Astrophysics

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Astrophysics is a science that employs the methods and principles of physics in the study of astronomical objects and phenomena. [1] [2] As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the heavenly bodies, rather than their positions or motions in space–what they are, rather than where they are." [3] Among the subjects studied are the Sun, other stars, galaxies, extrasolar planets, the interstellar medium and the cosmic microwave background. [4] [5] Emissions from these objects are examined across all parts of the electromagnetic spectrum, and the properties examined include luminosity, density, temperature, and chemical composition. Because astrophysics is a very broad subject, astrophysicists apply concepts and methods from many disciplines of physics, including classical mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.

Contents

In practice, modern astronomical research often involves a substantial amount of work in the realms of theoretical and observational physics. Some areas of study for astrophysicists include their attempts to determine the properties of dark matter, dark energy, black holes, and other celestial bodies; and the origin and ultimate fate of the universe. [4] Topics also studied by theoretical astrophysicists include Solar System formation and evolution; stellar dynamics and evolution; galaxy formation and evolution; magnetohydrodynamics; large-scale structure of matter in the universe; origin of cosmic rays; general relativity, special relativity, quantum and physical cosmology, including string cosmology and astroparticle physics.

History

Early 1900s comparison of elemental, solar, and stellar spectra NIEdot362.jpg
Early 1900s comparison of elemental, solar, and stellar spectra

Astronomy is an ancient science, long separated from the study of terrestrial physics. In the Aristotelian worldview, bodies in the sky appeared to be unchanging spheres whose only motion was uniform motion in a circle, while the earthly world was the realm which underwent growth and decay and in which natural motion was in a straight line and ended when the moving object reached its goal. Consequently, it was held that the celestial region was made of a fundamentally different kind of matter from that found in the terrestrial sphere; either Fire as maintained by Plato, or Aether as maintained by Aristotle. [6] [7] During the 17th century, natural philosophers such as Galileo, [8] Descartes, [9] and Newton [10] began to maintain that the celestial and terrestrial regions were made of similar kinds of material and were subject to the same natural laws. [11] Their challenge was that the tools had not yet been invented with which to prove these assertions. [12]

For much of the nineteenth century, astronomical research was focused on the routine work of measuring the positions and computing the motions of astronomical objects. [13] [14] A new astronomy, soon to be called astrophysics, began to emerge when William Hyde Wollaston and Joseph von Fraunhofer independently discovered that, when decomposing the light from the Sun, a multitude of dark lines (regions where there was less or no light) were observed in the spectrum. [15] By 1860 the physicist, Gustav Kirchhoff, and the chemist, Robert Bunsen, had demonstrated that the dark lines in the solar spectrum corresponded to bright lines in the spectra of known gases, specific lines corresponding to unique chemical elements. [16] Kirchhoff deduced that the dark lines in the solar spectrum are caused by absorption by chemical elements in the Solar atmosphere. [17] In this way it was proved that the chemical elements found in the Sun and stars were also found on Earth.

Among those who extended the study of solar and stellar spectra was Norman Lockyer, who in 1868 detected radiant, as well as dark, lines in solar spectra. Working with chemist Edward Frankland to investigate the spectra of elements at various temperatures and pressures, he could not associate a yellow line in the solar spectrum with any known elements. He thus claimed the line represented a new element, which was called helium, after the Greek Helios, the Sun personified. [18] [19]

In 1885, Edward C. Pickering undertook an ambitious program of stellar spectral classification at Harvard College Observatory, in which a team of woman computers, notably Williamina Fleming, Antonia Maury, and Annie Jump Cannon, classified the spectra recorded on photographic plates. By 1890, a catalog of over 10,000 stars had been prepared that grouped them into thirteen spectral types. Following Pickering's vision, by 1924 Cannon expanded the catalog to nine volumes and over a quarter of a million stars, developing the Harvard Classification Scheme which was accepted for worldwide use in 1922. [20]

In 1895, George Ellery Hale and James E. Keeler, along with a group of ten associate editors from Europe and the United States, [21] established The Astrophysical Journal: An International Review of Spectroscopy and Astronomical Physics. [22] It was intended that the journal would fill the gap between journals in astronomy and physics, providing a venue for publication of articles on astronomical applications of the spectroscope; on laboratory research closely allied to astronomical physics, including wavelength determinations of metallic and gaseous spectra and experiments on radiation and absorption; on theories of the Sun, Moon, planets, comets, meteors, and nebulae; and on instrumentation for telescopes and laboratories. [21]

