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.
Contents
- Schechter luminosity function
- Integrals of the Schechter function
- White dwarf luminosity function
- References
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).
Schechter luminosity function
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
It is often more convenient to rewrite the Schechter function in terms of magnitudes, rather than luminosities. In this case, the Schechter function becomes:
Note that because the magnitude system is logarithmic, the power law has logarithmic slope
Integrals of the Schechter function
Integrals of the Schechter function can be expressed via the incomplete gamma function
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.