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).

Collins Dictionary of Astronomy © Market House Books Ltd, 2006

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.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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 L_b and mass m

L_b = 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 M_b of less than 7.5. For brighter stars, up to a bolometric stellar magnitude of M_b = -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.

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References in periodicals archive

The stellar mass-luminosity relation, which is the main empirical relation of observational astrophysics, is compared by the authors to that derived in the framework of the liquid model.

Book review: " Inside Stars. A Theory of the Internal Constitution of Stars, and the Sources of Stellar Energy According to General Relativity"

For example, this mass-luminosity relation is only valid for the absolute luminosity, while a direct measurement yields only an apparent brightness.

Astronomers can observe a group of stars, estimate the stellar masses through the mass-luminosity relation (however imprecise that might be), and then check if Salpeter's law correctly applies.

The quest for the most massive star: astronomers are conducting a frenetic search for our galaxy's most massive star. (Our Galaxy's Biggest, Brightest Brutes

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.

and hence, because the luminosity of a star is [bar.L] = [??][[bar.R].sup.2], we obtain the mass-luminosity relation [bar.L] = [[bar.M].sup.3].

We therefore substitute the observed mass-luminosity relation [bar.L] = [[bar.M].sup.10/3] and the theoretical relation [bar.L] = [[bar.M].sup.3] into our formula for stellar energy reduced to the absolute mass and radius of a star [??] = [[bar.B].sup.5/2] = [[bar.M].sup.10]/[[bar.R].sup.10] (10).

In other words, for both the observed and theoretical mass-luminosity relation, our formula for stellar energy says that, On the basis of stellar energy being generated by the background space non-holonomity field, in Thomson dispersion of light in free electrons, the luminosity L of a star is proportional to its volume V = 4/3 [pi][R.sup.3], with a small progression with an increase of radius.

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.L] = [[bar.M].sup.3] - [[bar.M].sup.10/3]), should produce another correlation; mass-radius [bar.M] = [[bar.R].sup.1.1] - [[bar.R].sup.1.2].

from which, because [bar.L] = [??][[bar.R].sup.2], we obtain, with the observed mass-luminosity relation [bar.L] = [[bar.M].sup.10/3],

So the mass-luminosity relation [bar.L] = [[bar.M].sup.3] is derived from the energy drainage condition [??] = [bar.B]/[??][bar.R] = [[bar.M].sup.3]/[[bar.R].sup.2].

A source of energy for any kind of star