The Sun as a Guide to Stellar Physics

The Sun as a Guide to Stellar Physics illustrates the significance of the Sun in understanding stars through an
examination of the discoveries and insights gained from solar physics research. Ranging from theories to modeling
and from numerical simulations to instrumentation and data processing, the book provides an overview of what
we currently understand and how the Sun can be a model for gaining further knowledge about stellar physics.
Providing both updates on recent developments in solar physics and applications to stellar physics, this book
strengthens the solar–stellar connection and summarizes what we know about the Sun for the stellar, space, and
geophysics communities.

• Applies observations, theoretical understanding, modeling capabilities and physical processes first revealed by the sun to the study of stellar physics
• Illustrates how studies of Proxima Solaris have led to progress in space science, stellar physics and related fields
• Uses characteristics of solar phenomena as a guide for understanding the physics of stars

• Language: English
• Publisher: Elsevier Science
• Release date: Nov 15, 2018
• ISBN: 9780128143353

Book preview

The Sun as a Guide to Stellar Physics

Editors

Oddbjørn Engvold

Professor emeritus, Rosseland Centre for Solar Physics, Institute of Theoretical Astrophysics, University of Oslo, Oslo, Norway

Jean-Claude Vial

Emeritus Senior Scientist, Institut d'Astrophysique Spatiale, CNRS-Université Paris-Sud, Orsay, France

Andrew Skumanich

Emeritus Senior Scientist, High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado, United States

Table of Contents

Cover image

Title page

Copyright

List of Contributors

Preface

Chapter 1. Discoveries and Concepts: The Sun's Role in Astrophysics

Chapter 2. Stellar and Solar Chromospheres and Attendant Phenomena

Chapter 3. The Sun's Atmosphere

Chapter 4. Helioseismic Inferences on the Internal Structure and Dynamics of the Sun

Chapter 5. Atmospheric structure, Non-Equilibrium Thermodynamics and Magnetism

Chapter 5.2. Models of Solar and Stellar Atmospheres

Chapter 5.3. Spectropolarimetry and Magnetic Structures

Chapter 6. Coronal Magnetism as a Universal Phenomenon

Chapter 7. Magnetohydrodynamics and Solar Dynamo Action

Chapter 8. Solar and Stellar Variability

Chapter 9. High-Energy Solar Physics

Chapter 10. Space Weather at Earth and in Our Solar System

Chapter 11. The Solar–Stellar Connection

Chapter 12. Instrumentation

Chapter 12.2. High-Resolution Ground-Based Observations of the Sun

Chapter 13. Solar Data and Simulations

Chapter 14. Challenges and Prospects for the Future

Author Index

Subject Index

Copyright

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Notices

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(Main image) Anatomy of the Sun - Image of the Sun showing the Corona, Chromosphere and Photosphere, with a cut-away portion showing its interior, i.e. through the Convective and Radiative Zone into the Sun's Core. Credit: Bernhard Fleck, SOHO/ESA/NASA. (Left) An image of a sunspot group near solar disk center observed with the Swedish 1-m Solar Telescope on 15 July 2002. Credit: Göran B. Scharmer and Mats G. Löfdahl, Institute for Solar Physics, Stockholm University. (Middle) Composite image of the Sun showing a Coronal Mass Ejection heading for Earth's magnetic field and an artistic view of the Earth's bullet-shaped magnetosphere. Credit: ESA/NASA/SOHO/LASCO/EIT. (Right) Coronal loops seen above the solar edge with the TRACE (Transition Region and Coronal Explorer) instrument in the light of eight times ionized Iron (Fe 17.1 nm). Credit: Alan Title, Solar Astrophysics Laboratory, Lockheed Martin Advanced Technology Center, Palo Alto, California.

List of Contributors

Thomas R. Ayres,     University of Colorado, 389-UCB (CASA), Boulder, CO, United States

Gibor Basri,     University of California, Berkeley, CA, United States

Sarbani Basu,     Yale University, Department of Astronomy, New Haven, CT, United States

William J. Chaplin,     University of Birmingham, School of Physics and Astronomy, Edgbaston, United Kingdom

Oddbjørn Engvold,     Rosseland Centre for Solar Physics, Institute of Theoretical Astrophysics, University of Oslo, Oslo, Norway

Marianne Faurobert,     University of Nice-Sophia Antipolis, Lagrange Laboratory, Nice, France

Petr Heinzel,     Astronomical Institute, Czech Academy of Sciences, Ondřejov, Czech Republic

H.S. Hudson

School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom

Space Sciences Laboratory, University of California, Berkeley, CA, United States

Neal Hurlburt,     Lockheed Martin Advanced Technology Center, Palo Alto, CA, United States

Kiyoshi Ichimoto

Astronomical Observatory, Graduate School of Science, Kyoto University, Hida Observatory, Kurabashira Kamitakara-cho, Takayama-city, Japan

National Astronomical Observatory of Japan, Solar-C Project, Mitaka, Japan

Philip G. Judge,     National Center for Atmospheric Research, High Altitude Observatory, Boulder, CO, United States

B.C. Low,     High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO, United States

Noé Lugaz,     Space Science Center and Department of Physics, University of New Hampshire, Durham, NH, United States

A.L. MacKinnon,     School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom

Hardi Peter,     Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany

E.R. Priest,     School of Mathematics and Statistics, University of St. Andrews, St Andrews KY16 9SS, United Kingdom

Alexander I. Shapiro,     Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany

Andrew Skumanich,     Senior Scientist Emeritus, High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado, United States

Sami K. Solanki

Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany

School of Space Research, Kyung Hee University, Yongin, Korea

Alan Title,     Lockheed Martin Advanced Technology Center, Physics Department Stanford University Hanover Street, Palo Alto, California, United States

Jean-Claude Vial,     Senior Scientist Emeritus, Institut d'Astrophysique Spatiale, CNRS-Université Paris-Sud, Orsay, France

Jack B. Zirker,     National Solar Observatory, Sunspot, NM, United States

Preface

It has been said that solar physics is astronomy with a zoom lens. Modern observations of the Sun yield overwhelming complex details and dynamics of its variable corona, chromosphere, photosphere, and heliosphere, with ever-increasing spatial and temporal resolution. Observations and theory have led to the entirely new field of helioseismology. The Sun is generally assumed to represent a typical case of cool, magnetically active stars. However, it remains to be proven that the Sun qualifies fully as a standard star. Solar–stellar comparisons are mutually beneficial to both fields as well for a number of fields in physics.

