Astrophysical Formulae: Space, Time, Matter and Cosmology

455 Pages·1978·29.405 MB·English

by  Kenneth R. Lang (auth.)

Quantity Symbol Value
Hubble constant t Ho 100 h km s-1 Mpc-1
Normalized Hubble constant t h=Ho/100 0.50 < h < 0.85
Hubble timet 1/Ho 9.778 13 x 109 h-1 years
Age ofUniverset to 15(5) x 109 years
Critical density of Universe t p.= 3H~/8nG 1.878 82(24) x 10-29 h2 g cm-3
2.775 366 27 x 1011 h2 M0 Mpc-3
1.053 94(13) x 10-5 h2 GeV cm-3
Density parameter of Universe t 0.1 <0 <2
0
(p0 =present mass density of Universe)
Local disk density p disk 3-12 x 10-24 g cm-3
Local halo density p halo 3 - 7 x IQ-25 g cm-3
Cosmic background radiation T0 2.726 ± 0.005 K
(CBR) temperature t
Solar velocity with respect to CBR 369.5 ± 3.0 km s-1
Energy density of CBR Pr 4.647 7 x 10-34 (T/2.726)4 g cm-3
0.260 71 (T/2.726)4 eV cm-3
Number density of CBR photons ny 410.89 (T/2.726)3cm-3
Conversion Factors
Parsec pc = 1Nl arc second 3.085 677 582 x 1018 em= 3.2616ly
Megaparsec Mpc = 106pc 3.085 677 582 x 1024 em
Light year ly 9.460 730 47 >< 1017 em= 0.306 601 pc
Day d 86 400 seconds
Julian century JC 36 525 days
Radian rad 2.062 648 062 5 x 105 seconds of arc
Steradian* str 3283 (degree)2=4.25x 1010(arcsec)Z
Jansky Jy = 1 flux unit 10-23 erg cm-2 s-I Hz-I
Solar flux unit sfu = 104 flux units 10-19 erg cm-2 s-I Hz-I
t Subscript 0 denotes present-day values
* A sphere subtends 4n steradians = 41253 square degrees
1 Adapted from LANG, K.R.: Astrophysical Data: Planets and Stars (New York: Springer-Verlag,
1992), Siedelmann, K.P.: Explanatory Supplement to the Astronomical Almanac (Mill Valley, CA:
University Science Books, 1992), and Physical Review D50, 1234 (1994). The figures in parenthesis
after the values give the one-standard-deviation uncertainties in the last digits.
\STRONOMY AND
\STROPHYSICS LIBRARY
LIBRARY
Series Editors: G. Borner, Garching, Germany
A. Burkert, Miinchen, Getmany
W. B. Burton, Charlottesville, VA, USA and
Leiden, The Netherlands
M.A. Dopita, Canberra, Australia
A. Eckart, Koln, Germany
T. Encrenaz, Meudon, France
B. Leibundgut, Garching, Germany
J. Lequeux, Paris, France
A. Maeder, Sauverny, Switzerland
V. Trimble, College Park, MD, and Irvine, CA, USA
K. R. Lang
Astrophysical
Formulae
Volume II: Space, Time, Matter
and Cosmology
Third Enlarged and Revised Edition
With 41 Figures and 22 Tables
~Springer
Kenneth R. Lang
Tufts University
Department of Physics and Astronomy
Robinson Hall
Medford, MA 02155, USA
Cover picture Vo/ume II: Hotstars with powerful winds shape this glowing gas into a comet-Iike apparition. It is called
a cometary globule, or CO for short, and designated CO 4. This cometary globule is surrounded by a diffuse red glow
of hydrogen liberated from it by the radiation of nearby stars. These same stars are probably responsible for creating
the green, dusty tail that absorbs some of the light from background reftection nebulosity. Courtesy of David Malin,
Anglo-Australian Telescope Board.
Library of Congress Control Number: 2005934623
3rd Edition 1999, 2nd printing 2006
ISSN 0941-7834
ISBN 978-3-662-21641-5 ISBN 978-3-662-21639-2 (eBook)
DOI 10.1007/978-3-662-21639-2
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To Marcella
Ebbene, forse voi credete
che l'arco senza fondo della volta spaziale
sia un vuoto vertiginoso di silenzi.
