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Astrophysics
of
Gaseous Nebulae
uclei
Second Edition
IP*
-* #
Donald E. Osterbrock
Gary J. Ferland

SECOND EDIT I O N
Astrophysics of Gaseous Nebulae
and Active Galactic Nuclei

NGC 1976, the Orion Nebula, probably the most-studied H II region in the sky. The contrast in
this image, which was taken in the light of Ha, has been reduced to allow both the bright inner
regions and the faint outer regions to be visible. The Trapezium is the group of four stars near
the center of the nebula. The nebula to the upper left (northeast) is NGC 1982. (John Bally,
KPNO)

SECOND EDIT1 O N
Astrophysics of
Gaseous Nebulae
and Active Galactic
Nuclei
Donald E. Osterbrock
TRENTO
^ UNIVERSITY
LIBRARY
PETERBOROUGH. ONTARIO
Lick Observatory, University of California, Santa Cruz
Gary J. Ferland
Department of Physics and Astronomy, University of Kentucky
UNIVERSITY SCIENCE BOOKS
Sausalito, California

University Science Books
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or 108 of the 1976 United States Copyright Act without the permission of the copyright
owner is unlawful. Requests for permission or further information should be addressed to the
Permissions Department, University Science Books.
Uibrary of Congress Cataloging-in-Publication Data
Osterbrock, Donald E.
Astrophysics of gaseous nebulae and active galactic nuclei.—2nd ed. /
Donald E. Osterbrock, Gary J. Ferland.
p. cm.
ISBN 1-891389-34-3 (alk. paper)
1. Nebulae. 2. Galactic nuclei. 3. Astrophysics. I. Ferland, G. J. II. Title.
QB855.55.088 2005
523.1'125—dc22 2005042206
Printed in the United States of America
10 987654321

Contents
Preface xi
Preface to the First Edition .xv
General Introduction 1
1.1 Introduction 1
1.2 Gaseous Nebulae 1
1.3 Observational Material 3
1.4 Physical Ideas 7
1.5 Diffuse Nebulae 8
1.6 Planetary Nebulae 10
1.7 Nova and Supernova Remnants
1.8 Active Galactic Nuclei 12
1.9 Star Formation in Galaxies
Photoionization Equilibrium 17
2.1 Introduction 17
2.2 Photoionization and Recombination of Hydrogen 19
2.3 Photoionization of a Pure Hydrogen Nebula 23
2.4 Photoionization of a Nebula Containing Hydrogen and Helium
2.5 Photoionization of He+ to He++ 33
2.6 Further Iterations of the Ionization Structure 35
2.7 Photoionization of Heavy Elements 35
Thermal Equilibrium 45
3.1 Introduction 45
3.2 Energy Input by Photoionization 45
3.3 Energy Loss by Recombination 47
3.4 Energy Loss by Free-Free Radiation 49

vi Contents
3.5 Energy Loss by Collisionally Excited Line Radiation
3.6 Energy Loss by Collisionally Excited Line Radiation of H
3.7 Resulting Thermal Equilibrium 60
Calculation of Emitted Spectrum 67
4.1 Introduction 67
4.2 Optical Recombination Lines 68
4.3 Optical Continuum Radiation 77
4.4 Radio-Frequency Continuum and Line Radiation 88
4.5 Radiative Transfer Effects in H I 92
4.6 Radiative Transfer Effects in He I 97
4.7 The Bowen Resonance-Fluorescence Mechanisms for O III and O I
4.8 Collisional Excitation in He I 100
99
Comparison of Theory with Observations 107
5.1 Introduction 107
5.2 Temperature Measurements from Emission Lines 108
5.3 Temperature Determinations from Optical Continuum
Measurements 114
5.4 Temperature Determinations from Radio-Continuum Measurements
5.5 Temperature Determinations from Radio and UV Absorption Lines
5.6 Electron Densities from Emission Lines 121
5.7 Electron Temperatures and Densities from Infrared Emission Lines
5.8 Electron Temperatures and Densities from Radio Recombination
Lines 127
5.9 Filling and Covering Factors 133
5.10 Ionizing Radiation from Stars 135
5.11 Abundances of the Elements in Nebulae 142
5.12 Calculations of the Structure of Model Nebulae 148
116
120
127
Internal Dynamics of Gaseous Nebulae 157
6.1 Introduction 157
6.2 Hydrodynamic Equations of Motion 158
6.3 Free Expansion into a Vacuum 161
6.4 Shocks 162
6.5 Ionization Fronts and Expanding H+ Regions 164
6.6 Magnetic Fields 169
6.7 Stellar Winds 170

Contents vii
Interstellar Dust 177
7.1 Introduction 177
7.2 Interstellar Extinction 177
7.3 Dust within H II Regions 184
7.4 Infrared Thermal Emission 190
7.5 Formation and Destruction of Dust Particles 194
7.6 Grain Opacities 195
7.7 Effects of Grains on Surrounding Gas 197
7.8 Dynamical Effects of Dust in Nebulae 200
Infrared Radiation and Molecules 207
8.1 Introduction 207
8.2 The Structure of a PDR 207
8.3 The H2 Molecule 211
8.4 The CO Molecule 214
8.5 Comparison with Observations 216
8.6 Molecules Around H II Regions 221
HII Regions in the Galactic Context 225
9.1 Introduction 225
9.2 Distribution of H II Regions in Other Galaxies 225
9.3 Distribution of H II Regions in Our Galaxy 227
9.4 Stars in H II Regions 230
9.5 Abundances of the Elements 232
9.6 Newly Formed Stars in H II Regions 240
9.7 Starburst Galaxies 242
Planetary Nebulae 247
10.1 Introduction 247
10.2 Distance Determinations 247
10.3 Space Distribution and Kinematics of Planetary Nebulae 251
10.4 The Origin of Planetary Nebulae and the Evolution of Their Central
Stars 253
10.5 The Expansion of Planetary Nebulae 258
10.6 Morphology and Composition 261
10.7 Planetary Nebulae with Extreme Abundances of the Elements 264

Contents
10.8 Molecules in Planetary Nebulae 266
10.9 Mass Return from Planetary Nebulae 268
10.10 Planetary Nebulae in Other Galaxies 269
11 Heavy Elements and High-Energy Effects 277
11.1 Introduction 277
11.2 Physical Processes Involving Bound Electrons 277
11.3 Physical Processes at Still Higher Energies 283
11.4 Physical Conditions from X-ray Spectroscopy 286
11.5 Collisional Excitation of H° 290
Nova and Supernova Remnants 295
12.1 Introduction 295
12.2 Nova Shells 295
12.3 The Crab Nebula 301
12.4 The Cygnus Loop 307
12.5 CasA 314
12.6 Other Supernova Remnants 316
12.7 Spectroscopic Differences Between Shock-Heated and Photoionized
Regions 316
12.8 i) Car 317
Active Galactic Nuclei—Diagnostics and Physics
13.1 Introduction 325
13.2 Historical Sketch 326
13.3 Observational Classification of AGNs 328
13.4 Densities and Temperatures in the Narrow-Line Gas
13.5 Photoionization 340
13.6 Broad-Line Region 345
325
336
Active Galactic Nuclei—Results
14.1
14.2
14.3
14.4
Introduction 353
Energy Source 353
Narrow-Line Region
LINERs 361
356
353

Contents
14.5 Broad-Line Region 363
14.6 Dust in AGNs 372
14.7 Internal Velocity Field 374
14.8 Physical Picture 382
APPENDIX A. Measures of Light 395
A 1.1 Specific Intensity / 395
A 1.2 Flux F 396
A 1.3 Mean Intensity 7 397
A 1.4 Energy Density and Radiation Pressure 397
A 1.5 Emittance 398
A 1.6 Surface Brightness S 399
A 1.7 Emissivity and Observed Quantities 399
2
APPENDIX ^ Milne Relation Between Capture and Photoionization Cross
Sections 401
3
APPENDIX Emission Lines of Neutral Atoms 405
APPENDIX 4 Nebular Quantum Mechanics 407
APPENDIX 5 Atomic Data for Heavy Element Ionization Balance 423
APPENDIX ^ Quantum Mechanics of Molecules 433
Glossary of Physical Symbols 437
Glossary of Telescope and Instrument Acronyms 443
Index 445

Preface
This book is a revised, updated, and expanded edition of Astrophysics of Gaseous Neb¬
ulae and Active Galactic Nuclei (1989) by one of us (D. E. O.), and that book was
based in turn on an earlier volume. Astrophysics of Gaseous Nebulae (W. H. Freeman,
1974) by the same author. Over the 30 years between the publication of that first book
and the completion of the manuscript of the present one the subject of ionized-gas
astrophysics has grown phenomenally. Astronomers have long studied gaseous neb¬
ulae, and the cooler, less intrinsically luminous dust and molecular clouds associated
with them, for their intrinsic interest. In addition, stars are almost completely opaque,
and it is impossible to observe their interiors directly, or to measure their internal
temperatures, pressures, densities, or abundances of the elements within them except
by indirect methods. Many nebulae, on the other hand, are relatively transparent, and
we can measure these quantities directly.
Since Walter Baade’s discovery of the two stellar populations, which turned out
to be young stars and old, and the working out of the main nuclear reaction chains
that release energy on stars by Hans Bethe, C. F. von Weizsacker, and others, we
have begun to understand the way in which most stars evolve. Much remains to be
filled in, both observationally and theoretically, and we have learned how to trace
star formation and evolution not only from stars themselves, but from their effect on
the gas around them as well. We can estimate or measure the star formation rate not
only with nebulae in our Galaxy, but throughout distant galaxies in the universe, from
emission lines emitted in nebulae, clouds, associations, and spiral arms in galaxies,
and even from entire galaxies.
Interpreting the measurements is not straightforward; the path between is through
"nebular astrophysics”, as explained in this book. Fikewise we can measure abun¬
dances of the elements in all these objects with the same basic tools. We can directly
observe, in some planetary nebulae and supernova remnants, the changed abundances
of the elements that resulted within the stars themselves, leading to slow mass loss,
shells thrown off from the star, or thermonuclear reactions at the surfaces of highly
evolved stars.
Active galactic nuclei and their close relatives, quasars and other types of quasis-
tellar objects, are a field of research only 40 years old, which has grown explosively.
Almost all we know about them came from study of their spectra, and especially their
emission-line spectra, very similar to but not identical with those of gaseous nebulae.
Maarten Schmidt, J. Beverly Ole, and Jesse F. Greenstein’s giant leap in understand¬
ing the basic nature of 3C 273 and 3C 48 depended on their knowledge of nebular
xi

Preface xii
emission lines, and the subsequent study of all these objects has paralleled the study
of gaseous nebulae.
Cosmology has advanced tremendously in the past decade or two, based on the
availability of new, very large telescopes, either on high mountains like Keck I and II
on Mauna Kea, Hawaii, and the VLT on Paranal, Chile, or in space, like the Hubble
Space Telescope, and their fast, digital imaging systems and spectrometers. All the
most distant objects we know have been identified and measured by their “nebular
emission lines emitted within them, from HI Lo' to [OII] X3121, [O III] AA4959, 5007,
and Her. How can we be sure it is one of these lines that an astronomer has observed?
If it was, what other lines should be seen? If they are not seen, should that purported
identification be rejected? If the identification is correct, what physical information
(besides redshift and hence distance and look-back time) can be drawn from it? These
are some of the questions which nebular astrophysics can help to answer.
In all these subjects, going beyond simply using a formula or canned interpre¬
tation from a previously published paper, is a necessity, in our opinion. We have
tried to explain and illustrate the methods used, but also to express reasonable doubts
about some far-reaching conclusions drawn from minimal data, without examining
possible alternative interpretations. In the final chapter of the book we have outlined
several questions about active galactic nuclei which shall await full explanations. The
methods of the book will be useful in deciding the answers, we feel certain.
The fundamental outline and style of exposition of Astrophysics of Gaseous Neb¬
ula and Active Galactic Nuclei, often referred to as (AGN)2, has been preserved in
this new edition, but we have carefully gone through every chapter, weeding out the
old and including many new results, measurements, and ideas. Each chapter was com¬
pletely rewritten, and then revised several times. Furthermore, since its publication of
the first edition, results from two fast-developing observational techniques, infrared
astronomy and X-ray astronomy, have multiplied many fold. Hence we not only up¬
dated the material in these two fields for this edition, which we call AGN3, but have
added much more new material, so it now includes two more chapters, one on each
of these topics. In both these chapters, and in the rest of the book as well, we have
emphasized the continuity of the physical ideas across the boundaries of “spectral
regions” and the importance of observing and analyzing data over as wide a range of
wavelengths as possible.
From comments of many recent students and current researchers who are using
(AGN)2, we are aware that beginning graduate students of astrophysics today gener¬
ally know much more about applications of quantum mechanics to nuclear physics
than the previous generation, but much less about its applications to atomic spec¬
troscopy, so necessary in nebular astrophysics. Hence we have added a completely
new appendix on “nebular quantum mechanics”, and also a shorter one on “molecu¬
lar quantum mechanics” (which neither generation of astrophysics graduate students
know very well) to help bring them in to the fold.
Most of the figures are new, based on recent published measurements and inter¬
pretations, and on images obtained with the most advanced telescopes and detecting
systems of today. We are grateful to many colleagues who gave us permission to use
them in AGN3.

Preface xiii
All the chapters, after the first five, which deal with basic material, have been
reviewed for us by colleagues and friends who are active research experts in the
various fields. We are most grateful to the following for their efforts on our behalf, who
either contributed material or reviewed chapters: Jack Baldwin, John Bally, Robert
Bauman, Mark Bottorff, Eugene Capriotti, John Danziger, Kris Davidson, Reginald
Dufour, Robert Fesen. Donald Garnett, William Henney, Richard B. Henry, Luis Ho,
Roberta Humphries, George Jacoby, Sveneric Johansson, Steven Kahn, Kirk Korista,
Steven Kraemer, Karen Kwitter, Sun Kwok, Xiaowei Liu, John Mathis, Jon Morse,
C. Robert O'Dell, Manuel Peimbert, Richard Shaw, Gregory Shields, Joseph Shields,
Lewis Snyder, Phillip Stancil, Barry Turner, Sidney van den Bergh, Peter van Hoof,
Sylvain Veilleux, Nolan Walborn, Joseph Weingartner, Robin Williams, Robert E.
Williams, Mark Wolfire, and Stan Woosley. We also are extremely grateful to Nick
Abel who carefully read the entire manuscript. We thank Jeffrey Mallory and John
Rickard for help in producing the final manuscript. Any errors which may remain are
our responsibility, not theirs.
D. E. O.
G. J. F.