The aim of The Sun as a Guide to Stellar Physics is to review and illustrate how proxima solaris, where structures and time variabilities can be studied in detail from a full solar disk, have led to breakthroughs and progress in stellar science, as well as new discoveries and insight in associated areas of physics. This involves observations, theories, modeling, numerical simulations, instrumentation, and data processing. The 17 individual chapters represent various solar physics subfields. A brief overview of why interest in studying the Sun started and how is followed by more detailed descriptions and discussions of observational challenges and possibilities, a theoretical understanding, and modeling capacities behind the current level of insight and knowledge.

This book is prepared and written by solar and stellar physicists for a broader audience of interested astronomers, astrophysicists, and physicists.

The editors are most grateful to the 19 authors for their enthusiasm and willingness to contribute to the various specialized chapters. The insight and expertise of the chapter authors have been vital for the presentations of interpretations and understanding of frequently intricate interrelated solar phenomena. A multiauthor book will inevitably also risk repetitions in description and interpretation of particular phenomena in chapters covering related issues. Because authors often have their personal style and the book is aiming for a broad audience of readers, repeated descriptions and explanations of a discovery or idea as examined under different lights may be valuable to the reader.

The editors deeply thank R.M. Bonnet, J. Harvey, M. Knoelker, J. Leibacher, and S. Tremaine for their encouragements and B. Fleck for his help in this endeavor.

Oddbjørn Engvold

Jean-Claude Vial

Andrew Skumanich

Chapter 1

Discoveries and Concepts

The Sun's Role in Astrophysics

Jack B. Zirker¹, and Oddbjørn Engvold²     ¹National Solar Observatory, Sunspot, NM, United States     ²Rosseland Centre for Solar Physics, Institute of Theoretical Astrophysics, University of Oslo, Oslo, Norway

Abstract

The Sun has had an important role in the development of stellar astrophysics. The discoveries of solar magnetism, solar wind, and global acoustic vibrations, to name only a few, have launched completely new topics for research in stellar physics. In addition, concepts such as magnetic reconnection and neutrino mass first arose in attempts to explain puzzling solar phenomena.

This volume is intended to remind astronomers, physicists, and students of the Sun's key role, which is based in part on its proximity and its commonality with other stars. After a short survey of the subject, successive chapters will describe the status and future progress in several topics in solar physics that are relevant to stellar physics. We begin with the simplest characteristic of the Sun, its luminosity.

Keywords

Chemical composition; Coronal mass ejections; Earth–Sun connection; Magnetic fields; Solar cycle; Solar neutrinos

Chapter Outline

1. The Solar Constant

2. The Sun's Chemical Composition

2.1 Spectroscopic Methods

2.2 Modeling of the Sun's Atmosphere

2.3 Settling of Light Elements

3. Internal Structure and Helioseismology

3.1 Detection of Oscillatory Pattern

3.2 Interpretation of Solar Oscillations

4. The Magnetic Sun and Its Variability

4.1 Solar Cycle

4.2 Magnetic Fields

4.3 Internal Structure and Location of the Magnetic Dynamo

5. The Solar Corona and Wind

5.1 The Temperature of the Corona

5.2 The Shape of the Corona

5.3 The Solar Wind

6. Earth–Sun Connection

6.1 Aurora and Geomagnetic Storms

6.2 The Carrington Event

6.3 Solar Flares, X-Rays and Energetic Particles

6.4 Reconnection of Magnetic Fields

6.5 Coronal Mass Ejections

7. Testing Two Concepts

7.1 Neutrino Oscillations in the Sun

7.2 Testing General Relativity

8. Concluding Remarks

Acknowledgments

References

1. The Solar Constant

The amount of energy the Earth receives from the Sun is critically important to astronomers, physicists, and meteorologists. This constant is defined as the flux of energy (in watts/m²) above the Earth's atmosphere, at the mean distance of the Earth from the Sun's surface. The constant includes all electromagnetic radiation summed over all wavelengths.

The theory of stellar evolution predicts that the luminosity of the Sun changes only very slowly, over billions of years. The question is, what is its current value?

The main difficulty in determining the constant from measurements at the Earth's surface is the correction for the absorption of the atmosphere. In 1838, French physicist C. Pouillet obtained a value of 1.228  kW/m², which (perhaps by chance) was close to the best modern value. S.P Langley determined a value of 2.9  kW/m² at the top of Mount Whitney in 1884, in strong discord with Pouillet.

C.G. Abbot, who followed Langley as the director of the Smithsonian Astrophysical Observatory in 1907, spent 40  years in search of a reliable estimate. He established observing stations at high dry locations such as Mount Wilson; Bassour, Algeria; and Calama, Chile. His best estimates (1.318–1.548  kW/m²) were obtained with balloon sondes, some of which reached an altitude of 25  km. Abbot was convinced the Sun actually varied by such an amount within a few years.

Measurements of extreme precision became possible with the use of satellites and with the development of a sensitive detector, the Active Cavity Radiometer Irradiation Monitor (ACRIM). Richard C. Willson, a physicist at the National Aeronautics and Space Administration’s (NASA's) Jet Propulsion Laboratory, was principally responsible for its development.

The first series of measurements was made during the flight of the Solar Maximum Mission (1980–89). It showed a distinct decrease of about 0.06% (from 1366.5 to 1365.8  W/m² in 1980–85 and a return to 1366.6  W/m² in 1986–89) with a day-to-day noise of about 0.3%. This noise was actually the response to the appearance and disappearance of sunspots.

In a tour de force, Woodard and Hudson (1983) analyzed the first 10  months of ACRIM data and extracted 5-min oscillations of low degree (long horizontal wavelength). Frequencies, amplitudes, and line widths were obtained for individual pulsations. This result was a tribute to the precision and stability of ACRIM 1.

A succession of satellites carried improved versions of ACRIM detectors, and with extensive calibration and cross-comparisons, an 11-year record of genuine variations was pieced together (Fig. 1.1, from Foukal et al., 2006). The solar luminosity varies in step with the sunspot cycle (Willson and Hudson, 1991). The reasons for this correlation will be addressed in Chapter 8.

