Luminosity function (astronomy)

For the luminosity function in photometry, see Luminosity function.

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.

Schechter luminosity function

The Schechter luminosity function gives the space density of galaxies within a luminosity bin. The form of the function is

$n(x)\ \mathrm {d} x=\phi ^{*}x^{a}\mathrm {e} ^{-x}\mathrm {d} x,$

where $x=L/L^{*}$, and $L^{*}$ is a characteristic galaxy luminosity where the power-law form of the function cuts off. The parameter $\,\!\phi ^{*}$ 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 $a=-1.25,\ \phi ^{*}=1.2\times 10^{-3}h^{3}\mathrm {Mpc} ^{-3}$.

White dwarf luminosity function

The white dwarf luminosity function (WDLF) gives the number of white dwarf stars with a given luminosity. As this is determined by the rates at which these stars form and cool, it is of interest for the information it gives about the physics of white dwarf cooling and the age and history of the Galaxy.