Preface to the First Edition
Fifteen years ago I sent to the publisher my book on Astrophysics of Gaseous Nebulae.
It was a graduate-level text and research monograph that evidently filled a need, for it
soon became widely used and quoted. Over the years since then the book has found
increasing use, not only in nebular research, but also in problems connected with
quasars, Seyfert galaxies, quasistellar objects, and all the other fascinating types of
active galactic nuclei whose emission-line spectra are similar, in general terms, to
those of gaseous nebulae. My own research had turned in those directions since I came
to Lick Observatory in 1973 and began obtaining data with its superbly instrumented
3-m Shane reflecting telescope, as it now is named.
Hence as AGN (for so my first book is often referred to) gradually became
dated, particularly in its tables of observational results and theoretical calculations,
it was natural for me to think of revising it, and of extending it to Astrophysics of
Gaseous Nebulae and Active Galactic Nuclei at the same time. Many of my friends
and colleagues urged me to do so. Thus the present {AGN)2 came about.
Like the earlier AGN, it is both a graduate-level text and an introduction to nebular
and AGN research. The first nine chapters are based upon the first nine chapters of
the earlier book, but have been heavily revised and updated. The last three chapters
are completely new, one on nova and supernova remnants, and the final two chapters
on active galactic nuclei. The emphasis is very strongly on the ionized gas in AGNs
and the emission-line spectra they emit; their X-ray and radio-frequency radiations
are only briefly mentioned.
The book is based upon graduate courses that I have given often at the University
of California, Santa Cruz. It represents the material I consider necessary to understand
research papers that are now being published in its fields. So much is known today,
and so many new results are pouring out, that it is probably impossible to go straight
from studying any book to doing frontier research oneself. But I believe that this book
will enable the reader to get up to speed, so that he or she will be able to read and
understand current research, and then begin to add to it.
The reader for whom {AGN)2 was written is assumed to have a reasonably
good preparation in physics, and some knowledge of astronomy and astrophysics.
The simplest concepts of radiative transfer are used without explanation, since the
reader almost invariably has studied stellar atmospheres before gaseous nebulae and
active galactic nuclei. Physical parameters, such as collision cross sections, transition
probabilities, and energy levels, are taken as known quantities; no attempt is made to
derive them. When I teach this material I usually include some of these derivations,
linking them to the quantum-mechanics textbooks with which the students are most
xv

XVI Preface to the First Edition
familiar. Omitting this material from the book left room to include more interpretation
and results on gaseous nebulae and active galactic nuclei.
References are given at the end of each chapter, in a separate section. They are
not inserted in the text, partly so that they will not break up the continuity of the
discussions, and partly because the text is a complicated amalgam of many papers,
with no obvious single place at which to refer to many of them. Almost all the
references are to the American, English, and European astronomical literature, with
which I am most familiar; it is also the literature that will be most accessible to the
readers of this book.
I would like to express my deep gratitude to my teachers at the University of
Chicago, who introduced me to the study of gaseous nebulae; Thornton L. Page, S.
Chandrasekhar, W. W. Morgan, and the late Bengt Stromgren. I am also very grateful
to my colleagues and mentors at the Mount Wilson and Palomar Observatories, as
it was then named, the late Walter Baade and the late Rudolph Minkowski, who
encouraged me to apply what I knew of nebular astrophysics to the study of galaxies.
I owe much to all these men, and I am grateful to them all for their continued
encouragement, support, and stimulation.
I am extremely grateful to my colleagues and friends who read early drafts of
various chapters in this book and sent me their suggestions, comments, and criticisms
on them: Donald P. Cox, Gary J. Ferland, William G. Mathews, John S. Mathis,
Manuel Peimbert, Richard A. Shaw, Gregory A. Shields, Sidney van den Bergh,
Robert E. Williams, and Stanford E. Woosley. In addition, my two current graduate
students, Richard W. Pogge and Sylvain Veilleux, carefully read the entire manuscript;
their comments and corrections greatly improved it, as did those of Dieter Hartmann
and Philip A. Pinto, both of whom carefully read the supernova material. I am most
grateful to them all.
Though these readers found many misprints and errors, corrected many misstate¬
ments, and clarified many obscurities, the ultimate responsibility for the book is mine.
I have tried very hard to find and remove all the errors, but some must surely remain,
to be discovered only after publication. I can do no better than repeat once again the
words of a great physicist, Richard P. Feynman. “Listen to what I mean, not to what
I say.” If the reader finds an error, I am sorry I did not catch it, but he or she will have
proved his or her real understanding of the material, and I shall be very pleased to
receive a correction.
I am greatly indebted to Gerri McLellan, who entered on the word processor the
first drafts of all the chapters, and all the successive revisions of the manuscript, and to
Pat Shand, who made the final editorial revisions and prepared the camera-ready copy
for publication. I deeply appreciate the skill, accuracy, and dedication with which they
worked on this book. I am also most grateful to my wife, Irene H. Osterbrock, who
prepared the index for the book.
My research on gaseous nebulae and active galactic nuclei has been supported
over the past fifteen years by the University of California, the John Simon Guggen¬
heim Memorial Foundation, the University of Minnesota, the University of Chicago,
the Institute for Advanced Study, the Ohio State University, and especially by the
National Science Foundation. I am grateful to all of these organizations for their gen-

Preface to the First Edition XVII
erous support. Much of my own research, and of the research of the graduate students
and postdocs who have worked and are working with me, has gone into this book; I
could never have written it without doing that research myself.
I am especially grateful to my friends George H. Herbig, Paul W. Hodge, Guido
Munch, and Robert E. Williams, who provided original photographs included in this
book. I am grateful to them and also to Palomar Observatory, Lick Observatory, and
the National Optical Astronomy Observatories for permission to use the photographs
(which are all credited individually) in this book. Publication of the photographs from
NOAO does not imply the endorsement by NOAO, or by any NOAO employee, of this
book! Many of the other figures are derived from published papers, and I am grateful
to their authors for permission to modify and use their figures in this book.
Lastly, I wish to express my sincere thanks to my friends Bruce Armbruster,
president of University Science Books, and Joseph S. Miller, my colleague, former
student, and astronomy co-editor with me for USB, both of whom encouraged me
time after time to go on with revising AGN and writing the additional new chapters
for {AGN)2. Bruce was the astronomy editor for W. H. Lreeman and Company when I
wrote the earlier book, and he helped me greatly with it then, as he has helped me with
{AGN)2 now. It was a great pleasure for me to work with him on both these books. I
am also grateful to W. H. Lreeman and Company for releasing me from my obligation
to them, and allowing me to publish this book with USB.
Donald E. Osterbrock

1
General Introduction
1.1 Introduction
Many important topics in astrophysics involve the physics of ionized gases and the
interpretation of their emission-line spectra. The subject is fascinating in itself. In
addition, H II regions allow us to probe the evolution of the elements and the star-
formation history of the far reaches of our own Galaxy, and of distant galaxies.
Planetary nebulae let us see the outer remaining envelopes of dying stars. Supernova
remnants allow us to observe material from the burned-out deep interiors of exploded,
massive stars. Starburst galaxies, quasars, and QSOs are the most luminous objects
in the universe, and hence the most distant that we can observe. Spectra can reveal
details surrounding the first generations of star birth and the formation of the heavy
elements in the young universe. All of these are subjects we shall cover in this book.
Further applications, such as the properties of intergalactic material. X-ray flows, and
primordial galaxies, though not treated here, are straightforward extensions of the
physics that forms the spine of this volume.
1.2 Gaseous Nebulae
Gaseous nebulae are observed as bright extended objects in the sky. Those with
the highest surface brightness, such as the Orion Nebula (NGC 1976) or the Ring
Nebula (NGC 6720), are easily observed on direct images, or even at the eyepiece
of a telescope. Many other nebulae that are intrinsically less luminous or that are
more strongly affected by interstellar extinction are faint on ordinary images, but
can be imaged on long exposures with filters that isolate a narrow wavelength region
around a prominent nebular emission line, so that the background and foreground
stellar and sky radiations are suppressed. The largest gaseous nebula in the sky is
the Gum Nebula, which has an angular diameter of the order of 30°, while many
familiar nebulae have sizes of the order of one degree, ranging down to the smallest
objects at the limit of resolution of the largest telescopes. The surface brightness of a
nebula is independent of its distance, but more distant nebulae have (on the average)
smaller angular size and greater interstellar extinction; so the nearest members of any
particular type of nebula tend to be the most-studied objects.
1

General Introduction
Figure 1.1
The ultraviolet, optical, and near infrared spectrum of inner regions of the Orion Nebula. A
few of the strongest lines are identified in the plot; their wavelengths and those of all the other
emission lines, from C III] A1909 to [S III] AA9069, 9531 (except the H I and He I lines)
may be found in Chapter 3. The flux scale is normalized to the flux in H/l = 1. (Original data
provided by Reginald Dufour and Jack Baldwin.)
Gaseous nebulae have emission-line spectra. Their spectra are dominated by
forbidden lines of ions of common elements, such as [O III] AA4959, 5007, the famous
green nebular lines once thought to indicate the presence of the hypothetical element
nebulium; [NII] AA6548, 6583 and [S III] AA9069,9523 in the red; and [OII] AA3726,
3729, the ultraviolet doublet which appears as a blended A3727 line on low-dispersion
spectrograms of almost every nebula (Figure 1.1). In addition, the permitted lines of
hydrogen, Ha A6563 in the red, H/l A4861 in the blue, Hy A4340 in the violet, and
so on, are characteristic features of every nebular spectrum, as is He I A5876, which
is considerably weaker, while He II A4686 occurs only in higher-ionization nebulae.
Long-exposure spectrophotometric observations extending to faint intensities, show
progressively weaker forbidden lines, as well as faint permitted lines of common
elements, such as C II, C III, C IV, O II, and so on. Nebular emission-line spectra, of
course, extend into the infrared, where [Ne II] A 12.8 /Tin and [O III] A88.4 /rm are
among the strongest lines measured, and into the ultraviolet, where Mg II AA2796,
2803, C III] AA1907, 1909, C IV AA1548, 1551, and even La A1216 are also observed.
It is seldom possible to observe all important stages of ionization in a particular
spectral region. In these cases one must model the physical system or obtain spectra

1.3 Observational Material 3
outside of the traditional visible/near-IR bands to get an accurate picture of the system
in question.
Gaseous nebulae have weak continuous spectra, consisting of atomic and reflec¬
tion components. The atomic continuum is emitted chiefly by free-bound transitions,
mainly in the Paschen continuum of H I at A > 3646 A, and the Balmer continuum at
o o
912 A < A < 3646 A. In addition, many nebulae have reflection continua consisting
of starlight scattered by dust. The amount of dust varies from nebula to nebula, and
the strength of this continuum fluctuates correspondingly. In the infrared, the nebular
continuum is largely thermal radiation emitted by the dust.
In the radio-frequency region, emission nebulae have a reasonably strong con¬
tinuous spectrum, mostly due to free-free emission or bremsstrahlung of thermal
electrons accelerated on Coulomb collisions with protons. Superimposed on this con¬
tinuum are weak emission lines of H, such as 109o' at A = 6 cm, resulting from
bound-bound transitions between very high levels of H. Weaker radio recombi¬
nation lines of He and still weaker lines of other elements can also be observed
in the radio region, slightly shifted from the H lines by the isotope effect. In the
infrared spectral region most nebulae have strong continuous spectra, emitted by
heated dust particles within them. These emission continua have bands, some iden¬
tified as resulting from silicate or graphite in the particles, others still not positively
identified.
1.3 Observational Material
Nebulae emit a broad range of “light”, by which we mean the full range of electro¬
magnetic radiation, although only a few wavelengths pass easily through the Earth's
atmosphere. Figure 1.2 shows the altitude above which atmospheric attenuation (“ab¬
sorption”) is negligible. Visible light, and some infrared and radio radiation, can be
studied from the ground, but most other wavelength regions can only be observed
from high-altitude aircraft, balloons, or orbit.
The resolution that can be achieved is limited by the telescope and the detector,
and also by the refractive effects of the air. Spatial resolution is measured by the
apparent diameter of a point source, usually expressed in arcsec. It is influenced by
the aperture of the telescope, the number of resolution elements per unit area on the
detector, and “seeing”, the blurring of an image caused by refraction of light in the
Earth’s atmosphere. Spectroscopic resolution specifies the smallest wavelength or
energy interval that can be discerned, and is usually measured in the most convenient
units for a particular form of light. The angstrom unit is commonly used for the
wavelength resolution <5A in visible light. Resolution has the disadvantage that while
1A resolution is very low resolution for A « 5 A X-rays, it is very high resolution
for infrared wavelengths near 10,000 A. The resolving power, the ratio A/<5A, is
more convenient for many purposes. It is inversely proportional to the radial-velocity
resolution bu since A/<5A = c/8u for the Doppler effect. Resolving powers of 103-
104 correspond to radial-velocity resolutions of 30-300 kms"1. Typically, a radial
velocity can be measured with an accuracy that is roughly a tenth of the velocity
resolution, for lines that have symmetric profiles.

General Introduction
102 i nr2 10“4 1CT6 1CT8 10 10 cm
1 m
1 1
1 cm 1 mm
1
1 /im 1 A Wavelength
Figure 1.2
The wavelength regions of the electromagnetic spectrum (upper panel) and the altitude above
sea level where this radiation can be detected. Most bands can only be observed from high¬
flying aircraft or space.
Figure based on http://www.mpifr-bonn.nipg.de/div/hhertz/general_info4.html
The following paragraphs outline observational aspects of various regions of the
electromagnetic spectrum.
1.3.1 Ground Based Optical
Investigations in the optical spectral region have a long and rich history. Modem
telescopes must be large to be competitive, since light gathering power is proportional

1.3 Observational Material 5
to the area of the primary mirror. Consortia of universities or countries have built
most ot today's new research facilities. The leading examples, with 8-m or larger
telescopes, include at present the Keck Observatory, the United States’ National
Optical Astronomy Observatories (NOAO), and the European Southern Observatory
(ESO).
Spectroscopic resolving powers up to 105 can often be achieved on moderately
bright sources, and ~103 on faint ones. Spatial resolution is limited to just under 1"
by atmospheric seeing. It can be partly overcome by adaptive optics, in which the
optical surfaces of the telescope move to compensate for atmospheric distortions, but
to date it has only been completely removed by observations from space.
Optical emission from nebulae include emission lines from warm ionized gas,
and continua produced either by atomic processes in the nebula or by scattering of
light from the photospheres of stars within it. Absorption lines are produced in the
spectra of background stars or nebulae by ions or atoms of interstellar matter (ISM).
1.3.2 Ultraviolet
° °
The vacuum ultraviolet (912A < X < 3000A) can only be observed from space. Ini¬
tially this spectral region was observed from high-altitude balloons and sounding
rockets; today from long-lived orbital missions. The early successes of the Orbit¬
ing Astronomical Observatories (OAO) spacecraft, and the International Ultraviolet
Explorer (IUE) were followed by the Far Ultraviolet Spectroscopic Explorer (FUSE)
and the Hubble Space Telescope (HST). HST may be able to operate through much
of the decade 2000-2010 with more modest ultraviolet missions expected to follow
it. HST is also highly competitive in the optical region because of the freedom from
seeing, despite its modest aperture. Spatial resolution of 0.1" can be achieved rou¬
tinely, and spectroscopic resolving powers similar to ground-based detectors (up to
105, but more typically 103— 104) are possible.
Emission lines in the vacuum ultraviolet generally originate in higher-ionization
species than the optical, and are produced in warm ionized gas. Interstellar matter
(ISM) absorption lines from a broad range of species can also be found. Hotter stars
and atomic processes in the emitting gas generally produce the continuum.
E3.3 X-ray
X-rays have photon energies between 0.1 keV and 10 keV, corresponding to wave¬
lengths between 100 A and ~1 A. (The region between the short-wavelength limit
of the vacuum ultraviolet, 912 A, and the long-wavelength limit of X-rays, 25 A, is
heavily absorbed by the ISM and hence is nearly unobservable.) Early observations
were made from sounding rockets, but long-lived orbital missions, such as Uhuru,
Einstein. ROSAT, ASCA, and at this writing Chandra and XMM, have had the great¬
est impact. Early missions were limited by the technology available then, and used
small grazing incidence telescopes and proportional counting detectors. For instance,
Einstein had two imagers, the Imaging Proportional Counter with E resolution and a
High Resolution Imager with 3" resolution. The spectral resolving power of the HRI
was between 10-50. The current missions have, for the first time, achieved resolutions
similar to optical observations.