Vi posso dire allora che verso
questa terra sospettabile appena
l'universo gia dilaga di pensieri.
(Mario Socrate, Favole paraboliche)
Well, maybe you think
That the endless arch of the space vault
Is a giddy, silent hollowness.
But I can tell you that,
Overflowing with thought,
the universe is approaching
this hardly guessable earth.
(Mario Socrate, Parabolic Fables)
Preface to the Third Edition
When the first edition of Astrophysical Formulae was published in 1974, it was
designed as a fundamental reference for the student and researcher in the field
of astrophysics. Here the reader could find that long-forgotten formula or
reference to the more comprehensive article. Anyone interested in learning
about a new area of astrophysics could first turn to Astrophysical Formulae to
obtain an introductory background and guidance to the relevant literature. In
all these ways, the book has succeeded far beyond my initial expectations,
becoming a widely-used, standard reference.
I am grateful to the many astronomers and astrophysicists who have told
me how useful this book has been to them. Such comments have helped sustain
my writing and led to this revised, updated version. It could not have been
written without the caring, steadfast support of my wife, Marcella. This third
edition remains dedicated to her; we courted and were married during the
writing and publication of the first edition.
It is more disappointing than astonishing that today's astronomers and
astrophysicists so quickly forget the exciting moments of yesterday's science,
and often inadequately acknowledge the important work of their predecessors.
This can be partly attributed to the accelerated pace of our celestial science; it is
difficult to stay abreast of rapid developments in one's own field, let alone
others. By providing a comprehensive reference for fundamental formulae and
original articles, Astrophysical Formulae provides a foundation for overcoming
these difficulties. It can also help researchers in all areas to enjoy the
development and exciting new discoveries of astronomy and astrophysics.
This completely revised, third edition of Astrophysical Formulae more than
doubles the number of formulae and references found in the previous versions.
There are now more than 4 000 formulae. The references are now gathered
together alphabetically for the entire book, rather than by chapter as in
previous versions. The authors, titles and journal information have now been
provided for more than 5 000 journal articles!
Astrophysical Formulae has now been divided into two volumes. The first
Volume 1: Radiation, Gas Processes and High Energy Astrophysics, contains the
classical physics that underlies astrophysics, updated with recent work and
references in their applications to the cosmos. Volume II: Space, Time, Matter
and Cosmology includes many of the topics that are under active scrutiny by
contemporary astronomers and astrophysicists.
The first Volume 1: Continuum Radiation, Monochromatic (Line) Radiation,
Gas Processes, and High Energy Astrophysics retains the classical material of
previous versions, including the suggestions of the Russian translators of the
first edition. Some new sections have now been provided, such as those on
X Preface to the Third Edition
helioseismology, solar neutrinos, neutrino oscillations, neutrino emission from
stellar collapse and supernovae, and energetic particles and radiation from
solar flares. These chapters have additionally been updated with references to
important review articles and books. Many of the tables have been removed
from these chapters, since more comprehensive tabular information can now
be found in Kenneth R. Lang's Astrophysical Data: Planets and Stars (New
York: Springer-Verlag 1992).
New formulae and supporting data in Volume I include, in order of
presentation, those dealing with: synchrotron radiation, gyrosynchrotron
radiation, synchrotron self-absorption, bremsstrahlung, dispersion measures
and time delays of pulsar emission, longitudinal waves, Cerenkov radiation,
inverse Compton radiation, interstellar dust, interstellar extinction, interstellar
polarization, interstellar scintillation, transition probabilities, emission lines
from planetary nebulae and H II regions, recombination lines, LS coupling, 21-
cm line of interstellar hydrogen, Fraunhofer lines, solar emission lines, Zeeman
effect and cosmic magnetic fields, gravitational redshifts, impact broadening,
polytropes, Stromgren radius and its expansion, white dwarf stars and neutron
stars, equations of state for degenerate gases, limiting masses for compact
objects, rotation of fluid masses, Roche limit, Roche lobes, solar and stellar
coronas, solar and stellar winds, heating of the Sun's chromosphere and
corona, sound waves and solar oscillations, depth of the solar convection zone,
rotation and gas currents inside the Sun, shock waves, gravitational collapse in
the presence of a magnetic field, star formation in molecular clouds,
magnetohydrodynamic waves, accretion, variable stars, nonradial stellar
oscillations, fluid instabilities, pinch instability, magnetic reconnection, funda
mental particles, nucleosynthesis, atomic mass excesses, thermonuclear reac
tion rates, electron screening, neutrinos, neutron star cooling, origin and
abundance of the elements, spallation reactions of cosmic ray particles with
interstellar matter, formation of lithium, beryllium, and boron, supernova
explosions, supernova remnants, supernova SN 1987 A, the solar neutrino
problem, neutrino astrophysics, gamma-ray lines from solar flares, nonthermal
hard X-ray bremsstrahlung of solar flares, particle acceleration in solar flares,
observed cosmic rays, ultra-high-energy cosmic rays, shock wave acceleration
of cosmic rays, and gamma ray bursts.
