Eddington Formulates the Mass-Luminosity Law for Stars

Arthur Stanley Eddington’s demonstration of the relationship between a star’s mass and its luminosity led to an understanding of how stars evolve.

Summary of Event

In the early twentieth century, astronomy was changing. Until that time, astronomers had concerned themselves chiefly with the motions of heavenly objects and the laws and forces that describe those motions. With the advent of the analysis of starlight (spectrography) Spectrography and the use of photography, the science of astrophysics Astrophysics began to take shape. Scientists could now learn more about the properties of stars other than their motions and could begin the task of understanding what stars are like internally, how they form, and what fuels their existence. New data were becoming available that scientists could use to discover patterns or relationships among different properties of stars, as revealed by their light. The interpretation of these patterns and relationships was to be one of the first tasks of the science of astrophysics. [kw]Eddington Formulates the Mass-Luminosity Law for Stars (Mar., 1924)
[kw]Mass-Luminosity Law for Stars, Eddington Formulates the (Mar., 1924)[Mass Luminosity Law for Stars, Eddington Formulates the (Mar., 1924)]
[kw]Luminosity Law for Stars, Eddington Formulates the Mass- (Mar., 1924)
[kw]Stars, Eddington Formulates the Mass-Luminosity Law for (Mar., 1924)
Stars;mass-luminosity relationship[mass luminosity relationship]
Mass-luminosity law[Mass luminosity law]
Stellar evolution
[g]England;Mar., 1924: Eddington Formulates the Mass-Luminosity Law for Stars[06030]
[c]Science and technology;Mar., 1924: Eddington Formulates the Mass-Luminosity Law for Stars[06030]
[c]Astronomy;Mar., 1924: Eddington Formulates the Mass-Luminosity Law for Stars[06030]
Eddington, Arthur Stanley
Halm, Jacob Karl Ernst
Campbell, William Wallace
Hertzsprung, Ejnar
Russell, Henry Norris

Arthur Stanley Eddington.

(Library of Congress)

One type of new data concerned the luminosities (brightnesses) and spectral types of stars. A star’s spectral type is a classification assigned to it after a study of its light, as spread out by a prism or a grating (its spectrum). A program at Harvard College Observatory Harvard College Observatory and other research provided astronomers with catalogs of spectral type and luminosity for many stars. In 1905, Ejnar Hertzsprung, a Danish astronomer, revealed a relationship between a star’s brightness and its type. This relationship was demonstrated in the Hertzsprung-Russell (H-R) diagram, developed by Hertzsprung and Henry Norris Russell in the United States. Its discovery raised issues regarding the meaning of this relationship and its implications for why stars are of differing colors and brightnesses.

Another type of new data concerned the masses of stars. When studying double-star systems, Double stars astronomers can use one of the laws formulated by Johannes Kepler in the seventeenth century to determine the sum of the masses of the two stars in the system. In some cases, a ratio of the masses of the two stars can also be obtained, and this information can be used to determine the mass of each individual star. This can be done either with stars that are visibly pairs of stars (visual doubles) or with stars that look like a single star to the eye but have spectra that reveal that two stars are actually present.

Jacob Karl Ernst Halm, at the Cape Observatory in South Africa, reviewed research conducted by William Wallace Campbell and by Russell with these double-star masses and postulated a relationship between a star’s mass and its spectral class. Halm then combined these two relationships in 1911 (spectral type-brightness and mass-spectral type) and suggested that there is a relationship between a star’s mass and its brightness. This possible relationship was also discussed by Russell in 1913 and by Hertzsprung in 1918.

In 1924, Arthur Stanley Eddington was a professor of astronomy at the University of Cambridge in England and director of the Royal Observatory in Greenwich. He analyzed mass and luminosity data for many stars and plotted a diagram of mass versus luminosity. The diagram showed a relationship between the two that generally indicated that the brighter a star is, the more massive it is. Stars range from dim low-mass stars to bright high-mass stars along a diagonal line stretching across the plot. Eddington not only demonstrated this relationship but also began the discussion of its cause and implications.