Around 1920, following the discovery of the Hertzsprung–Russell diagram still used as the basis for classifying stars and their evolution, Arthur Eddington anticipated the discovery and mechanism of nuclear fusion processes in stars, in his paper The Internal Constitution of the Stars. [23] [24] At that time, the source of stellar energy was a complete mystery; Eddington correctly speculated that the source was fusion of hydrogen into helium, liberating enormous energy according to Einstein's equation E = mc2. This was a particularly remarkable development since at that time fusion and thermonuclear energy, and even that stars are largely composed of hydrogen (see metallicity), had not yet been discovered. [25]

In 1925 Cecilia Helena Payne (later Cecilia Payne-Gaposchkin) wrote an influential doctoral dissertation at Radcliffe College, in which she applied ionization theory to stellar atmospheres to relate the spectral classes to the temperature of stars. [26] Most significantly, she discovered that hydrogen and helium were the principal components of stars. Despite Eddington's suggestion, this discovery was so unexpected that her dissertation readers convinced her to modify the conclusion before publication. However, later research confirmed her discovery. [27]

By the end of the 20th century, studies of astronomical spectra had expanded to cover wavelengths extending from radio waves through optical, x-ray, and gamma wavelengths. [28] In the 21st century it further expanded to include observations based on gravitational waves.

Observational astrophysics

Supernova remnant LMC N 63A imaged in x-ray (blue), optical (green) and radio (red) wavelengths. The X-ray glow is from material heated to about ten million degrees Celsius by a shock wave generated by the supernova explosion. N 63A- Chandra and Hubble - Heic0507f.tif
Supernova remnant LMC N 63A imaged in x-ray (blue), optical (green) and radio (red) wavelengths. The X-ray glow is from material heated to about ten million degrees Celsius by a shock wave generated by the supernova explosion.

Observational astronomy is a division of the astronomical science that is concerned with recording and interpreting data, in contrast with theoretical astrophysics, which is mainly concerned with finding out the measurable implications of physical models. It is the practice of observing celestial objects by using telescopes and other astronomical apparatus.

The majority of astrophysical observations are made using the electromagnetic spectrum.

Other than electromagnetic radiation, few things may be observed from the Earth that originate from great distances. A few gravitational wave observatories have been constructed, but gravitational waves are extremely difficult to detect. Neutrino observatories have also been built, primarily to study our Sun. Cosmic rays consisting of very high-energy particles can be observed hitting the Earth's atmosphere.

Observations can also vary in their time scale. Most optical observations take minutes to hours, so phenomena that change faster than this cannot readily be observed. However, historical data on some objects is available, spanning centuries or millennia. On the other hand, radio observations may look at events on a millisecond timescale (millisecond pulsars) or combine years of data (pulsar deceleration studies). The information obtained from these different timescales is very different.

The study of our very own Sun has a special place in observational astrophysics. Due to the tremendous distance of all other stars, the Sun can be observed in a kind of detail unparalleled by any other star. Our understanding of our own Sun serves as a guide to our understanding of other stars.

The topic of how stars change, or stellar evolution, is often modeled by placing the varieties of star types in their respective positions on the Hertzsprung–Russell diagram, which can be viewed as representing the state of a stellar object, from birth to destruction.

Theoretical astrophysics

Theoretical astrophysicists use a wide variety of tools which include analytical models (for example, polytropes to approximate the behaviors of a star) and computational numerical simulations. Each has some advantages. Analytical models of a process are generally better for giving insight into the heart of what is going on. Numerical models can reveal the existence of phenomena and effects that would otherwise not be seen. [29] [30]

Theorists in astrophysics endeavor to create theoretical models and figure out the observational consequences of those models. This helps allow observers to look for data that can refute a model or help in choosing between several alternate or conflicting models.

Theorists also try to generate or modify models to take into account new data. In the case of an inconsistency, the general tendency is to try to make minimal modifications to the model to fit the data. In some cases, a large amount of inconsistent data over time may lead to total abandonment of a model.

