# mass-luminosity relation

## mass-luminosity relation,

in astronomy, law stating that the luminosityluminosity,
in astronomy, the rate at which energy of all types is radiated by an object in all directions. A star's luminosity depends on its size and its temperature, varying as the square of the radius and the fourth power of the absolute surface temperature.
of a star is proportional to some power of the mass of the star. More massive stars are in general more luminous. For stars on the main sequence of the Hertzsprung-Russell diagramHertzsprung-Russell diagram
[for Ejnar Hertzsprung and H. N. Russell], graph showing the luminosity of a star as a function of its surface temperature. The luminosity, or absolute magnitude, increases upwards on the vertical axis; the temperature (or some temperature-dependent
, it is found empirically that the luminosity varies as the 3.5 power of the mass. This means that if the mass is doubled, the luminosity increases more than tenfold. The law can be derived theoretically and was confirmed by independently measuring the masses of many visual binary stars, all at approximately the same distance. A more exact formulation of the law takes into account the chemical composition of the star. One important use of the mass-luminosity relation is in estimating the mass of a star of known luminosity that is not in a binary system.

## mass-luminosity relation

(M-L relation) An approximate relation between the mass and luminosity of main-sequence stars, predicted by Eddington in 1924. Although having some basis in theory it is obtained empirically from a graph of absolute bolometric magnitude against the logarithm of mass (in solar units), i.e. M /M O, for a large number of binary stars. Most points lie on an approximately straight line. Since a star's absolute bolometric magnitude is a function of the logarithm of its luminosity (in solar units), i.e. L /L O, this line is represented by the M-L relation:
log(L /L O) = n log(M /M O )
L /L O = (M /M O )n
n averages about 3 for bright massive stars, about 4 for Sun-type stars, and about 2.5 for dim red dwarfs of low mass. The relation holds for main-sequence stars, which all have a similar chemical composition and have similar internal structures and nuclear power sources. It is not obeyed by white dwarfs (degenerate matter) or red giants (extended atmospheres).

## Mass-Luminosity Relation

in astronomy, the relation, deduced from observations of binary stars, between the mass and the luminosity of a star. Such a relation was theoretically predicted by the British astronomer A. Eddington in the early 20th century. In practice, all types of stars, except white dwarfs, conform to the empirically found law. However, the parameters of the relation between the star’s bolometric luminosity Lb and mass m

Lb = kmn

may differ significantly for different groups of stars. Thus, according to the most complete data available by the early 1970’s, k = 0.1 and n = 1.5 for faint stars with bolometric stellar magnitudes Mb of less than 7.5. For brighter stars, up to a bolometric stellar magnitude of Mb = -0.3, k ≈ 1 and n = 4.0.

The mass-luminosity relation, extended to include stars that are not members of binary systems, permits the masses of stars to be estimated from the observationally evaluated luminosities of the stars.

### REFERENCE

Martynov, D. Ia. Kurs obshchei astrofiziki. Moscow, 1965.

## mass-luminosity relation

[′mas ‚lü·mə′näs·əd·ē ri‚lā·shən]
(astrophysics)
A relation between stellar magnitudes and mass of the stars; when the absolute magnitudes of stars are plotted versus the logarithms of their masses, the points fall closely along a smooth curve.
References in periodicals archive ?
This was the first indication of the mass-luminosity relation, later elaborated by others.
The authors match the calculated energy production of the suggested mechanism of thermonuclear fusion of the light atomic nuclei in the Hilbert core (the "inner sun") of the stars to the empirical mass-luminosity relation of observational astrophysics, to determine the density of the liquid stellar substance in the Hilbert core.
The mass-luminosity relation for very massive stars is an open problem," he said.
We compare the mechanism to the relations of observational astrophysics--the mass-luminosity relation and the stellar energy relation.
We analyze this result, taking the mass-luminosity relation into account.
We therefore substitute the observed mass-luminosity relation [bar.
In other words, for both the observed and theoretical mass-luminosity relation, our formula for stellar energy says that,
If such a correlation (the condition of energy production) is true, the correlation, in common with the energy drainage condition (the mass-luminosity relation [bar.
2], we obtain, with the observed mass-luminosity relation [bar.
M] by the mass-luminosity relation (the energy drainage condition), and also (2) their radii [bar.

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