Figure 1.1  Active cavity radiometer irradiation monitor measurements of solar constant during 11-year sunspot cycles ( Foukal et al., 2006 ).

2. The Sun's Chemical Composition

The chemical abundance of the Sun is a fundamental yardstick in astronomy. Knowing the Sun's chemical composition became essential for discovering energy generation in the Sun and stars. The final breakthrough came in 1936 with the discovery by Hans Bethe, Charles Crichfield, and Carl Friedrich von Weizäcker of nuclear reactions taking place under the extreme pressure and temperatures in the core of the Sun (Foukal, 2004).

2.1. Spectroscopic Methods

Spectral observations of the solar photosphere are currently possible and available with very high spectral resolution and signal-to-noise ratio because of the great brightness of the source, allowing the profiles of a multitude of weak or blended absorption lines to be measured accurately. Element abundances of essentially all astronomical objects are referenced to the solar composition and basically every process involving the Sun and stars depend on their compositions. The abundance of elements in the Sun has become more extensively and reliably known than in any other star.

The German optician Joseph von Fraunhofer was the first to observe and describe the multitude of dark lines in the emission spectrum of the Sun. He designated the principal absorption features with the letters A through K, and weaker lines with lowercase letters. Physicist Gustav Kirchoff, also from Germany, realized that the dark lines corresponded to the emission lines that he and his colleague Robert Bunsen observed in emission from heated gases. Kirchhoff concluded that the lines on the spectrum of the Sun were dark because they resulted from absorption by cooler layers of gas in the Sun's atmosphere above hotter layers where the continuous emission spectrum originated. Kirchhoff's formulated the following three laws that enabled solar scientists to exploit the potential of spectrometry in chemical analysis of the Sun and subsequently in stars: (1) A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum; (2) a low-density gas excited to emit light will do so at specific wavelengths, and this produces an emission spectrum; and (3) if light composing a continuous spectrum passes through a cool, low-density gas, the result will be an absorption spectrum.

The emission spectra of elements, which could be vaporized by the Bunsen burner, were examined and compared with solar absorption line spectra. This became a truly fundamental astrophysical tool and a breakthrough in the science of astronomy. Kirchoff and Bunsen discovered lines from cesium and rubidium in the Sun. Swiss mathematician and physicist Johann Jakob Balmer observed the visible line spectrum of hydrogen and determined its wavelengths. The dominant red Fraunhofer line C, at wavelength 6563  Å, is referred to by astronomers as Hα of the Balmer series.

At a solar eclipse in India in 1868, French astronomer Pierre-Jules Janssen recorded the emission spectrum of a solar prominence, which contained a yellow line (Fraunhofer's D3) at 5875  Å, which had not yet been seen in laboratory spectra. This led Janssen and his contemporaries to conclude that it must represent a purely solar element, which soon was named helium after helios, the Greek word for Sun. In 1895, Swedish chemists Cleve and Langlet could confirm the presence of terrestrial helium gas coming out of a uranium ore called cleveite.

The availability of spectral data and an understanding of the origin of the absorption lines stimulated development of analytical techniques to determine the constitution and structure of the solar atmosphere, including its chemical composition.

2.2. Modeling of the Sun's Atmosphere

Before around 1940, calculations of solar spectral lines were based on the Schuster–Schwarzschild model of the atmosphere, in which the photosphere radiated a continuous spectrum and was overlaid by a cooler layer that resulted in pure absorption. This crude approximation, which was most appropriate to use for strong resonance lines, was often applied in combination with the so-called curve of growth technique developed by Dutch astronomer Marcel Minnaert and collaborators C. Slob and G.F.W. Mulders in the early 1930s (Goldberg et al., 1960). The curve of growth is a graph showing how the equivalent width of an absorption line, or the radiance of an emission line, increases with the number of atoms producing the line and depends on the oscillator strength of the transition.

The Milne–Eddington model is considerably more sophisticated. Here, the condition for spectral line formation, i.e., the ratio of the emission coefficient to the absorption coefficient, which is denoted the line source function, may vary with optical depth in the atmosphere. However, solar and stellar abundance determinations are only as accurate as the modeling ingredients. The most recent determinations of the solar chemical composition are based on the use of state-of-the art three-dimensional atmospheric modeling and the calculation of spectral line formation, which also accounts for departures from local thermodynamic equilibrium (Asplund et al., 2009).

A comprehensive listing of element abundances in the solar photosphere and in meteorites is provided by Nicolas Grevesse and Jacques Sauval (1998).

2.3. Settling of Light Elements

When the solar abundances of lithium, beryllium, and boron are compared with their abundances in carbonaceous chondrite meteorites, in younger stars, and in the interstellar medium, it is found that the current solar lithium abundance is about a factor of 160 lower than in the primordial material, whereas the abundances of beryllium and boron are about normal.

The variations in abundance of light elements with stellar age is associated with the existence of a subsurface convective layer in solar-type stars. The core region where nuclear fusion takes place is followed by the radiative zone out to 70% of the radius where the energy is transported outward by radiation whereas the remaining outer layer is the convection zone. A layer of thickness 0.02  Rʘ between the base of the convection zone and the top of the radiative zone is termed the solar tachocline (Elliot and Gough, 1999). This layer occurs because the inner radiative region rotates as a solid body while the convection zone rotates faster at the solar equator than near the poles.

Because lithium burns at about 2.4  ×  10⁶K whereas beryllium requires 3.5  ×  10⁶K, its surface abundance is considerably affected, because the surface convection zone reaches down to the dynamic tachocline layer, at a temperature around 2  ×  10⁶K, where some exchange of material with the radiative zone takes place. This process also explains the observed increased lithium depletion in cooler, low-mass stars, which are expected to have deeper convection zones than the Sun (Vauclaire, 1998).

An additional settling of elements will also result from the migration of elements through the interface between the convection zone and the radiative zone. A 10% reduction in helium abundance relative to hydrogen from the solar surface downward to the tachocline has been demonstrated from helioseismic studies and is explained as element migration (Grevesse and Sauval, 1998). This effect is active in both the Sun and stars.

3. Internal Structure and Helioseismology

3.1. Detection of Oscillatory Pattern

In 1960, Robert Leighton, professor of physics at Caltech, and his students (R. F. Noyes and G. W. Simon) discovered a cellular pattern of vertical oscillations of the solar surface. Within a decade, the discovery would lead to the development of a new tool for solar physics (helioseismology) and the exploration of the solar interior.