Eddington’s theoretical explanation for the mass-luminosity relationship was based on the law of perfect gases. Perfect gas law This law describes the relationship between the pressure, volume, and temperature of a gas. The temperature of a star is related to its luminosity, which is actually a measure of the amount of energy radiated away from the star in a given amount of time (“brightness” is commonly used as an equivalent term for luminosity, given that energy is seen in the form of visible light). At the time, H-R diagrams of spectral type versus luminosity for groups of stars showed that there are two types of stars: those recognized by Hertzsprung as being larger (the giants) and the main-sequence stars, Main-sequence stars[Main sequence stars] or dwarf stars. Dwarf stars The giant stars Giant stars occupy one place on the diagram, with fairly constant luminosity and varying spectral types. The dwarf stars demonstrate Hertzsprung’s color-luminosity relationship: Color-luminosity relationship of stars[Color luminosity relationship] Blue stars Blue stars are brighter than yellow stars, Yellow stars which, in turn, are brighter than red stars. Red stars At the time when Eddington formulated this explanation, it was thought that only giant stars were composed of gases that would follow the perfect gas laws (which applied only under certain conditions), thus the mass-luminosity relationship should apply only to giant stars. Eddington tested the idea that only giants should exhibit the relationship between their masses and their luminosities and was surprised to discover that the relationship held for stars on the main sequence too. This was in conflict with the prevailing assumption that main-sequence stars were too dense for the perfect gas laws to apply to them and their relatively low luminosities (relative to the giants) were accounted for by their high densities. Eddington’s discovery indicated that their low luminosities could be accounted for simply by their low masses. He explained that the perfect gas laws applied at higher densities than expected for stars, because the material of which the stars were composed was highly ionized; that is, the individual atoms were missing some of their electrons because of the presence of high temperatures. This ionization reduced the bulk of the atoms, and the net result was that the perfect gas laws “worked” for much higher densities than could otherwise have been expected.

An interesting feature of the mass-luminosity diagram is the relatively broad range of luminosities and much smaller range of masses. The most massive star then known was estimated to be about one hundred times the mass of the Sun; the least massive was about one-sixth the mass of the Sun. Eddington had also considered the problem of radiation pressure in a star, and he used radiation pressure to explain the relatively small range of stellar masses. He showed that there is a condition of equilibrium in a star, with gravitational pressure inward balanced by gas pressure and radiation pressure outward. Beyond a certain mass, the radiation pressure becomes so great that a star would be blown apart by it; therefore, mass is the upper limit to stellar masses. (Today, the most massive star known has been estimated to be only about sixty-five times the mass of the Sun.) Eddington developed an equation to describe equilibrium in a star that is still used today. This equation involved the assumption of perfect gas conditions and therefore at first he thought it should apply only to giant stars. The discovery that perfect gas conditions are also maintained in dwarf or main-sequence stars extended the applicability of this equation and the model of a star’s interior that resulted.

The demonstration of the mass-luminosity relationship for stars gave astronomers new areas to investigate and revealed something about the conditions in main-sequence stars that had not been known before. It was an important step in the development of the current understanding of what makes stars shine and how they change over time.


After documenting the mass-luminosity relationship, Eddington began sorting out problems of the structure of stars and their energy sources. The fact that the perfect gas law can be applied to both main-sequence and giant stars was a great help to scientists studying stellar structure. The basic problem of stellar structure is that of producing a model star, that is, a description of the physical properties of a star at various depths below the star’s surface, such as the temperature and density. In order to know these properties, one must know the degree to which the gas prevents the free outward flow of radiation. The perfect gas law gives astronomers a tool for calculating this quantity, calculating the temperature and density at various depths in the star, and producing stellar models that are compared with actual stars. Eddington’s calculations assumed an average particle mass (for the particles of gas in stars) that today is known to be too high. This resulted from the fact that at the time the proportions of the various gases composing the stars were not known. It was not until Russell’s discovery that the Sun is almost entirely hydrogen that astronomers could use a particle weight more closely corresponding to reality.

