luhmann, J. G., Y. Li, C. N. Arge, P. R. Gazis, and R. Ulrich, Solar cycle changesin coronal holes and space weather cycles, Journal of Geophysical Research (SpacePhysics), 107 , 1154, 2002.

Lukianova, R., and K. Mursula, Changed relation between sunspot numbers, solarUV/EUV radiation and TSI during the declining phase of solar cycle 23, Journalof Atmospheric and Solar-Terrestrial Physics, 73 , 235–240, 2011.

Maunder, E. W., Note on the distribution of sun-spots in heliographic latitude, 1874-1902,Monthly Notices of the Royal Astronomical Society , 64 , 747–761, 1904.

44

McComas, D. J., H. A. Elliott, J. T. Gosling, D. B. Reisenfeld, R. M. Skoug, B. E. Gold-stein, M. Neugebauer, and A. Balogh, Ulysses’ second fast-latitude scan: Complexitynear solar maximum and the reformation of polar coronal holes, Geophysical ResearchLetters, 29 , 090,000–1, 2002.

McComas, D. J., R. W. Ebert, H. A. Elliott, B. E. Goldstein, J. T. Gosling, N. A.Schwadron, and R. M. Skoug, Weaker solar wind from the polar coronal holes and thewhole Sun, Geophysical Research Letters, 35 , 18,103, 2008.

Mursula, K., and T. Hiltula, Bashful ballerina: Southward shifted heliospheric currentsheet, Geophysical Research Letters, 30 , 220,000–1, 2003.

Ness, N. F., and J. M. Wilcox, Solar Origin of the Interplanetary Magnetic Field, PhysicalReview Letters, 13 , 461–464, 1964.

Neugebauer, M., and C. W. Snyder, Solar Plasma Experiment, Science, 138 , 1095–1097,1962.

Newton, H. W., and A. S. Milsom, Note on the observed differences in spottedness of theSun’s northern and southern hemispheres, Monthly Notices of the Royal AstronomicalSociety , 115 , 398, 1955.

OMNI database, National Space Science Data Center, http://nssdc.gsfc.nasa.gov/space/,http://nssdc.gsfc.nasa.gov/space/ , 2012.

Owens, M. J., C. N. Arge, N. U. Crooker, N. A. Schwadron, and T. S. Horbury, Estimatingtotal heliospheric magnetic flux from single-point in situ measurements, Journal ofGeophysical Research, 113 , 12,103–+, 2008.

Parker, E. N., Hydromagnetic Dynamo Models., Astrophysical Journal , 122 , 293, 1955.

Parker, E. N., Dynamics of the interplanetary gas and magnetic fields, AstrophysicalJournal , 128 , 664–676, 1958.

Pesnell, W. D., Predictions of Solar Cycle 24, Solar Physics, 252 , 209–220, 2008.

Pneuman, G. W., and R. A. Kopp, Gas-Magnetic Field Interactions in the Solar Corona,Solar physics, 18 , 258–270, 1971.

Richardson, J. D., and K. I. Paularena, Streamer belt structure at solar minima, Geo-physical Research Letters, 24 , 1435–1438, 1997.

Rightmire-Upton, L., D. H. Hathaway, and K. Kosak, Measurements of the Sun’s High-latitude Meridional Circulation, Astrophysical Journal Letters, 761 , L14, 2012.

Riley, P., J. A. Linker, Z. Mikić, R. Lionello, S. A. Ledvina, and J. G. Luhmann, AComparison between Global Solar Magnetohydrodynamic and Potential Field SourceSurface Model Results, Astrophys. J., 653 , 1510–1516, 2006.

Rosenbauer, H., et al., A survey on initial results of the HELIOS plasma experiment,Journal of Geophysics Zeitschrift Geophysik , 42 , 561–580, 1977.

Rosenberg, R. L., and P. J. Coleman, Heliographic latitude dependence of the dominantpolarity of the interplanetary magnetic field, Journal of Geophysical Research, 74 ,5611 – 5622, 1969.

Schatten, K. H., J. M. Wilcox, and N. F. Ness, A model of interplanetary and coronalmagnetic fields, Solar Physics, 6 , 442–455, 1969.

45

Schrijver, C. J., and Y. Liu, The Global Solar Magnetic Field Through a Full SunspotCycle: Observations and Model Results, Solar Physics, 252 , 19–31, 2008.

Schwabe, M., Sonnenbeobachtungen im Jahre 1843. Von Herrn Hofrath Schwabe inDessau, Astronomische Nachrichten, 21 , 233, 1844.

Schwadron, N. A., An explanation for strongly underwound magnetic field in co-rotatingrarefaction regions and its relationship to footpoint motion on the the sun, GeophysicalResearch Letters, 29 , 1663, 2002.

Schwadron, N. A., and D. J. McComas, The sub-Parker spiral structure of the heliosphericmagnetic field, Geophysical Research Letters, 32 , 3112, 2005.