Leighton had joined the faculty in 1949 and had built a reputation as an inventive experimentalist, a keen researcher, and a fine teacher. His main scientific interest had been the decay products of cosmic rays, but in the late 1950s, he turned his attention to solar physics, specifically to the velocity fields of the solar surface.

To pursue his objective, Leighton modified an existing instrument, the spectroheliograph at Mount Wilson's 65-foot solar tower (Leighton et al., 1962). George Ellery Hale (and independently, Henri-Alexandre Deslandres) had invented this instrument in the 1890s. It was designed to form an image of the solar surface in monochromatic light and record it as a photograph.

The instrument contained two narrow slits. The first slit selected a narrow strip on the solar image and passed its white light to a second slit, which was the entrance to a monochromator. This device contained a prism or a diffraction grating that dispersed the white light and isolated a chosen spectrum line. The light from the monochromator was focused on the photographic plate. As the spectroheliograph was driven slowly across the solar image, it recorded a monochromatic image of the solar surface.

To measure vertical velocities, Leighton introduced a beam splitter just behind the exit of the monochromator and installed two glass blocks, one for each beam. The blocks could be tilted by equal amounts in opposite directions, thus shifting one beam to the red wing and the other beam to the blue wing of a symmetrical line such as Ca 6103  Å. A Doppler shift of the line thus increased the brightness in one wing and decreased the brightness in the other wing. The two monochromatic beams were recorded on a photographic plate as the spectroheliograph moved across the solar image.

After the scan was completed, the red channel on the photograph was subtracted from the blue channel by the use of a clever photographic technique. This brightness difference is proportional to the Doppler shift, or equally, the velocity of the solar surface and was recorded on a new plate. Thus, the velocity at each point in a strip of the solar image (within the length of the scanning slit) was presented as a brightness pattern. Bright elements are rising; dark elements are receding.

Successive scans were made from north to south and in reverse over a period of many minutes. When the results were examined, two global cellular patterns emerged from the data.

In large cells were detected typically 16,000-km-diameter, horizontal flows from center to boundary that persisted for several hours. The root mean square (rms) speed of the flow depended on the height of formation of the spectral line: for example, 0.4  km/s for Ca 6103  Å and 1.8  km/s for Ca II 8542  Å. The similarity to the flows in photospheric granulation suggested the name super granulation.

A second pattern of smaller cells (on the order of 2000  km) was also found. The researchers expected that the vertical velocity in such small cells would vary randomly in time. To their surprise, they found instead that cell velocity was quasioscillatory with a unique period of 296  s, a mean amplitude of 0.4  km/s, and a lifetime of at least three periods. Moreover, the cell brightness varied in phase with the velocity and with nearly the same period: bright plasma was rising and dark plasma was receding. The cell diameters increased from 1700 to 3500  km with increasing height above the surface.

3.2. Interpretation of Solar Oscillations

The authors proposed several possible explanations for the oscillations but cautioned that more and better observations would be needed to choose one. They were persuaded, however, that the oscillations were determined only on local properties of the solar atmosphere.

During the following decade, a variety of explanations were proposed for the oscillations, but none was definitive. However, Roger Ulrich, a postdoctoral student at the University of California Los Angeles, proposed in 1970 that the oscillations were the surface manifestations of a three-dimensional system of resonant acoustic waves that were trapped below the surface (Ulrich, 1970). Leibacher and Stein (1971) proposed a similar explanation.

Standing acoustic waves in a three-dimensional cavity are distinguished by their horizontal and vertical wavelengths and by their frequencies. In the Sun, the observed horizontal wavelengths of the 5-min oscillations (around 2000  km) are small compared with the solar radius, so that a plane parallel geometry is a useful approximation. The vertical wavelengths however, are determined by the steep temperature and ionization gradients below the surface. Therefore, to construct a realistic model of the standing wave system, Ulrich needed an adequate model of the deep layer below the surface. Fortunately, he had calculated just such a model for his doctoral dissertation.

Ulrich predicted that acoustic power at the surface would be observed primarily at particular combinations of horizontal wavelength (or wave number Kh) and frequency of oscillation ω. In other words, power exists only along curved lines in the Kh – ω diagram (Fig. 1.2). He wrote that previous observations of the oscillations were not long enough and did not cover a sufficient area to resolve the curved lines, and he specified the necessary limits. Deubner (1975) carried out the definitive observations and so confirmed Ulrich's theory. The rest, as they say, was history.

Figure 1.2  Observations of low-wavenumber nonradial eigenmodes of the Sun. The curved lines are theoretical ( Deubner, 1975 ; Ando and Osaki, 1977 ).

4. The Magnetic Sun and Its Variability

The Sun is far from a static state. The so-called quiet Sun that may be described by relatively restricted, simple solar and stellar models is subjected to a variety of nonstationary active processes that represent the multitude of features and characteristics of solar as well as stellar activity.

The variable Sun and subsequently its cyclic variability became known initially as a result of the German–Dutch spectacle maker Hans Lipperhey's invention of telescopes in 1608. As a result of this new invention, Galileo Galilei and a handful of contemporary scientists realized in the following years that the solar surface was blemished with dark spots and their associated bright faculae that came and went. Trackable spots on the Sun's surface informed the quick intuitive mind of Galilei and the pertinent observer and Jesuit priest Christoph Scheiner that the Sun rotates and that its axis of rotation is tilted close to 7  degrees relative to the normal to the ecliptic plane, a discovery that led to the end of the geocentric model.

Even the Sun's differential rotation was noticed by these very early scientists (Engvold and Zirker, 2016).

4.1. Solar Cycle

The 11-year solar activity cycle was first noticed by Heinrich Schwabe in 1843, who patiently recorded the number of sunspots over 17  years. This cycle, usually referred to as the Schwabe cycle, is the most prominent variability in the sunspot-number series. Rudolf Wolf of the Zürich observatory collected observations of sunspots from the 1600s onward and introduced the index known as the Zürich Wolf Sunspot number Rz, which was generally used in following years:

where g is the number of sunspot groups, n is the number of individual sunspots, and k is constant correction factor that brings each observer to a common scale. Solar activity in all of its manifestations is dominated by the 11-year Schwabe cycle, but it has a variable length of 9–14  years for individual cycles. Hoyt and Schatten (1998) derived also a more robust series of sunspot activity indices, which is based on the more easily identified sunspot groups and excluded the number of individual spots.

