Luminosity function (astronomy)

In astronomy, the luminosity function gives the number of stars or galaxies per luminosity interval. Luminosity functions are used to study the properties of large groups or classes of objects, such as the stars in clusters or the galaxies in the Local Group.

Note that the term "function" is slightly misleading, and the luminosity function might better be described as a luminosity distribution. Given a luminosity as input, the luminosity function essentially returns the abundance of objects with that luminosity (specifically, number density per luminosity interval).

The Schechter luminosity function provides a parametric description of the space density of galaxies as a function of their luminosity. The form of the function is

where ${\displaystyle x=L/L^{*}}$, and ${\displaystyle L^{*}}$ is a characteristic galaxy luminosity where the power-law form of the function cuts off. The parameter ${\displaystyle \,\!\phi ^{*}}$ has units of number density and provides the normalization. The galaxy luminosity function may have different parameters for different populations and environments; it is not a universal function. One measurement from field galaxies is ${\displaystyle \alpha =-1.25,\ \phi ^{*}=1.2\times 10^{-2}h^{3}\mathrm {Mpc} ^{-3}}$.

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