General Introduction
X-ray continuum sources are either very hot material, radiating thermal spectra,
or very energy-rich material, radiating by non-thermal processes such as synchrotron
emission. They are often coronae of “normal stars or accreting material very near a
collapsed object in AGN, cataclysmic binaries, or pulsars. Emission lines are often
produced by atomic processes involving inner shells of heavy-element ions, and can
come from a wide range of ionization.
1.3.4 Infrared
The infrared spectral region covers wavelengths between 1 fim and several hundred
microns, although there is no agreed boundary between the far infrared and the sub¬
millimeter radio. Some wavelengths can be observed from the ground or from aircraft
(Figure 1.2), while other wavelengths require high-altitude balloons or orbiting space¬
craft. KAO, IRAS, and ISO were among the most prominent airborne and orbital
missions. The lifetime of orbiting IR missions has been limited by the need to cool
parts of the telescope and detectors cryogenically to very low temperatures, to mini¬
mize thermal emission. The resolution has been limited by technology to ~T and a
resolving power between 10 and 1000. The infrared is the spectral region in which,
with SOFIA, the Spitzer Space Telescope, and the James Webb Space Telescope, the
greatest technical advances will take place over the next several years.
Cool thermal emission from grains, atomic processes in nebulae, and photo¬
spheres of cooler stars are efficient sources of IR continua. Emission lines from ions
and atoms with a wide range of ionization potentials are observed, along with molec¬
ular rotational and vibrational transitions. Infrared light can penetrate through dusty
regions more easily than optical light, making it possible to use the IR to detect oth¬
erwise heavily obscured objects.
1.3.5 Radio
Many radio wavelengths can be studied from the ground; such investigations date back
to the mid-twentieth century. Very long waves are reflected by the Earth's ionosphere
and can only be detected from orbit (Figure 1.2), while other radio waves are absorbed
by water vapor in the atmosphere and can only be studied from dry mountain-top sites,
such as the Atacama Large Millimeter Array (ALMA). Radio telescopes are often
interferometers because the long wavelengths result in very poor diffraction limits
for single-dish telescopes. The spectroscopic and spatial resolutions that are possible
in the radio region are the very best; spatial resolutions of 10-3" and resolving powers
of over 105 are relatively routine.
1.3.6 Returned Data
In nearly all types of observing, digital data is returned from the telescope. Most
observatories have software reduction packages specifically designed to handle data
from their instrument. The final product may be an image or the emission-line fluxes
or measures of the continuum at selected energies. Most missions produce large data
archives that form a rich data set. These archives are now so extensive that many pilot
projects can be carried out solely using them. Although the biggest discoveries will

1.4 Physical Ideas 7
come from new observations, archival research is usually the first step in starting a
large research program.
1.4 Physical Ideas
The source of energy that enables emission nebulae to radiate is, almost always,
ultraviolet radiation from stars within or near the nebula. There are one or more
hot stars, with effective surface temperature 7* > 3 x 104 K, near or in almost every
nebula; and the ultraviolet photons these stars emit transfer energy to the nebula by
photoionization. In nebulae and in practically all astronomical objects, H is by far
the most abundant element, and photoionization of H is thus the main energy-input
mechanism. Photons with energy greater than 13.6 eV, the ionization potential of H,
are absorbed in this process, and the excess energy of each absorbed photon over
the ionization potential appears as kinetic energy of a newly liberated photoelectron.
Collisions between electrons, and between electrons and ions, distribute this energy
and maintain a Maxwellian velocity distribution with temperature T in the range
5,000 K < 7 < 20,000 K in typical nebulae. Collisions between thermal electrons
and ions excite the low-lying energy levels of the ions. Downward radiation transitions
from these excited levels have very small transition probabilities, but at the low
densities (ne < 104 cm"3) of typical nebulae, collisional deexcitation is even less
probable; so almost every excitation leads to emission of a photon, and the nebula
thus emits a forbidden-line spectrum that is quite difficult to excite under terrestrial
laboratory conditions.
Thermal electrons are recaptured by the ions, and the degree of ionization at
each point in the nebula is fixed by the equilibrium between photoionization and
recapture. In nebulae in which the central star has an especially high temperature, 7*,
the radiation field has a correspondingly high number of high-energy photons, and
the nebular ionization is therefore high. In such nebulae collisionally excited lines up
to [Ne V] and [Fe VII] may be observed, but the high ionization results from the high
energy of the photons emitted by the star, and does not necessarily indicate a high
nebular temperature 7, defined by the kinetic energy of the free electrons.
In the recombination process, recaptures occur to excited levels, and the excited
atoms thus formed then decay to lower and lower levels by radiative transitions,
eventually ending in the ground level. In this process, line photons are emitted, and
this is the origin of the H I Balmer- and Paschen-line spectra observed in all gaseous
nebulae. Note that the recombination of H+ gives rise to excited atoms of H° and thus
leads to the emission of the H I spectrum. Likewise, He+ recombines and emits the
He I spectrum, and in the most highly ionized regions, He++ recombines and emits
the He II spectrum, the strongest line in the ordinary observed region being A4686.
Much weaker recombination lines of C II, C III, C IV, and so on, are also emitted;
however, the main excitation process responsible for the observed strengths of such
lines with the same spin or multiplicity as the ground term is resonance fluorescence
by photons, which is much less effective for H and He lines because the resonance
lines of these more abundant elements have greater optical depth.

8 General Introduction
In addition to the bright-line and continuous spectra emitted by atomic processes,
many nebulae also have an infrared continuous spectrum emitted by dust particles
heated to a temperature of order 100 K by radiation derived originally tiom the
central star.
Gaseous nebulae may be classified into two main types, diffuse nebulae or H II
regions, and planetary nebulae. Though the physical processes in both types are quite
similar, the two groups differ greatly in origin, mass, evolution, and age of typical
members; so for some purposes it is convenient to discuss them separately. Nova shells
are rare but interesting objects: tiny, rapidly expanding, cool photoionized nebulae.
Supernova remnants, an even rarer class of objects, differ greatly from both diffuse
and planetary nebulae. We will briefly examine each of these types of object, and then
discuss Seyfert galaxies and other active galactic nuclei, in which much the same
physical processes occur, although with differences in detail because considerably
higher-energy photons are involved.
1.5 Diffuse Nebulae
Diffuse nebulae or H II regions are regions of interstellar gas (Figure 1.3) in which
the exciting star or stars are O- or early B-type stars. Figure 1.3 is an example. They
are young stars, which use up their nuclear energy quickly. Often there are several
exciting stars, a multiple star, or a galactic cluster whose hottest two or three stars
are the main sources of ionizing radiation. These hot, luminous stars undoubtedly
formed fairly recently from interstellar matter that would otherwise be part of the
same nebula they now ionize and thus illuminate. The effective temperatures of the
stars are in the range 3 x 104 K < 7* < 5 x 104 K; throughout the nebula, H is
ionized. He is singly ionized, and other elements are mostly singly or doubly ionized.
Typical densities in the ionized part of the nebula are of order 10 or 102 cm-3,
ranging to as high as 104 cm-3, although undoubtedly small denser regions exist
close to or even below the limit of resolvability. In many nebulae dense neutral
condensations are scattered throughout the ionized volume. Internal motions occur
in the gas with velocities of order 10 km s-1, approximately the isothermal sound
speed. Bright rims, knots, condensations, and so on, are apparent to the limit of
resolution. The hot, ionized gas tends to expand into the cooler surrounding neutral
gas, thus decreasing the density within the nebula and increasing the ionized volume.
The outer edge of the nebula is surrounded by ionization fronts running out into the
neutral gas.
The spectra of these “H II regions,” as they are often called (because they contain
mostly H+), are strong in H I recombination lines and [N II] and [O II] collisionally
excited lines, but the strengths of [O III] and [N II] lines may differ greatly, being
stronger in the nebulae with higher central-star temperatures.
These H II regions are observed not only in our Galaxy but also in other nearby
galaxies. The brightest H II regions can easily be seen on almost any large-scale
images, but those taken in a narrow wavelength band in the red, including Ha
and the [N II] lines, are especially effective in showing faint and often heavily

1.5 Diffuse Nebulae 9
Figure 1.3
The HII region NGC 1499, also known as the California Nebula. The O star which photoionizes
the gas, 'i Per, is off the picture to the right, just outside the bright emission nebula. (Photo ©
UC Regents/Lick Observatory)

10 General Introduction
reddened H II regions in other galaxies. The H II regions are strongly concen¬
trated to the spiral arms, and indeed are the best objects for tracing the structure
of spiral arms in distant galaxies. Radial-velocity measurements of H II regions then
give information on the kinematics of Population I (young) objects in our own and
other galaxies. Typical masses of observed H II regions are of order 10“ to 10
Mq, with the lower limit depending largely on the sensitivity of the observational
method used.
1.6 Planetary Nebulae
Planetary nebulae are isolated nebulae, often (but not always) possessing a fair degree
of bilateral symmetry, that are actually shells of gas that have been lost in the fairly
recent past by their central stars (Figure 1.4). The name “planetary ’ is purely historical
and refers to the fact that some of the bright planetaries appear as small, disk-like,
greenish objects in small telescopes. The central stars of planetary nebulae are old
stars, typically with rt«5x 104 K, even hotter than galactic O stars, and often less
luminous (Mv = -3 to +5). The stars are in fact rapidly evolving toward the white-
dwarf stage, and the shells are expanding with velocities of order of several times the
velocity of sound (25 km s~' is a typical expansion velocity). However, because they
are decreasing in density, their emission is decreasing, and on a cosmic time scale
they rapidly become unobservable, with mean lifetimes as planetary nebulae of a few
times 104 years.
As a consequence of the higher stellar temperatures of their exciting stars, typical
planetary nebulae are generally more highly ionized than HII regions, often including
large amounts of He++. Their spectra thus include not only the HI and He I recombi¬
nation lines, but often also the He II lines; the collisionally excited lines of [O III] and
[Ne III] are characteristically stronger in their spectra than those in diffuse nebulae,
and [Ne V] is often strong. There is a wide range in the temperatures of planetary-
nebula central stars, however, and the lower-ionization planetaries have spectra that
are quite similar to those of H II regions.
The space distribution and kinematic properties of planetary nebulae indicate
that, on the cosmic time scale, they are fairly old objects, usually called old Disk
Population or old Population I objects. This indicates that the bulk of the planetaries
we now see, though relatively young as planetary nebulae, are actually near-terminal
stages in the evolution of quite old stars.
Typical densities in observed planetary nebulae range from 104 cm-’ down to
102 cm-3, and typical masses are of order 0.1 MQ to 1.0 MQ. Many planetaries
have been observed in other nearby galaxies, especially the Magellanic Clouds and
M 31, but their luminosities are so much smaller than the luminosities of the brightest
H II regions that they are more difficult to study in great detail. However, spec¬
troscopic measurements of these planetaries give good information on velocities,
abundances of the elements, and stellar evolution in these galaxies, and HST im¬
ages show that they have forms quite similar to those of planetary nebulae in our
Galaxy.