German astronomer Gustav Spörer noted that observations of the Sun in several decades close to 1700 revealed few sunspots. Later studies by Hoyt et al. (1994) confirmed that the Sun was well-observed during the extended period from about 1645 until 1715 and showed few spots, which J. Eddy (1976) referred as the Maunder minimum, in recognition of the impressive contribution to studies of sunspot variability by the solar astronomers Annie and Walter Maunder. The following period, from 1795 to 1823, which had a remarkably low sunspot index, he termed the Dalton minimum.

Early observations by Carrington and Spörer showed that the locations of spots migrated toward the equator throughout the cycle; these were followed up by Maunders, who visualized this phenomenon in a time–latitude histogram, which is referred to as the butterfly diagram (Maunder, 1904).

4.2. Magnetic Fields

George Ellery Hale used the powerful Snow Telescope at the Mount Wilson Observatory when he noticed Zeeman split lines in spectral observations of sunspots, and he argued that they must be magnetic in origin (Hale, 1908). Sunspots became the first astronomical objects known to harbor magnetic fields. Father and son Harold and Horace Babcock invented the magnetograph around 1950, which enabled mapping of distribution, strength of the order of 1  G, and polarity of magnetic fields over the entire solar surface. The magnetic role of all aspects of solar activity were realized and settled (Babcock and Babcock, 1955).

After the remarkable discoveries of sunspots, the Sun's activity cycle, the peculiar time–latitude pattern, and the overall magnetic link, Hale et al. (1919) showed that spots often emerged in bipolar pairs oriented roughly east–west and that most westward or leading spots in the northern hemisphere have the same magnetic polarity during a cycle. Similarly, most of those in the southern hemisphere have the opposite polarity. Hale's empirical rule provided fundamental clues about the interaction of emerging magnetic fields with the Sun's differential rotation then thought to give rise to the spots and their distribution on the solar surface.

In fact, the solar surface contains two types of magnetically active regions. There are polar and equatorial areas of the Sun, both of which are dominated by magnetic fields and structures. Work by Grotrian and Künzel (1950) showed that the polar and equatorial fluxes are comparable in magnitude.

Babcock and Livingston (1958) found that the time of maximum of the polar fields was delayed by 3  years after sunspot minimum. Sheeley (2008) used solar faculae visible on white-light images as proxies of magnetic fluxes from a much longer time period and confirmed that polar magnetic fluxes undergo a cyclic variation, disappearing at sunspot maximum and appearing in large numbers around sunspot minimum. These results serve to shed light on the poleward migration of solar magnetic fields.

The cyclic variations in intensity and distribution of magnetic flux on the solar surface demonstrate that the magnetic cycle is actually 22  years.

The maxima of individual Schwabe cycles vary considerably and it is usual to distinguish among three long-lasting episodes containing around a dozen cycles, i.e., Grand maxima, Grand minima, and episodes of regular variations (de Jager et al., 2016). A long-term trend in the Schwabe cycle amplitude is called the secular Gleissberg cycle, with the mean period of about 90  years, or rather, a modulation in the cycle envelope with a varying timescale of 60–120  years (Gleissberg, 1971; Ogurtsov et al., 2002).

The Sun's proximity and resulting traceable effects of its variable activity on the Earth, such as ¹⁴C in tree rings and ¹⁰Be in polar ice, have enabled reconstructions of solar activity on multimillennial timescales (Solanki et al., 2004; Usoskin et al., 2016). According to these reconstructions, the level of solar activity during the past 70  years is exceptional, and the previous period of equally high activity occurred more than 8000  years ago. Such reconstructed data from the previous 11,000  years show numerous activity minima of duration ranging from 50 to 150  years.

4.3. Internal Structure and Location of the Magnetic Dynamo

Our knowledge of the Sun's interior is founded solely on theoretical models based on assumptions about physical conditions and processes that are likely to prevail there. The models were later successfully confirmed via helioseismology and the measured neutrino flux from the Sun's inner core (Bahcall and Ulrich, 1988).

Eugene Parker showed how isolated toroidal magnetic flux tubes could rise from the depth of the tachocline layer (see Section 2.3) by magnetic buoyancy through the convection zone and form sunspots where they break through the solar surface (Parker, 1955). His work stimulated a search for the origin of solar magnetic fields. The Solar Dynamo action is discussed in detail in Chapter 7.

Recent progress in our understanding of the solar magnetic dynamo and the nature of the solar tachocline, have stimulated further investigation of the origin of the variable period of the Schwabe cycles and of the episodes of changing cycle amplitudes. The unusual long-lasting minimum following the previous Schwabe cycle #23 in solar activity, which is being referred to as a transitional period, has inspired further studies of long term variations in the solar tachocline (de Jager et al., 2016).

5. The Solar Corona and Wind

5.1. The Temperature of the Corona

In the centuries preceding the invention of the telescope, astronomers in Babylonia and China might have noted the appearance of a faint ring of light around the Sun during a total eclipse. They may have speculated on the source of the light. Was it some fluke of the air? Was it attached to the Moon or the Sun? Not until the total eclipse of May 22, 1724 did an Italian astronomer, Giacomo Filippo Maraldi, realize that the ring of light was a part of the Sun, because it did not follow the motion of the Moon.

Progress in understanding the nature of this corona had to await the invention of the telescope (around 1600) and the spectroscope (around 1814, by Joseph Fraunhofer). Fraunhofer found hundreds of dark lines in the spectrum of sunlight, which were later identified as absorptions by chemical elements in the solar atmosphere.

The earliest spectra of the corona, taken at total eclipse, showed these dark Fraunhofer lines. This suggested that coronal light was simply scattered photospheric light.

Then, at the total eclipse of Aug. 7, 1869, Charles Augustus Young and William Harkness independently discovered a bright line (brighter than the surrounding continuum) at a wavelength of 5303  Å. More bright lines were discovered at the 1879 eclipse and in later eclipses. Their wavelengths corresponded to no known element. Therefore, the observers postulated the existence of a new element, coronium.