Topics studied by theoretical astrophysicists include stellar dynamics and evolution; galaxy formation and evolution; magnetohydrodynamics; large-scale structure of matter in the universe; origin of cosmic rays; general relativity and physical cosmology, including string cosmology and astroparticle physics. Astrophysical relativity serves as a tool to gauge the properties of large-scale structures for which gravitation plays a significant role in physical phenomena investigated and as the basis for black hole (astro)physics and the study of gravitational waves.

Some widely accepted and studied theories and models in astrophysics, now included in the Lambda-CDM model, are the Big Bang, cosmic inflation, dark matter, dark energy and fundamental theories of physics.

Popularization

The roots of astrophysics can be found in the seventeenth century emergence of a unified physics, in which the same laws applied to the celestial and terrestrial realms. [11] There were scientists who were qualified in both physics and astronomy who laid the firm foundation for the current science of astrophysics. In modern times, students continue to be drawn to astrophysics due to its popularization by the Royal Astronomical Society and notable educators such as prominent professors Lawrence Krauss, Subrahmanyan Chandrasekhar, Stephen Hawking, Hubert Reeves, Carl Sagan, Neil deGrasse Tyson and Patrick Moore. The efforts of the early, late, and present scientists continue to attract young people to study the history and science of astrophysics. [31] [32] [33]

See also

Related Research Articles

Arthur Eddington British astrophysicist (1882–1944).

Sir Arthur Stanley Eddington was an English astronomer, physicist, and mathematician. He was also a philosopher of science and a populariser of science. The Eddington limit, the natural limit to the luminosity of stars, or the radiation generated by accretion onto a compact object, is named in his honour.

Big Bang Cosmological model

The Big Bang theory is the prevailing cosmological model explaining the existence of the observable universe from the earliest known periods through its subsequent large-scale evolution. The model describes how the universe expanded from an initial state of high density and temperature, and offers a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure.

Physical cosmology Branch of astronomy

Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its origin, structure, evolution, and ultimate fate. Cosmology as a science originated with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood. Physical cosmology, as it is now understood, began with the development in 1915 of Albert Einstein's general theory of relativity, followed by major observational discoveries in the 1920s: first, Edwin Hubble discovered that the universe contains a huge number of external galaxies beyond the Milky Way; then, work by Vesto Slipher and others showed that the universe is expanding. These advances made it possible to speculate about the origin of the universe, and allowed the establishment of the Big Bang theory, by Georges Lemaître, as the leading cosmological model. A few researchers still advocate a handful of alternative cosmologies; however, most cosmologists agree that the Big Bang theory best explains the observations.

Dark matter Hypothetical form of matter comprising most of the matter in the universe

Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe and about 27% of its total mass–energy density or about 2.241×10−27 kg/m3. Its presence is implied in a variety of astrophysical observations, including gravitational effects that cannot be explained by accepted theories of gravity unless more matter is present than can be seen. For this reason, most experts think that dark matter is abundant in the universe and that it has had a strong influence on its structure and evolution. Dark matter is called dark because it does not appear to interact with the electromagnetic field, which means it does not absorb, reflect or emit electromagnetic radiation, and is therefore difficult to detect.

Quasar Active galactic nucleus containing a supermassive black hole

A quasar is an extremely luminous active galactic nucleus (AGN), in which a supermassive black hole with mass ranging from millions to tens of billions of times the mass of the Sun is surrounded by a gaseous accretion disk. As gas in the disk falls towards the black hole, energy is released in the form of electromagnetic radiation, which can be observed across the electromagnetic spectrum. The radiant energy of quasars is enormous; the most powerful quasars have luminosities thousands of times greater than a galaxy such as the Milky Way. Usually, quasars are categorized as a subclass of the more general category of AGN. The redshifts of quasars are of cosmological origin.

Redshift Eventual increase of wavelength in radiation during travel

In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation. The opposite change, a decrease in wavelength and simultaneous increase in frequency and energy, is known as a negative redshift, or blueshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum.

Gravitational lens Light bending by mass between source and observer

A gravitational lens is a distribution of matter between a distant light source and an observer, that is capable of bending the light from the source as the light travels towards the observer. This effect is known as gravitational lensing, and the amount of bending is one of the predictions of Albert Einstein's general theory of relativity.