1.7 Nova and Supernova Remnants 11
Figure 1.4
The planetary nebula IC 418. Note the fine structure, including the low narrow arc-like
filaments, and the second smaller structure within the main nebula. (STScI)
1.7 Nova and Supernova Remnants
Many recent novae are surrounded by small, faint shells with emission-line spec¬
tra. As we shall see, they are tiny photoionized nebulae. A few emission nebulae
are known to be supernova remnants. The Crab Nebula (NGC 1952), the rem¬
nant of the supernova of A.D. 1054, is the best known example, and small bits of
scattered nebulosity are the observable remnants of the much more heavily red¬
dened objects, Tycho’s supernova of 1572 and Kepler’s supernova of 1604. All
three of these supernova remnants have strong non-thermal radio spectra, and several
other filamentary nebulae with appearances quite unlike typical diffuse or planetary

12 General Introduction
nebulae have been identified as older supernova remnants by the tact that they have
similar non-thermal radio spectra. Two of the best known examples are the Cygnus
Loop (NGC 6960-6992-6995) and IC 443. In the Crab Nebula, the non-thermal
synchrotron spectrum observed in the radio-frequency region extends into the opti¬
cal region, and extrapolation to the ultraviolet region indicates that this synchrotron
radiation is probably the source of the photons that ionize the nebula. However,
in the other supernova remnants no photoionization source is seen, and much of
the energy is instead provided by the conversion of kinetic energy of motion into
heat. In other words, the fast-moving filaments collide with ambient interstellar gas,
and the energy thus released provides ionization and thermal energy, which later is
partly radiated as recombination- and collisional-line radiation. Thus these supernova
remnants are objects in which collisional ionization occurs, rather than photoion¬
ization. However, note that in all the nebulae, collisional excitation is caused by
the thermal electrons that are energized either by photoionization or by collisional
ionization.
1.8 Active Galactic Nuclei
Many galaxies, in addition to having H II regions and planetary nebulae, show
characteristic nebular emission lines in the spectra of their nuclei. In most of these
objects, the gas is evidently photoionized by hot stars in the nucleus, which is thus
much like a giant H II region, or perhaps a cluster of many H II regions. The galactic
nuclei with the strongest emission lines of this type are often called “extragalactic
H II regions”, “star-forming regions”, or “starburst galaxies.” Besides these objects,
however, a small fraction of spiral galaxies have ionized gas in their nuclei that emits
an emission-line spectrum with a wider range of ionization than any H II region.
Usually the emission-line profiles show a significantly greater range of velocities than
in starburst galaxies. These galaxies, totaling a few percent of all spiral galaxies, are
called Seyfert galaxies. Many of the most luminous radio galaxies, typically N, cD,
D, or E galaxies in form, have nuclei with very similar emission-line spectra. Quasars
(quasistellar radio sources) and QSOs (quasistellar objects) are radio-loud and radio¬
quiet analogues of radio galaxies and Seyfert galaxies; they have similar optical
spectra and even greater optical luminosities, but are much rarer in space. All these
objects together are called active galactic nuclei. Among them are the most luminous
objects in the universe, quasars and QSOs with redshifts up to z ~ 6, corresponding
to recession velocities of more than 0.9c.
Much if not all of the ionized gas in active galactic nuclei appears to be photoion¬
ized. However, the source of the ionizing radiation is not a hot star or stars. Instead,
it is probably an extension to high energies of the blue “featureless continuum” ob¬
served in these objects in the optical spectral region. This is probably emitted by an
accretion disk around a black hole, or by relativistic particles and perhaps a mag¬
netic field associated with the immediate environs of the black hole. The spectrum of
the ionizing radiation, whatever its source, certainly extends to much higher energies

1.9 Star Formation in Galaxies 13
than the spectra of the hot stars that ionize H II regions and planetary nebulae. Also,
the particle and energy densities are much larger in some ionized regions in active
galactic nuclei than in nebulae.
1.9 Star Formation in Galaxies
Newly born stars "appear ’ in or near the interstellar matter from which they and their
neighbors tormed. Generally, when stars are formed under conditions we can observe
in other galaxies, they do so in large numbers and some of them are O and B stars.
These hot stars immediately begin photoionizing the residual ISM around themselves,
creating large emission-line diffuse nebulae or huge regions of nebulosity. Thus we
observe many star-forming regions (in nearby galaxies), or star-forming galaxies
(more distant objects). The galaxies with the strongest nebular emission lines (such
as H/I or Ha or Pa or Bra) are called starburst galaxies, as unusually large numbers
of stars are being formed within them within a short time interval.
The first survey of the infrared (5-500 /am) sky by the Infrared Astronomical
Satellite (IRAS) discovered a class of galaxies that emit more energy in the infrared
than in all the other pass bands combined. Previous optical surveys of galaxies had
deduced a “luminosity function”, a description of the fraction of that population that
has various luminosities. From low to high luminosities, the range went from dwarf
irregular galaxies like the Magellanic Clouds, to normal spiral galaxies like the Milky
Way, to Seyfert galaxies (mostly early-type or distorted spirals), giant ellipticals, and
quasars, which have the greatest luminosities we know. Among the spirals are many
star-forming galaxies and fewer starburst ones. All of these sources radiate most of
their energy in the optical passband. The infrared luminous sources discovered by
IRAS were too faint to be included in optical surveys but are among the most luminous
infrared sources in the sky. When these are included, it appears that most of the very
most luminous galaxies (L > 10nLo) emit the majority of their luminosity in the
infrared.
These infrared luminous galaxies are among the most luminous starburst galax¬
ies. The infrared continuum that carries most of their luminosity is emitted by inter¬
stellar dust heated to 30-60 K by hot stars and by the emission lines they produce in
the gas, creating a peak in the energy distribution near 60 /am. The underlying source
of the great luminosity is a “super starburst”, in which a large fraction of a galaxy’s
mass is involved in vigorous star formation. Interstellar dust then absorbs the energy
emitted by the hot stars, which is eventually reradiated in the infrared. The obser¬
vations can be understood if a very large fraction of a galaxy’s mass, ~10lu MQ, is
quickly converted into stars in a dusty environment.
The starburst phenomenon is thought to be the result of interactions and mergers
of gas-rich spirals. The host galaxies tend to show signs of interacting with other
galaxies or of being an otherwise disturbed system. During such galactic collisions
some of the gas in the ISM loses its angular momentum and quickly falls towards the
merger nuclei. Models suggest that as much as 101(l MQ of gas and dust can build up

14 General Introduction
within a few hundred parsecs of the center, resulting in vigorous star formation. Most
of this star formation occurs in regions that are heavily obscured by dust, so many
parts of the system can only be observed directly in the infrared. For this reason it is
necessary to develop emission line diagnostics that use only infrared lines, the subject
of a later chapter.
The basic physical principles that govern the structures and emitted spectra
of active galactic nuclei are largely the same as those that apply in H II regions
and planetary nebulae. However, because of the large proportion of high-energy
photons in the ionizing flux, some new physical processes become important in active
galactic nuclei, and these cause their structures to differ in important details from
those of classical nebulae. These differences can best be analyzed after H II regions
and planetary nebulae are well understood. Hence we treat nova shells, supernova
remnants, and active galactic nuclei in the final chapters of this book.
References
General reviews on astronomical research are found in a variety of places. Three of the best
series are
Annual Reviews of Astronomy and Astrophysics, by Annual Reviews Inc. These come
out once per year and feature articles on a variety of research topics.
Astronomical Society of the Pacific Conference Series, by the Astronomical Society of
the Pacific. Each book of this series summarizes a specialist conference on a chosen topic,
many of them organized by the International Astronomical Union. The articles are a mix
of longer reviews and shorter research summaries.
The Saas Fe Conference Series. These are the proceedings from summer schools held
each year. Each book is on a chosen topic and features a few longer articles.
A brief historical sketch of the development of nebular astrophysics is contained in an article
on “pioneer nebular theorists” (which also includes some of the main observational results on
which they built):
Osterbrock, D. E. 2001, Revista Mexicana de Astronomia, Serie d. Conferencias, 12, 1
(in English).
The following are on-line data bases of astronomical sources. At this time most archives are
limited to space-based data, but archives of ground-based are being developed. The main
archives at the time of this writing are
ADS, the NASA Astrophysics Data System, has links to much of the published astronom¬
ical literature, http://adsabs.harvard.edu/
HEASARC, the High Energy Astrophysics Science Archive Research Center, is “a source
of gamma-ray. X-ray, and extreme ultraviolet observations of cosmic (non-solar) sources”.
http://heasarc.gsfc.nasa.gov/
SIMBAD, a database operated at CDS, France. This “brings together basic data, cross¬
identifications, observational measurements, and bibliography, for celestial objects out¬
side the solar system: stars, galaxies, and non-stellar objects within our galaxy, or in
external galaxies”. http://cdsweb.u-strasbg.fr/Simbad.html

References 15
The Hubble Data Archive provides access to data obtained with the Hubble Space Tele¬
scope. http://archive.stsci.edu/
MAST, the Multi-mission Archive at STScI, provides access to data from a variety of
missions ranging from the extreme UV through near IR. http://archive.stsci.edu/mast.html
1PAC, the Infrared Processing and Analysis Center, has access to NASA’s infrared pro¬
gram. http://www.ipac.caltech.edu/
NED, the NASA/1PAC Extragalaetic Database at JPL, can be searched by object name,
type of data, literature, or tools, http://nedwww.ipac.caltech.edu/
Additionally, meta-archives, collections of links to individual archives, are being developed. A
good one is
Canadian Astronomy Data Centre, at http://cadcwww.hia.nrc.ca/
The following gives an overview of various ways to find information in these databases:
Skiff, Brian A. 2002, Sky & Telescope, 103, 50.

2
Photoionization Equilibrium
2.1 Introduction
Emission nebulae result from the photoionization of a diffuse gas cloud by ultraviolet
photons from a hot “exciting” star or from a cluster of exciting stars. The ionization
equilibrium at each point in the nebula is fixed by the balance between photoion¬
izations and recombinations of electrons with the ions. Since hydrogen is the most
abundant element, we can get a first idealized approximation to the structure of a
nebula by considering a pure H cloud surrounding a single hot star. The ionization
equilibrium equation is:
(2.1)
= nenp a(H°, T)[cm 3 s ']
where Jv is the mean intensity of radiation (in energy units per unit area, per unit time,
per unit solid angle, per unit frequency interval) at the point. Thus </>„ = 4nJv/hv is
the number of incident photons per unit area, per unit time, per unit frequency interval,
and av(H°) is the ionization cross section for H by photons with energy hv (above
the threshold hv0); the integral [denoted by T(H0)] therefore represents the number
of photoionizations per H atom per unit time. The neutral atom, electron, and proton
densities per unit volume are n(H°), ne, and np, and c^H0,!) is the recombination
coefficient; so the right-hand side of the equation gives the number of recombinations
per unit volume per unit time.
To a first approximation, the mean intensity Jv [see Appendix 1 for definitions
of it and other observed (or measured) quantities connected with radiation] is simply
the radiation emitted by the star reduced by the inverse-square effect of geometrical
dilution. Thus
(2.2)
17

Photo ionization Equilih ri um
where R is the radius of the star, n Fv(0) is the flux at the surface of the star, r is the
distance from the star to the point in question, and Lv is the luminosity of the star per
unit frequency interval.
At a typical point in a nebula, the ultraviolet radiation field is so intense that the
H is almost completely ionized. Consider, for example, a point in an H II region,
with density 10 H atoms and ions per cm3, 5 pc from a central 07.5 star with T* =
39,700 K. We will examine the numerical values of all the other variables later, but
for the moment, we can adopt the following very rough values:
poo r
Q(H°) = / — dv 1 x 1049 [photons s-1];
Jvq hv
fly(H0) ~6 x 10“18 [cm2];
f°° ^av(H°)dv « 1 x 10~8 = x~l [s-1];
Jvq hv F
a(H°, T) & 4 x 10“13 [cm3 s-1]
where zph is the lifetime of the atom before photoionization. Substituting these
values and taking ^ as the fraction of neutral H, that is, ne = np = (1 — £)n(H) and
n(H°) = cJ/7 (H), where n(H) = 10 cm-3 is the density of H, we find (^4x 10-4;
that is, H is very nearly completely ionized.
On the other hand, a finite source of ultraviolet photons cannot ionize an infinite
volume, and therefore, if the star is in a sufficiently large gas cloud, there must be
an outer edge to the ionized material. The thickness of this transition zone between
ionized and neutral gas, since it is due to absorption, is approximately one mean free
path of an ionizing photon {/ [« (H°) av] cm}. Using the same parameters as
before, and taking £ — 0.5, we find the thickness
d
1
n(H0)au
O.lpc,
or much smaller than the radius of the ionized nebula. Thus we have the picture of
a nearly completely ionized “Stromgren sphere" or H II region, separated by a thin
transition region from an outer neutral gas cloud or H I region. In the rest of this
chapter we will explore this ionization structure in detail.
First we will examine the photoionization cross section and the recombination
coefficients for H, and then use this information to calculate the structure of hypo¬
thetical pure H regions. Next we will consider the photoionization cross section and
recombination coefficients for He, the second most abundant element, and then cal¬
culate more realistic models of H II regions, that take both H and He into account.
Finally, we will extend our analysis to other, less abundant heavy elements; these
often do not strongly affect the ionization structure of the nebula, but are always quite
important in the thermal balance to be discussed in the next chapter.

2.2 Photoionization and Recombination of Hydrogen 19
2.2 Photoionization and Recombination of Hydrogen
Figure 2.1 is an energy-level diagram of H; the levels are marked with their quantum
numbers n (principal quantum number) and L (angular momentum quantum number),
and with S, P, D, F, . . . standing for L = 0, 1, 2, 3, ... in the conventional notation.
Permitted transitions (which, for one-electron systems, must satisfy the selection
rule AL = ± 1) are marked by solid lines in the figure. The transition probabilities
A(nL. n'L') of these lines are of order 104 to 108 s-1, and the corresponding mean
lifetimes of the excited levels,
T-nL
1
E E
L'=L± 1
1nL.n'L'
(2.3)
Figure 2.1
Partial energy-level diagram of H I, limited to n < 7 and L < G. Permitted radiative transitions
to levels n < 4 are indicated by solid lines.

Photoionization Equilibrium
are therefore of order 10“4 to 10“8 s. The only exception is the 2 2S level, from
which there are no allowed one-photon downward transitions. However, the transition
2 2S —> 1 2S does occur with the emission of two photons, and the probability
of this process is A(2 2S, 1 2S) = 8.23 s-1, corresponding to a mean lifetime for
the 2 2S level of 0.12 s. Even this lifetime is quite short compared with the mean
lifetime of an H atom against photoionization, which has been estimated previously
as rph 108 s for the 1 2S level, and is of the same order of magnitude for the
excited levels. Thus, to a very good approximation, we may consider that very nearly
all the H° is in the 1 2S level, that photoionization from this level is balanced by
recombination to all levels, and that recombination to any excited level is followed
very quickly by radiative transitions downward, leading ultimately to the ground level.
This basic approximation greatly simplifies calculations of physical conditions in
gaseous nebulae.
The photoionization cross section for the 1 25 level of H°, or, in general, of a
hydrogenic ion with nuclear charge Z, may be written in the form
(Z) = /M4 exp {4 - [(4 tan^
\ i) / 1 — pyn (—9
9 /£]}
Tr'rYT - 1
where
29tt 1
3e4 V 137.0
nar 6.30 x 10“18 [cm2],
£ =
and
hvx = Z2hv0 = 13.6Z2 eV
is the threshold energy. This cross section is plotted in Figure 2.2, which shows
that it drops off rapidly with energy, approximately as v~3 not too far above the
threshold, which, for H, is at vD = 3.29 x 1015 s-] or A.0 = 912 A, so that the higher-
energy photons, on the average, penetrate further into neutral gas before they are
absorbed.
The electrons produced by photoionization have an initial distribution of en¬
ergies that depends on Jvav/hv. However, the cross section for elastic scattering
collisions between electrons is quite large, of order 4jt(e2/mu2)2 ^ 10-13 cm2, and
these collisions tend to set up a Maxwell-Boltzmann energy distribution. The recom¬
bination cross section, and all the other cross sections involved in the nebulae, are so
much smaller that, to a very good approximation, the electron-distribution function
is Maxwellian, and therefore all collisional processes occur at rates fixed by the local

2.2 Photoionization and Recombination of Hydrogen 21
Figure 2.2
Photoionization absorption cross sections of H°, He0, and He+.
temperature defined by this Maxwellian. Therefore, the recombination coefficient to
a specified level n2L may be written
poo
a„ 2L(H°, T)= uan 2L(H°, u) f(u) clu [cm3 s_1] (2.5)
Jo
where
f(u) = u2 exp(-raw2 / kT) (2.6)
7 \2kT /
is the Maxwell-Boltzmann distribution function for the electrons, and anL{H°, u) is
the recombination cross section to the term n 2L in H° for electrons with velocity u.
These cross sections vary approximately as w-2, and the recombination coefficients,
which are proportional to ucr, therefore vary approximately as A selection of
numerical values of an iL is given in Table 2.1. Since the mean electron velocities at

