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TheSunasaGuide
toStellarPhysics
Edited by
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-Universite´Paris-Sud, Orsay, France
Andrew Skumanich
Emeritus Senior Scientist, High Altitude Observatory, National Center
for Atmospheric Research, Boulder, Colorado, United States

Elsevier
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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: Go¨ran B. Scharmer and Mats G.
Lo¨fdahl, 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, Ondrejov, 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
Noe´Lugaz
Space Science Center and Department of Physics, University of New Hampshire,
Durham, NH, United States
xv

A.L. MacKinnon
School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
Hardi Peter
Max-Planck-Institut fu¨r Sonnensystemforschung, Go¨ttingen, 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 fu¨r Sonnensystemforschung, Go¨ttingen, Germany
Andrew Skumanich
Senior Scientist Emeritus, High Altitude Observatory, National Center for
Atmospheric Research, Boulder, Colorado, United States
Sami K. Solanki
Max-Planck-Institut fu¨r Sonnensystemforschung, Go¨ttingen, 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-Universite´
Paris-Sud, Orsay, France
Jack B. Zirker
National Solar Observatory, Sunspot, NM, United States
xviList of Contributors

Preface
It has been said that solar physics is astronomy with a zoom lens. Modern observa-
tions 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. Solarestellar comparisons are mutually beneﬁcial to
both ﬁelds as well for a number of ﬁelds in physics.
The aim ofThe Sun as a Guide to Stellar Physicsis 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 pos-
sibilities, 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 willing-
ness to contribute to the various specialized chapters. The insight and expertise of
the chapter authors have been vital for the presentations of interpretations and under-
standing 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 de-
scriptions 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
xvii

Discoveries and Concepts:
The Sun’s Role in
Astrophysics
1
Jack B. Zirker
1
, Oddbjørn Engvold
2
National Solar Observatory, Sunspot, NM, United States
1
;
Rosseland Centre for Solar Physics, Institute of Theoretical Astrophysics, University of Oslo,
Oslo, Norway
2
CHAPTER OUTLINE
1. The Solar Constant ................................................................................................. 2
2. The Sun’s Chemical Composition............................................................................. 3
2.1 Spectroscopic Methods............................................................................ 3
2.2 Modeling of the Sun’s Atmosphere............................................................ 4
2.3 Settling of Light Elements........................................................................ 5
3. Internal Structure and Helioseismology ................................................................... 6
3.1 Detection of Oscillatory Pattern ................................................................ 6
3.2 Interpretation of Solar Oscillations............................................................ 7
4. The Magnetic Sun and Its Variability ....................................................................... 8
4.1 Solar Cycle ............................................................................................. 9
4.2 Magnetic Fields ...................................................................................... 9
4.3 Internal Structure and Location of the Magnetic Dynamo .......................... 10
5. The Solar Corona and Wind .................................................................................. 11
5.1 The Temperature of the Corona............................................................... 11
5.2 The Shape of the Corona........................................................................ 13
5.3 The Solar Wind ..................................................................................... 13
6. EartheSun Connection.......................................................................................... 14
6.1 Aurora and Geomagnetic Storms............................................................. 14
6.2 The Carrington Event ............................................................................. 15
6.3 Solar Flares, X-Rays and Energetic Particles ............................................ 16
6.4 Reconnection of Magnetic Fields ............................................................ 17
6.5 Coronal Mass Ejections.......................................................................... 18
7. Testing Two Concepts........................................................................................... 19
7.1 Neutrino Oscillations in the Sun ............................................................. 19
7.2 Testing General Relativity ...................................................................... 22
8. Concluding Remarks............................................................................................. 23
Acknowledgments ..................................................................................................... 24
References ............................................................................................................... 24
CHAPTER
1
The Sun as a Guide to Stellar Physics.https://doi.org/10.1016/B978-0-12-814334-6.00001-7
Copyright©2019 Elsevier Inc. All rights reserved.

1.THE SOLAR CONSTANT
The amount of energy the Earth receives from the Sun is critically important to as-
tronomers, physicists, and meteorologists. This constant is deﬁned as the ﬂux of en-
ergy (in watts/m
2
) 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/m
2
, which (perhaps by
chance) was close to the best modern value. S.P Langley determined a value of
2.9 kW/m
2
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 Astrophys-
ical Observatory in 1907, spent 40 years in search of a reliable estimate.
He established observing stations at high dry locations such as Mount Wilson; Bas-
sour, Algeria; and Calama, Chile. His best estimates (1.318e1.548 kW/m
2
)
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 Irra-
diation Monitor (ACRIM). Richard C. Willson, a physicist at the National Aeronau-
tics 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 (1980e89). It showed a distinct decrease of about 0.06%
(from 1366.5 to 1365.8 W/m
2
in 1980e85 and a return to 1366.6 W/m
2
in
1986e89) 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 wave-
length). Frequencies, amplitudes, and line widths were obtained for individual pul-
sations. 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 var-
iations was pieced together (Fig. 1.1, fromFoukal 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.
2 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

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 dis-
covery by Hans Bethe, Charles Crichﬁeld, and Carl Friedrich von Weiza¨cker of nu-
clear reactions taking place under the extreme pressure and temperatures in the core
of the Sun (Foukal, 2004).
2.1SPECTROSCOPIC 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 ab-
sorption lines to be measured accurately. Element abundances of essentially all as-
tronomical 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
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 Composition3

lowercase letters. Physicist Gustav Kirchoff, also from Germany, realized that the
dark lines corresponded to the emission lines that he and his colleague Robert Bun-
sen 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 emis-
sion 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 wave-
lengths, and this produces an emission spectrum; and (3) if light composing a contin-
uous 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 A˚, is referred to by astronomers as Ha
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 A˚, 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 afterhelios, the Greek word for “Sun.”
In 1895, Swedish chemists Cleve and Langlet could conﬁrm the presence of terres-
trial helium gas coming out of a uranium ore called cleveite.
The availability of spectral data and an understanding of the origin of the absorp-
tion lines stimulated development of analytical techniques to determine the consti-
tution and structure of the solar atmosphere, including its chemical composition.
2.2MODELING OF THE SUN’S ATMOSPHERE
Before around 1940, calculations of solar spectral lines were based on the
“SchustereSchwarzschild” model of the atmosphere, in which the photosphere radi-
ated 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.
4 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

The MilneeEddington model is considerably more sophisticated. Here, the con-
dition for spectral line formation, i.e., the ratio of the emission coefﬁcient to the ab-
sorption 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).
2.3SETTLING 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 inter- stellar 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 remain-
ing outer layer is the convection zone. A layer of thickness 0.02 R
ʘbetween the base
of the convection zone and the top of the radiative zone is termed the solartacho-
cline(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 2.4ʘ10
6
K whereas beryllium requires
3.5ʘ10
6
K, its surface abundance is considerably affected, because the surface con-
vection zone reaches down to the dynamictachoclinelayer, at a temperature around
2ʘ10
6
K, 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 down-
ward to thetachoclinehas 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.
2.The Sun’s Chemical Composition5

3.INTERNAL STRUCTURE AND HELIOSEISMOLOGY
3.1DETECTION 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 spectro-
heliograph at Mount Wilson’s 65-foot solar tower (Leighton et al., 1962). George
Ellery Hale (and independently, Henri-Alexandre Deslandres) had invented this in-
strument in the 1890s. It was designed to form an image of the solar surface in mono-
chromatic 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 amonochromator. This device contained a prism or a diffraction grating that
dispersed the white light and isolated a chosen spectrum line. The light from the
monochromatorwas 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 themonochromatorand 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 A˚. 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 bright-
ness 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.
6 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

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 A˚and 1.8 km/s for Ca II 8542 A˚. 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 “qua-
sioscillatory” 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.
3.2INTERPRETATION 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 os-
cillations, 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)pro-
posed 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 tem-
perature and ionization gradients below the surface. Therefore, to construct a real-
istic 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 K
h) and fre-
quency of oscillationu. In other words, power exists only along curved lines in
the K
heudiagram (Fig. 1.2). He wrote that previous observations of the oscilla-
tions 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.
3.Internal Structure and Helioseismology7

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 character-
istics of solar as well as stellar activity.
The variable Sun and subsequently its cyclic variability became known initially
as a result of the GermaneDutch 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.
FIGURE 1.2
Observations of low-wavenumber nonradial eigenmodes of the Sun. Thecurved linesare
theoretical (Deubner, 1975; Ando and Osaki, 1977).
8 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

Even the Sun’s differential rotation was noticed by these very early scientists
(Engvold and Zirker, 2016).
4.1SOLAR 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 se-
ries. Rudolf Wolf of the Zu¨rich observatory collected observations of sunspots from
the 1600s onward and introduced the index known as the Zu¨rich Wolf Sunspot num-
ber R
z, which was generally used in following years:
R
z¼kð10 gþnÞ
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 9e14 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 Spo¨rer noted that observations of the Sun in several
decades close to 1700 revealed few sunspots. Later studies byHoyt et al. (1994)
conﬁrmed that the Sun was well-observed during the extended period from about
1645 until 1715 and showed few spots, whichJ. Eddy (1976)referred as the
Maunder minimum, in recognition of the impressive contribution to studies of sun-
spot 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 Spo¨rer showed that the locations of spots
migrated toward the equator throughout the cycle; these were followed up by Maun-
ders, who visualized this phenomenon in a timeelatitude histogram, which is
referred to as the “butterﬂy diagram” (Maunder, 1904).
4.2MAGNETIC FIELDS
George Ellery Hale used the powerful Snow Telescope at the Mount Wilson Obser-
vatory 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 map-
ping 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 real-
ized and settled (Babcock and Babcock, 1955).
4.The Magnetic Sun and Its Variability9

After the remarkable discoveries of sunspots, the Sun’s activity cycle, the pecu-
liar timeelatitude pattern, and the overall magnetic link,Hale et al. (1919)showed
that spots often emerged in bipolar pairs oriented roughly eastewest and that most
westward or “leading” spots in the northern hemisphere have the same magnetic po-
larity during a cycle. Similarly, most of those in the southern hemisphere have the
opposite polarity. Hale’s empirical rule provided fundamental clues about the inter-
action 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 byGrotrian and Ku¨nzel (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 vari-
ation, disappearing at sunspot maximum and appearing in large numbers around
sunspot minimum. These results serve to shed light on the poleward migration of so-
lar 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 60e120 years (Gleissberg, 1971;
Ogurtsov et al., 2002).
The Sun’s proximity and resulting traceable effects of its variable activity on the
Earth, such as
14
C in tree rings and
10
Be 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.
4.3INTERNAL 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).
10 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

Eugene Parker showed how isolated toroidal magnetic ﬂux tubes could rise from
the depth of thetachoclinelayer (seeSection 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 na-
ture of the solartachocline, have stimulated further investigation of the origin of the
variable period of the Schwabe cycles and of the episodes of changing cycle ampli-
tudes. 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
5.1THE 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 photo-
spheric 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 con-
tinuum) at a wavelength of 5303 A˚. 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.
5.The Solar Corona and Wind11

Part of the confusion arose from the fact that the outer and inner corona have
different spectra. In1934, 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 cal-
cium appeared in the spectrum of the solar disk (3933 and 3358 A˚), a weak depres-
sion of the continuum appeared. It was only a few percent deep and over 100 A˚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 Edle´n, a Swedish physicist, had deter-
mined 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 A˚. Simi-
larly, the separation of two levels of Fe XI corresponded to the wavelength of the
coronal line at 7892 A˚.
According toP. Swings (1943), Edle´n 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 A˚. 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 1e3 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 Lab-
oratory 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 A˚were detected above 87 km and UV
radiation around 1200 and 1500 A˚above 70 and 95 km, respectively. But what were
12 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

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.
5.2THE 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.
5.3THE SOLAR WIND
Ludwig Biermann (Max Planck Institutefu¨rNaturforschung) 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 500e1500 km/s and densities at the orbit of Earth of 500 to 10
5
particles
per cm
3
.
In1958, Eugene Parker developed a gas-dynamic theory to explain Biermann’s
estimates. He showed how a hot corona must expand at supersonic speeds into inter-
planetary 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 mag-
netic 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
USMariner IIen route to Venus, in 1962. The study of the wind has grown into a
major subdiscipline within solar physics.
5.The Solar Corona and Wind13

6.EARTHeSUN CONNECTION
6.1AURORA 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 Earthe
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, north-
ern 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 Augus-
tus in Rome, where the aurora shows up occasionally. The 17th century French sci-
entist 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 1.3shows 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 6300A˚line of atomic oxygen whereas the
100e200 km region is dominated by the green line at 5577 A˚, also from oxygen.
Credit: Dr. Nja˚l Gulbrandsen, University of Tromsø, Norway.
14 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

Swedish physicists Anders Celsius and Olof Hiorter started systematic observa-
tions in the 1740s with magnetic needles. They were able to conﬁrm a strong corre-
lation between aurora events and geomagnetic ﬂuctuations. As solar activity
resumed after the Maunder minimum (1645e1715), 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 sug-
gested 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 rota-
tion 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.
6.2THE 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 mal- functioned 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 lati-
tudes 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 compara-
ble 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 par-
ticles from the Sun could trigger the aurora. In 1896, he presented his theory that
6.EartheSun Connection15