Astronomy Scientific study of celestial objects and phenomena

Astronomy is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, galaxies, and comets. Relevant phenomena include supernova explosions, gamma ray bursts, quasars, blazars, pulsars, and cosmic microwave background radiation. More generally, astronomy studies everything that originates beyond Earth's atmosphere. Cosmology is a branch of astronomy that studies the universe as a whole.

Astronomical spectroscopy

Astronomical spectroscopy is the study of astronomy using the techniques of spectroscopy to measure the spectrum of electromagnetic radiation, including visible light, ultraviolet, X-ray, infrared and radio waves that radiate from stars and other celestial objects. A stellar spectrum can reveal many properties of stars, such as their chemical composition, temperature, density, mass, distance and luminosity. Spectroscopy can show the velocity of motion towards or away from the observer by measuring the Doppler shift. Spectroscopy is also used to study the physical properties of many other types of celestial objects such as planets, nebulae, galaxies, and active galactic nuclei.

Edward Arthur Milne

Edward Arthur Milne FRS was a British astrophysicist and mathematician.

Tests of general relativity Scientific experiments

Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury, the bending of light in gravitational fields, and the gravitational redshift. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions of general relativity were performed in 1919, with increasingly precise measurements made in subsequent tests; and scientists claimed to have measured the gravitational redshift in 1925, although measurements sensitive enough to actually confirm the theory were not made until 1954. A more accurate program starting in 1959 tested general relativity in the weak gravitational field limit, severely limiting possible deviations from the theory.

Cosmology Scientific study of the origin, evolution, and eventual fate of the universe

Cosmology is a branch of astronomy concerned with the study of the chronology of the universe. Physical cosmology is the study of the universe's origin, its large-scale structures and dynamics, and the ultimate fate of the universe, including the laws of science that govern these areas.

Theoretical astronomy is the use of analytical and computational models based on principles from physics and chemistry to describe and explain astronomical objects and astronomical phenomena. Theorists in astronomy endeavor to create theoretical models and from the results predict observational consequences of those models. The observation of a phenomenon predicted by a model allows astronomers to select between several alternate or conflicting models as the one best able to describe the phenomena.

Outline of astronomy

The following outline is provided as an overview of and topical guide to astronomy:

Nuclear astrophysics

Nuclear astrophysics is an interdisciplinary part of both nuclear physics and astrophysics, involving close collaboration among researchers in various subfields of each of these fields. This includes, notably, nuclear reactions and their rates as they occur in cosmic environments, and modeling of astrophysical objects where these nuclear reactions may occur, but also considerations of cosmic evolution of isotopic and elemental composition (often called chemical evolution). Constraints from observations involve multiple messengers, all across the electromagnetic spectrum (nuclear gamma-rays, X-rays, optical, and radio/sub-mm astronomy), as well as isotopic measurements of solar-system materials such as meteorites and their stardust inclusions, cosmic rays, material deposits on Earth and Moon). Nuclear physics experiments address stability (i.e., lifetimes and masses) for atomic nuclei well beyond the regime of stable nuclides into the realm of radioactive/unstable nuclei, almost to the limits of bound nuclei (the drip lines), and under high density (up to neutron star matter) and high temperature (plasma temperatures up to 109 K). Theories and simulations are essential parts herein, as cosmic nuclear reaction environments cannot be realized, but at best partially approximated by experiments. In general terms, nuclear astrophysics aims to understand the origin of the chemical elements and isotopes, and the role of nuclear energy generation, in cosmic sources such as stars, supernovae, novae, and violent binary-star interactions.

Fulvio Melia

Fulvio Melia is an Italian-American astrophysicist, cosmologist and author. He is professor of physics, astronomy and the applied math program at the University of Arizona and was a scientific editor of The Astrophysical Journal and an associate editor of The Astrophysical Journal Letters. A former Presidential Young Investigator and Sloan Research Fellow, he is the author of six English books and 230 refereed articles on theoretical astrophysics and cosmology.

Gravitational-wave astronomy Emerging branch of observational astronomy using gravitational waves

Gravitational-wave astronomy is an emerging branch of observational astronomy which aims to use gravitational waves to collect observational data about objects such as neutron stars and black holes, events such as supernovae, and processes including those of the early universe shortly after the Big Bang.