The discovery of the mass-luminosity relation was important to theories of how stars change with time. In 1913, Russell had presented a scheme of stellar evolution in which all the stars on the main sequence were of different ages. The main sequence represented the path a star took throughout its lifetime, beginning as a bright blue star and cooling down to a dim red star as its energy source (heat from contraction under gravitational force) ran out. With Eddington’s discovery, however, astronomers realized that stars on the main sequence had differing masses (because mass and luminosity are related and they have different luminosities): The stars on the dim red end of the main sequence were less massive than stars at the bright blue end. If the main sequence is an evolutionary path that stars follow, then mass loss must occur as stars age. This was difficult to explain; it was not until later discoveries on stellar evolution that astronomers realized that the main sequence is not an evolutionary path.

The questions of how stars evolve and what their energy source is were solved in the 1930’s with the discovery of atomic fusion and the realization that fusion is occurring in stars. When two atoms fuse in the interior of a star, energy is released, and it is this energy that is seen as starlight and other types of radiation. Scientists now know that the mass of a star determines how quickly the fusion reactions take place inside it (how long it lives) and its place on the main sequence. A more massive star is brighter, hotter, and bluer, and when it comes to the end of its fuel supply, it has a more spectacular ending to its life than do less massive, cooler stars. Astronomy;stars
Stars;mass-luminosity relationship[mass luminosity relationship]
Mass-luminosity law[Mass luminosity law]
Stellar evolution

Further Reading

  • Abell, George O. Realm of the Universe. 5th ed. Philadelphia: Saunders College Publishing, 1994. Introductory college textbook explains various stellar properties and introduces the mass-luminosity relation and the diagram of this relation. Explains how data are gathered on masses of binary stars and discusses the Hertzsprung-Russell diagram and its relevance to stellar masses and evolutions. Includes illustrations, diagrams, glossary, and annotated bibliography.
  • Degani, Meir H. Astronomy Made Simple. Rev. ed. Garden City, N.Y.: Doubleday, 1976. Explains the mass-luminosity law in the context of the sequences of stars on the Hertzsprung-Russell diagram. Discussion of stellar evolution emphasizes the importance of a star’s mass in determining how it will change with time. Includes line diagrams and glossary.
  • Eddington, A. S. Stars and Atoms. New Haven, Conn.: Yale University Press, 1927. Collection of a series of lectures given in 1926. Describes the then-current knowledge of stellar structure in a manner intended for the amateur willing to apply new ideas. First section concerns stellar interiors and the mass-luminosity relation. Dated, but valuable for Eddington’s own view of the work he performed and for his clear, engaging style.
  • Motz, Lloyd, and Jefferson Hane Weaver. The Story of Astronomy. New York: Plenum, 1995. Presents the history of astronomy from ancient times to the end of the twentieth century. Chapter 15 is devoted to the origin and development of the field of astrophysics. Features bibliography and index.
  • Pannekoek, A. A History of Astronomy. 1961. Reprint. Mineola, N.Y.: Dover, 1989. Scholarly classic work includes a chapter titled “Common Stars” that discusses the mass-luminosity relation in the context of the development of astrophysics in the early twentieth century, the development of the H-R diagram, and theories of stellar evolution. Includes some line drawings and black-and-white photographs.
  • Struve, Otto, and Velta Zebergs. Astronomy of the Twentieth Century. New York: Macmillan, 1962. Discusses the work on stellar properties that culminated in Eddington’s discovery of the mass-luminosity law, including mass determination for binary stars. Also gives background on stellar evolution and H-R diagrams. Cowritten by an astronomer who participated in some of the astronomical history he describes. Includes drawings, diagrams, black-and-white photographs, glossary, and bibliography.
  • Zeilik, Michael, and Stephen A. Gregory. Introductory Astronomy and Astrophysics. 4th ed. Monterey, Calif.: Brooks/Cole, 1997. Provides a useful overview of general astronomy, including basic spectral issues and the use of H-R diagrams.

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