SIDC-team, The International Sunspot Number, Monthly Report on the InternationalSunspot Number, online catalogue, 2012.

Simpson, J. A., M. Zhang, and S. Bame, A Solar Polar North-South Asymmetry forCosmic-Ray Propagation in the Heliosphere: The ULYSSES Pole-to-Pole Rapid Tran-sit, Astrophys. J., 465 , L69+, 1996.

Smith, E. J., What causes the flux excess in the heliospheric magnetic field?, Journal ofGeophysical Research (Space Physics), 116 , 12,101, 2011.

Smith, E. J., and A. Balogh, Ulysses observations of the radial magnetic field, GeophysicalResearch Letters, 22 , 3317–3320, 1995.

Smith, E. J., M. Neugebauer, A. Balogh, S. J. Bame, G. Erdös, R. J. Forsyth, B. E.Goldstein, J. L. Phillips, and B. T. Tsurutani, Disappearance of the heliospheric sectorstructure at ulysses, Geophysical Research Letters, 20 , 2327–2330, 1993.

Smith, E. J., A. Balogh, R. F. Forsyth, B. T. Tsurutani, and R. P. Lepping, RecentObservations of the Heliospheric Magnetic Field at Ulysses: Return to Low Latitude,Advances in Space Research, 26 , 823–832, 2000a.

Smith, E. J., J. R. Jokipii, J. Kóta, R. P. Lepping, and A. Szabo, Evidence of a North-South Asymmetry in the Heliosphere Associated with a Southward Displacement ofthe Heliospheric Current Sheet, Astrophysical Journal , 533 , 1084–1089, 2000b.

Smith, E. J., A. Balogh, R. J. Forsyth, and D. J. McComas, Ulysses in the south polarcap at solar maximum: Heliospheric magnetic field, Geophysical Research Letters, 28 ,4159–4162, 2001.

Solanki, S. K., N. A. Krivova, M. Schüssler, and M. Fligge, Search for a relationship be-tween solar cycle amplitude and length, Astronomy and Astrophysics, 396 , 1029–1035,2002.

Solanki, S. K., I. G. Usoskin, B. Kromer, M. Schüssler, and J. Beer, Unusual activity ofthe Sun during recent decades compared to the previous 11,000 years, Nature, 431 ,1084–1087, 2004.

Stix, M., The Sun, an introduction, Springer, 1989.

Stone, E. C., A. C. Cummings, F. B. McDonald, B. C. Heikkila, N. Lal, and W. R. Web-ber, Voyager 1 Explores the Termination Shock Region and the Heliosheath Beyond,Science, 309 , 2017–2020, 2005.

Stone, E. C., A. C. Cummings, F. B. McDonald, B. C. Heikkila, N. Lal, and W. R.Webber, An asymmetric solar wind termination shock, Nature, 454 , 71–74, 2008.

46

Sun, X., Y. Liu, J. T. Hoeksema, K. Hayashi, and X. Zhao, A New Method for PolarField Interpolation, Solar Physics, 270 , 9–22, 2011.

Svalgaard, L., T. L. Duvall, Jr., and P. H. Scherrer, The strength of the sun’s polar fields,Solar Physics, 58 , 225–239, 1978.

Tapping, K. F., Recent solar radio astronomy at centimeter wavelengths - The temporalvariability of the 10.7-cm flux, Journal of Geophysical Research, 92 , 829–838, 1987.

Tapping, K. F., and J. J. Valdés, Did the Sun Change Its Behaviour During the Declineof Cycle 23 and Into Cycle 24?, Solar Physics, 272 , 337–350, 2011.

Temmer, M., J. Rybák, P. Bendík, A. Veronig, F. Vogler, W. Otruba, W. Pötzi, andA. Hanslmeier, Hemispheric sunspot numbers Rn and Rs from 1945-2004: cata-logue and N-S asymmetry analysis for solar cycles 18-23, Astronomy and Astrophysics,447 , 735–743, 2006.

Ulrich, R. K., Analysis of Magnetic Fluxtubes on the Solar Surface from Observations atMt. Wilson of A5250; A5233, in Cool Stars, Stellar Systems, and the Sun, edited byM. S. Giampapa and J. A. Bookbinder, vol. 26 of Astronomical Society of the PacificConference Series, p. 265, 1992.

Ulrich, R. K., Solar Meridional Circulation from Doppler Shifts of the Fe I Line at 5250Å as Measured by the 150-foot Solar Tower Telescope at the Mt. Wilson Observatory,Astrophysical Journal , 725 , 658–669, 2010.

Ulrich, R. K., S. Evans, J. E. Boyden, and L. Webster, Mount wilson synoptic magneticfields: Improved instrumentation, calibration, and analysis applied to the 2000 july 14flare and to the evolution of the dipole field, The Astrophysical Journal SupplementSeries, 139 , 259, 2002.

