An Etymological Dictionary of Astronomy and Astrophysics

A mathematical expression that describes the → luminosity function of galaxies. The function correctly reflects the facts that the luminosity function decreases with increasing luminosity and that the decrease is particularly marked at high luminosities. It is expressed as:

φ(L) = φ(L/L)^α exp (-L/L), which has two parts and three parameters: φ is an empirically determined amplitude, α is an empirically derived exponent, and L is a characteristic luminosity which separates the low and high luminosity parts.
For small luminosities (L much smaller than L) the Schechter function approaches a power law, while at high luminosities (L much larger than L) the frequency of galaxies drops exponentially. φ, L^*, and the faint-end slope α depend on the observed wavelength range, on the → redshift, and on the environment where the galaxies are observed.

See also: Named after the American astronomer Paul Schechter (1948-), who proposed the function in 1976 (ApJ 203, 297); → function.