The spectrum of the corona was the subject of vigorous debate until at least 1918, however (Perrine, 1918). Some astronomers claimed to observe the Fraunhofer lines in the coronal spectrum whereas others observed only a smooth continuum devoid of lines. The issue is critical. A spectrum with lines would imply that the corona is composed of small particles that scatter photospheric light. A spectrum without lines would suggest that the corona is composed of incandescent gas that emits a continuum.

Part of the confusion arose from the fact that the outer and inner corona have different spectra. In 1934, Grotrian separated the two components of the coronal light using eclipse spectra. He discovered that the K component (K for Kontinuum) is polarized and decreases in intensity rapidly with increasing distance from the Sun. He postulated that it is caused by the scattering of free electrons. The F component (F for Fraunhofer) contains dark lines and falls off slowly with the distance from the Sun. It is caused by diffraction by solid dust particles along the line of sight to the Sun. Near the Sun, the dust evaporates. Thus, the inner corona is predominantly K and the outer corona is predominantly F.

Grotrian thought he found a clue to the temperature of the electrons that produce the K corona (Grotrian, 1933). When he examined the spectrum taken at the total eclipse of 1929, he discovered that it lacked the dark lines almost entirely. However, at the wavelengths at which two exceptionally broad and dark lines of ionized calcium appeared in the spectrum of the solar disk (3933 and 3358  Å), a weak depression of the continuum appeared. It was only a few percent deep and over 100  Å wide. If confirmed, it would suggest that the particles that scatter photospheric light broaden the calcium lines almost to the point of extinction by virtue of their Doppler effect. That would imply a very high temperature for the K corona.

Unfortunately, observations at later eclipses failed to confirm Grotrian's broad, shallow depression. The precision of his measurements have also been called into question (Menzel and Pasachoff, 1968).

Grotrian was not deterred, however,. He was about to make a crucial connection. In 1939, he received preliminary measurements of the energy levels of atoms that had lost 10 or more valence electrons. Bengt Edlén, a Swedish physicist, had determined these levels from the extreme UV spectra of excited atoms. He forwarded these data to Grotrian in preparation for a report on the nebular phases of novae at the Paris meeting on novae.

Grotrian noticed that the separation of two energy levels of Fe X (nine times ionized iron) corresponded to the wavelength of the coronal red line at 6374  Å. Similarly, the separation of two levels of Fe XI corresponded to the wavelength of the coronal line at 7892  Å.

According to P. Swings (1943), Edlén became deeply interested in Grotrian's remark. From his unpublished measurements of the spectra of Ca XII and XIII, he found coincidences with two faint coronal lines at 3328 and 4086  Å. Assuming these four identifications to be correct, he predicted the forbidden lines of Fe XIII, XIV, Ni XII, and others. He found more coincidences too remarkable to be caused by pure chance.

The coronal spectrum problem was solved! These highly ionized atoms could only be formed in a plasma at temperatures of 1–3  million K.

Confirmation of the high temperature of the corona was not long in coming. On Sep. 29, 1949, Herbert Friedman and his colleagues at the US Naval Research Laboratory launched a V-2 rocket that carried an x-ray photon counter to an altitude of 150  km (Friedman et al., 1951). X-rays of 8  Å were detected above 87  km and UV radiation around 1200 and 1500  Å above 70 and 95  km, respectively. But what were the physical implications? What could heat the corona to such temperatures? Surely, the mechanism had to be nonthermal because heat does not flow from low to high temperatures. This question would challenge solar astronomers for the next 70  years (Zirker and Engvold, 2017).

The relative abundances of different stages of ionization of an element could be predicted later with the development of the nonlocal thermodynamic equilibrium theory. Stellar astrophysics has benefitted considerably from the application of the theory, as applied to atmospheres of extremely low particle density, the coronal approximation. The theory has been developed further to cover multilevel atoms and radiative transfer in denser atmospheres.

5.2. The Shape of the Corona

Before the invention of photography, observers at total eclipse could only draw a quick sketch of the corona or commit its shape to memory. The early daguerreotypes were too slow to record the extensive plumes that can be seen at totality. Despite these handicaps, French astronomer Jules Janssen noticed a change in the shape of the corona between the eclipses of 1871 and 1878. It was initially round and later enhanced mainly at the solar equator. He realized that the corona changed shape in step with the 11-year sunspot cycle that Schwabe had discovered in 1843: round in 1871 at sunspot maximum and equatorial in 1878  at minimum. This result would later suggest a magnetic framework for the structure of the corona.

5.3. The Solar Wind

Ludwig Biermann (Max Planck Institute für Naturforschung) was a theoretical astrophysicist who made important contributions to the theory of stellar convection, stellar interiors, comet nuclei, interstellar magnetic fields, and plasma physics. Around 1951, he noticed that the tails of comets always pointed away from the Sun while orbiting the Sun (Biermann, 1951). That observation led him to postulate a radial streaming of particles from the Sun. In subsequent articles, he estimated speeds of 500–1500  km/s and densities at the orbit of Earth of 500 to 10⁵ particles per cm³.

In 1958, Eugene Parker developed a gas-dynamic theory to explain Biermann's estimates. He showed how a hot corona must expand at supersonic speeds into interplanetary space. An isothermal corona of 2  million K would reach the Earth at a speed of 500  km/s. Moreover, the radial flow of ions would draw a weak dipole magnetic field into an Archimedes spiral, as seen from interplanetary space.

Parker's theory was met with considerable skepticism at first but was vindicated by the detection of the solar wind by the Soviet satellite Luna I in 1959 and by the US Mariner II en route to Venus, in 1962. The study of the wind has grown into a major subdiscipline within solar physics.

6. Earth–Sun Connection

6.1. Aurora and Geomagnetic Storms

The auroral polar light displays in the northern and southern hemispheres are now seen as the most dramatic visual feature of a whole new science referred to as space weather (cf. Chapter 10). Our current understanding of the central aspects of Earth–Sun connections is based on tireless efforts by many scientists over 250  years. The connections include several components: coronal mass ejections (CMEs), the solar wind, flare particle and x-ray emissions, geomagnetic storms, and auroras.

Northern lights, i.e., the Aurora Borealis, are one of nature's most spectacular light phenomena that can be observed with the naked eye. Through millennia, northern lights have triggered the human imagination, curiosity, and fear, as reflected in a number of mythologies from those of Nordic areas where the northern lights occur most frequently to those of North Dakota Indians and that of Tiberius Caesar Augustus in Rome, where the aurora shows up occasionally. The 17th century French scientist Pierre Gassendi applied the name aurora to the northern lights after Aurora, the Goddess of Dawn in Roman mythology, which has become the commonly used name for the northern lights. Figure 1.3 shows an aurora display observed from the Svalbard archipelago.