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 the-
ory of the aurora today.
One of Birkeland’s experiments was based on his magnetizedterrella,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 theterrellamimicking the Earth’s magnetic ﬁeld. The atmo-
sphere 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 astrophysi-
cists long after his death in 1917. It took over 60 years before Birkeland’s theory
could be conﬁrmed, when NASA’sMariner IIspacecraft, on its way to Venus in
1962, measured the presence of ionized gas with speeds up to 300e700 km/s, i.e.,
the solar wind.
6.3SOLAR 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 Haby 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 10
25
J. An impulsive release, within a few minutes, could be fol-
lowed 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 ob-
servations from satellites have shown that large eruptive ﬂares can emit radiation
from radio wavelengths to gamma rays and particle emission up to 1000 megaelec-
tron 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
10e100 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
16 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

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 mech-
anism could account for the rapid conversion of energy?R.G. Giovanelli (1948),an
Australian physicist, proposed the reconnection of twisted magnetic ﬁelds.
6.4RECONNECTION 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 reconﬁg-
ured, with the release of kinetic, thermal, and accelerated particle energy.
In1958, 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
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 formU-shaped linesthat retract,
pulling plasma toward the top and bottom as in (C).
6.EartheSun Connection17

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 trans-
formation 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 Alfve´n speed.
In principle, a steady state could be reached as long as the supply of plasma and ﬁeld
was maintained.
Sweet adopted a plausible chromospheric temperature (10
4
K), sheet length
(10
4
km), and ﬁeld strength (10
3
Gauss). He calculated that the total energy released
could reach 10
33
erg in a ﬂare lifetime of 10
4
s, which he thought reasonable. More-
over, the electric ﬁeld in the current sheet seemed sufﬁcient to account for the accel-
eration 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 SweeteParker
theory.
Actually, Sweet’s ﬂare model was too slow by a factor of 10
3
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 evi-
dence for reconnection. Flare observers therefore often apply some form of recon-
nection theory to analyze their observations (Shibata and Magara, 2011; Vilmer,
2012).
The frontier in reconnection theory is the extension to three dimensions. Mag-
netic reconnection is described in Chapter 7.
6.5CORONAL 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) be-
tween 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 unprece-
dented studies of the evolution of the outer solar corona. A slit-less spectrograph
on boardSkylabrecorded emission at extreme UV and UV wavelengths, which
18 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

enabled observations of coronal structures in a range of temperatures from 10
4
to
10
6
K 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 theSolar and Heliospheric Observatoryallowed 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 sun-
spot 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
Skylabmission in 1973e1974, near the minimum of the activity cycle, they suggest
that 40% are associated with ﬂares and that 70% of the recorded CMEs were associ-
ated 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 ﬁla-
ments. 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
7.1NEUTRINO 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 exis-
tence 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. It would interact with dense matter so weakly that it
could pass through the Earth without being deﬂected. His Italian American
colleague, Enrico Fermi, named it the “neutrino,” or little neutron.
7.Testing Two Concepts19

The neutrino was also invoked in the quest to explain the source of the Sun’s radi-
ated energy. In 1938, Hans Bethe and Charles Critchﬁeld constructed a chain of nu-
clear reactions that converts four protons into a helium nucleus, with the emission of
one neutrino and 26.7 MeV of energy in gamma rays. Their work would earn them
the Nobel Prize in Physics for 1967, only after the existence of the neutrino was
proven.
Twenty-ﬁve years would pass before this elusive particle would be detected.
Clyde Cowan and Frederick Reines (Los Alamos National Laboratory) realized in
1951 that a nuclear reactor would emit intense ﬂuxes of antineutrinos, which differ
from ordinary neutrinos only by the direction of a kind of spin. (Every elementary
particle has a twin with the same mass but different electrical charge or spin.) If they
could trap antineutrinos, they would prove the existence of neutrinos. Their exper-
iment in 1956 at the reactor at Savanna, Georgia, was successful: electron neutrinos
are real particles.
With this conﬁrmation, the path was open to test the validity of the Bethee
Critchﬁeld theory of solar energy production. In 1963, Ray Davis and John Bahcall
(Brookhaven National Laboratory) made plans for a critical experiment. Davis was
the experimentalist and Bahcall the theorist. They planned to count solar antineutri-
nos and compare theory and observation.
Davis used a 100,000-gallon tank of tetrachloroethylene (a common dry-
cleaning ﬂuid) as his antineutrino detector. To avoid false signals from cosmic
rays, Davis set his tank 1500 m deep in the Homestake Gold Mine in South Dakota.
A passing neutrino could convert an atom of chlorine-37 to a radioactive argon-37
atom, with a vanishingly small probability. Davis invented an exquisitely sensitive
technique to collect argon-37 atoms about every 2 months by ﬂushing his tank
with helium. He was able to detect single argon atoms. Using the best model of
the solar interior and combining it with the BC theory, Bahcall calculated the rate
of neutrino captures Davis should see if the BC theory was valid. He predicted about
two captures per week.
Davis ran his experiment for 5 years until he had sufﬁcient captures to compare
with theory. His preliminary results in 1968 showed a rate one-third as large as the-
ory predicted. Where were the missing neutrinos? His result provoked a serious
crisis in stellar and nuclear physics.
Over the following two decades, Davis scrutinized his procedures and reﬁned his
estimates of possible experimental error. Bahcall examined the possible sources of er-
ror in his calculations. These included uncertainties in nuclear reaction cross-sections
and in the theoretical models of the solar interior. Nothing was large enough to ac-
count for a factor of three discrepancy. Davis continued his experiment until 1984.
Meanwhile, several discoveries were made elsewhere that bore on the solar neu-
trino problem. A second type of neutrino, associated with the muon particle, was
discovered in 1962 by three scientists at CERN. They bombarded a target with a
powerful proton beam to produce measurable muon neutrinos. A third type of
low-mass particle, the Tau particle, was detected in 1978 by the Stanford Linear
Accelerator Center and its associated neutrino in 2000 by CERN.
20 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

When the ﬁrst results from the Homestake experiment were published, Bruno
Pontocorvo and Vladimir Gribov proposed a radical solution to the solar neutrino
problem: neutrinos mightoscillateamong the three “ﬂavors”: electron, muon, and
tauon. (This was possible in the weird world of quantum mechanics.) If solar
neutrinos arrived at Earth as either muon or tauon neutrinos, Davis’s tank would
not detect them. Particle physicists were skeptical and there was no way to test
the idea.
In any case, a more plausible solution had to be explored. The production of
electron neutrinos is extremely sensitive to the temperature distribution in the
solar interior. Could the uncertainty in the temperature account for the missing
neutrinos?
Helioseismology is the technique of using the observed vibrations of the solar
surface to determine the properties of the solar interior. There are two ways to go
about this. In the forward method, one computes a solar model of temperatures
and densities and predicts the oscillation frequencies of many different modes.
Then one compares the predicted and observed frequencies and modiﬁes the model
until they match. In the inverse method, one uses the fact that acoustic modes of
different frequency are refracted (internally reﬂected) at different distances from
the Sun’s center. Therefore, it is possible to combine modes to sample the speed
of sound (and hence, temperature) at a chosen depth in the Sun. If the empirical
and model temperatures disagree, the model has to be modiﬁed.
As the quality and duration of observations steadily improved during the past two
decades, agreement between empirical and computational sound speed distributions
matched to within 0.1% through most of the Sun’s depth. This precision eliminates
the possibility that temperature uncertainty is the cause of the solar neutrino
problem.
That conclusion lent support to Pontocorvo’s idea that neutrinos oscillate among
three types as they propagate from the Sun’s center to the Earth. The only way to test
the idea was to count the different types. Indeed, that is what two neutrino observa-
tories have done: one in Sudbury, Canada, and the other in Kamioka, Japan. The
Sudbury Neutrino Observatory counts only electron neutrinos whereas the Japanese
neutrino observatory counts the sum of all three types. From the difference in
counts, one could determine the fraction of muon and tauon neutrinos. It turned
out that only a third of all neutrinos arriving from the Sun are electron neutrinos;
the other two-thirds arrive as muon or tauon neutrinos. Physicists could breathe a
sigh of relief. The missing neutrinos have been found; the Bethe-Critchﬁeld theory
of energy production is valid!
However, a new challenge has arisen. The standard theory of elementary particle
physics assumed that neutrinos have no rest mass, whereas the observed oscillation
of ﬂavors requires that they do indeed have mass. The challenge is to determine their
masses. The difﬁculty is that each ﬂavor does not have a permanent mass as it moves
through a material body such as the Sun. Instead, each ﬂavor has a superposition of
three absolute masses, with different probabilities. As of 2016, it was known that the
sum of the three masses is less than 10
6
of the electron mass.
7.Testing Two Concepts21

7.2TESTING GENERAL RELATIVITY
In1916, Albert Einstein published his General Theory, which describes gravity as a
curvature of space in the presence of a material body. Relatively few scientists were
able to follow his argument, whereas those who did awaited experimental conﬁrma-
tion. By 1918, Einstein’s prediction of the advance of the perihelion of Mercury by
43 arcsec per century convinced some astronomers, but the theory was still in doubt.
Therefore, Einstein proposed another test of his theory. He encouraged astrono-
mers to measure the deﬂection of starlight in the vicinity of the Sun at a total solar
eclipse. He predicted that a ray of starlight that grazed the edge of the eclipsed Sun
would be deﬂected by precisely 1.76 arcsec. He also predicted the deﬂections at
different distances from the Sun.
Einstein was evidently unaware of the earlier work of Johann Georg von Soldner,
a German astronomer. In1804, von Soldner used Isaac Newton’s formula for the
gravitational attraction of two bodies to calculate the deﬂection of a ray of starlight
near the Sun. In this estimate, von Soldner assumed, as did Newton, that light con-
sists of a stream of tiny corpuscles that have mass. von Soldner obtained a deﬂection
angle of 0.875 arcsec.
To carry out Einstein’s suggested test of his theory, an astronomer would photo-
graph the positions of as many stars as possible during an eclipse. Then, a few
months later, when the Sun was no longer present in the same ﬁeld of stars, he would
photograph the same stars with the same telescope. By subtracting one photograph
from another, he could determine the deﬂections and compare them with Einstein’s
predictions.
A team from the Lick Observatory was the ﬁrst to attempt this test. They
observed the total eclipse of Jun. 1918 in Washington State, but the clouds allowed
them to see only a few stars. The test was inconclusive. Therefore, the British astron-
omers resolved to try their luck at the eclipse of May 29, 1919.
They sent one expedition to Sobral, Brazil, and another one to the island of Prin-
cipe, in the Gulf of Guinea. Arthur Eddington, who would become one of the fore-
most theorists of the century, joined the team in Principe as an observational
astronomer.
The eclipse was partly cloudy at Principe. After returning to Oxford, Eddington
could measure the positions of only four stars, but he derived a deﬂection of
1.61 arcsec at the Sun’s edge.
The Sobral team had better luck. They found seven stars on their photographic
plates. After measurement and interpolation, they obtained a deﬂection at the
Sun’s edge of 1.98 arcsec, compared with the prediction of 1.76 arcsec. The British
concluded that a deﬂection does occur at the edge of the Sun, in an amount compat-
ible with Einstein’s prediction, but with a relatively large random error of 0.3 arcsec.
They urged their colleagues to repeat this critical test.
Over the next 40 years, a dozen measurements were obtained at total eclipses,
with varying random errors. It became clear that systematic errors introduced by a
22 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

host of external factors were larger than random errors and very difﬁcult to evaluate.
A major effort was made at the 7-min eclipse in 1973 by a team from Princeton and
the University of Texas. That team obtained a value of 1.660.18 arcsec at the
Sun’s edge, in close agreement with Einstein’s prediction. Moreover, their measured
deﬂections of 40 stars, at different distances from the Sun, followed Einstein’s curve,
but with huge scatter.
That was where the issue stood when radio astronomers entered the game,
around 1969. They had used interferometers with long baselines to measure the po-
sition of radio sources with millliarcsec precision. In particular, they measured the
positions of two quasars that are very close to each other in the sky and pass near
the Sun during the year. By 1972, theory and observations agreed to within 3%.
In 1974 and 1976 the two scientists A.Fomalont and R. Sramek (1975)were able
to observe three sources that lie in a straight line in the sky. They obtained
1.7610.016 arcsec, or within 1% of Einstein’s number.
The latest measurement (2009) was made by Fomalont and colleagues using the
Very Long Baseline Interferometer, a 5000-mile chain of radio telescopes between
Europe and the United States. They achieved agreement between theory and obser-
vation of less than 1%. Fomalont projects that this uncertainty can soon be reduced
by a factor of four.
The bending of light rays by a massive object has produced some surprising im-
ages and has developed into a subtopic in astronomy: gravitational lensing. In 1979,
three astronomers discovered a double image of a distant quasar in visible light. It
turned out that a nearby galaxy was acting as a lens for the rays from the quasar. Sub-
sequently, examples were found of complete rings, or a pattern of arcs. Background
stars or galaxies can act as sources of light or radio waves that pass by nearby
massive galaxies and seem to vary in brightness. Searches for such events have un-
covered the imprint of dark matter.
8.CONCLUDING REMARKS
The focus of this chapter has been on breakthroughs in studies of the Sun that have
stimulated stellar physics. Stellar global oscillations and stellar activity cycles are
two examples of this impact. Olin C. Wilson’s initial survey of variations in stellar
activity from observations of Ca II H and K lines (Wilson, 1963) opened a momen-
tous new ﬁeld of astrophysics and a comprehensive literature, as reviewed by
Vidotto et al. (2014), Testa et al. (2015), and others. Conversely, stellar studies
have given essential context to the behavior of the Sun. Relationships between
large-scale surface magnetic ﬁelds, stellar age, and rotation are well-documented.
Empirical relations between stellar rotation periods and the length of corresponding
activity periods shed light on the dynamo actions in the Sun and sun-like stars. We
look forward to further fruitful cross-fertilization.
8.Concluding Remarks23

