Mass–luminosity relation
A mass - luminosity relation is a relation between the mass of an object, for example a star and its luminosity dar.
Main-sequence stars
For main sequence stars, the mass - luminosity relation is well known. For the first time it was described in the 1926 book " The Internal Constitution of Stars" (hence, the internal structure of stars) by Sir Arthur Stanley Eddington. The mass-luminosity relation can be used to estimate the mass of a star solely from the observation of the luminosity. Alternatively, the brightness may also be the effective temperature or spectral of a star can be used as a measure of its luminosity. These sizes are usually easier to determine than the luminosity itself.
The empirically determined mass-luminosity relation for main-sequence stars is
The exponent (in this case the value of 3.5 ) results from the adjustment of the relationship of measured data. Using the basic equations of stellar structure can also derive a mass - luminosity relation. Here one obtains a value of 3 for the exponent.
However, the relation thus obtained is not an exact solution of the equations but are merely an estimate and true in view of the fairly good agreement with the observed mass - luminosity relation. The derivation of the relationship from the basic equations of stellar structure (basically are regarded only mean values ) by the way is a degree of similarity ( homology) of the structure of stars with different masses ahead. The confirmation of the relationship by observations can thus already to certain conclusions on the interior of the star.
The mass - luminosity relation actually means that a star with twice the mass of the sun has 11.3 times the luminosity of the sun. A star with 4 solar masses is already 128 times as bright as the sun. The strong dependence causes massive stars have a much shorter residence time ( "lifetime" ) on the main sequence as a low-mass, because the nuclear fuel is consumed much faster.
The relationship is only valid for main-sequence stars and can not simply be on giant stars or brown dwarfs transferred.