Photoionization Equilibrium
Table 2.1
Recombination coefficients (in cm3 s^1) a„ 2L for H
5,000 K 10,000 K 20,000 K
a\ 2S
2.28 x 10“13 1.58 x 10-13 1.08 x 10-13
a2 2S 3.37 x 10~14 2,34 x 14“14 1.60 x 10“14
2 po 8.33 x 10-14 5.35 x 10“14 3.24 x 10“14
a3 2S
1.13 x I0“14 7.81 x 10~15 5.29 x 10-15
0( 2 po 3.17 x 10-14 2.04 x 10~14 1.23 x 10"14
a3 2D
3.43 x 10"14 1.73 x 10“14 9.49 x 10“15
a4 2S
5.23 x 10~15 3.59 x 10“15 2.40 x 10~15
^4 2 po 1.51 x I0"14 9.66 x 10-15 5.81 x 14-15
a4 2D
1.90 x 10~14 1.08 x 10~14 5.68 x 10“15
C^4 2 po 1.09 x 10~14 5.54 x 10~15 2.56 x 10“15
“10 2S
4.33 x 10-16 2.84 x 10-16 1.80 x 10“16
a10 2C
2.02 x 10“15 9.28 x 10-'6 3.91 x 10-16
“10 2m
2.7 x 10“17 1.0 x 10“17 4.0 x 10^18
«A
6.82 x 10~13 4.18 x 10-13 2.51 x 10“13
aB 4.54 x 10“13 2.59 x 10"13 1.43 x 10“13
the temperatures listed are of order 5 x 107 cm s_1, it can be seen that the recom¬
bination cross sections are of order 10~20 cm2 or 10-21 cm2, much smaller than the
geometrical cross section of an H atom.
In the nebular approximation discussed previously, recombination to any
level n 2L quickly leads through downward radiative transitions to 1 2 S, and
the total recombination coefficient is the sum over captures to all levels, ordinarily
written
«a = 2>« 2L(H°, T) [cnr's-1]
n,L
n—\
(2.7)
n L= 0
= Ea«(H°’
n
where a„ is thus the recombination coefficient to all the levels with principal quantum
number n. Numerical values of aA are also listed in Table 2.1. A typical recombination
time is zr = l/ne aA « 3 x 1 012/ne s « 105/ne yr, and deviations from ionization
equilibrium are ordinarily damped out in times of this order of magnitude.

2.3 Photoionization of a Pure Hydrogen Nebula 23
2.3 Photoionization of a Pure Hydrogen Nebula
Consider the simple idealized problem of a single star that is a source of ionizing
photons in a homogeneous static cloud of H. Only radiation with frequency v > v0
is effective in the photoionization of H from the ground level, and the ionization
equilibrium equation at each point can be written
n(H°) / --av dv = npneaA(H°, r)[cm-3 s-1]. (2.8)
Jv0 hv
The equation of transfer for radiation with v > u0 can be written in the form
~~ = —n(H°)avIv + jv (2.9)
as
where Iv is the specific intensity of radiation and jv is the local emission coefficient (in
energy units per unit volume, per unit time, per unit solid angle, per unit frequency)
for ionizing radiation.
It is convenient to divide the radiation field into two parts, a “stellar” part,
resulting directly from the input radiation from the star, and a “diffuse” part, resulting
from the emission of the ionized gas:
Iv = Ivs + IVd- (2-10)
The stellar radiation decreases outward because of geometrical dilution and
absorption, and since its only source is the star, it can be written
47zJvs = nFvs (r) = 7tFvs (R) R CXP,( Tv) [erg cm-2 s-1 Hz-1], (2.11)
rl
where jt Fvs(r) is the standard astronomical notation for the flux of stellar radiation
(per unit area, per unit time, per unit frequency interval) at r, nFvs(R) is the flux at
the radius of the star R. and rv is the radial optical depth at r,
rv (r) = [ rc(H°, r) avdr', (2.12)
JO
which can also be written in terms of r0, the optical depth at the threshold:
(r) = — r0 (r)
c,v0
The equation of transfer for the diffuse radiation I vd is

Photoionization Equilibrium
and for AT <$C hv0 the only source of ionizing radiation is recaptures of electrons from
the continuum to the ground 1 2S level. The emission coefficient for this radiation is
(erg cm-2 s_1 Hz-1 sr_l)
0 7. .,3 / 7.2 \ T2
jv (T) = —— ( --— ) avexp[-h (v - v0)/kT]npne (v > v0) (2.14)
cz \2tt mkl /
which is strongly peaked to v = v0, the threshold. The total number of photons gener¬
ated by recombinations to the ground level is given by the recombination coefficient
f oo ■
47r/ —dv = npne a](H°, T)[cm_3 s-1], (2.15)
Jv0 hv
and since a, = < aA, the diffuse field Jvd is smaller than Jvs on the average, and
may be calculated by an iterative procedure. For an optically thin nebula, a good first
approximation is to take Jvd ~ 0.
On the other hand, for an optically thick nebula, a good first approximation is
based on the fact that no ionizing photons can escape, so that every diffuse radiation-
field photon generated in such a nebula is absorbed elsewhere in the nebula:
4n f ^LdV = 4;r f n(n°)^^-dV, (2.16)
J hv J hv
where the integration is over the entire volume of the nebula. The so-called “on-the-
spot” approximation amounts to assuming that a similar relation holds locally:
J vd
Jv
n (H°) av
(2.17)
This, of course, automatically satisfies (2.16), and would be exact if all photons were
absorbed very close to the point at which they are generated (“on the spot”). This is
not a bad approximation because the diffuse radiation-field photons have v ~ v0, and
therefore have large av and correspondingly small mean free paths before absorption.
Making this on-the-spot approximation and using (2.11) and (2.15), we find that
the ionization Equation (2.8) becomes
n(H0)/?2 7tFv(R)
hv
av exp(—rv) dv = npneaB(H{), T) (2.18)
where
«s(H°, D=aA(H°, T)-ax{H°, T)
OO
= T)
2
The physical meaning is that in optically thick nebulae, the ionizations caused by
stellar radiation-field photons are balanced by recombinations to excited levels of

2.3 Photoionization of a Pure Hydrogen Nebula 25
Table 2.2
Calculated ionization distributions for model H II regions
r (pc)
rt = 4x 10~4 K
Blackbody Model
nP n (H°)
F = 3.74 x 10“4 K
Model stellar
atmosphere
np «(H°)
nP + n( H°) nP + n (H°) nP +/i(H°) nP + «(H°)
0.1 1.0 4.5 x 10“7 1.0 4.5 x 10“7
1.2 1.0 2.8 x 10“5 1.0 2.9 x 10"5
2 2 0.9999 1.0 x 10“4 0.9999 1.0 x 10-4
3.3 0.9997 2.5 x 10“4 0.9997 2.5 x 10~4
4.4 0.9995 4.4 x 10“4 0.9994 4.5 x 10“4
5.5 0.9992 8.0 x 10“4 0.9992 8.1 x 10“4
6.7 0.9985 1.5 x 10-3 0.9985 1.5 x 10~3
7.7 0.9973 2.7 x 10-3 0.9973 2.7 x 10“3
OO oo 0.9921 7.9 x 10~3 0.9924 7.6 x 10-3
9.4 0.977 2.3 x 10~2 0.979 2.1 x 10"2
9.7 0.935 6.5 x 10~2 0.940 6.0 x 10“2
9.9 0.838 1.6 x 10“' 0.842 1.6 x 10-’
10.0 0.000 1.0 0.000 1.0
H, while recombinations to the ground level generate ionizing photons that are
absorbed elsewhere in the nebula but have no net effect on the overall ionization
balance.
For any stellar input spectrum 7rFv(R), the integral on the left-hand side of (2.18)
can be tabulated as a known function of r0, since av and zv are known functions of v.
Thus, for any assumed density distribution,
rcH(r) = n(H°, r) + np(r)
and temperature distribution T(r), equations (2.18) and (2.12) can be integrated
outward to find n(H°, r) and np(r) = ne(r). Two calculated models for homogeneous
nebulae with constant density n(H) = 10 H atoms plus ions cm'3 and constant
temperature T = 7,500 K are listed in Table 2.2 and graphed in Figure 2.3. For
one of these ionization models, the assumed nFV(R) is a blackbody spectrum with
F = 40,000 K, chosen to represent approximately an 07.5 main-sequence star, while
for the other, the n FV(R) is a computed model stellar atmosphere with 7* = 37,450 K.
The table and graph clearly show the expected nearly complete ionization out to a
critical radius rh at which the ionization drops off abruptly to nearly zero. The central
ionized zone is often referred to as an “H II region ’ (”H+ region would be a better
name), and it is surrounded by an outer neutral H° region, often referred to as an “H I
region”.

Photoionization Equilibrium
Figure 2.3
Ionization structure of two homogeneous pure-H model H II regions.
The radius rx can be found from (2.18), substituting from (2.12),
drv
dr
= n(H°) av
and integrating over r:
R-
f
nFv(R)
hv
dv
poo
/ d[.
Jo
poo
exp(—rv)] = / n neaBr2 dr
Jo
r:
=r2I
nFv (R)
hv
dv
Using the result that the ionization is nearly complete [np = ne ^ n(H)] within rh
and nearly zero (n „ = ne ~ 0) outside rh this becomes
4n R > r = f
Jvn hv Ju
oo
L,
dv
V0 hv
= Q( H°) = fryHa„.
(2.19)
Here 47r R2tt Fv(R) = Lv is the luminosity of the star at frequency v (in energy units
per time per unit frequency interval), and the physical meaning of (2.19) is that the
total number of ionizing photons emitted by the star just balances the total number
of recombinations to excited levels within the ionized volume 4nr2, often called the

2.4 Photoionization of a Nebula Containing Hydrogen and Helium 27
Table 2.3
Calculated Stromgren radii as function of spectral types spheres
Spectral
type T*(K) My
log <2(H°)
(photons/s)
log nenpr]
n in cm-3;
in pc
log nenpr3
n in cm-3;
i]in pc
r\ (pc)
ne = np
= 1 cm-3
03 V 51,200 -5.78 49.87 49.18 6.26 122
04 V 48,700 -5.55 49.70 48.99 6.09 107
04.5 V 47,400 -5.44 49.61 48.90 6.00 100
05 V 46,100 -5.33 49.53 48.81 5.92 94
05.5 V 44,800 -5.22 49.43 48.72 5.82 87
06 V 43,600 -5.11 49.34 48.61 5.73 81
06.5 V 42,300 -4.99 49.23 48.49 5.62 75
07 V 41,000 -4.88 49.12 48.34 5.51 69
07.5 V 39,700 -4.77 49.00 48.16 5.39 63
08 V 38,400 -4.66 48.87 47.92 5.26 57
08.5 V 37,200 -4.55 48.72 47.63 5.11 51
09 V 35,900 -4.43 48.56 47.25 4.95 45
09.5 V 34,600 -4.32 48.38 46.77 4.77 39
BOV 33,300 -4.21 48.16 46.23 4.55 33
BOA V 32,000 -4.10 47.90 45.69 4.29 27
03 III 50,960 -6.09 49.99 49.30 6.38 134
B0.5 III 30,200 -5.31 48.27 45.86 4.66 36
03 la 50,700 -6.4 50.11 49.41 6.50 147
09.5 la 31,200 -6.5 49.17 47.17 5.56 71
Note: T = 7,500 K assumed for calculating aB.
Stromgren sphere. Numerical values of radii calculated by using the model stellar
atmospheres discussed in Chapter 5 are given in Table 2.3.
2.4 Photoionization of a Nebula Containing Hydrogen and Helium
The next most abundant element after H is He, whose relative abundance (by number)
is of order 10 percent, and a much better approximation to the ionization structure
of an actual nebula is provided by taking both these elements into account. The
ionization potential of He is hv2 = 24.6 eV, somewhat higher than H; the ionization
potential of He+ is 54.4 eV, but since even the hottest O stars emit practically no
photons with hv > 54.4 eV, second ionization of He does not occur in ordinary H II
regions. (The situation is quite different in planetary nebulae, as we shall see later
in this chapter.) Thus photons with energy 13.6 eV < hv < 24.6 eV can ionize H
only, but photons with energy hv > 24.6 eV can ionize both H and He. As a result,
two different types of ionization structure are possible, depending on the spectrum
of ionizing radiation and the abundance of He. At one extreme, it the spectrum is

28 Photoionization Equilibrium
concentrated to frequencies just above 13.6 eV and contains only a few photons with
hv > 24.6 eV, then the photons with energy 13.6 eV < hv < 24.6 eV keep the H
ionized, and the photons with hv > 24.6 eV are all absorbed by He. The ionization
structure thus consists of a small central H+, He+ zone surrounded by a larger H+,
He0 region. At the other extreme, if the input spectrum contains a large fraction of
photons with hv > 24.6 eV, then these photons dominate the ionization of both H and
He, the outer boundaries of both ionized zones coincide, and there is a single H+,
He+ region.
The He0 photoionization cross section ay(He°) is plotted in Figure 2.2, along
with flv(H°) and ay(He+) calculated from Equation (2.4). The total recombination
coefficients for He to configurations L > 2 are, to a good approximation, the same as
for H, since these levels are hydrogen-like, but because He is a two-electron system,
it has separate singlet and triplet levels and
an iL(He°, T) « -jan 2L(H°, T)
a„3L(He°, T)^^an 2L(H°, T)
(2.20)
For the P and particularly the S terms there are sizeable differences between the He
and H recombination coefficients. Representative numerical values of the recombi¬
nation coefficients are included in Table 2.4.
The ionization equations for H and He are coupled by the radiation field with
hv > 24.6 eV, and are straightforward to writedown in the on-the-spot approximation,
Table 2.4
Recombination coefficients (in cm’s-1) for He
T
5,000 K 10,000 K 20,000 K
cqHe0, 1 '5) 2.17 X 10“
-13
1.54 X 10-
-13
1.10 X 10-
-13
a(He°, 2 XS) 7.62 X 10-
-15
5.55 X 10-
-15
4.07 X 10”
-15
cr(He0, 2
\p°)
1.97 X 10”
-14
1.26 X 10"
-14
7.57 X 10”
-15
a(He°, 3 XS) 2.20 X 10"
-15
1.62 X io-
-15
1.19 X io-
-15
a(He°, 3 ]P°) 7.87 X io-
-15
5.01 X 10”
-15
2.99 X 10-
-15
a(He°, 3 lD) 7.53 X io-
-15
4.31 X 10-
-15
2.26 X 10-
-15
aB(He°, [L) 1.09 X 10“
-13
6.23 X 10-
-14
3.46 X 10-
-14
a(He°, 2 3S) 1.97 X 10"
-14
1.49 X 10"
-14
1.16 X 10"
-14
a(He°, 2 3 p°) 8.52 X 10
-14
5.60 X 10-
-14
3.52 X 10-
-14
a(He°, 3 3 *5) 4.78 X io-
-15
3.72 X 10-
-15
2.96 X 10-
-15
cOHe0, 3 3D) 2.95 X 10"
-14
1.95 X 10-
-14
1.23 X 10-
-14
as (He0, En: *6) 3.57 X 10"
-13
2.10 X 10-
-13
1.21 X 10-
-13
aB(He°) 4.66 X 10"
-13
2.72 X 10-
-13
1.56 X 10-
-13

