luminosity function

A luminosity function for some type of astronomical object, is an empirical unnormalized probability density function that yields the number of them at each possible luminosity. Example object types are galaxies (galaxy luminosity function) and globular clusters (globular cluster luminosity function). For example, the Schechter luminosity function for galaxies (aka Schechter function, an example of a galaxy luminosity function), which is a modified power law:

Φ(L)dL = Φ*(L/L*)αexp(-L/L*)d(L/L*)

• L - luminosity.
• dL - differential of the luminosity.
• Φ(L)dL - number density of galaxies with luminosity within interval dL.
• L^* - parameter: a luminosity value around which this function is adjusted, i.e., within the function's regime.
• Φ^* - parameter: normalization factor: the value of the function at L^*.
• α - parameter: exponent that fits observation data.

The parameters are chosen to fit observation. Example case:

• L^* = 1.4 × 10¹⁰
• Φ^* = 1.77 × 10^-2
• α = -1.15

Other variations of luminosity functions are galaxy cluster luminosity functions, planetary nebula luminosity functions, and luminosity functions of particular bands, spectral lines, or the lines of a specific molecule (e.g., carbon monoxide). It is assumed that luminosity functions might evolve, e.g., vary with redshift.