ACKNOWLEDGMENTS
The authors are grateful for comments and suggestions from Aad van Ballegooijen, Sara F.
Martin, and Jean-Claude Vial in their preparation of this chapter.
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26 CHAPTER 1Discoveries and Concepts: The Sun’s Role in Astrophysics

Stellar and Solar
Chromospheres and
Attendant Phenomena
2
Thomas R. Ayres
University of Colorado, 389-UCB (CASA), Boulder, CO, United States
CHAPTER OUTLINE
1. Introduction .........................................................................................................27
2. Why Chromospheres Exist.....................................................................................28
2.1 Stellar Convection Zones........................................................................ 28
2.2 The Solar Chromosphere ........................................................................ 29
2.3 Stellar Chromospheres........................................................................... 31
2.4 Why Are Chromospheres So Thick? ......................................................... 32
2.5 The WilsoneBappu Effect ...................................................................... 43
3. The RotationeAgeeActivity Connection .................................................................45
3.1 Background .......................................................................................... 45
3.2 PosteSkumanich Law Insights Into the RotationeAgeeActivity
Connection ........................................................................................... 46
3.3 Theory Behind the Skumanich Law ......................................................... 50
4. Stellar Activity Cycles ..........................................................................................52
References ...............................................................................................................56
1.INTRODUCTION
One might surmise that the physics of the stars and that of the Sun must be intimately
connected. After all, physics is physics and the Sun is a star. However, any common
ground fails at a granular level for the simple reason that sets the Sun apart from all
the other stars: it is possible to observe the solar surface (and the interior, thanks to
helioseismology) in remarkable detail with almost arbitrarily high temporal, spatial,
and spectral resolution, free of interstellar absorption.
Furthermore, as a singular object of attention, the Sun has inspired long−term
records of various phenomena such as the enigmatic sunspot cycle, for which
detailed surface maps of the dark spots (initially drawings, more recently digital im−
ages) extend back four centuries or more. Meanwhile, the stars are so distant that
observational limitations dictate more superﬁcial examinations, certainly spatially
unresolved, except in a few special cases. Also, the stars are so numerous and diverse
CHAPTER
27
The Sun as a Guide to Stellar Physics.https://doi.org/10.1016/B978-0-12-814334-6.00002-9
Copyright©2019 Elsevier Inc. All rights reserved.

in size, mass, temperature, luminosity, chemical composition, age, etc., that statisti−
cal considerations must come into play. The wide but shallow view of the stars lends
itself to equally superﬁcial physical modeling. Thus, there is little to be learned
about the ﬁne details of solar phenomena from the necessarily more global exami−
nations of the stars.
That said, studies of the stars can help our understanding of the Sun in a number
of important ways. We have learned much from our privileged solar vantage point
but still must appeal to the broader collection of sunlike stars to understand pivotal
aspects of the solar condition. For example, is the Sun typical of G−type dwarfs? Or
is the Sun special in some way that has allowed life to develop and ﬂourish on one of
its planets? What might the Sun have been like in its youth, when the solar system
was still forming? Will normal evolutionary changes in our star someday threaten
planetary habitability? Are there infrequent events on the Sun that might affect
our technology−laden civilization right now, for which there is little or no historical
experience because these episodes are rare? Observations of stars can help answer
such questions. This is the playing ﬁeld of the Solar−Stellar Connection laid out
by Leo Goldberg a half−century ago in a prestigious Russell Lecture before the
American Astronomical Society.
There is one more point to be made in favor of the stellar viewpoint: the neces−
sarily macroscopic views of stars potentially can act as a ﬁlter to isolate important
global phenomena that might be glossed over in the microscopic details of solar ob−
servations: a forest view despite the trees.
2.WHY CHROMOSPHERES EXIST
2.1STELLAR CONVECTION ZONES
The chromosphere story begins with convection. The presence of an outer convec−
tive envelope is the main characteristic that distinguishes late−type (cool) stars from
their early type (hot) cousins. Convection zones make their appearance at the early F
spectral types, for which the effective temperature,T
eff, is about 7000K; increase in
thickness through the solar spectral types (G2 V:T
effz5770K), down to the K−
types (T
effz4500K); then into the cooler M’s (T effz3500K), which become fully
convective by mid−M.
Convection plays several key roles in deﬁning the physical state of the stellar
outer atmosphere (sequentially outward from the stellar surface):photosphere
(65004000K [at solarT
eff]),chromosphere(5000e8000K),transition zone(TZ)
(10
4
10
5
K), andcorona

TT10
6
K

:
1.Convective turbulence, and collapse of convective granules, together produce
acoustic noise, which powers internal seismic waves and leaks into the chro−
mosphere, inducing shocks and other dynamical effects.
2.Convection transforms the solid body rotation of a star into differential zonal
ﬂows (the Sun’s equator rotates almost 40% faster than the poles). Differential
rotation, in turn, has a central role in the (a−U) dynamo generation of strong
28 CHAPTER 2Stellar and Solar Chromospheres and Attendant Phenomena

magnetic ﬁelds in the stellar interior, at the interface between the convective and
radiative zones. The internal magnetic ﬂux ropes occasionally become buoyant,
rise through the convective envelope, then erupt into the surface layers as active
regions, often showing a great deal of complexity. These dynamic magnetic
ecosystems cause heating in the chromosphere, and transient events such as
ﬂares and coronal mass ejections.
3.Convective turbulence also can directly produce (by thea−aeffect) small−scale
magnetic ﬁelds in the near−surface layers, which can bubble up into the
photosphere as ephemeral bipoles and other types of disorganized ﬁeld.
4.Chaotic ﬂows associated with the overturning convection cells kinematically
buffet the photospheric footpoints of small−scale magnetic ﬂux tubes, launching
various types of Alfve´n waves and magnetosonic disturbances that can dissipate
heat higher up. Organized larger−scale horizontal convective ﬂows can sweep up
the small−scale ﬁeld and collect it into discrete surface patterns called the
supergranulation network. There, ﬂux concentrations of opposite polarity are
driven against one another by turbulence in the subduction lanes of the large−
scale pattern. Reconnection heating can occur as a consequence, sometimes
ejecting high−speed gas plumes.
Given the myriad roles of convection, it is unsurprising that solar−like high−
energy activity is conﬁned mainly to late−type stars.
2.2THE SOLAR CHROMOSPHERE
Fig. 2.1depicts a full−disk ﬁltergram of the Sun taken in the Ca II 3933 A˚K reso−
nance line during a period of moderate solar activity. The K line brightens in
magnetically disturbed areas where local chromospheric heating is elevated. The im−
age illustrates several of the magnetic−related features mentioned earlier, speciﬁcally
their chromospheric counterparts. Numerous sunspots, some organized in groups,
appear as small, dark, roughly circular patches (dim in visible light; apparently
also in chromospheric Ca II emission). Surrounding the dark spots are halos of bright
Ca II plage. These are extensive, moderately magnetic areas (z100 G, spatially
averaged) initially associated with emerging sunspots, but often persist long after
the magnetically intense spots (z1000 G) have decayed. Further from the active re−
gions are additional Ca II bright mottles organized in the lacy pattern of the super−
granulation network. At a ﬁner spatial scale, one also would see a peppering of Ca II
bright points in the network cell interiors, which represent transient chromospheric
excitation mainly by shock waves.
As illustrated inFig. 2.2,Ha6563 A˚ﬁltergrams have a signiﬁcantly different
appearance. This is partly because the formation of the subordinate hydrogen line
has a more complex relationship to plasma properties owing to the difﬁculty of
populating the 10 eV lower level of the transition and partly because, as the lightest
element, hydrogen is the most affected by thermal Doppler broadening. The Ha
feature can be seen in relative absorption or emission, depending on local physical
conditions and also at what velocity displacement the line proﬁle is sampled
2.Why Chromospheres Exist29

(primarily owing to the Doppler broadening effect). Unlike Ca II images, which are
dominated by collections of small−scale bright features near the lower−altitude foot−
points of magnetic structures, the Hapictures are composed of light and dark hor−
izontal striations of various lengths, sometimes organized in radially spoked
rosettes, all of which trace the higher altitude extensions of the magnetic ﬁeld, form−
ing the complex topology of the chromospheric canopy.
A common feature of full−disk Haﬁltergrams are long, dark, narrow curvilinear
features called ﬁlaments (prominences when seen in emission at the limb). These are
unusually cool (z10
4
K) and dense plasma structures, in the otherwise hot (z10
6
K)
tenuous corona, suspended high above the surface inside long−lived magnetic ﬂux
ropes.
In fact, prominence−like structures are inferred to exist on a few fast−rotating,
active stars such as the K dwarf AB Doradus (Collier Cameron et al., 1990) and
the G giant FK Comae Berenices (Huenemoerder et al., 1993). The signature is
Doppler−shifted components in Hathat are synchronized with the rotation period,
FIGURE 2.1
Ca II K-line (3933 A˚) full-disk ﬁltergram of solar chromosphere. Smaller dark areas are
sunspot umbrae; surrounding lighter patches are chromospheric plage. Away from the
spot groups, the brighter, lacy patterns are part of the supergranulation network. Not
visible in this global image are small-scale transient Ca II bright points found in the
internetwork regions.
From the Big Bear Solar Observatory.
30 CHAPTER 2Stellar and Solar Chromospheres and Attendant Phenomena

but whose projected velocities exceed that of the stellar surface by as much as a fac−
tor of two, which suggests a physical extension to perhaps a stellar radius above the
photosphere. The fast rotation of the host stars makes high−altitude prominence−like
structures especially easy to detect spectroscopically. Nevertheless, such coronal
condensations probably are common among cool stars.
2.3STELLAR CHROMOSPHERES
Like the solar counterpart, stellar chromospheres are known principally from optical emission lines, especially Ca II H and K and Ha(the latter usually is seen in absorp−
tion, although emission is common in more active stars). As shown inFig. 2.3, the
Ca II emission cores sit at the bottoms of broad, deep photospheric absorption fea−
tures, which completely dominate the 3900−4000 A˚wavelength interval in stars such
as the Sun. In fact, thanks to favorable atomic physics, the Ca II resonance doublet is
the strongest feature in the visible solar spectrum, even through calcium is not partic−
ularly abundant (compared with iron, for instance). In contrast, the most prominent
hydrogen line in the visible, Ha, is much weaker, despite the overwhelming abun−
dance of hydrogen, now owing to unfavorable atomic physics (the 10 eV lower level
of Hais only weakly populated in a cool atmosphere).
The chromospheric Ca II emission cores are doubly−reversed (M−shaped). They
barely are discernible in low−activity G dwarfs such as the Sun but strengthen in
active dwarfs (or solar plage regions). In late−type stars, the Ca II emission features
broaden systematically with increasing absolute visual luminosity over a remarkable
FIGURE 2.2
High-resolution Ha(6563 A˚) ﬁltergram of solar chromosphere. Scales are in arcseconds.
From the Swedish Solar Observatory.
2.Why Chromospheres Exist31