2.4 Photoionization of a Nebula Containing Hydrogen and Helium 29
though complicated in detail. First, the photons emitted in recombinations to the
ground level of Fie can ionize either H or He, since these photons are emitted with
energies just above hv2 = 24.6 eV. The fraction absorbed by H is
n(U°)a (H°)
y= _A_ (2 21)
n(H°) aV2(H°) + n(He°) aV2(He°),
and the remaining fraction, 1 — y, is absorbed by He. Second, following recombina¬
tion to excited levels of He, various photons are emitted that ionize H. Of the recom¬
binations to excited levels of He, approximately three-fourth are to the triplet levels
and approximately one-fourth are to the singlet levels. All the captures to triplets lead
ultimately through downward radiative transitions to 2 3S, which is highly metastable,
but which can decay by a one photon forbidden line at 19.8 eV to 1 'S, with transition
probability A(2 3S, 1 'S) = 1.26 x 10-4 s-1. Competing with this mode of depopula¬
tion of 2 3S, collisional excitation to the singlet levels 2 1S, and 2 1 P° can also occur
with fairly high probability, while collisional transitions to 1 1S or to the continuum are
less probable. Since the collisions leading to the singlet levels involve a spin change,
only electrons are effective in causing these excitations, and the transition rate per
atom in the 2 3S level is
ne q{2 3S, 2 lL) = ne uo{2 3S, 2 lL, u) f{u)du (2.22)
where the cr(2 3S, 2 lL) are the electron collision cross sections for these excitation
processes, and the x are their energy thresholds. These rate coefficients are listed in
Table 2.5, along with the critical electron density ne(2 3S), defined by
nc(2 3S) =
_A(2 3S, 1 *5)_
<7(2 3S, 2 >5) + q(2 35, 2 XP°)
(2.23)
Table 2.5
Collisional rate coefficients (in cm3 s_1) from He°(235)
T( K) <7(2 35, 2 *5) <7(23S, 2XP°) nca
6,000 1.95 x 10-8 2.34 x 10”9 6.2 x 103
8,000 2.45 xl0“8 3.64 xlO-9 4.6 x 103
10,000 2.60 x 10-8 5.92 x 10-9 3.9 x 103
15,000 3.05 x 10-8 7.83 x 10"9 3.3 x 103
20,000 2.55 x 10“8 9.23 x 10“9 3.3 x 103
25,000 2.68 x 10“8 9.81 x 10“9 3.4 x 103
a. Critical density in cm

Photoionization Equilibrium
at which collisional transitions are equally probable with radiative transitions. In
typical H II regions, the electron density ne < I02 cm”3, is considerably smaller than
nc, so practically all the atoms leave 2 3S by emission of a 19.8 eV-line photon. In
contrast, in typical bright planetary nebulae, ne ~ 104 cm”3, somewhat larger than
ne, and therefore many of the atoms are transferred to 2 *5 or 2 1P" before emitting
a line photon. From the ratio of excitation rates, it can be seen that, for instance, at T
= 104 K. a fraction 0.83 of the transitions lead to 2 *5, and 0.17 to 2 1P". If the less
probable collisional deexciting collisions to I 'S are also included, these tractions
become 0.78 and 0.16, respectively.
Of the captures to the singlet-excited levels in Fie, approximately two-thirds lead
ultimately to population of 2 ] P°, while approximately one-third lead to population
of 2 '5. Atoms in 2 1 P° decay mostly to 1 !S with emission of a resonance-line photon
at 21.2 eV, but some also decay to 2 '5 (with emission of 2 'S' — 2 1 P° at 2.06 /rm)
with a relative probability of approximately 10~3. The resonance-line photons are
scattered by He0, and therefore, after approximately 103 scatterings, a typical photon
would, on the average, be converted to a 2.06-yum line photon and thus populate 2 '5.
However, it is more likely that before a resonance-line photon is scattered this many
times, it will photoionize an H atom and be absorbed. He atoms in 2 1 A- decay by
two-photon emission (with the sum of the energies 20.6 eV and transition probability
51.3 s'”1) to 1 '5. From the distribution of photons in this continuous spectrum, the
probability that a photon is produced that can ionize H is 0.56 per radiative decay
from He0 2 !S.
All these He bound-bound transitions produce photons that ionize H but not
He, and they can easily be included in the H ionization equation in the on-the-spot
approximation. The total number of recombinations to excited levels of He per unit
volume per unit time is n(He+)neaB(He°, T), and of these a fraction p generate
ionizing photons that are absorbed on the spot. As shown by the preceding discussion,
in the low-density limit rte <^C nc
p ~
2 1
— + - (0.56)
3 3
0.96,
but in the high-density limit ne 5>> nc,
3 „ 11 3 1 2
(0.78) + - • - (0.56) + -(0.16) +-
4 4 3 4 4 3
0.66.
Thus, in the on-the-spot approximation, the ionization equations become
n(H°) R-
r
Jv0
-——-av(H°) exp( — tv) dv + yn(He+)rceo'l(He°, T)
hv
+ pn(He+) neaB(He0, T) = npneaB(H°, T)\
(2.24)

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block perforated to correspond with the needles, and driven at the
speed of a quarter of a revolution for each two picks. The pegs on it
carry the pattern plates round with the block. The needles are
arranged horizontally, points facing pattern block. The outer needles
regulate whether the right or left leg of the fork shall be in contact
with the wheel on pinion shaft, to determine whether the
reciprocation shall be upwards or downwards. A hole in either one
side or the other of the plate regulates this; should both sides be
perforated, the fork remains in its previous position. The fork is
raised and depressed by a lever, actuated by one of two cams—one
to move the boxes one shelf, and the other to skip a shelf, thus
moving two boxes. These cams are changeable, and operate on one
end of the lever, while the fork is suspended to the other end. The
central needle decides which shall be in action, as it carries a
projection which, when pushed back, thrusts the larger sweep cam
into action. It is easy, therefore, to understand the action of these
cards; three holes give no movement; two holes, with a blank at one
side, put the fork into gear with the corresponding side of the pinion
wheel; and in the case of two blanks, the one in the centre puts
two-box stroke in action, and the side blank puts the fork in gear at
one side. One blank at the right side causes a rise, or, at the left
side, a fall. The five forms of plate are:—
Rising one means that the box is risen to the next shelf; rising two is
risen to the next shelf but one, skipping one. This style of drop box

can be driven at the speed of 170 picks per minute. Generally, a
weaver attends to three of these looms, and an overlooker to from
50 to 60. For the check shirting trade looms to weave from 30-inch
to 37-inch cloth are used.
OTHER MOTIONS.
An ingenious drop-box motion is manufactured by a Burnley firm, by
which the weight of supporting the boxes, etc., is altogether
removed from the pattern chain, which is consequently made of less
cumbrous construction. Other firms claim decided advantages in
respect of a greater skip than either Diggle’s or Wright Shaw’s
motions—e.g., from the first to the sixth box. Skips of this extent are
obtained principally by using several eccentric cams. One of these
may lift a single box, a second may raise the boxes two spaces, and
their effect in combination is a lift of three shuttles, and so on for
greater effects.
CIRCULAR BOXES.
Circular boxes are seldom used for cotton goods. In this
arrangement the shuttles are fixed in grooves formed in a block
revolving at the slay end, and drawn round in either direction by
hooks, one being placed at each side of the revolving barrel. The
movement of the hooks is regulated by a pattern chain. The speed is
about the same as a Wright Shaw motion.
GENERAL.
Any of these types of boxes may be used with the over-pick, and
either with tappets, dobby, or jacquard shedding. Attempts have
recently been made to apply the drop-box principle to a system of
replenishing the loom with three or four cops of weft without a
stoppage, by having them previously placed in the shelves and
lowered on the breakage or running-off of the previous weft.

Coloured Spots.
Additional colour is introduced into cotton fabrics in spots and
figures after the manner of embroidery, by using circle swivels or
lappets. If a series of small spots in colour are required to be made,
by using a drop-box loom with a jacquard or dobby the object is
easily attained, but it necessitates the cutting away of much of the
coloured yarn which has been picked across the cloth, and only a
portion of which is required for the figure. Now, by using extra twist
or weft, and only interweaving as much as is required for the figure
alone, much waste can be prevented, and a firmer spot obtained.
Take, for example, the spotted muslin so frequently used for window
curtains; each figure only consists of a few inches of coarse yarn so
loosely passed through the ground cloth, and apparently so entirely
independent of the other spots, that a tyro can form no other
explanation of their appearance there than that they have been
sewn on.
Circle Weaving .
Circle weaving has been used in these cases. In addition to the
ground weft, which is carried across the cloth in the ordinary shuttle,
there is a frame above the shed of the warp carrying several circular,
or rather horseshoe-shaped attachments with a small bobbin of weft
pivoted at the upper part (farthest from the opening in the ring).
These rings are driven round by gearing with a rack. When the
figure has to be formed by the weft passing round, say 20 ends,
these are raised above the level of the top of the ordinary shed,
inside the ring, which then makes one complete revolution, and the
ends are depressed. Maybe a plain pick or two is then inserted, and
afterwards more spotting, until the desired figure is embroidered on
the muslin, when plain weaving is resumed for a few inches.
Lappets .

In lappet weaving, extra bobbins of warp are placed below the loom,
and the ends from them carried to a set of upright needles, which
slide in a groove immediately in front of the end, a false reed being
arranged for the guidance of the shuttle. The needles are regulated
by a cam, and, with their point projecting, raise the thread into the
shed, so that it may be bound into the cloth by the weft; after which
the needles are removed the distance of a few threads, and again
raise the coloured end, so that it may be bound into the cloth. The
cam causes the needles to be slid to and fro in this manner until a
figure is formed as desired. By this latter method the colour in the
figure largely predominates on one side of the cloth, that which is
the under side in the loom. The upper side merely shows the outline
of the figure where the thread has passed through to be bound. In
the circle swivel figures the weft usually shows equally on both
sides.

CHAPTER IX.
MILL CALCULATIONS—YARN COUNTS, REEDS,
HEALDS, COST OF CLOTH, WARPING AND SIZING
LENGTHS, WAGES, SPEEDS, ENGINES.
It is desirable that the calculations connected with cotton
manufacturing in all its bearings be treated in a separate
chapter. This is not only necessary from their number, but from
their great variety and difficulty of classification under different
chapter headings, inasmuch as many are applicable to more than
one process.
Yarn Calculations .
The fineness of cotton yarn is indicated by the counts (otherwise
numbers or grist). The counts refer to the number of hanks in a
pound (avoirdupois). The cotton hank is always 840 yards; and,
therefore, if we speak of 10’s, we refer to yarn of which 10 hanks or
8400 yards weigh one pound; or in referring to 36’s, of that which
36 × 840 or 30,240 yards weigh one pound. This applies to either
twist or weft. The cotton yarn measure is—
120 yards = 1 lea.
7 leas or 840 yards = 1 hank.
and the cotton yarn weight is peculiar, being an avoirdupois pound
divided into pennyweights and ounces as in the troy weight.
24 grains = 1 pennyweight.
437-1/2 grains = 18-11/48 pennyweights = 1 ounce.

7000 grains = 16 ounces = 1 lb.
Wrapping .
1’s are taken as the standard with 840 yards in 7000 grains, and a
higher count means finer yarn; then 840 yards of, say 2’s, would
weigh 3500 grains, or of 70’s, would weigh 100 grains. If we
measure a hank of yarn, and find that it weighs 100 grains, then
7000, divided by 100, gives the counts. It is inconvenient in
wrapping yarn to measure 840 yards, therefore a lea of 120 yards is
taken as the standard length for 1’s, and also the proportionate
weight = 1000 grains. Instead of taking 840 yards and 7000 grains it
is usual, then, to take 120 yards and 1000 grains. A wrap reel is 1-
1/2 yards in circumference, and, by revolving it 80 times, we can
wind 120 yards from a cop placed in the machine. Suppose this lea
of 120 yards weighs 25 grains, then 10000/25 = 40’s. Should less
than a lea be taken, say 60 yards, then 500 grains must be the
dividend. Generally, however, to obtain the counts of any yarn, 120
yards are weighed, and the weight, in grains, divided into 1000.
Having the Length and Counts given, to find the Weight.—9240
yards of 44’s weft = 9240 yards ÷ 840 = 11 hanks. In the given
counts 44 hanks weigh 1 lb., then 11 hanks weigh 11/44 or 1/4 of a
lb.
Counts of Silk, Worsted, Linen.—Single silk is counted same as
cotton, except that in two-fold patent silk the actual wrapping is
given—say, 30’s/2 in silk will wrap 30’s. In cotton, 2/30’s would wrap
15’s. The worsted hank is 560 yards. The linen “lea” is 300 yards.
The French cotton standard is 1000 metres in 500 grammes—
equivalent to 992·4 yards in 1 lb. Thus, 1·181’s in English would be
1’s in French. To transfer cotton measure to any other take the
cotton count, proportion it inversely to the number of yards in the
hanks, say—
20’s cotton equals 30’s worsted,
(20 × 840)/560 = 30’s

20’s cotton equals 56’s linen,
300 : 840 :: 20’s : 56’s.
20’s cotton equals 20’s silk.
20’s English equals 16·93’s French.
1·18 : 1 :: 20’s : x
x = (1 × 20)/1·181 = 16·93
Double Yarns (Cotton).—Two-fold yarns are numbered according to
the single yarn counts—thus, 2/80’s = two ends of 80’s twined
together, which would wrap 40’s. Actually, to make the resultant
count 40’s, the single yarn should be finer than 80’s, because the
twist put in the folded yarn contracts it in length and causes the
two-fold to be really coarser than would appear. However, neglecting
this, suppose we twine one end of 40’s and one of 20’s, the counts
would not be 15’s, as a first glance would indicate, but 13·33. This
can be proved by taking the weight of a lea of 40 = 25 grains, and
of 20’s = 50 grains; total, 75. 75 divided into 1000 gives the counts
as 13-1/3. Another rule is, multiply the two counts and divide by
their sum—
(40 × 20)/(40 + 20) = 800/60 = 13-1/3
3/300’s = 100’s.
3-fold yarn of 40’s, 80’s, and 120’s would be 21·81.
A lea of 40’s   = 25     gr ains.
A lea of 80’s   = 12-1/2    "
A lea of 120’s =   8-1/8   "
——
45-5/6
1000/(45-5/6) = 21·81