New advances, both observational and theoretical, have come at an ever
increasing rate, including the discovery of the cosmic microwave background
radiation with its anisotropy; improved tests of the special and general theories
of relativity; new measurements of the extragalactic distance scale and age of
the Universe; the discovery of, and search for, invisible dark matter; the
discovery of the binary pulsar and its implications for gravitational radiation;
the mature development of radio and X-ray astronomy; the discovery of
gravitational lenses; the development of theories for accretion onto compact
objects; a new knowledge of white dwarfs, neutron stars and pulsars; the
discovery of candidate black holes at the centers of galaxies and the
establishment of a comprehensive theory for black holes; a new inflationary
model for the earliest stages of the Universe; the discovery of superluminal
motions in quasars and nearby micro-quasars; the development of theories for
Preface to the Third Edition XI
active galactic nuclei; improved computations of big bang nucleosynthesis; new
observations of deuterium and helium throughout the cosmos; and dramatic
improvements in our knowledge of the shape, structure, content and formation
of the Universe. All of these comparatively recent developments are included in
a completely new Volume II: Space, Time, Matter and Cosmology. I am
indebted to my colleagues for the opportunity to learn about so many
captivating new ideas and discoveries.
Over one hundred of the seminal contributions to twentieth century
astronomy and astrophysics, through to the year 1975, are now reproduced in,
A Source Book in Astronomy and Astrophysics 1900--1975 by Kenneth R. Lang
and Owen Gingerich (Cambridge, Mass.: Harvard University Press 1979). It
contains a dozen new English translations of articles originally in German,
French or Dutch, and includes a historical introduction to each. It is
heartening to realize that every article in the Source Book was previously
referenced in the first edition of Astrophysical Formulae, and that several of
these articles include the work of subsequent winners of the Nobel Prize in
Physics- including Subramanyan Chandrasekar, William A. Fowler, Antony
Hewish, Arno A. Penzias, Sir Martin Ryle, and Robert F. Wilson. When the
Source Book is updated to the turn of the millennium in the year 2000, it will
surely consist of articles referenced in this third edition of Astrophysical
Formulae.
The library at the Harvard-Smithsonian Center for Astrophysics has been
an invaluable resource, and special thanks go to Seth Redfield for helping to
locate material there.
I have profited from the advice of many experts who have read individual
sections of this version. Those who have read portions of the new material and
have supplied critical comment include: Neil Ashby, John N. Bahcall, Roger
D. Blandford, Margaret Geller, Jack Harvey, Mark Haugan, Bruce Partridge,
Martin Rees, David Schramm, and Kenneth Seidelmann. Persons who have
provided suggestions for new formulae and references include: E. H. Avrett, K.
Borkowski, R. Catchpole, K. P. Dere, T. Forbes, J. Franco, V. G. Gurzadyan,
H. J. Haubold, M. Hernanz, R. W. John, K. I. Kellermann, K. Krisciunas, W.
Kundt, M. A. Lee, J. Linsley, G. P. Malik, W. C. Martin, J.-M. Perrin, V. A.
Razin, D. 0. Richstone, N. N. Shefov, B. V. Somov, J. Terrell, R. Woo, S.
Woosley, and J. Yang.
Medford Kenneth R. Lang
October, 1998