Leibniz Institute for Astrophysics Potsdam

Leibniz Institute for Astrophysics Potsdam (AIP) is a German research institute. It is the successor of the Berlin Observatory founded in 1700 and of the Astrophysical Observatory Potsdam (AOP) founded in 1874. The latter was the world's first observatory to emphasize explicitly the research area of astrophysics. The AIP was founded in 1992, in a re-structuring following the German reunification.

Computational astrophysics refers to the methods and computing tools developed and used in astrophysics research. Like computational chemistry or computational physics, it is both a specific branch of theoretical astrophysics and an interdisciplinary field relying on computer science, mathematics, and wider physics. Computational astrophysics is most often studied through an applied mathematics or astrophysics programme at PhD level.

References

  1. Maoz, Dan. Astrophysics in a Nutshell. Princeton University Press. p. 272.
  2. "astrophysics". Merriam-Webster, Incorporated. Archived from the original on 10 June 2011. Retrieved 2011-05-22.
  3. Keeler, James E. (November 1897), "The Importance of Astrophysical Research and the Relation of Astrophysics to the Other Physical Sciences", The Astrophysical Journal, 6 (4): 271–288, Bibcode:1897ApJ.....6..271K, doi:10.1086/140401
  4. 1 2 "Focus Areas – NASA Science". nasa.gov.
  5. "astronomy". Encyclopædia Britannica.
  6. Lloyd, G. E. R. (1968). Aristotle: The Growth and Structure of His Thought . Cambridge: Cambridge University Press. pp.  134–135. ISBN   978-0-521-09456-6.
  7. Cornford, Francis MacDonald (c. 1957) [1937]. Plato's Cosmology: The Timaeus of Plato translated, with a running commentary. Indianapolis: Bobbs Merrill Co. p. 118.
  8. Galilei, Galileo (1989-04-15), Van Helden, Albert (ed.), Sidereus Nuncius or The Sidereal Messenger, Chicago: University of Chicago Press (published 1989), pp. 21, 47, ISBN   978-0-226-27903-9
  9. Edward Slowik (2013) [2005]. "Descartes' Physics". Stanford Encyclopedia of Philosophy . Retrieved 2015-07-18.
  10. Westfall, Richard S. (1983-04-29), Never at Rest: A Biography of Isaac Newton , Cambridge: Cambridge University Press (published 1980), pp.  731–732, ISBN   978-0-521-27435-7
  11. 1 2 Burtt, Edwin Arthur (2003) [First published 1924], The Metaphysical Foundations of Modern Science (second revised ed.), Mineola, NY: Dover Publications, pp. 30, 41, 241–2, ISBN   978-0-486-42551-1
  12. Ladislav Kvasz (2013). "Galileo, Descartes, and Newton – Founders of the Language of Physics" (PDF). Institute of Philosophy, Academy of Sciences of the Czech Republic . Retrieved 2015-07-18.Cite journal requires |journal= (help)
  13. Case, Stephen (2015), "'Land-marks of the universe': John Herschel against the background of positional astronomy", Annals of Science, 72 (4): 417–434, Bibcode:2015AnSci..72..417C, doi: 10.1080/00033790.2015.1034588 , PMID   26221834, The great majority of astronomers working in the early nineteenth century were not interested in stars as physical objects. Far from being bodies with physical properties to be investigated, the stars were seen as markers measured in order to construct an accurate, detailed and precise background against which solar, lunar and planetary motions could be charted, primarily for terrestrial applications.
  14. Donnelly, Kevin (September 2014), "On the boredom of science: positional astronomy in the nineteenth century", The British Journal for the History of Science, 47 (3): 479–503, doi:10.1017/S0007087413000915
  15. Hearnshaw, J.B. (1986). The analysis of starlight. Cambridge: Cambridge University Press. pp. 23–29. ISBN   978-0-521-39916-6.