Or take the highest count and divide it by each of the others and by
itself, then divide the total of the quotients into the highest—
120 ÷ 80 = 1-1/2
120 ÷ 40 = 3
120 ÷ 120 = 1
——
5-1/2
120/5-1/2 = 21·81
Testing Yarns.
In addition to wrapping warp yarn to ascertain actual counts, it is
frequently tested as to strength; the lea from the reel is placed
between two hooks on a testing machine, and by a wheel worm and
screw the lower hook is moved downwards, increasing the tension
on the yarn. By an index finger this tension is indicated on a face
plate, and when the lea is broken the finger stops at the highest
weight or strain that the yarn has stood. Below is a table, which will
give a general idea of the comparative strength of mule twists,
having, for the American cotton, the standard turns in—i.e., square
root of counts multiplied by 3-3/4.
20’s American Cotton = 80lb.
30’s American Cotton = 54lb.
40’s {
American Cotton = 40lb.
Egyptian Cotton = 50lb.
50’s {
American Cotton = 28lb.
Egyptian Cotton = 37lb.
60’s Egyptian Cotton = 30lb.
70’s Egyptian Cotton = 26lb.
In yarn the diameters of the threads do not vary inversely as the
counts, but inversely as the square root of the counts. Thus, 16’s is

not four times as thick as 64’s, but twice as thick, the square roots
being four and eight respectively.
Reed Counting .
Before entering into the calculations regarding the weight of cloth, it
is necessary to familiarise ourselves with some method of counting
the ends of warp in the cloth. On the Exchange the system adopted
both for ends and pick is their number per quarter inch—e.g., a 16
by 14 means 16 ends per 1/4-inch, or 14 picks per quarter. The
methods used in the manufactory are based on the counts of reed.
Formerly many systems of reed counts prevailed, each town or
district having a method peculiar to itself; thus, Blackburn counts,
Preston counts and many others were at one time adhered to in
their respective districts, but have now fallen into disuse, and almost
been forgotten. The Stockport counts is commonest in Lancashire,
and is based on the number of dents or splits of the reed in two
inches, and as cloth is generally wrought two ends on a dent, this
system is often taken as the number of ends in one inch. It is in use
in almost every Lancashire manufacturing district, being adopted in
consequence of its simplicity and suitability for calculation purposes.
The Bolton counts is still used in some mills in that town and also in
Bury and some few other districts. It is based on the number of
beers in 24-1/4 inches—a beer comprising 20 dents. A Stockport 40’s
reed would have 485 dents on 24-1/4 inches, or 24-1/4 beers
Bolton. A Bolton 24-1/4 reed is then equal to a Stockport 40’s. To
find the number of splits per inch in a reed having Bolton counts
given, multiply those counts by ·8249, or vice versâ. This rule shows
the number of dents and decimal parts; 8·245 is more often taken,
but it gives the number with less exactitude. The fraction is only
taken to two places of decimals, showing thus the 100th parts of
dents—e.g., a 30
0
Bolton has 24-74/100 splits per inch (8·249 × 30
= 24·747). To convert Stockport into Bolton counts multiply by
·60625. To convert Bolton into Stockport multiply by 1·6495. This
rule gives the number of ends per inch in Bolton counts, supposing

the cloth to be wrought two ends in a dent. The Scotch systems are
to take the number of dents or splits in the old Scotch ell, 37 inches,
or by the number of porters on the same length. The Scotch porter
is equal to the Lancashire beer—20 splits. In the first system, the
splits per ell are expressed in hundreds—thus, 17
00
indicates 1700
splits on 37 inches, almost equal to a 92 reed, Stockport; or a 46 on
the Scotch inch scale, which is the number of splits in one inch, and
corresponding to the old Radcliffe and Pilkington method in
Lancashire.
By the porter system, a 40-porter reed would give 40 × 20 dents =
800 on 37 inches, equal to a 43 reed, Stockport, In Scotland (as in
Lancashire) the old complicated systems show a tendency to give
way in favour of the simpler systems of counting the dents or ends
in one inch.
In the reed table given below, the first row of figures shows the
proportion which these reeds bear to one another, and the lower
rows indicate the fineness of the different systems for 33 and 40
splits per inch respectively—the calculation results being given,
which same might not frequently appear in practice—
The Inch
Scale.
Stockport Bolton Scotch.Scotch Porter.
Dents per
Inch.
Dents on 2
Inches.
Beers on 24-
1/4 Inches.
100 ends 37
Inches.
Porters on 37
Inches.
1 2 1·2125 0·37 1·85
33 66 40· 12·20 61
40 80 48·5 14·80 74
Healds.
In Stockport counts four healds are considered as a set, and having
one thread through each eye are dubbed of similar counts to the
reed—e.g., a 60’s set of healds has 15 stitches per inch in each set,

equalling 60 ends per inch in the reed, which is a 60’s reed,
Stockport.
In spaced healds some are knitted finer than others and
consequently numbered differently. In this point draft:—
5 5
4 4 4 4
3 3 3
2 2
1
twelve ends are drawn on five healds, one end on the 1st heald, two
on the 2nd, three on the 3rd, four on the 4th, and two on the 5th.
Four different degrees of fineness are required in the five heald
staves, and the above draft is given to the knitter with instructions
for so many patterns to the inch. Say five patterns per inch: 5 × 12
would give a 60 reed, and the number of stitches per inch would be
respectively 5, 10, 15, 20 and 10—the front one being equal to a
Stockport 20’s, for if there were four similar to it in a set, the
number of ends would be 20. Similarly the second stave equals a
Stockport 40’s, the third 60’s, the fourth 80’s, and the fifth same as
the second, a 40’s. To prove this, the requisite set of five staves
might be obtained by taking one stave out of a plain 20’s set, two
staves of a plain 40’s, one stave from a 60’s, and one from an 80’s
set.
Weight of a Piece.
In calculating the weight of a piece, the warp weight is obtained
from the number of ends, based upon the width in the reed. This is
multiplied by the sizing length and brought into hanks, from which
the weight can be obtained by dividing by the counts. The weft is
calculated from the picks to the inch, the reed width, and the actual
length of piece. Example—A piece has to be made full dimensions,
36 inches wide, 36 yards long, 16 square (1/4 inch)—i.e., 64 ends

per inch and 64 picks; yarns 30’s/36’s, the first number being the
warp, sized 25 per cent. In the reed it would stand 38 inches, about
six per cent. being allowed for contraction. Of course, if the yarn
were coarser, the pick heavier, and the reed finer, more than this
would be allowed. Supposing that a 60’s reed (Stockport) is used,
the number of ends would be 38 × 60 = 2280; the length of warp,
say 38 yards, allowing six per cent.—then
(2280 × 38)/840 = 103-1/7 hanks,
Divided by 30’s gives 3lb. 7oz.
Weft.—The weft, 37-1/2 inches wide, 64 picks; length of piece, 36
yards.
(37-1/2 × 64 x 36)/(840 × 36’s) = 2lb. 13-3/4oz.
37-1/2 × 64 gives the number of inches of weft in one inch of cloth,
or, what is the same, yards of weft in one yard of cloth.
Size.—
3lb. 7oz. = 55oz.
25 per cent. on 55 =
55 × 25 ÷ 100 = 13-3/4oz.
The weight of the piece is then—
Twist 3 : 7
Size 13-3/4
——————————
4 : 4-3/4
Weft 2 : 13-3/4
—————
7 : 2-1/2
When the piece is measured by the long stick, about half an inch
more to the yard must be reckoned—e.g., 38-inch: 14/14, 37-1/2
yards L.S., 38’s weft, to be 8-1/4lb. in weight; this would be perhaps
38-1/4 yards long S.S.

Weft.—
(40 × 56 × 38-1/4)/(840 × 38) = 2 : 10-3/4
Leaving 5: 9-1/4 for twist and size, say of the latter 100 per cent.,
then 2: 12-1/2 would be twist—
(40 × 52 × 41)/840 = 101-1/2 hanks
required to be found in 2: 12-1/2 of yarn; then if 2: 12-1/2 = 101-
1/2 hank:: 1lb. equals 36’s twist about.
This cloth would then be composed of—
Warp2 : 12-1/4
Size 2 : 13
Weft2 : 10-3/4
————
8 : 4
For quoting purposes the weight of the yarn is taken at the market
price, say that of the cloth No. 1—
lb. oz.
3 7 of 30’ s T at 8d. = 2 : 3-1/2
2 13-3/4 of 36’s W at 8d. = 1 : 11
Weaving Price = 9-1/2
To this is added a sum sufficient to cover cost—winding, warping,
sizing, power, miscellaneous expenses, waste (which sum varies
considerably, and depends mainly upon the situation of the
producers as regards the amount at which he can produce this
cloth). Often, for lightly-sized goods, the weaving price is doubled,
making this piece cost 5s. 9-1/2d. Should it be a dhootie, then an
addition is made for coloured yarns for heading and border, and if a
figured cloth extras are included for increased cost of production.
The examples given are supposititious ones, for, as has been said,
the exact details of weight and quoting prices are decided purely by
local or temporary position, and fixed data cannot be given as a
standard for every case.

Stripe Patterns .
In case of stripes with two counts of warp yarn, for example, the
number of ends of each must be obtained. If there are 38 stripes
each of 15 ends, 40’s twist, with a ground cloth between each of 45
ends warp, 60’s T, separate calculations for each must be made.
38 × 15 = 570 stripe ends.
38 × 45 = 1710 ground ends.
Altering .
When the pick or reed is altered, the weight of the weft or warp is
altered in proportion; when the length or width is altered, the weight
of the piece is altered in proportion; when the counts of yarn are
altered, the weight alters inversely proportionately.
Other Reeds.
Although the 1/4-inch scale is mostly used for calculating warps in
Lancashire, we give an example of a calculation with the Bolton
reed. To get the number of ends, multiply the reed counts by the
width of your warp in the reed, and by 1·6495—thus, Bolton 36’s, 39
inches in the reed, would give 2238 ends. The calculation is then
proceeded with in the ordinary manner. In the Scotch ell standard
system, the dimensions of the cloth before-mentioned would be 36
inches wide, 36 yards long, 11
00
reed, 11-1/2 shots to the glass,
yarns 30’s/36’s. To calculate the weight of warp, add six per cent. to
the 36 inches, making it 38 inches wide in the reed. If there are
1100 splits on 37 inches, then the number on 38 inches will be
proportional.
(1100 × 38)/37 = 1130.
Multiply by 2, as it is always understood that there are two ends in a
split, and we get 2260 ends. The calculation is then continued in the

usual way.
(2260 × 38)/(840 × 30) = 3·407lb.
Weft.—— The meaning of shots on the glass refers to a counting
glass used in Glasgow district, one two-hundredth part of a yard in
width; 11-1/2 shots will then give 11-1/2 × 200 = 2300 picks in a
yard.
(2300 × 37-1/2 inches wide)/(36’s × 36 inches to the yard × 840) =
2·85lb.
If required to be left in hank, omit to divide by the counts in each
case. In other materials, the length of the hank varies, and, in the
case of single worsted, we should have divided in the previous
calculations by 560 instead of 840, in linen by 300, or in single silk
by 840.
Warping and Sizing Calculations .
In getting an order passed through a weaving shed the first point,
after calculating the particulars for each piece or cut, is to get the
length for warping and sizing. In the case of an order for 3750
pieces of the before-mentioned dimensions, the total length of warp
is calculated thus—38 yards for one piece × 3750 = 142,500 yards,
allowing nothing for waste in length, as the tension on the yarn in
process will stretch it sufficiently to allow for that, and perhaps a
little more. At the warping mill the length is taken in wraps of 3564
yards, subdivided into teeth of 27 yards. In this case, four wraps or
14,256 yards would be taken to a set of back beams; therefore, this
order would be run in ten separate sets.
The number of back beams for the sizing machine is proportioned to
the capacity of the warping mill—say five beams, the length on each
beam must be 14,256 yards, and the total number of ends on the
beams equal to the ends in the piece—say 5 at 456 each = 2280.
To Calculate the Counts of Yarn after Warping.—Divide the length by
the weight and 840. A beam weighs 301lb., carrying 504 ends, each

14,256 yards long—
(14,256 × 504)/(301 × 840) = 28·41’s.
Having 375 pieces to make from the set of beams, which will
probably weigh about 1300lb. for 30’s twist, to this add 25 per cent.
for size =
(1300 × 325)/100 = 325
1300
——
1625
Divide by 375) 1500 (4lb. 5oz.
——
125
16
——
2000
4lb. 5oz. being about the size required (vide page 150).
Actual Size.—To find the size actually put on the yarn, subtract the
weight of the unsized yarn less waste from the sized yarn—e.g.,
1639 Actual sized weight.
1300
——
339 = Weight of size.
1300) 33900 (26·07 per cent. actual.
2600
———
7900
7800
——
100
Counts after Sizing.—
(14256 × 2280) / (1639 × 840) = 23·61’s