Usoskin, I. G., A history of solar activity over millennia, Living Reviews in Solar Physics,5 , 2008.

Usoskin, I. G., K. Mursula, and G. A. Kovaltsov, Was one sunspot cycle lost in late XVIIIcentury?, Astronomy and Astrophysics, 370 , L31–L34, 2001.

Usoskin, I. G., K. Mursula, and G. A. Kovaltsov, Lost sunspot cycle in the beginning ofDalton minimum: New evidence and consequences, Geophysical Research Letters, 29 ,2183, 2002.

Usoskin, I. G., S. K. Solanki, and G. A. Kovaltsov, Grand minima and maxima of solaractivity: new observational constraints, Astronomy and Astrophysics, 471 , 301–309,2007.

Usoskin, I. G., K. Mursula, R. Arlt, and G. A. Kovaltsov, A Solar Cycle Lost in 1793-1800:Early Sunspot Observations Resolve the Old Mystery, The Astrophysical Journal Let-ters, 700 , L154–L157, 2009.

von Steiger, R., T. H. Zurbuchen, and D. J. McComas, Oxygen flux in the solar wind:Ulysses observations, Geophysical Research Letters, 37 , 22,101, 2010.

Waldmeier, M., Die Zonenwanderung der Sonnenflecken, Astronomische Mitteilungen derEidgenössischen Sternwarte Zurich, 14 , 470–481, 1939.

Waldmeier, M., Ergebnisse und Probleme der Sonnenforschung., 1955.

Wang, Y.-M., and E. Robbrecht, Asymmetric Sunspot Activity and the Southward Dis-placement of the Heliospheric Current Sheet, The Astrophysical Journal , 736 , 136–+,2011.

47

Wang, Y.-M., and N. R. Sheeley, Jr., Solar wind speed and coronal flux-tube expansion,The Astrophysical Journal , 355 , 726–732, 1990.

Wang, Y.-M., and N. R. Sheeley, Jr., On potential field models of the solar corona, TheAstrophysical Journal , 392 , 310–319, 1992.

Wang, Y.-M., and N. R. Sheeley, Jr., Solar Implications of ULYSSES Interplanetary FieldMeasurements, The Astrophysical Journal Letters, 447 , L143, 1995.

Wang, Y.-M., J. Lean, and N. R. Sheeley, Jr., The long-term variation of the Sun’s openmagnetic flux, Geophysical Research Letters, 27 , 505–508, 2000.

Wang, Y.-M., E. Robbrecht, and N. R. Sheeley, Jr., On the Weakening of the PolarMagnetic Fields during Solar Cycle 23, The Astrophysical Journal , 707 , 1372–1386,2009.

Webber, W. R., and F. B. McDonald, Recent Voyager 1 data indicate that on 25 August2012 at a distance of 121.7 AU from the Sun, sudden and unprecedented intensitychanges were observed in anomalous and galactic cosmic rays, Geophysical ResearchLetters, 40 , 1665–1668, 2013.

Wenzler, T., S. K. Solanki, N. A. Krivova, and C. Fröhlich, Reconstruction of solarirradiance variations in cycles 21-23 based on surface magnetic fields, Astronomy andAstrophysics, 460 , 583–595, 2006.

Wilcox, J. M., and N. F. Ness, Quasi-Stationary Corotating Structure in the Interplane-tary Medium, Journal of Geophysical Research, 70 , 5793–5805, 1965.

Wilcox Solar Observatory, PFSS model documentation, http://wso.stan-ford.edu/words/pfss.pdf, 2009.

Withbroe, G. L., A. K. Dupree, L. Goldberg, M. C. E. Huber, R. W. Noyes, W. H.Parkinson, and E. M. Reeves, Coronal electron density maps for 7 march, 1970, derivedfrom mgx λ 625 spectroheliograms, Solar Physics, 21 , 272–280, 1971.

Wolf, R., Extract of a Letter to Mr. Carrington, Monthly Notices of the Royal Astronom-ical Society , 19 , 85–86, 1859.

Zhang, L., K. Mursula, I. Usoskin, and H. Wang, Global analysis of active longitudes ofsunspots, Astronomy and Astrophysics, 529 , A23, 2011.

Zhang, L., K. Mursula, and I. Usoskin, Consistent long-term variation in the hemisphericasymmetry of solar rotation, Astronomy and Astrophysics, 552 , A84, 2013.

Zhao, X. P., J. T. Hoeksema, and P. H. Scherrer, Prediction and understanding of thenorth-south displacement of the heliospheric current sheet, Journal of GeophysicalResearch, 110 , 10,101–+, 2005.

Zirker, J. B., Coronal holes and high-speed wind streams, Reviews of Geophysics andSpace Physics, 15 , 257–269, 1977.

Zolotova, N. V., and D. I. Ponyavin, Synchronization in Sunspot Indices in the TwoHemispheres, Solar Physics, 243 , 193–203, 2007.