  16. Kirchhoff, Gustav (1860), "Ueber die Fraunhofer'schen Linien", Annalen der Physik, 185 (1): 148–150, Bibcode:1860AnP...185..148K, doi:10.1002/andp.18601850115
  17. Kirchhoff, Gustav (1860), "Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht", Annalen der Physik, 185 (2): 275–301, Bibcode:1860AnP...185..275K, doi: 10.1002/andp.18601850205
  18. Cortie, A. L. (1921), "Sir Norman Lockyer, 1836 – 1920", The Astrophysical Journal, 53: 233–248, Bibcode:1921ApJ....53..233C, doi:10.1086/142602
  19. Jensen, William B. (2004), "Why Helium Ends in "-ium"" (PDF), Journal of Chemical Education, 81 (7): 944–945, Bibcode:2004JChEd..81..944J, doi:10.1021/ed081p944
  20. Hetherington, Norriss S.; McCray, W. Patrick, Weart, Spencer R. (ed.), Spectroscopy and the Birth of Astrophysics, American Institute of Physics, Center for the History of Physics, archived from the original on September 7, 2015, retrieved July 19, 2015
  21. 1 2 Hale, George Ellery (1895), "The Astrophysical Journal", The Astrophysical Journal, 1 (1): 80–84, Bibcode:1895ApJ.....1...80H, doi:10.1086/140011
  22. The Astrophysical Journal. 1(1).
  23. Eddington, A. S. (October 1920), "The Internal Constitution of the Stars", The Scientific Monthly, 11 (4): 297–303, Bibcode:1920Sci....52..233E, doi:10.1126/science.52.1341.233, JSTOR   6491, PMID   17747682
  24. Eddington, A. S. (1916). "On the radiative equilibrium of the stars". Monthly Notices of the Royal Astronomical Society. 77: 16–35. Bibcode:1916MNRAS..77...16E. doi: 10.1093/mnras/77.1.16 .
  25. McCracken, Garry; Stott, Peter (2013-01-01). McCracken, Garry; Stott, Peter (eds.). Fusion (Second ed.). Boston: Academic Press. p. 13. doi:10.1016/b978-0-12-384656-3.00002-7. ISBN   978-0-12-384656-3. Eddington had realized that there would be a mass loss if four hydrogen atoms combined to form a single helium atom. Einstein’s equivalence of mass and energy led directly to the suggestion that this could be the long-sought process that produces the energy in the stars! It was an inspired guess, all the more remarkable because the structure of the nucleus and the mechanisms of these reactions were not fully understood.
  26. Payne, C. H. (1925), Stellar Atmospheres; A Contribution to the Observational Study of High Temperature in the Reversing Layers of Stars (PhD Thesis), Cambridge, Massachusetts: Radcliffe College, Bibcode:1925PhDT.........1P
  27. Haramundanis, Katherine (2007), "Payne-Gaposchkin [Payne], Cecilia Helena", in Hockey, Thomas; Trimble, Virginia; Williams, Thomas R. (eds.), Biographical Encyclopedia of Astronomers, New York: Springer, pp. 876–878, ISBN   978-0-387-30400-7 , retrieved July 19, 2015
  28. Biermann, Peter L.; Falcke, Heino (1998), "Frontiers of Astrophysics: Workshop Summary", in Panvini, Robert S.; Weiler, Thomas J. (eds.), Fundamental particles and interactions: Frontiers in contemporary physics an international lecture and workshop series. AIP Conference Proceedings, 423, American Institute of Physics, pp. 236–248, arXiv: astro-ph/9711066 , Bibcode:1998AIPC..423..236B, doi:10.1063/1.55085, ISBN   1-56396-725-1
  29. Roth, H. (1932), "A Slowly Contracting or Expanding Fluid Sphere and its Stability", Physical Review , 39 (3): 525–529, Bibcode:1932PhRv...39..525R, doi:10.1103/PhysRev.39.525
  30. Eddington, A.S. (1988) [1926], Internal Constitution of the Stars, New York: Cambridge University Press, ISBN   978-0-521-33708-3, PMID   17747682
  31. D. Mark Manley (2012). "Famous Astronomers and Astrophysicists". Kent State University . Retrieved 2015-07-17.
  32. The science.ca team (2015). "Hubert Reeves – Astronomy, Astrophysics and Space Science". GCS Research Society. Retrieved 2015-07-17.
  33. "Neil deGrasse Tyson". Hayden Planetarium. 2015. Retrieved 2015-07-17.

Further reading