15 stellar magnitudes. This is called the Wilson−Bappu effect (WBE), named after its
codiscoverers (Wilson and Bappu, 1957); it is illustrated inFig. 2.4.
2.4WHY ARE CHROMOSPHERES SO THICK?
The chromospheric temperature inversion exists because nonradiative heating above
the photosphere disrupts the classical radiative equilibrium (RE) stratiﬁcation. A
remarkable characteristic of chromospheres that begs explanation is why they are
so thick. Semiempirical solar models (Vernazza et al., 1981) indicated that the layer
is about 1500 km in extent, roughly 10 pressure scale heights, three times thicker
than the photosphere. Empirical measurements, especially at total eclipses, have
proposed even larger extents.
As we will see subsequently, this key structural property of the chromosphere can
be addressed even without full knowledge of the possible heating mechanisms.
How Is the Chromosphere Cooled?The chromosphere is an ideal environment
to explore the balance, or lack of balance, between heating and cooling processes.
The reason is that although the heating mechanisms might be varied and complex,
the cooling is straightforward: creation of photons by collisional interactions and
then their escape from the chromosphere. This radiative cooling dominates in the
FIGURE 2.3
Ca II H and K lines in the solar spectrum, dominating the violet region. Inset shows blowup
of K-line core in quiet Sun (lower, thicker curve) and three plage regions (thinner, higher
curves):x-axis is wavelength displacement from line center in A˚. Note that the full widths
at half maximum (FWHM) (delimited by vertical dashed lines) are similar; theK
1
minimum features become broader with increasing activity (stronger K-line emission) but
theK
2peak separations become perhaps slightly narrower.
From the National Solar Observatory Fourier transform spectrometer archive.
32 CHAPTER 2Stellar and Solar Chromospheres and Attendant Phenomena

low−density layers because the gas is optically thin, so local convection is inhibited;
while the temperature gradients are relatively mild, so heat conduction is suppressed
(except at the steep TZ interface at the top of the chromosphere).
A lucky consequence of radiative cooling control is that, in principle, solar ob−
servers can record the escaping chromospheric radiation directly, so it is a simple
matter conceptually to count all the radiative losses to determine the cooling, and
thus also the incident heating. However, given the observational challenges to record
often subtle chromospheric emissions across a wide range of species and wave−
lengths, a more practical way to carry out the radiative cooling inventory is to calcu−
late the individual contributions using a chromospheric model, especially when it is
“calibrated” against the more robust chromospheric signatures (Mg II and Ca II).
By this approach,Anderson and Athay (1989)estimated chromospheric radiative
losses for the quiet Sun of 1.410
7
erg/cm
2
s. The authors found that Fe II was
responsible for about half the total line cooling (Mg II and Ca II accounted for
much of the rest), and that the energy dissipation was nearly constant across the
chromospheric temperature plateau, 6000e8000K.
FIGURE 2.4
Left: stacked photographic spectra of 18 representative late-type stars (higher intensities
are darker) in the Ca II region. Star 3 has narrow H and K emissions, whereas star 15 has
noticeably broader, doubly reversed proﬁles (see schematic tracing of reversal shapes in
inset). Right: stellar WilsoneBappu effect: full width at half maximum intensity (W
0,
expressed in equivalent velocity units) of the Ca II K-line emission core increases
systematically with absolute visual magnitude.
Adapted from Wilson, O.C., Bappu, V.M.K., 1957.Astrophys. J.125, 661.
2.Why Chromospheres Exist33

The chromospheric energy loss is only about 0.02% of the solar bolometric sur−
face ﬂux,F
1
bol
¼610
10
erg=cm
2
s. The corresponding fractions for the TZ and
corona are down by additional orders of magnitude. In this light, the outer atmo−
spheric heating might seem trivial. Nevertheless, one must keep in mind that it is
source of the Sun’s high−energy activity that feeds Earth−affecting space weather.
Chromospheric Structure. In the early−1960s,Thomas and Athay (1961)argued
that the chromospheric temperature rise resulted in part from a shift in the radiative
cooling from the negative hydrogen ion, H

(dominant visible and near−infrared [IR]
broadband opacity) to hydrogen bound−bound transitions (Lya,Ha) and bound−free
continua (Balmer and Paschen), which can be excited at higher temperatures than
H

.
In the late−1970s,T. Ayres (1979)pointed out that the H

continuum cooling and
that of important chromospheric resonance lines all are similar in magnitude and all
have the same dependence on the electron density. So, it might be that the electron
density itself was the key to understanding the chromospheric temperature inversion.
In fact, solar and stellar semiempirical models available at the time almost invariably
had remarkably constant electron densities [n
e(cm
3
)] in the chromospheric layers
despite the typical factor of 10
4
exponential decline of the hydrogen density [proto−
nsþneutrals:n
H(cm
3
)] over the same height range.
The Ionization Valve Effect. A simple analytical framework was proposed by
Ayres (1979)to understand the basic foundations of chromospheric structure. The
underlying mechanism later was called the ionization valve effect. Here is how it
works.
Photospheric temperatures of a cool star decrease monotonically outward in RE,
eventually stabilizing at a boundary value (Tz0.8T
effz4850K for the Sun) in the
optically thin layers. At these temperatures, hydrogen is almost completely neutral,
but a soft lower boundary on the ionization fraction,n
e/nHz10
4
, is maintained by
the easily ionized metals (such as iron). The atmosphere can remain in balance at
these low temperatures because both the radiative heating and cooling are controlled
by mirror−image processes in the same species (H

).
However, if there is extra,nonradiativeenergy deposition (e.g., acoustic shocks,
magnetosonic waves, magnetic reconnection, and so forth) in these high layers, the
gas cannot rid itself of the additional heat in its baseline low ionization state. The
reason is that the radiative cooling (per gram of material) is proportional to the elec−
tron density, and thus must follow the precipitous outward hydrostatic decline of the
hydrogen density (because at low temperatures,n
ez10
4
nH). Given the outwardly
falling radiative cooling, any increased energy input will cause a thermal instability,
forcing the temperatures to rise above the RE boundary value, until enhanced ioni−
zation boosts the collisionally induced thermal emission. This tipping point deﬁnes
the initial chromospheric temperature rise.
Above that point, increasing ionization can keep up with a more or less height−
independent extra heating over many pressure scale heights, even despite the rapid
outward decline ofn
H, because when hydrogen begins to ionize (T>5000K), there
are lots of electrons available (i.e.,n
e/nHcan increasefour orders of magnitudefrom
34 CHAPTER 2Stellar and Solar Chromospheres and Attendant Phenomena

the metal−dominated limit 10
4
at and below about 4500K; up tow1 near 8000K,
where hydrogen is fully stripped). This region of slowly rising temperatures but
rapidly increasing ionization is the middle chromosphere.
Once the hydrogen is almost completely ionized, however, the gas has run out of
new cooling electrons and no longer can compensate for extra heating by slowly
increasing the temperatures outward. Rather, a catastrophic thermal instability
must ensue, imposing a sharp temperature rise (10
4
/10
6
K) at the top of the thick,
nearly isothermal (6000e8000K), middle chromosphere. This second inversion is
the chromosphere−corona TZ.
Now, let us consider the scenario more quantitatively, piece by piece.
Low-Temperature Metal Ionization. Near the top of the photosphere
(T<5000K), hydrogen is essentially neutral (owing to its high 13.6 eV ionization po−
tential) and electrons come mainly from the big−three easily ionized metals: Mg, Si,
and Fe, each about 3.510
5
by number relative to hydrogen. Between 3000 and
5000K, the ionization fractions of these species are close to unity, so:
n
ezðA MgþASiþAFeÞnHz1:210
4eAn
H, where theA’sare abundances
relative to hydrogen, andeAis a relative metallicity factor introduced for the general
stellar case

eA
1h1

.
H

Cooling and Heating. In a normal late−type atmosphere, the broadband
visible and near−IR opacity (i.e., that which controls the bolometric ﬂow of radiative
energy through the photosphere) is dominated by the loosely bound (0.75 eV) nega−
tive hydrogen ion, H

. Under such conditions, in the Sun, temperatures fall steadily
outward from about 6500K in the deep photosphereðs
H
z1Þuntil they reach a
boundary value of about 4850K roughly 500 km aboves
H
z1. (The continuum
optical depth unity surface could be called thesee level, the deepest layers visible
to an external observer.)
H

cools the gas by associative attachment (analogous to recombination for
ions): a free electron interacts with the polarization electric ﬁeld of a neutral
hydrogen atom and can be captured into the single weakly bound state of the qua−
simolecule. The kinetic energy of the captured electron plus the binding energy,
0.75 eV, is liberated as a photon (with wavelength,l(1.6m). The packet of energy
carried away by the photon represents a net drain from the local “thermal pool,” i.e.,
cooling.
Radiative heating mainly is by the complementary process, photodetachment of
H

: a sufﬁciently energetic photon (below the dissociation limit at 1.6m) ejects the
loosely bound electron. The freed hot electron then thermalizes its energy by colli−
sions with other particles in the gas, thereby heating the plasma.
In the solar outer photosphere, near the radiative boundary temperature (4850K),
the H

heating and cooling are in balance. On either side of the equilibrium temper−
ature, thenetheating (or cooling) scales asDT=Trelative to the (large) absolute H

cooling. Consequently, thenetH

cooling is signiﬁcantly reduced near the boundary
temperature, but on the other hand, the substantial H

heating term is largely
canceled.
2.Why Chromospheres Exist35

Radiative Cooling by Lines. The most signiﬁcant chromospheric cooling lines
are Mg II h and k at 2800 A˚, Ca II H and K at 3950 A˚, and a series of strong tran−
sitions of singly ionized iron, mainly in the 2400−2600 A˚interval. Of secondary
importance are H I 1215 A˚Lya(primarily at the top of the chromosphere), Ha,
and the Ca II subordinate IR triplet (near 8500 A˚).
All of the parent species are the dominant ionization stages of the respective el−
ements under chromospheric conditions. Mg II and Ca II have low−lying excited
levels easily populated by collisions and connected to the ground state by pairs of
strong near−UV resonance transitions. Mg II is more important than Ca II because
magnesium is 15 times more abundant. Fe II has generally weaker resonance tran−
sitions than Mg II, but more of them; and like Mg II, is important owing to the large
abundance of iron.
The resonance line cooling works differently from the H

associative attachment
described earlier, but follows the same principle: a collisional interaction creates a
photon, which then escapes from the region, carrying away the energy of formation.
In this case, the interaction is an inelastic collision between a fast free electron and
the ion, which promotes one of the bound electrons into a higher orbital at the
expense of most of the kinetic energy of the incident electron. Electrons are the
dominant colliding partners, because the light particles have faster thermal speeds
than the heavier hydrogen atoms and thus higher collision frequencies.
Resonance transitions such as Ca II H and K are characterized by very fast spon−
taneous radiative decays (Einstein A−values typically of order 10
8
s
1
). Conse−
quently, an initial inelastic collisional excitation usually is followed by a
spontaneous decay, producing a photon. If the newly minted photon travels a long
distance, the energy it carries away would represent a net drain locally, thus cooling.
However, the most common situation at low densities is scattering: a resonance
transition initially isphoto−excited and then almost immediately decays radiatively.
The new photon is essentially identical to that absorbed in all respects (except
perhaps the direction of ﬂight). The main way in which a scattered photon is
destroyed is when the radiative decay that normally follows the photo−excitation
is short−circuited by an inelastic collisional de−excitation.
When the collisional−deactivation rates are slow, as at low density, an absorbed
photon is less likely to be removed from the radiation ﬁeld after each photo−
excitation, and thus ultimately might escape the atmosphere after a long journey
of many scatterings. On the other hand, when deactivation rates are fast, as at
high density, an absorbed photon more likely would be thermalized by a downward
collision after each photo−excitation. In the high−collision−rate limit, photons are
able to travel only a single optical depth, on average, before being destroyed.
The multiple scattering process is characterized by a thermalization depth,L, the
average number of vertical line−center optical depths a newly created photon can tra−
verse before destruction. When collision rates are high,Lz1. However, when
collision rates are low,Lcould be very large, thousands or many thousands of op−
tical depths for chromospheric resonance lines.
36 CHAPTER 2Stellar and Solar Chromospheres and Attendant Phenomena

Several aspects of the scattering process controlL, especially frequency redistri−
butions. This effect causes photons to random−walk not only in physical space but
also diffuse through the line proﬁle in frequency. This diffusion is important because
photons escape more readily in the transparent line wings than in the opaque line
core. Such nuances make the calculation of thermalization depths and associated
escape probabilities tricky.
Regardless, resonance lines of abundant species are capable of removing colli−
sionally−created photons efﬁciently from deep in the chromosphere, and thus can
be potent radiative coolants. When a species is emitting within a thermalization
depth of the surface, we call the transition effectively optically thin, or simply effec−
tively thin.
The collision−induced radiative cooling can be expressed as a differential incre−
ment to the local energy ﬂux,F, with respect to height. For our purposes, the most
convenient height scale is the mass column densitym(g/cm
2
), the mass of gas in a
cm
2
column above a given altitude. In the solar atmosphere,mdecreases two orders
of magnitude from 4 g/cm
2
atsH
z1 to 0.03 g/cm
2
atsH
z10
4
(top of the
photosphere); then another four orders of magnitude through the chromosphere it−
self. In these variables, the line cooling can be written asdF
cooling
[

dm.
For strong resonance lines under chromospheric conditions, the radiative cooling
is directly proportional to the upward collisional rate because virtually every excita−
tion results in emission of a photon; but with a correction for the fraction able to
escape the region:
dF
cooling
[
dm
zw
nlClu
r

hc
l
lu

erg=sg;wheren
lis the population of the
lower level;C
luis the upward collision rate;l luis the transition wavelength (paren−
thetical term is the photon energy);wis a cooling escape fraction that accounts for
the collisionally created photons that actually cool the gas; andris the matter den−
sity (g/cm
3
). The latter factor converts the expression from physical height,z,to
mass column density,m(becausedm¼rdz). (A useful relation for later:
rz1.4m
HnHfor a 10% helium abundance by number;m His the mass of the
hydrogen atom.)
If the species is the dominant ionization stage of the element, and most of the
population resides in the ground state (normally the case), then:n
lzAelnH, where
A
elis the abundance of the element by number relative to hydrogen.
In the effectively thin layers, the minimum value ofwlikely isz½, representing
the photons scattering in the outward hemisphere, which ultimately escape the atmo−
sphere. Note thatw/0 in the effectively thick limit, where all the photons are ther−
malized more or less locally.
The collision rate can be written asC
lu¼neUluðT=5000Þ
1=2
e
hc=lkT
s
1
.
Here,U
luis the collision strength, which can be evaluated asg
luðTÞ

g l
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
5000
p
,
whereg
lu(T) is the factor tabulated in, for example, theChianti Atomic Database,
andg
lis the statistical weight of the lower level. For ions,g lu(T) has a slow logarith−
mic dependence on temperature (Burgess and Tully, 1992).
2.Why Chromospheres Exist37