Figure 1.3  An aurora display observed from the European Incoherent Scatter Scientific Association (EISCAT) antenna site in the Svalbard archipelago on Nov. 10, 2010. The characteristic upper red emission from above 200   km results from the 6300Å line of atomic oxygen whereas the 100–200   km region is dominated by the green line at 5577   Å, also from oxygen. 

Credit: Dr. Njål Gulbrandsen, University of Tromsø, Norway.

Swedish physicists Anders Celsius and Olof Hiorter started systematic observations in the 1740s with magnetic needles. They were able to confirm a strong correlation between aurora events and geomagnetic fluctuations. As solar activity resumed after the Maunder minimum (1645–1715), some intense auroras were observed at midlatitudes. In 1733, French geophysicist and astronomer Jean-Jacques d'Ortous de Mairan noticed an apparent link between sunspots and auroras and suggested that auroral light could result from solar fluid impinging upon the Earth's atmosphere.

German amateur astronomer Samuel Heinrich Schwabe, who first publicly suggested the existence of the sunspot cycle, followed with an additional discovery in 1843 when he noticed a correlation between aurora and geomagnetic activity and the number of sunspots. A few years later, Scottish geophysicist J.A. Broun found that geomagnetic storms had a tendency to recur after 27  days, a time close to the rotation period of the Sun seen from the Earth.

These clues, indicating that activity on the Sun somehow influences the Earth's magnetic field were further strengthened by a dramatic event in 1859.

6.2. The Carrington Event

A white light solar flare within a huge sunspot that was observed and recorded by British astronomers Richard Carrington and Richard Hodgson on Sep. 1, 1859 was followed by a powerful geomagnetic storm the next day. They saw two patches of very intense light. Carrington immediately thought that his equipment had malfunctioned but soon realized that he saw a real solar feature (Carrington, 1859). The storm is now referred to as the Carrington event. The storm caused interruptions of telegraph systems, which were sensitive to strong geomagnetic signals, throughout the world for several hours. The storm was followed by sparkling bright aurora that could be seen by people around the world and was visible even at latitudes of Italy, England, and France.

It is well-known today that clouds of particles from very strong solar eruptions penetrate deeper into the geomagnetic magnetic fields and thus cause geomagnetic storms and aurora at lower latitudes than normal.

Solar storms of the same magnitude occurring today can cause life-threatening power outages, satellite damage, communication failures, and navigation. A very large X15-class solar flare on Mar. 6, 1989 resulted in a geomagnetic storm on the following Mar. 9, with disturbing consequences on Earth. The storm began with extremely intense auroras at the poles. Satellites in polar orbits lost control for several hours and Geostationary Operational Environmental Satellite weather communications were interrupted. Strong fluctuations in the Earth's magnetic field resulted in serious electric power failure in Quebec, Canada. An eruption comparable in strength to the 1859 Carrington event took place on Jul. 23, 2012 but it missed hitting the Earth that time.

Norwegian physicist Kristian Birkeland was the first to claim that charged particles from the Sun could trigger the aurora. In 1896, he presented his theory that the northern lights result from electric charged particles from the Sun being deflected by Earth's magnetic field and pulled down toward the poles, where they collide with the atmosphere and create this magical light. This is essentially the theory of the aurora today.

One of Birkeland's experiments was based on his magnetized terrella, which consisted of a small model of the globe containing an electromagnet in a vacuum-sealed chamber simulating the Earth. Using the electromagnet, he could create a magnetic field around the terrella mimicking the Earth's magnetic field. The atmosphere was like a layer of fluorescent paint that would give off light when it was struck by charged particles.

Birkeland's theory of the aurora remained dismissed by mainstream astrophysicists long after his death in 1917. It took over 60  years before Birkeland's theory could be confirmed, when NASA's Mariner II spacecraft, on its way to Venus in 1962, measured the presence of ionized gas with speeds up to 300–700  km/s, i.e., the solar wind.

6.3. Solar Flares, X-Rays and Energetic Particles

Solar flares are sudden releases of energy in the solar atmosphere. They were first detected and studied as chromospheric outbursts in the light of Hα by observers such as G.E. Hale, H.A. Deslandres, and M.A. Ellison. They learned that flares occur in regions of intense magnetic field that are located among groups of sunspots. Their frequency varied in step with the 11-year sunspot cycle. Their area and intensity ranged over several orders of magnitude and the total amount of energy released could reach up to 10²⁵  J. An impulsive release, within a few minutes, could be followed by a slow release over several hours.

Evidence of a terrestrial response to most flares continued to accumulate. G.E. Hale (1931) listed a dozen especially large flares that were followed in a day or two by geomagnetic storms. That suggested to him that flares can emit streams of charged particles. S.E. Forbush (1946), pioneer observer of galactic cosmic rays, detected sudden decreases in cosmic ray intensity after some flares. This was later interpreted as resulting from CMEs that swept away the protective geomagnetic field. In addition, he measured sporadic increases of giga-electron volt protons after very energetic flares.

Rocket observations of flares in the 1950s revealed the emission of soft x-rays (about 1  kiloelectron-volt [keV]) that caused ionospheric fadeouts. Subsequent observations from satellites have shown that large eruptive flares can emit radiation from radio wavelengths to gamma rays and particle emission up to 1000  megaelectron  volts (MeV). In fact, up to half of the total energy released may be in the form of energetic charged particles.

In so-called proton events, the initial flare brightening is detected in 10–100  keV x-rays (electron bremsstrahlung) and type III decimeter bursts. After a few minutes, the products of the CMEs are detected. These include 10- to 100-MeV gamma rays and up to 600-MeV protons and helium nuclei. A fraction of these very energetic protons may penetrate the Earth's geomagnetic field, enhance the ionosphere at 50- to 80-km altitudes, and reach ground level.

Researchers soon agreed that the huge amounts of flare energy could be derived only from the energy stored in strong nonpotential magnetic fields. But what mechanism could account for the rapid conversion of energy? R.G. Giovanelli (1948), an Australian physicist, proposed the reconnection of twisted magnetic fields.