To Calculate the Percentage of Waste.—Multiply the waste made by
100 and divide by the weight of yarn used. If eleven skips of twist,
weighing 3189lb., make 33lb. of waste—
3189 ) 3300 ( 1·034 per cent.
3189
———
11100
9567
———
15330
Wages—Standard Lists.
In those towns where a uniform class of goods is made of simple
weave, it is possible to formulate and adhere to a standard method
of payment such as is done in Burnley, Blackburn, and other towns.
In other districts, such as Bolton and Preston, the sorts are so varied
and difficult to classify that at many mills a private list is adhered to
with satisfaction to the employer and employed. For the benefit of
some readers a typical calculation will be given, based on the 1853
Blackburn list, as in 1883 this list was adopted in Preston, Chorley,
and other towns. This may be considered a list of medium position
with regard to other lists—Burnley being lower for plains, Ashton list
being considered a low one for fancies.
The Blackburn list is based on a 40-inch loom, weaving from 36 to 41-inch cloth,
60 reed Stockport counts, 16 picks per 1/4 inch, 37-1/2 yards, from 30’s to 60’s
weft, and from 28’s to 45’s twist, for 12·25d.
Reeds.—A 60 reed or 30 dents, being the standard, is made the starting point, and
3/4 per cent. is deducted for every two ends or counts of reeds, from 60 to 48;
but no deduction is made below 48 reed, and 3/4 per cent. is added for every two
ends or counts of reed above 60.
Weft.—All weft from 30’s to 60’s, both included, is considered medium, and
reckoned equal, but all weft above 60’s to be allowed 1 per cent. for every 10
hanks,

and all below 30’s to 26’s to be allowed 2 to be allowed
and all below 26’s to 20’s to be allowed 5 to be allowed
and all below 20’s to 16’s to be allowed 8 to be allowed
and all below 16’s to 14’s to be allowed 10 to be allowed
Twist.—All twist from 28’s to 45’s, both included, is considered medium, and
reckoned equal, but all twist above 45’s up to 60’s to be allowed 1-1/2 per cent.,
and all above 60’s 1 per cent. for each 10 hanks,
and all below 28’s to 20’s to be allowed 1 per cent. on list.
and all below 20’s to 14’s to be allowed 2 per cent. on list.
Additions for Picks.—All picks above 8 and up to 18 are considered proportionate,
but 8 picks and all below and all above 18, to have 1 per cent. allowed for every
pick over and above the proportionate difference in the number of picks.
Width of Looms.—A 40-inch loom being the standard, is taken as the starting
point, and all additions or deductions are made therefrom. (The reed space is
measured from back board to forkgrate.)
25-inch loom has 2-1/2 per cent. deducted from 30-inch loom.
30-inch " 5 " " 35-inch "
35-inch " 5 " " 40-inch "
40-inch loom (45-inch reed space) the standard—
45-inch loom has 5 per cent. added to 40-inch loom.
50-inch loom has 10 per cent. added to 45-inch "
55-inch loom has 10 per cent. added to 50-inch "
60-inch loom has 10 per cent. added to 55-inch "
Looms of Intermediate Width.—One per cent. per inch is to be deducted from 40
down to 30-inch loom; below 30 to 26-inch loom 5/8 per cent. per inch to be
deducted. Above 40-inch and up to 45-inch loom, 1 per cent. per inch to be
added, and all above 45-inch 2 per cent. per inch.
Narrow Cloth in Broad Looms.—Suppose a 40-inch loom should be weaving cloth
36 to 31-1/4 inches in width, take off one-half the difference between 40 and 35-
inch loom price; and if weaving cloth 31 to 27-1/4 inches wide, take off one-half
the difference between 40 and 30-inch loom price; or if weaving 41-1/4 to 46-inch
cloth in a 50-inch loom, take off one-half the difference between 50 and 45-inch
loom, and so on with all other widths.
Range of Cloths.—

26-inch loom allowed to weave cloth up to 27 inches.
35-inch loom allowed to weave cloth from 31 to 36 inches.
40-inch loom allowed to weave cloth 36 to 41 inches.
45-inch loom allowed to weave cloth 41 to 46 inches.
50-inch loom allowed to weave cloth 46 to 52 inches.
Basis of Calculations.—The calculations in the Blackburn list are based upon the
picks counted by the glass when the cloth is laid upon the counter. Forty yards
short stick to be taken as 39 yards long stick.
To find price for a 44-inch cloth in 45-inch loom = 66’s reed, 44
change pinion, 528 dividend, 75 yards long, 34’s/36’s—
12·25 Standard.
Add 5 per cent. loom ·61
———
12·86
Add 2-1/4 per cent. reed ·28
———
13·14
Calculate in proportion to pick 16 to 12 = 9·86
Calculate proportion length 37-1/2 to 75 = 19·72 = List price.
Double
Deduct 10 per cent. = 1·97
———
17·78 = Present price.
or from list under heading, 45-inch loom—
66 reed, 37-1/2 yards = ·822 for 1 pick.
9·86 for 12 picks.
19·72 for 75 yards.
Speeds of Shafts, Etc.
In calculating the speed of a shaft driven from another by pulleys or
gearing, multiply the speed of the first shaft by the driving pulley or
wheel, and divide by the driven one. A shaft makes 100 revolutions

per minute and carries a 40-inch drum driving a 16-inch pulley on
another shaft; the speed of the second shaft would be 250, thus:—
(100 × 40)/16 = 250.
The same rule and calculation would apply if the first shaft had
carried a 40-teeth cog-wheel, and the second a 16-teeth wheel.
In taking the dimensions of a pulley for calculations the diameter is
often taken; it does not matter, though, if the circumference be
taken, but care must be exercised in taking the same dimension for
the driven as is taken for the driver. If the diameter is taken of one,
the diameter must be taken of the other.
To get Speed of Loom from Engine.—Multiply the engine speed by all
the driving pulleys, and divide by the driven ones. If the engine
make 46 strokes per minute, spur-wheel 105 teeth, second motion
pinion 52 teeth; also on same a 52 driving a 49 on line shaft in shed.
Pulley on line shaft on which is a 15-inch drum driving a loom pulley
on the crank-shaft of 8 inches.
The driving and driven pulleys are always alternate; then as the first
must be a driver—
(46 × 105 × 52 × 15)/(52 × 49 × 8) = 185 nearly.
The answer gives the calculated picks per minute. About 4 per cent.
must, however, be allowed for slippage, reducing the 185 to an
actual speed of about 177.
To find the Size of Pulley for any required Speed.—Find the ratio of
the given speed and arrange size of pulley accordingly. Suppose a
shaft running at 100 revolutions per minute has to drive a loom-
shaft at a speed of 180 picks per minute the ratio of speed is as 100
to 180 or as 5 to 9; arrange the pulleys in this proportion—say 10
inches and 18 inches, the larger pulley being on the driving shaft.
To alter Speeds.—Calculate in proportion to the alteration. If a twill-
shaft is driven by a 30-cog wheel, and revolves at a speed of 45
revolutions per minute for a 4-leaf twill, and it is desirable to change

this to a 3-leaf twill with the twill-shaft at 60 revolutions per minute,
then, as 45 is to 60, so 30: x—
x = (60 × 30)/45 = 40
A 40 wheel must now drive the wheel on the twill-shaft, and the
speed will be increased one-third more.
Engines .
The strength of a steam engine is indicated in horse-powers. A
horse-power is taken as the capacity of performing 33,000 foot-
pounds of work in one minute; lifting 3300lb. 10 feet high, or 10lb.
3300 feet high would be 33,000 foot-pounds of work.
To obtain the Indicated Horse-power—the most usual Standard.—A
diagram is taken from the engine by a small apparatus, and this
diagram, when measured and averaged at different points of its
length, gives the mean pressure of steam in the cylinder. Multiply
this by the speed of the piston, by the area of the piston, and divide
by 33,000, and the I.H.P. is to hand. 39·81 average pressure per
square inch, area of piston 400 square inches, length of stroke 5-1/2
feet, strokes per minute 40 (or 11 feet both ways)—
(39·81 × 400 × 11 × 40)/33,000 = 212·32 I.H.P.
Nominal horse-power (condensing) = area of piston divided by 22;
ditto high pressure = area of piston divided by 11.
2-1/2 to 3 looms, with preparation, are reckoned to 1 indicated
horse-power.
Coal.—A good quality of coal should evaporate 8lb. of water for each
1lb. burnt, and for a manufacturing concern (including sizing, which
takes a great amount of steam) the consumption of coal should be
about 3-1/4lb. per I.H.P. per hour. Thus 600 horse-power should use
about 24 tons per week; excluding sizing, 2-3/4lb. would suffice.
To find the Circumference of a Circle.—Multiply the diameter by
3·1416 or (roughly) by 3-1/7.

To find the Area of a Circular Space.—Square the diameter and
multiply by ·7854.
To find the Cubical Contents of a Rectangular Block.—Multiply the
depth, length and breadth together.

City and Guilds of London Institute
FOR THE ADVANCEMENT OF
TECHNICAL EDUCATION.
TECHNOLOGICAL EXAMINATIONS.
19B.—COTTON MANUFACTURE.
Section I.—COTTON SPINNING.
I. Syllabus.—The Examination will include questions founded on
such subjects as the following:—
1. The geographical position of the world’s cotton fields, and suitable
regions to which it may be introduced.
2. Cotton cultivation and the various causes of damage to the fibre
during growing and picking seasons, with the dates of planting and
picking in all cotton-growing countries.
3. The mode of preparing the raw material, cotton gins, ginning,
packing, &c. Means and methods of adulteration.
4. Commercial handling of the raw material up to the spinning mill.
5. The nature and properties of the various kinds of raw material—
Sea Island, Queensland, Fiji, Egyptian, New Orleans, Uplands,
Boweds, Dollerah, Hinghinghat, Surat, Brazilian, &c.
6. The selection of, and advisability, or otherwise, of mixing various
cottons with a view to the full utilization of every kind.
7. The development of and the principles involved in the construction
of the several machines used in cotton spinning.

8. Cleaning cotton by opening, scrutching, carding and combing
machines.
9. Processes of attaining a parallel arrangement of fibres by carding,
and the attenuation of the sliver through drawing, slubbing,
intermediate and finishing roving frames.
10. Spinning operations upon the throstle, mule, and ring frames.
11. The doubling of single yarns for lace, hosiery, sewing thread, and
kindred purposes.
12. Warping and bundling for the home trade and export, with the
accompanying processes of winding and reeling.
13. Packing and commercial dealing with yarns in the process of
distribution.
In the Honours Examination more difficult questions in the above
subjects will be set than in the Ordinary Grade.
II. Full Technological Certificate.—The candidate, who is not
otherwise qualified (see Regulations 33 and 34), will be required, for
the full Certificate in the Ordinary Grade, to have passed the Science
and Art Department’s Examination, in the Elementary Stage at least,
and for the full Certificate in the Honours Grade, in the Advanced
Stage at least, in two of the following Science subjects:—
II. Machine Construction and Drawing.
III. Building Construction.
VI. Theoretical Mechanics.
VII. Applied Mechanics.
XV. Elementary Botany.
Certificates, showing that the candidate has passed the Second
Grade Examination of the Science and Art Department in
Geometrical Drawing as well as in Freehand or Model Drawing, will

be accepted in lieu of one of the above Science subjects for the full
Technological Certificate in either grade of the Examination.
Section II.—COTTON WEAVING.
The Examination in the Ordinary Grade will consist of a paper of
questions only.
I. Syllabus.—The Examination will include questions founded on
such subjects as the following:—
1. Winding Machines for warping and pirns.
2. Warping.—Mill, beam and sectional.
3. Sizing.—Ball, hank, dressing, slashing upon both cylinder and hot-
air frames.
4. Beaming and Scotch Dressing.
5. Reeds and Healds (Counts Setting, &c.), Drawing in and Twisting.
6. Comparative merits of Hand and Power Looms.
7. The Power Loom—its parts, the principle governing each, with the
relation and timing of each to the other.
8. Shedding Motions—as Tappets with their over and under motions.
Dobbies or witches.
9. Picking motions, alternate and “pick and pick.”
10. Beating up, shuttle box, and minor motions.
11. Necessary calculations for the power loom.
12. The various makes of cloth produced by Tappets and Dobbies as
plain cloth, twills, satins, and small figured effects, with one warp
and weft, or with the addition of extra warp for figuring, as in
Dhooties.
13. Method of making designs, drafts, and tie-ups for the above.

14. Colour and colour blending as applied to the coloured branches
of the industry.
15. Calculations for warp and weft and method of costing goods.
The Examination for the Honours Grade will consist of more
advanced questions on the preceding subjects, especially those
enumerated in Sections 7 to 11; and, in addition, questions relating
to the following:—
1. Construction of the various Jacquard machines in use, and their
relative suitability to various goods, and the system of mounting
Jacquard looms.
2. Construction, merits and uses of the hand loom.
3. Principles of cloth structure, and the mechanism required for the
production of the following typical fabrics:—Plain cloth, twills,
diapers, brocades, damasks, coloured stripes and checks, warp
spots, repps, weft spots produced with circles, swivels or extra
shuttles, backed cloths, double cloths, 3, 4, 5, &c., ply fabrics,
tapestries, velveteens, cords, Terry fabrics, plain and figured gauze,
lappets, plain and figured leno.
4. Principles of designing and card cutting involved in producing the
above fabrics, giving preference to the actual designing and working
of such patterns as shall be practically useful as articles of
commerce.
5. Analysis of samples of woven fabrics to determine pattern, draft,
tie-up, and counts of material used.
6. Composition of the various yarns used in the production of mixed
fabrics.
7. Latent and other defects in fabrics caused by faulty construction
and unequal balancing of warp and weft.

8. Selection of warp and weft yarns suitable for the fabrics required.
9. Proportioning of fabrics so as to maintain the original structure
with an increased or diminished weight.
10. Method of calculating the cost of a fabric from given data of
values of material and labour, by ascertaining the fibre, counts, ends,
picks and weight.
11. Actual Weaving.—Each candidate will be required, during the
year preceding the Examination, to design and execute in suitable
material an original pattern, of not less than 200 ends and 200 picks
in a complete pattern, and to forward the same (carriage paid) to
London a fortnight prior to the day of the Examination, together with
a certificate signed by his employer, or by the class teacher and a
member of the School Committee, stating that the work has been
executed by the candidate without assistance. The specimen of
weaving, showing the complete pattern, must not be less than one
yard in length and at least 24 inches in width: it must be properly
dyed or finished, and constructed in such a manner as to be a
saleable article.
II. Full Technological Certificate.—The candidate, who is not
otherwise qualified (see Regulations 33 and 34), will be required, for
the full Certificate in the Ordinary Grade, to have passed the Science
and Art Department’s Examination, in the Elementary Stage at least,
and for the full Certificate in the Honours Grade, in the Advanced
Stage at least, in two of the following Science subjects:—
II. Machine Construction and Drawing.
III. Building Construction.
VI. Theoretical Mechanics.
VII. Applied Mechanics.
XV. Elementary Botany.
Certificates, showing that the candidate has passed the Second
Grade Examination of the Science and Art Department in
Geometrical Drawing as well as in Freehand or Model Drawing, will

be accepted in lieu of one of the above Science subjects for the full
Technological Certificate in either grade of the Examination.

GLOSSARY OF TRADE TERMS.
Am.—American . Sc.—Scotch.]
Some words not mentioned here are explained in previous parts of
the book, and will be found in the General Index.
Apex—The tip or point—e.g., of a cone or wedge.
Backed Cloth—Cloth which, in addition to the faced fabric,
bears bound underneath a layer either of extra weft, extra warp,
or of another cloth. The term is usually applied to the first-
named variety.
Bar—A term applied to a single strip of coloured weft, used as
heading or cross border.
Beam—The flanged roller on which the warp yarn is wound,
either at the beam, warping, sizing, or dressing machines; also
applied to the full beam.
Beer—Twenty dents or splits in a reed, also 40 ends—i.e., two
ends to each split.
Bevel—A cog wheel, having the teeth set at an angle with the
shaft on which it moves, but in the some plane, unless a skew-
gear bevel.
Bitting—Drawing in additional ends at the side of healds and
reeds in case of a wider warp having to be used.
Bobbin—A flanged wooden cylinder.
Borders—The stripe running along the side of a piece of cloth—
formed either by different colour, counts of yarn, or weave, from
the centre.

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