Mg II h and k provide a signiﬁcant fraction of the total resonance line cooling in
the solar chromosphere, perhaps as much as 30%, so are a useful bellwether for the
total effect. Substituting parameters appropriate for these lines fromChiantiinto the
previous equations, and takingwz1=2, yields:
dF
cooling
Mg II
dm
z
h
6:310
þ1
ðT=5000Þ
1=2
e
51390=T
i
eAn
eerg=sgz2:210
3eAn
e
ðT¼5000KÞ:
Here, the magnesium abundance was assumed to scale as the stellar metallicity.
A similar calculation for Ca II H and K yields a coefﬁcient of 1.510
3
(5000K).
Important Fe II is more complicated, given its numerous strong UV transitions.
An estimate can be obtained by considering the ground state and four lowest excited
levels, and the associated resonance transitions to higher levels. Assuming pure−
collisional population ratios and theChianticollision strengths yields a numerical
factor of 3.610
3
(5000K), comparable to Mg IIþCa II (i.e., Fe II accounts
for about half the resonance line total, as concluded byAnderson and Athay
(1989)from their numerical modeling).
Instabilities and Stabilities.When nonradiative heating is present at the top of
the photosphere, there should be a point (call itm
*), where the extra heating begins
to overwhelm the ability of the gas to cool itself at low temperature. At that tipping
point, the temperatures must break upward from the boundary value because of the
mismatch between heating and cooling. Beyond the initial inversion, the radiative
cooling can tap into the ionization valve to maintain quasistability with only slowly
increasing temperatures, independent of the outward decline in the hydrogen den−
sity, until all the bound electrons are exhausted. A one−dimensional semiempirical
reference model of the solar chromosphere inFig. 2.5illustrates some of these basic
structural features.
In the middle photosphere, where the metal resonance lines are effectively
thick and thus poor coolants, the H

netcoolingðwðDT=TÞn eÞstill can balance
a signiﬁcant nonradiative heat input with only a smallDTas long as the hydrogen
density is high enough (noting again thatn
ez10
4
nH). Thus, there could be, and
probably is, substantial nonradiative heating in the dense middle photosphere,
which nevertheless might not be obvious because the temperature proﬁle still could
beclosetothatexpectedinRE(Ayres, 1975). However, as the hydrogen density
continues to fall outward, and so too the radiative cooling, there will come a point
at which H

no longer can keep up with extra heating at smallDT(and low
ionization).
Generic Nonradiative Heating Rate.Because the radiative cooling is propor−
tional ton
e, regardless of whether H

or lines dominate, and the collective cooling
must balance the nonradiative input, the constancy of the electron density in
38 CHAPTER 2Stellar and Solar Chromospheres and Attendant Phenomena

semiempirical models suggests that the extra heating (per gram) is relatively con−
stant with altitude above the base of the chromosphere (here designatedm
), as
noted byAnderson and Athay (1989)from their model simulations.
FIGURE 2.5
Lower panel: VAL-C’ quiet Sun reference model ofMaltby et al. (1986). Thick, warm
chromospheric layer, aboveT
minregion at top of photosphere, is terminated at left by
steep rise to million-degree corona, through narrow transition zone. Critical mass column
density,m
*, described in the text, is located just aboveT
min. Height zero is continuum
optical depth unity at 5000 A˚(the “see level”). Dashed curve represents the scattering
source function (in equivalent temperatures) for the Ca II K line. The source function
breaks downward from the temperature proﬁle aboveT
minas Ca II photons begin to
escape from the open boundary.m
Lmarked on the upper mass column density scale
indicates the thermalization depth mentioned in the text. Different intensity features in the
Ca II proﬁle (Fig. 2.4:K
1,K
2, and K
3) are mappings of corresponding features in
the source function, as indicated. Upper panel: Hydrogen and electron densities for the
model, showing almost constantn
ein the chromosphere, as well as then ez10
4
nH
behavior in the photosphere where hydrogen is neutral and the electrons come from
singly ionized metals.
2.Why Chromospheres Exist39

With this assumption, the heating rate atm *(or indeed anywhere in the chromo−
sphere) can be estimated as
dF
heating
dm
¼const¼F totm
1

erg/sg,whereF totis theto-
talextra heat deposited in the chromosphere (z1.410
7
erg/cm
2
s for the quiet Sun,
as mentioned earlier).
We could generalize this expression to other stars if we knew how the total heat−
ing varied with surface gravity, effective temperature, and activity level. We can es−
timate these trends by considering the chromospheric ﬂuxes of different types of
stars (noting again that the radiative emissions are proxies for the nonradiative
heating).
Bolometrically Normalized Fluxes. A useful way to compare chromospheric
emission levels of different stars is to divide a cooling line ﬂux, sayf
Mg II, by the
bolometric ﬂux (total over all wavelengths)f
bol(both quantities in erg/cm
2
sat
Earth). The stellar bolometric ﬂux can be calculated from a formula based on,
say, the Johnson visualV−band, with a bolometric correction that depends mainly
on the stellar effective temperature.
Thef
Mg II/fbolindex tells us what fraction of the total stellar energy budget has
been diverted to produce the chromospheric Mg II emission, at least the part that es−
capes to be detected remotely, so it is something like an efﬁciency factor (and typi−
cally small,zfew10
5
). Thef Mg II/fbolratio has the great virtue that it is
independent of stellar sizes and distances, and thus is less biased in comparisons
of different types of stars, such as dwarfs and giants. Thef
Mg II/fbolratio is equivalent
toL
Mg II/Lbol(and often written that way). Another useful equivalence is
F
Mg II

sT
4
eff
;whereFis the surface ﬂux (erg/cm
2
s at the star).
Stellar Mg II Emission Trends.We now consider the Mg II emissions of stars to
gain insight into how the total chromospheric heating,F
tot, might vary with stellar
parameters. Mg II is superior to Ca II (or Fe II) for this purpose, because the near−UV
Mg II core emissions show larger intensity contrasts than the often barely visible Ca
II (or Fe II) reversals.
A valuable stellar Mg II inventory was provided by the venerable International
Ultraviolet Explorer satellite (1978e96). These measurements can be summarized
as follows:
1.At any given spectral type, there is a wide range ofL
Mg II/Lbolratios extending
upward from a soft lower limit, often called the basal ﬂux.
2.The spread ofL
Mg II/Lbolvalues above the basal limit appears to be controlled by
a hidden property of stars, which we might call their activeness (presumably
related to elevated magnetic activity).
3.Mg II time series of individual stars show variability at the rotation period and
also on longer time scales associated with stellar analogs of the decadal sunspot
cycle. Nevertheless, the variability amplitude generally is much smaller than the
L
Mg II/Lbolspread between inactive and active stars.
4.The basal ﬂux boundary, albeit fuzzy, displays a modest decline with decreasing
effective temperature, something likeF
Mg II

sT
4
eff
wT
þ22
eff
(Linsky and
Ayres, 1978).
40 CHAPTER 2Stellar and Solar Chromospheres and Attendant Phenomena

The item 4 dependence impliesF Mg IIwT
þ62
eff
along the basal ﬂux trend. In
other words, the baseline Mg II chromospheric surface ﬂux, powered by some com−
bination of acoustic shocks and the supergranulation network, falls off strongly with
decreasing stellar effective temperature, perhaps even a little faster than expected
from a strict proportionality with the bolometric surface ﬂux.
Given the empirical Mg II trend, and the absolute chromospheric cooling for
the quiet Sun, the total inferred stellar heating can be estimated as:
F
totw1:410
7eFeT
þ62
eff
erg=cm
2
s;whereeT effis the stellar effective tempera−
ture in solar units (T
1
eff
¼5770K), andeFis an activeness factor to account for de−
viations from the basal heating law. For example,
e
Fz1 for a low−activity star such
as the Sun, whereaseFz10 for a solar plage region, or a young, active G dwarf. The
(depth−independent) heating rate now can be written as:
dF
heating
dm
z1:410
7e
FeT
þ62
eff
m
1

.
Thickness of the Chromosphere.In equilibrium, the local cooling must balance
the local heating (radiative plus nonradiative) throughout the chromosphere, in
particular at the base, where temperatures are low enough that metal−dominated
ionization still holds. For the sake of argument, suppose that the radiative cooling
atm
*, evaluated at a chromospheric base temperature ofz5000K, is the Fe II
plus Ca II effectively thin result (Mg II is the most likely of the three to be effectively
thick). This acknowledges that the H

cooling essentially cancels the photospheric
radiative heating at that temperature, so we can safely ignore both contributions in
the energy equation. The Fe IIþCa II cooling rate is
dF
cooling
tot
dm
ðmÞz5:110
3eAn
e
erg/s g (5000K).The leading numerical factor shows only a mild increase over the
range 5000e8000K, so the metal cooling per gram depends mainly on the electron
density.
At low temperatures, as described earlier, the electron density is proportional to
the total hydrogen density,n
H. The latter, in turn, is related to the mass column den−
sity,m, through the hydrostatic equilibrium condition: gm¼1.1n
HkT, where g is
the stellar surface gravity (g
1¼2:7410
4
cm=s
2
) andkis Boltzmann’s constant.
The left−hand side represents the weight of the mass column and the right−hand side
is the gas pressure at the base of the column. The latter invokes the perfect gas law, a
10% helium abundance by number, and negligible ionization. Solving for the
hydrogen density, introducing the result into the metal−ionization, then substituting
forn

e
in the cooling function yields:
dF
cooling
tot
dm
ðmÞz2:210
10eA
2
egmerg=sg;
whereeg¼g

g
1accounts for nonsolar surface gravities. Here, the metallicity fac−
tor enters squared: one power for the line cooling and the other for the low−
temperature metal ionization. Equating the heating and cooling expressions at the
tipping point yields:m
z0:025eA
1
eF
þ
1
2
eg

1
2
eT
þ31
eff
g=cm
2
. Note that the chromo−
spheric thickness goes as the inverse square−root of the key structural parameter, sur−
face gravity. In other words, a lower−gravity atmosphere, with its lower densities,
2.Why Chromospheres Exist41

must push the chromospheric inversion inward in mass column density to reach a
depth where there are enough electrons to fuel the metal−ionization dominated cool−
ing. Together with the other dependencies, the relation says that chromospheres
become thicker in lower gravity stars (e.g., giants), metal−poor objects, more active
stars, and with increasing effective temperature.
In the semiempirical quiet Sun model VAL−C
0
ofMaltby et al. (1986), the col−
umn mass density at the base and initial rise of the chromosphere is about
0.01e0.05 g/cm
2
(for the height range 710530 km [50004400K]). The model−
ized location of the solar inversion agrees reasonably well with the numerical coef−
ﬁcient in them
scaling law, which is encouraging.
Mean Electron Density of the Chromosphere.Substituting them
relation into
the expression forn
H, then that result into the low−temperature metal ionization
(again for Tz5000K) yields a second scaling law:
n

e
w1:110
11eF
þ
1
2
eg
þ
1
2
eT
þ31
eff
cm
3
. Note that the metallicity factor has canceled
out. This relation says that a thin chromosphere (smallm
*, typically high g) must
have a larger mean electron density to radiate away the same total extra heat input
as a thick chromosphere (largem
, typically low g). In addition, the mean electron
density rises with increasing activeness. However, bothn

e
andm *depend on the
activeness factor in the same way: a more active atmosphere is thickerandhas a
higher electron density.
Curiously,m
depends strongly on metallicity (inversely), whereasn