6.4. Reconnection of Magnetic Fields

Reconnection of magnetic fields is an important process in astrophysics. It is thought to occur in the Sun, in the geomagnetic field, and in the magnetic dynamo. It is observed in laboratory plasmas and specifically in controlled fusion experiments. The process involves a flow of plasma and embedded field toward a neutral point, where the magnetic field strength vanishes and field lines can be cut and reconfigured, with the release of kinetic, thermal, and accelerated particle energy.

In 1958, Peter Sweet (University of London Observatory) proposed a model in which two bipolar sunspot groups collide, forcing their magnetic fields to contact at a neutral point. The subsequent development depends on the conductivity of the solar plasma at that point. In a perfectly conducting plasma, no merging of fields is possible. In plasma with a small but finite electrical resistance, opposite polarity field lines can cancel and release copious amounts of energy.

Sweet presented a theory for the development of the contact region, which he visualized as a thin linear current sheet of finite length (Fig. 1.4A). Plasma and embedded field lines with opposing directions approach the sheet from the left and right sides at a slow speed that is determined by the rate of cancellation of field lines, which in turn is fixed by the rate of diffusion across the thin sheet. The crucial transformation occurs at the ends of the sheet at point X, where the original field lines are reconfigured to form U-shaped lines. These in turn are pulled rapidly away from the ends by their magnetic tension. A heuristic hydrodynamical model (Fig. 1.4) was used to describe this flow. The speed of outflow could approach the Alfvén speed. In principle, a steady state could be reached as long as the supply of plasma and field was maintained.

Figure 1.4  Sweet's reconnection model ( Sweet, 1958 ). (A) Embedded field lines converge from left and right on neutral line N (B) The magnetic field strength and polarity change abruptly across the current sheet and reconfigure at X and Y to form U-shaped lines that retract, pulling plasma toward the top and bottom as in (C).

Sweet adopted a plausible chromospheric temperature (10⁴K), sheet length (10⁴  km), and field strength (10³ Gauss). He calculated that the total energy released could reach 10³³  erg in a flare lifetime of 10⁴  s, which he thought reasonable. Moreover, the electric field in the current sheet seemed sufficient to account for the acceleration of charged ions.

Stimulated by Sweet's theory, E. N. Parker (1957) used dimensional arguments to reach similar conclusions, and the theory became known as the Sweet–Parker theory.

Actually, Sweet's flare model was too slow by a factor of 10³ or more to accord with observations, and he sparked an intense effort to improve on it. Parker (1963) showed that the Sweet mechanism is efficient only when oppositely directed field lines are exactly aligned. In the following decades, theorists have explored a variety of possible models of reconnection in the context of flares (Petchek, 1964; Sturrock, 1968), but many details remain unresolved.

A current sheet is predicted to be only a few meters thick and perhaps some 100 km long, far below the resolution of current telescopes. However, after a flare, observations of the reconfiguration of large-scale fields are seen as compelling evidence for reconnection. Flare observers therefore often apply some form of reconnection theory to analyze their observations (Shibata and Magara, 2011; Vilmer, 2012).

The frontier in reconnection theory is the extension to three dimensions. Magnetic reconnection is described in Chapter 7.

6.5. Coronal Mass Ejections

Erupting prominences provided the first observed evidence of expulsion of mass into the higher coronal regions. Edison Pettit collected observations of prominences from a number of observatories (Meudon, Arcetri, Kodaikanal, Zurich, and Yerkes) between 1919 and 1931. He found that the upward rise of eruptive prominences started slowly but was followed by notably rapidly increasing velocities (Pettit, 1932).

The coronal response to solar eruptions was finally explored with instruments in space. Coronagraphs on board the orbiting OSO-7 Satellite (Tousey, 1973) and on Skylab (Gosling et al., 1974) during its nearly 8-month mission enabled unprecedented studies of the evolution of the outer solar corona. A slit-less spectrograph on board Skylab recorded emission at extreme UV and UV wavelengths, which enabled observations of coronal structures in a range of temperatures from 10⁴ to 10⁶K and revealed the thermal variations in the dynamic coronal responses to large flares and filament eruptions. Further instruments such as the Extreme-ultraviolet Imaging Telescope onboard the Solar and Heliospheric Observatory allowed for more detailed studies, from their initiation at the Sun out to their arrival at 1  AU. See Chapters 12.1 and 12.2 for further details and discussions on solar instruments.

The corona responds to flares and erupting filaments with sudden expulsions of magnetic flux and dense clouds of plasma into interplanetary space (Munro et al., 1979). These eruptions are termed CMEs, which are distinctly different from the continuous outflows of the solar wind. The events are observable in white light owing to Thomson scattering of photospheric light by the coronal electrons in the ejected mass.

The OSO-7 series showed violent CMEs occurring every couple of days during sunspot minimum and several times a day during sunspot maximum (Gopalswamy, 2016). Munro et al. (1979) claimed that eruptive prominences are rarely if ever seen without an accompanying mass ejection. From CME observations obtained during the first Skylab mission in 1973–1974, near the minimum of the activity cycle, they suggest that 40% are associated with flares and that 70% of the recorded CMEs were associated with erupting prominences both with and without flares. Whether the CMEs is a cause or effect of other activities remains a challenging issue in the interpretation of observations and theoretical modeling of dynamic coronal events.

The simplest form of CMEs is composed of a leading edge followed by a dark cavity and a bright core, which also can contain the remains of the erupting filaments. The mass in coronal ejection events is largely coronal matter being swept up on its way outward (Poland and Munro, 1976).

The high-energy particles associated with CMEs may strongly affect planetary environments (Gosling et al. 1991). One realized soon that interactions between CMEs and interplanetary magnetic fields is a major cause of large magnetic storms (Gopalswamy et al., 2000).

For detailed discussions of these issues, including models of mass ejections, we refer to Chapter 10.

7. Testing Two Concepts

7.1. Neutrino Oscillations in the Sun

The Sun has had a central role in confirming an exotic process in elementary particle physics, namely the changes in identifying a neutrino as it propagates.

In 1931, Wolfgang Pauli, a German theoretical physicist, postulated the existence of an unknown elementary particle to account for the missing momentum in radioactive beta decay events. This hypothetical particle had neither mass nor charge but moved at the speed of light.