The Mass-Luminosity
Relation

Detailed observations, particularly in binary star systems where masses can be determined with some reliability, indicate that there is a correlation between the mass of a star and its luminosity.

The Relationship of Mass and Luminosity

The adjacent image illustrates for main sequence stars by plotting the logarithm of the luminosity (in units of solar luminosity) against the logarithm of mass (in units of solar mass).

We see that on this plot most stars fall very near a straight line. This is called the mass-luminosity relation for main-sequence stars.

The adjacent plot implies a very strong dependence of the luminosity on the mass, since the mass enters raised to the power 3.5. For example, if I double the mass of a main sequence star, the luminosity increases by a factor 2 3.5 ~ 11.3. Thus, stars like Sirius that are about twice as massive as the Sun are more than 10 times as luminous.

Caveats and Implications

This particular relation between mass and luminosity holds only for stars on the main sequence. It does not hold, for example, for white dwarfs or for giant stars.

The observation of a correlation between mass and luminosity for particular classes of stars suggests important systematics relating the light output of stars to their intrinsic structure that will later be exploited in the Hertzsprung-Russell Diagram.


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