e
does not
at all, at least when metal ions dominate the radiative cooling. This says that a metal−
poor chromosphere will be thicker but will have thesamemean electron density
compared with a solar−abundance chromosphere of the same gravity and activity.
The numerical coefﬁcient compares well with then
ez1.01.710
11
cm
3
found above theT minin the VAL−C
0
model (1.110
11
at 5000K). Also, the model
C
0
electron density is relatively constant in the chromospheric layers, whereas the
hydrogen density falls outward about four orders of magnitude (seeFig. 2.5). The
near−constancy ofn
eover the same height range wheren His dropping precipitously
supports the basic premise of the ionization valve effect: It is all about the electrons.
A semiempirical chromospheric model for the red giant star Aldebaran (aTauri:
K5 III;T
eff¼3920K, log g¼1.25, solar metallicity), published byMcMurry
(1999), has logm
?0.5 g/cm
2
and a chromospheric electron density of
11010
8
cm
3
, with an average of about 810
8
cm
3
in the hotter layers
(6000e8000K). Over the same range in mass column, the hydrogen density drops
the familiar four orders of magnitude. For these stellar parameters, the scaling
laws predict logm
?0.5 g/cm
2
andn

e
¼910
8
cm
3
; again, not bad
agreement.
An older model chromosphere for the metal−deﬁcient red giant Arcturus (a
Boo¨tis; K1 III;T
effz4250K;log gz1:7;logeAz0:5), published byAyres
and Linsky (1975), has logmzþ0.25 and an electron density of
0.51.710
9
(5000e8000K). For the given stellar parameters, the scaling laws
predict: logmz0.15 andn

e
¼1:910
9
. Compared with the roughly similar
42 CHAPTER 2Stellar and Solar Chromospheres and Attendant Phenomena

red giantaTau, aside from metallicity, theaBoo chromosphere is thicker but has
about the same electron density. Again, the agreement with the scaling laws is
encouraging.
2.5THE WILSONeBAPPU EFFECT
An indirect way to test the chromospheric scaling laws is to assess their impact on
the WBE mentioned earlier. Observations suggestW
0weA
a
eF
b
eg
geT
d
eff
;whereW 0is
the FWHM of the Ca II K (or Mg II k) emission core. Consensus empirical values
for the power law indices are:az0,bz0,0.23g0.20, and
1.3d1.7 (Linsky, 1999).
The emission width thus displays, remarkably, almost no sensitivity to metallic−
ity or activeness. The dependence on effective temperature is mild, noting thatT
eff
varies only a factor of two from cool M−types to the warm F−types. The main sensi−
tivity is the inverse dependence on surface gravity, because g decreases three or four
orders of magnitude from dwarfs to supergiants. Despite the weak sensitivity ofW
0
to activeness, Ca II (and Mg II) proﬁles of solar plage and active G dwarfs reveal that
thebaseof the emission proﬁlebroadenswith increasingeF, whereas, counterintu−
itively, the separation of the peaks at thetopof the proﬁle seems tonarrow, leaving
the FWHM more or less unchanged (Ayres, 1979).
Now, we make a crucial assumption: the edges of the emission core just inside
theK
1minimum features are controlled by the Lorentzian wings of the line proﬁle.
In the wings, the opacity depends quadratically on the wavelength shift,Dl, from
line center:f(Dl)wDl
2
. In the central Doppler core, on the other hand, the
dependence is exponential,fðDlÞwe
Dl
2
=Dl
2
D
(here,Dl Dis the Doppler width,
related to local thermal and turbulent velocities).
The Lorentzian assumption is contrary to early attempts to understand the WBE,
which assumed that the emission features form in the Doppler core; consequently,
the width would be dictated by chromospheric velocity ﬁelds (e.g.,Hoyle and Wil−
son, 1958). This is a reasonable expectation in principle, but in practice the implied
velocities (already near−sonic in the Sun) would quickly become supersonic in giants
and supergiants (e.g.,Fig. 2.4, noting that the chromospheric sound speed is only
about 7 km/s). Such extreme dynamics would be difﬁcult to sustain in the face of
strong dissipation by shocks. In that respect, Lorentzian control of the outer proﬁle
seems physically more appealing.
To proceed further, we can apply one of the EddingtoneBarbier relations, based
on analytical solutions of the radiation transport equation. It says that at a given
wavelength in the line proﬁle,f(Dl), one can “see” down to the atmospheric depths
(and their associated thermal emission) corresponding tosz1at that wavelength.
Thus, as one tunes through the line proﬁle from the transparent far wings inward to
the opaque core, the optical depth unity surface sweeps upward through the atmo−
sphere, encountering progressively lower temperature layers and thus lower inten−
sities, ultimately passing through the chromospheric temperature inversion, which
then maps onto the proﬁle as the initialK
1/K 2emission rise.
2.Why Chromospheres Exist43

Making these assumptions, it is easy to show thatDl K1
wA
þ
1
2
Ca
m
þ
1 2
. In other words,
as the chromosphere thickens, the base of the emission reversal moves further from
line center. The speciﬁc square root relationship works only for species, such as Ca II
and Mg II, that are the dominant ionization stages at chromospheric temperatures.
Then, the column density of (ground−state) absorbers is directly proportional to
the column density of hydrogen,N
H(cm
2
), and thus also the mass column
(mz1.4m
HNH).
Substituting the scaling law form
yields:Dl K1
weF
þ
1
4
eg

1
4
eT
þ
3
2

1 2
eff
;assuming
that the calcium abundance follows the metallicity,eA;which then cancels that factor
inm
. This relation shows a similar mild inverse dependence on surface gravity as
the consensus index forW
0, a weak sensitivity to activeness, no dependence on met−
allicity, and a positive moderate dependence on effective temperature.
A similar scaling relation can be worked out for the separation of theK
2emission
peaks. The formulation is more complicated because the scattering thermalization
depth,L, mentioned earlier, comes into play. The key is that the latter tends to scale
inversely as the electron density,Lwn
1
e
. This has a signiﬁcant impact on theDl K2
relation, which turns out to beeF

1
4
eg

1
4
eT

3
2

1 2
eff
x
þ
1 2
;where the new quantityxis a
typical Doppler velocity in the upper chromosphere.
Note thatDl
K2
has thesamedependence on surface gravity asDl K1
and likewise
none on metallicity, butoppositesensitivities to the other two parameters, especially
activeness. This says thatDl
K2also widens with decreasing surface gravity, like
Dl
K1
, butnarrowswithincreasing activity, contrary toDl K1
. This matches the coun−
terintuitive behavior seen in plage proﬁles of Ca II.
Because the WBE width falls roughly midway betweenDl
K1
andDl K2
,the
contrary behavior with respect toeFandeT
effsuggests thatW 0will be less sensitive
to these parameters, with exponents intermediate, perhaps even close to zero (as is
the case foreFempirically). Also, becauseDl
K1
andDl K2
display no sensitivity to
metallicity, it stands to reason that the WBE width would not either, as observed.
In short, despite the enormous simpliﬁcations of the analytical arguments, the
remarkable agreement of the scaling law predictions with the general properties
of the WBE supports the idea that chromospheres owe their peculiar properties,
especially their great thickness, mainly to the ionization valve effect rather than,
say, to the speciﬁc heating mechanism(s) or the particular cooling opacities.
It used to be thought that the WBE was caused by a dramatic increase in atmo−
spheric turbulence, going from dwarfs to giants, which would greatly enhance the
Doppler broadening of the Ca II cores in the luminous stars. Now, we have seen
an alternative view in which the Ca II width is controlled by the thickness of the
chromosphere, which in turn adjusts itself to the impact of nonradiative heating ac−
cording to a pressure−dependent instability in the low−temperature cooling. In this
sense, the WBE is abarometer, not atachometer.
44 CHAPTER 2Stellar and Solar Chromospheres and Attendant Phenomena

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The Theatrocrat
A TRAGIC PLAY OF CHURCH AND STAGE BY JOHN
DAVIDSON
LONDON E. GRANT RICHARDS 1905
TO THE GENERATION KNOCKING AT THE DOOR
Break—break it open; let the knocker rust:
Consider no "shalt not", and no man's "must":
And, being entered, promptly take the lead,
Setting aside tradition, custom, creed;
Nor watch the balance of the huckster's beam;
Declare your hardiest thought, your proudest dream:
Await no summons; laugh at all rebuff;
High hearts and youth are destiny enough.
The mystery and the power enshrined in you
Are old as time and as the moment new:
And none but you can tell what part you play,
Nor can you tell until you make assay,
For this alone, this always, will succeed,
The miracle and magic of the deed.
John Davidson.
INTRODUCTION WORDSWORTH'S IMMORALITY AND MINE
Poetry is immoral. It will state any and every morality. It has done
so. There is no passion of man or passion of Matter outside its
province. It will expound with equal zest the twice incestuous

intrigue of Satan, Sin, and Death, and the discarnate adoration of
Dante for the most beatified lady in the world's record. There is no
horror of deluge, fire, plague, or war it does not rejoice to utter; no
evanescent hue, or scent, or sound, it cannot catch, secure, and
reproduce in word and rhythm. The worship of Aphrodite and the
worship of the Virgin are impossible without its ministration. It will
celebrate the triumph of the pride of life riding to victory roughshod
over friend and foe, and the flame-clad glory of the martyr who lives
in obloquy and dies in agony for an idea or a dream. Poetry is a
statement of the world and of the Universe as the world can know it.
Sometimes it is of its own time: sometimes it is ahead of time,
reaching forward to a new and newer understanding and
interpretation. In the latter case poetry is not only immoral in the
Universal order; but also in relation to its own division of time: a
great poet is very apt to be, for his own age and time, a great
immoralist. This is a hard saying in England, where the current
meaning of immorality is so narrow, nauseous, and stupid. I wish to
transmute this depreciated word, to make it so eminent that men
shall desire to be called immoralists. To be immoral is to be different:
that says it precisely, stripped of all accretions, barnacles and
seaweed, rust and slime: the keen keel swift to furrow the deep. The
difference is always one of conduct: there is no other difference
between man and man: from the first breath to the last, life in all its
being and doing is conduct. The difference may be as slight as a
change in the form of poetical expression or the mode of wearing
the hair; or it may be as important as the sayings of Christ, as vast
and significant as the French Revolution and the career of Napoleon.
Nothing in life is interesting except that differentiation which is
immorality: the world would be a putrid stagnation without it, and
greatness and glory impossible. Morality would never have founded

the British Empire in India; it was English piracy that wrested from
Iberia the control of the Spanish Main and the kingdom of the sea.
War is empowered immorality: poetry is a warfare.
What I mean by Wordsworth's immorality begins to appear. This
most naive and majestic person, leading the proudest, cleanest,
sweetest of lives, was, during all his poetical time, immoralist sans
tache. In his boyhood he can think of no other atonement for a
slight indignity done him than suicide; he is perverse and obstinate,
defies chastisement—is rather proud of it, and slashes his whip
through the family portrait; he breathes "among wild appetites and
blind desires": delights and exults in "motions of savage instinct":
sullen, wayward, intractable, nothing fascinates him except
"dangerous feats." Even when his poetical time is spent, he can still
do the thing that Wordsworth should do. Milton's watch being
handed round, he takes out his own, a procedure that makes the
company uneasy; and it is remembered against him by vulgar people
who were present and felt foolish; but Wordsworth would not have
been Wordsworth had he left this undone. In Paris of the Revolution
he "ranges the streets with an ardour previously unfelt," and
remembers that the destiny of man has always hung upon a few
individuals. Why should not he lead the Jacobins, carry freedom
through Europe, and be the master of the world? He withdraws,
however, and tells himself at the time it is lack of means; but "The
Prelude," that miracle of self-knowledge and inferior blank verse, is
more explicit:—
   "An insignificant stranger and obscure,
   And one moreover little graced with power
   Of eloquence even in my native speech,
   And all unfit for turmoil or intrigue."

Another "insignificant stranger and obscure," as "little graced with
power of eloquence," ranged the streets of Paris devouring his heart
about the same time as Wordsworth—devouring his heart and
considering whether the Seine at once might not be his best goal.
Had Wordsworth remained in Paris to contest the dictatorship with
Napoleon? It is a dazzling might-have-been. Carlyle's remark on
Wordsworth comes to mind at once:—
"He was essentially a cold, hard, silent, practical man, who, if he
had not fallen into poetry, would have done effectual work of some
sort in the world. This was the impression one got of him as he
looked out of his stern blue eyes superior to men and circumstances
… a man of immense head and great jaws like a crocodile's, cast in a
mould designed for prodigious work."
Carlyle's hatred of pleasure—an experience constitutionally
impossible to himself; and his dyspeptic, neurasthenic distrust of
happiness generally, corrupt all his judgments of men, and especially
stultify his opinions of poets and poetry. His insane jealousy of all his
contemporaries, which gave him a vision of Tennyson "sitting among
his dead dogs"; in fine, his damnable Scotch-peasant's hypocrisy and
agonized self-conceit as of a sinless and impotent Holy Willy, require
to be cancelled ruthlessly after a scrupulous calculation, if we wish
to disengage the actual features from the masterful caricature, lurid
colour, violent gesture, false lights and falser shades, that mark his
portraits. Having struck out Carlyle's contempt of Wordsworth as
poet—poetry being an art Thomas himself had failed in; and having
perceived the coldness, the hardness, the silence, and the stern look
in the blue eyes, to be the necessary configuration of Wordsworth's
intercourse with a personality so antagonistic to his own as Carlyle's,
we have remaining a being of great power and presence, whose

magnitude and influence are more convincing in Carlyle's sketch
than in any other account of the man, because of the limner's
absolute standard, because of his passionate veracity, and because
of the deep grudge overcome. Could Wordsworth, then, have been
in any effective way the rival of Napoleon? Could he even have held
together a strong opposition to be the bulwark of Napoleon's power?
the cradle, nursery and academe of an enduring Napoleonic
dynasty? It is the debated question of genius: is genius the gift of
perfect conduct that may be bestowed, as circumstances determine,
in war or poetry, in art or commerce? Men of the greatest ability
have thought so, or said so, Carlyle among them, and therefore it is
that I pause a moment, although on the very swell of this last
interrogation—made, also, as if I had never inquired it of the fates
before—I felt the answer to be an everlasting no. Caesar wrote good
journalistic prose, being his own war-correspondent, but his
hexameters were of the same mark as Cicero's; Dante possessed all
the eloquence Wordsworth lacked, and in his "De Monarchia"
exhibits the very soul of sovereignty, but his diplomacy and
soldiership ended in bitter bread and death by heartbreak; therefore
Caesar could have indited a monumental poem, and Dante could
have conquered Gaul and overthrown Pompey!
It is not probable that Wordsworth at any period in his youth
would rather have been Caesar than Dante. To have the world at
one's absolute commandment for power and pleasure is the desire
of most virile natures, and a desire seldom renounced by the highest
intelligences, however closely disgrace and misery may dog them to
the end. Accordingly, when intellect, health, and strength abdicate
their heritage of the world we look for some tragic circumstance
compulsive. In the case of Wordsworth we look in vain. The worst
that befell him was the failure of his hopes in the French Revolution.

