luminositetsfunksjon

In astronomy, the luminositetsfunksjon, or luminosity function, describes the comoving number density of objects as a function of luminosity. It gives the average number of objects per unit luminosity interval per unit volume and can be expressed in terms of luminosity L or absolute magnitude M. The luminosity function is a key tool for characterizing populations such as galaxies, quasars, or stars and for estimating the total light emitted by a population through integration over luminosity, yielding the luminosity density.

A common mathematical form for galaxies is the Schechter function: Phi(L) dL = Phi* (L/L*)^alpha exp(-L/L*) dL/L*. In magnitudes, this becomes phi(M) = 0.4 ln 10 Phi* [10^{0.4 (M*-M)}]^{alpha+1} exp(-10^{0.4 (M*-M)}). This function captures a power-law behavior at faint luminosities with a exponential cutoff at bright luminosities, characterized by parameters Phi*, L*, and alpha. Other populations, such as active galactic nuclei, are often described by double power-law or other tailored forms, and the luminosity function can evolve with redshift, described by L*(z) or Phi*(z).

Measurement challenges include survey flux limits, incompleteness, K-corrections, dust extinction, and the choice of cosmological parameters, all of which affect the derived Phi(L) or Phi(M). The luminosity function is a fundamental observable for tracing cosmic history, linking the light output of a population to its formation and evolution. Integrating the luminosity function yields the luminosity density, which informs estimates of star formation rate density and, with mass-to-light ratios, the stellar mass density of the universe.