He never sent down a personal root into the busy world at all: but
had from the beginning a primitive-Christian contempt for power and
wealth. His reluctance—it lasted for two years—to take up the
burden of poetry is to be ascribed to the shame and horror of their
destiny which great poets feel. A great poet fights against his fate as
high women fight against passion. There is degradation and dismay
in the ministration of poetry as in "the ruddy offices of love"; but
both the woman and the poet yield: for love and poetry, being of the
race, are stronger than the individual.
Wordsworth's immorality, like all dynamic immorality, was what is
called a return to nature. He wrote with perfect insight concerning
poetry. There are many pregnant and convincing passages in his
letters and prefaces: but I question if he ever found the terms
characteristic of his own innovation. He said: "It may be safely
affirmed that there neither is nor can be any essential difference
between the language of prose and metrical composition." Boldly,
but not safely; and the substitution of "metrical composition" for
"poetry" is distinctly equivocal. The discovery Wordsworth made was
this:—That poetry is the least artificial of the arts; that, compared
with music, painting, sculpture, architecture, poetry is not an art at
all. Given an artist, the first condition of the arts proper is the
possession of mechanical means. But the poet requires none; no
pencils, colours, canvas, compasses, strings, or pipes. Language, the
vehicle of his no-art, is part of the poet's, as of all men's, birthright;
like food and air, he has it. And when he requires to supplement the
language with which the conditions of existence endue him, the
founts are ready: there are no grapes to gather: that is not the
winepress the poet must tread: he has only to drink from the
sources of utterance. Thus poetry, like an artesian well, broaches the
heart of Matter directly, and is its most intimate expression. It is

almost sacrilegious to call poetry an art. Without any intermediary of
violins, drums, trumpets, oils, palettes, brushes, mallets, chisels,
furnaces, scaffolds, and conditioned only by language, the poet can
utter that which is: the heart and the brain, the flesh, the bones and
the marrow—Matter become subconscious, conscious, and self-
conscious—are the orchestra and canvas of the poet's music and
vision; marble and bronze, the Parthenon and Notre Dame, are
misleading, unstable, and fleeting expressions of man and nature
compared with poetry. The more I think of the true substance of
poetry, the more impossible it is for me to see the necessity of
Wordsworth's affirmation: and his own poetry, as has long been
recognized, gives it the lie effectually.
As soon as he perceived the true nature of poetry, Wordsworth
began to write it as if no one had ever written it before—an
adventure commonly resented by the moralists of art, and in the
case of Wordsworth attended by a lifetime of detraction. Why did
not the literary world rise up as one man and crown the poet who
wrote in 1798, in his twenty-eighth year, the lines on Tintern Abbey?
Why was Wordsworth left without an audience, driven back into
himself, and thwarted in all his purposes, so that we have only—in
"The Prelude" and "The Excursion"—the gateway, porch, and raw
material of the city he meant to build? Why, but because he was an
immoralist—he, and not Byron—saying in a new manner that which
had not been said before: meaning something that schools and
churches, theatres and institutions, the periodical press and the
literature of the day, did not mean. Wordsworth had to think and
imagine the world and the universe for himself: for him the creeds
were outworn; for him "the smug routine and things allowed," in
which the common mind and imagination and the estates of the
realm live in most ages, were a dungeon and miasma. The

imagination of Wordsworth could not breathe in any Greek
mythology, any Christian Heaven and Hell, or theological system of
the Universe. Out of all the mythologies, pagan and Christian, he
culled this one thing only—the idea of spirit: which he whittled down
finally in the ninth book of "The Excursion" to an "active principle"—
no longer a poetical but a metaphysical idea. Now, metaphysic is an
aborted poetry. Poetry is concrete, requiring the exercise of all the
material powers of body, mind, and soul, which, co-operating, are
imagination. I have to use these words "mind" and "soul," because
for what I wish to say there is as yet no language. I hold that men
can think and imagine things for which there are no words: and that
men must attend upon the expression of these things before all
others: that these unsaid things are of more moment than all the
literature and religion of the past: and that these things can in the
first instance be said only by the poet, by one who makes words
mean what he, that is, what Matter chooses. The mind, separating
itself from the body and the soul, can transmute a figure of speech
into a category; indeed, there is probably no figure of speech that
could not be petrified into a metaphysic: metaphysics are the fossil
remains of dead poetries. Also, the soul can separate itself from the
body and the mind, and petrify a figure of speech into a theology:
creeds are the fossil remains of dead religions. The body, the static
and dynamic integer of which mind and soul are only exponents, is
held in profound disesteem by both metaphysic and theology. The
metaphysician says, "The Universe is thought"; the theologian says,
"The Universe is soul." It is as if one were to say "amber is
electricity," or "iron is sound," or "the spindrift is the sea," or "this
sure and firm-set earth is a word": all possible figures of speech, and
therefore all liable in the hands of a pedant to be erected into a
dogma. That was the tragedy of Wordsworth; his poetry became a

pedantry. It was not age—a man may be a poet at eighty; it was not
disease, as Wordsworth's health lasted to the end—besides, having
once known what health and strength are, a man may be a poet
although glued to the floor with consumption of the spinal marrow;
it was not poverty, for Wordsworth was frugal, nor ever knew the
hell it is to have to write for bread—besides, a man may be a poet
starving in a London suburb: it was the want of a great audience
and the world's applause that left Wordsworth to the pernicious
obsession of a metaphysic, dried up his poetry and made him at last
little better than a moralist. But whenever imagination had its way,
when his powers of body, mind, and soul were in equipollence and
co-operating, Wordsworth's immorality could be as free as
Shakespeare's or Burns's, and could disport itself with a naïveté, as
in "The Farmer of Tilsbury Vale," impossible to Shakespeare and
Burns, who were, both of them, men of the world; and no speech of
Falstaff or of Hamlet, no song of the Jolly Beggars, approaches the
stark utterance in "Rob Roy's Grave" of that immutable immorality
which is the inmost complexion of the world.
What was it Wordsworth really wanted? He wanted what all great
poets want, to extend his self-consciousness into the self-
consciousness of the world. At whatever cost to himself, his actual
and avowed aim was to live in the imagination of posterity to the
end of time. In effect his poetry says, and his prefaces and his
letters:—"What I desire—I make a present of it to all the humorists;
I love them, and I wish I were a humorist: I make a present of it to
all the wits; I love them also, and I would that I were witty: I make
a present of it to all the fools, whom I love the most, for there I
belong by reason of my naïveté and unworldliness: and, further, I
make a present of it to all the impertinents and to all the malignants,
whom I do not hate, for they are part of the whole—what I desire is

to substitute for Christendom a William Wordsworthdom." The two
potentates of English literature in the nineteenth century, Carlyle and
Wordsworth, had the same ambition—to furnish imagination with a
new abiding-place: the Carlyledom, which the first would have
substituted for Christendom, he called Hero-worship:
Wordsworthdom is a Nature-worship.
Carlyle took the world of great men for his province. His Mirabeau,
Mahomet, Cromwell, Frederick, have a somewhat closer resemblance
to their historical originals than Shakespeare's Hamlet bears to the
Hamlet of Saxo Grammaticus, the Hamlet who accomplished an
unhesitating revenge, married two wives, and died in battle: yet into
his chosen heroes Carlyle projected himself as passionately as
Shakespeare projected himself into Macbeth and Lear, and his
Cagliostro is as sympathetically drawn as his Burns. But men reject
Carlyledom. Willing enough, temporarily, to worship themselves in
Mahomet or Cromwell, they find the cult of great men so pursued to
end in all unhappiness; which is intolerable. Two men did try to live
in Carlyledom—Ruskin and Froude: and the end of them was
asphyxiation: Carlyle had exhausted the air: they had only his breath
to breathe. Carlyledom is a strait-jacket for the world, and a dusty
way to death and to the dull hell of the drill-sergeant and the knout.
"Declined with thanks," says mankind.
Wordsworth's worship was of a higher strain than Carlyle's. He
projected his own beauty of soul and his own strength of character
into the world and into the universe. Tenderly he enters the delight
of the daffodils: through the mountains he smites his powerful spirit.
Into all beauty and into all grandeur he pours his own love and
greatness, now an "eternal soul" clothed with the "unwearied joy" of

the brook "dancing down its waterbreaks," now apparelled in "the
Mighty Being" that
"doth with his eternal motion make A sound like thunder
everlastingly."
The Solitary Reaper, singing a Gaelic song, becomes, under the
spell of Wordsworth, a living presence and a power as of an
incarnate melody: and the same prodigious spell inspires the gaunt
and dreadful Leech-gatherer. Conceive how harsh, how crude an
image, however powerful, Balzac would have given of this, one of
the most appalling figures in all literature; but Wordsworth so
inspires his terrible Leech-gatherer with his own antique virtue, and
so invests him with his own extraordinary majesty, that it is only now
as I point it out you recognize the indwelling horror of a portrait
beside which the outcasts of the Russian realists lose all significance.
But men reject Wordsworthdom. Two did try to live in it— John
Stuart Mill and Matthew Arnold: but these were men of inferior
temperament: and Mill also lacked imagination, while in Matthew
Arnold imagination was a thing trained, as a tendon may, by special
exercise, be developed into a muscle. Further, neither Mill nor Arnold
had any childhood: they were never boys. Nowhere in
Wordsworthdom is there any actual room for that which, failing a
known surname, we still call by the "fond, adoptious Christendom"
of Romance: there is little scope in Wordsworthdom for Napoleon or
Wagner, for a great tragedy or a great triumph: nor is the universe
the projection of a Wordsworthian humanity into space. Generation
after generation may visit Carlyledom and Wordsworthdom, and
there may always be a few vengeful or placid minds to make, or to
try to make, a permanent abode in the frowning donjon of the one,

or the pastoral peace of the other: but neither is an enduring
habitation for the spirit of an era.
And now I come to my own immorality.
My four Testaments, "The Vivisector," "The Man Forbid," "The
Empire Builder," and "The Prime Minister," may be likened to statues
with subsidiary groups about their feet, and with panels in relief on
the four sides of the pedestals. As a fresco in the series of my
Testaments, and in order to bring home the matter contained in
them by a closer application to life than is possible in dramatic
monologue, also desiring to extend the circle of my readers and the
effect of my message, I wrote in the autumn of 1904 "The
Theatrocrat: a Tragic Play of Church and Stage." My hope was to
have this tragedy published and another ready by this time; but like
my own Knight of the Phoenix, "delays" are
"the lackeys circumstance Provides abundantly for all
my schemes."
On the night I finished "The Theatrocrat," being unable to sleep, I
searched about for an anodyne, and fell upon Wordsworth, whom I
had not looked into for twenty years. Remembering the tedium and
general drowsiness of "The Excursion," I turned to it—to the last
book, which I had not come within six of before. The pleasant
catalogue of the opening began to operate when suddenly, like one
hoist with his own petard, I sat up more than broad awake upon the
perusal of the sixteenth line—
"This is the freedom of the Universe."

I had written this line twice in "The Theatrocrat"! My memory is as
treacherous as most memories, and although I had never read the
last book of "The Excursion," I must in early days have read this line
in scholastic writings on Wordsworth. Promptly I turned to my
manuscript to change the line: but how could I? It was my meaning.
Instead, I retained it; and placed it also on the title-page as my
motto. A poet shall use that which belongs to him: it is the first
characteristic of his genius that he cannot learn: he can only use;
whether it be his own experience or the experience of others, he
takes everywhere the matter and form that suit him.
Some account of "The Theatrocrat" and of how I came to write it
seems necessary. My relations with the theatre are rather unusual.
At a time when I was occupied with ballads and eclogues, Mr. Forbes
Robertson, having looked into the volume of plays I wrote in
Scotland, surprised me with an invitation to prepare a version of a
French poetical play. It is no mere fashion of speech to say
"surprised": during the five years I had been in London, I had only
once visited a theatre, and although I considered drama my true
province, my calling and election had not yet become effectual, and
I certainly had never dreamt of entering these regions under a
foreign flag. But the proposal gratified me, was also suitable in
several ways, and the play interesting. On the production of my
adaptation at the Lyceum, the success of Mr. Robertson and Mrs.
Patrick Campbell in the parts they played attracted the attention of
managers to the adapter, and various proposals for versions were
made: but no one as yet thought of giving me a commission for an
original play: an adaptation of mine had succeeded, or seemed to
succeed: therefore I was to be an adapter. Being somewhat mollified
by seeming success—it was, as I said, Mr. Robertson and Mrs.
Campbell who had actually succeeded—I began again upon a French

play with considerable license of adaptation: but this license I
overstepped, and the matter fell through. I then wrote a play of my
own, and read it in succession to three managers, who listened
politely: I afterwards published this play. Again I made a play of my
own, this time upon commission, for the theatre is gallant, and likes
perseverance: but the actor-manager for whom I wrote it, deemed it
unsuitable, and again I published. Being now under the lash of
necessity, and not yet ready to die, having my Testaments and
Tragedies to write, I accepted commissions for adaptations, and in
due course made versions of five foreign dramatic pieces, and an
adaptation of a French novel, besides writing, also upon commission,
but at my own urgency, two original plays. This is an unusual record,
and the comedy of it lies here:—Not one of these adaptations was in
any degree of my own initiation, nor although I prepared them all
faithfully and some of them con amore, would I have chosen any of
them; yet it is by them my ability as a playwright has been tested:
while my own plays, "Godfrida," "Self's the Man," "The Knight of the
Maypole," and an unpublished Arthurian play remain unproduced.
The dismay of it is this:—That my Testaments and Tragedies—the
matter wherewith I propose to change the mood of the world—
remain, those that are issued, unknown; and those that should be
written, unwritten: whereas the successful production of my four
plays, the likeliest poetical plays written for the English stage in
these times, would have placed me in an independent and dominant
position from which all my writings could have come with that
adventitious authority the world is powerless to disregard.
After the playgoing public had failed to appreciate an adaptation
of mine, despite Mr. Lewis Waller's greatness in the part he played,
and an adorable queen of Mrs. Patrick Campbell's, I discovered,
upon various attempts, appeals, and challenges, that the stage

would be well pleased to do without me in the meantime, and under
these auspices, which I took to be the true evolutionary
determinant, I began upon my own tragedies and wrote "The
Theatrocrat: a Tragic Play of Church and Stage." This play derives its
title from the rank and vocation of the protagonist, Sir Tristram
Sumner, proprietor and manager of the Grosvenor Theatre. The
meaning of the title will best appear in Sir Tristram's own words
addressed to his friend and patron, the Bishop of St. James's. "I,"
says Sir Tristram,
"Became at last an artist: think of it!
I found myself the master of the mood,
Enchanting folk and playing on their nerves
As though an audience were a zither; made
A name far-sounding; and, by your good will,
Am now—Heaven save the mark! the banal end!—
Am now Sir Tristram Sumner, nominal,
As well as actual, theatrocrat;"
and the significance of the sub-title will come home to the reader
in the following extract from the diatribe of an exasperated actor
addressed to Sir Tristram himself:—
"When plays were damned
By churchmen, and the player a citizen
Of rascaldom on sufferance living only,
Great was the stage …
When the monarch set
The lethal signet on the theatre
Of gross respectability, knighting you,
Sir Tristram, and other players unfortunate,

Ranking you in the state with grocers, brewers,
Distillers, lawyers, vicars, aldermen,
He dealt a double blow at church and stage,
And both are bleeding from the wound."
The reader notes the special application here, and distinguishes
also between religion and the church, remembering the religious
import of the Attic drama. The plot of the play is simple. Sir Tristram
Sumner, a man of remarkable ability, having led an inharmonious
life, has reached that period when the material powers of mind and
soul begin to rebel against the over-indulged body, and are apt to
declare themselves in megalomaniacal obsessions. His instinct, once
infallible, misleads him, and he determines, against all advice, to
produce Shakespeare's "Troilus and Cressida." His wife, originally a
beautiful and healthy woman, has shared her husband's sensuality,
and is now haggard and neurotic, her ill-used soul asserting itself
discordantly in trances and telepathic visions. She is haunted by the
fancy that the play will succeed if Warwick Groom, a disgraced actor
of genius, takes the part of Troilus. Sir Tristram, who knows that
Lady Sumner had loved Warwick in her youth, has developed a
fierce jealousy of his former rival and a deadly hate for his wife; but
his financial position is so perilous, and his wife's premonitions have
been hitherto so reliable, that he dare not disregard her brain-sick
counsel. Warwick Groom's besetting vice, drunkenness, prevents his
appearance as Troilus, and the play fails. Bankruptcy and the end
have come. But now the Bishop of St. James's intervenes, and
finances Sir Tristram in order to produce a play of his own. St.
James's has a message to deliver, and prefers the theatre to the
pulpit. On the night of the production of his play he himself is to
introduce it in a guarded speech: but soon—a true propagandist—

"He stands entranced,
With face uplifted like a seraph, pealing
Material music, from his prologue worlds
Away."
At last the incensed audience, led by a "fighting parson" from the
stalls, invades the stage. St. James's is mobbed and dies of his
injuries. Of Sir Tristram's liaison with Europa Troop, an American
actress; of Lady Sumner's suicide, and the murder of Sir Tristram by
Warwick Groom, I say nothing here. My present concern is with St.
James's message, which is also mine: my statement of the world,
and of the Universe as the world can know it. I should add that
there is no key to "The Theatrocrat": all the people in it are made
essentially out of the good and evil in myself. My statement of the
world and of the Universe as the world can know it has offended and
will offend; but I have no purpose of offence; nor am I concerned to
please: my purpose is to say that which is, to speak for the Universe.
I mean nothing occult or mystical; only the natural mystery of
Matter. Man consists of the same Matter as the sun and the stars
and the omnipresent Ether; he is therefore the Universe become
conscious; in him the Universe thinks and imagines; and every man
who trusts himself trusts the Universe, and can say that which is. I
announced at the outset that I wished to transmute the depreciated
word "immorality," and admitted the difficulty of such a feat of
verbal alchemy in England, where the current meaning of immorality
is so narrow, nauseous, and stupid. And yet nothing could be simpler
than such a transmutation. We know now that there is no moral
order of the Universe, but that everything is constantly changing and
becoming and returning to its first condition in a perpetual round of
evolution and devolution; and this eternal tide of Matter, this restless
ebb and flow, I call Immorality. All men and things have a Will to be

Moral, have a Will to Righteousness—the metaphysic of religion. The
omnipresent Ether would fain be an established moral order of Ether,
pure, imponderable, invisible, constant; but that thorn in the flesh,
electricity, evolves from the Ether while still interpenetrated by it,
and the moral order of the Ether is at end. Electricity, the first
analysable form of Matter, for we have not yet isolated a sample of
the Ether, would fain be electricity, pure and perfect bi-sexuality and
nothing else; but hardly has it had time to adjust its negative and
positive poles when it begins to secrete hydrogen, and this wanton
seminary of Matter once opened, some seventy or eighty elements
are soon scored against the demoralized electricity. Among men
there is the same intense Will to Morality. How slowly a moral order
decays! Apollo and Aphrodite are still alive in the fancy of men! The
massacre of Saint Bartholomew, the depletion of the manhood of
France by the revocation of the edict of Nantes, the war of the
Fronde, the horrors of the Revolution, of the wars of Napoleon, of
the Franco-German war and of the Commune, which were the
evolution of the French Republic, witness the tenacity of an old
order, and how utterly regardless of the cost of its establishment a
new order is. The Universe is immoral, and no sooner has a morality
of any order established itself than the Universe begins to undo it.
To me the centuries of Christendom are only as a moment of time
which has ended, and in my heart I believe
"Terrific war
Will burst the chrysalis, the Christendom,
That hangs in rags about the eager soul,
Already wing'd and rich with crimson stains,
With sulphur plumes and violet, green and gold,
Psyche at last, pure Matter of itself!"

I have repeatedly attempted to speak this that I am writing, and
have always failed, coming out of it in a dumb rage. It is true that no
man, great or small, was ever so tongue-tied as I am; but it is also
true that the people one talks with who are consciously interested in
the Universe are almost always either theologians or metaphysicians,
men of dogma and system who can neither think nor imagine
beyond their rubrics: poetry to them is on the other side of the
hedge; it may be a vineyard, but they are tethered in their own plot
of thistles, and very well satisfied too. I have no system; I have no
dogma: it is a new poetry I bring. For me there is nothing
immaterial; for me everything matters; for me there is nothing
behind phenomena: the very "thing in itself" is phenomenon;
phenomena are the Universe. I, doubtless, prefer to drop such
words as "phenomenon," such phrases as "thing in itself," specialized
out of all meaning, precisely as the Bishop of St. James's and I drop
all legends
"Of dead men come alive, and signs and shows
Of tongues and thunders, cures and stigmata,
Which are no mystery but the quaint alarm
Of ignorance, that harnessed vision against
The things that be in sterile dreams of spirit,
As banal, venomous-moral, hard and fast
As Matter is mysterious, fluent, pure,
Filling the Universe with miracle,
Filling and being the Universe itself."
I am not an atheist. The words atheist and atheism, infidel and
infidelity, seem to me misnomers, mere childish nicknames,
unpoetical, inapplicable, feebly malignant; you cannot disbelieve in
what is not; so violent a reaction as disbelief intimates the existence

of that which is antagonized: one might as well say, "There is no
Hamlet; there is no Don Quixote," as affirm the nonentity of God.
Indeed and indeed there has been nothing but God for many a
century. For the active world, the money-making, breeding,
pleasure-seeking, power-loving world, the rulers, artists, poets,
merchants, soldiers, the great world as distinguished from the
studious faction of scientists, theologians, philosophers, and men of
letters—an insignificant and negligible minority in this particular: for
this great world, God sums imagination; not an idea; no, the Ancient
of Days, the Almighty; called a spirit, but a most Material, most
poetical God, who created the world out of nothing, with the sun to
light it by day and the moon and stars by night; who made man in
His own image; who sent His son to atone for His creatures'
backslidings; and who provided Heaven for the repentant sinner, and
Hell for the unregenerate; for God and Sin and Heaven and Hell that
are not
"Are yet the very texture of the world,
Kings, magistracies, warriors, wisdom, love,
Being knit in Heaven and Hell, in God and Sin,
Like blood, nerve, sinew, bone in living flesh."
But a minority are no longer knit up in this divine texture. When
science found out that the world and man had not been created at
all—could not possibly have been created or made in any sense of
these terms; that instead of the sun being specially prepared as a
lantern to light the earth, the earth is really an offscouring of the
sun; and when it searched the Universe and sampled it with its
telescope, discovering although it plunged vision through thousands
of millions of miles that there was no lodge anywhere for Heaven, no
pit to be the continent of Hell, but only illimitable tracts of

incandescent orbs, each the centre of a system to which our solar
nook of space is as a little room by candle-light compared with that
very sunlit space itself, then science knew, as I know, that the
theological system of the Universe is an error of man's ignorance: an
error so wonderful and so significant that I still attend upon the
adequate expression of its true intention. In the Matter of God and
Sin and Heaven and Hell, men of letters are apt to be lukewarm—
not all, but the majority. I exclude poets from the class of men of
letters. Men of letters are humane, moral, civilized, cultured,
sceptical; whereas poets are inhuman, immoral, barbaric,
imaginative, and trustful. With most literary critics, publicists,
journalists, dealers in the humanities, and professional people
generally, God and Sin and Heaven and Hell are not debateable
subjects. Why should anyone nowadays concern himself about these
things? If they are not dead and done with, it is bad taste to discuss
them in a secular work; if they are dead and done with, it is worse
taste, and a waste of time to lug them into the light of day:
arguments that seem to me unanswerable; but here am I with these
dead things to bury, and my message to deliver.
What the theologian calls God, the metaphysician calls by various
names. One will tell you that the world is a Will to Live rushing into
being. Another will say, "That does not account for man: if a Will to
Live is the thing in itself, man is de trop, for man is the greatest foe
life has. Other animals kill only to satisfy hunger; but man, although
for food and for sport he preserves life, yet for sport, for food, for
adornment, and to make room for himself, man has destroyed, and
continues to destroy, life by whole species, including those of his
own kind. No, there is something behind the Will to Live, and that is
the Will to Power. A Will to Power accounts for man; man, the tamer
of the tide, of the lion and the lightning; and man, the tamer of

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