Schechterfunksjon

A Schechter function is a mathematical formula commonly used in astrophysics to describe the distribution of galaxy luminosities within a specific volume of space. Named after the astronomer Paul Schechter, who introduced the function in 1976, it provides a parametric model that characterizes the number density of galaxies as a function of their brightness or luminosity.

The function is typically expressed as a combination of a power law and an exponential cutoff, capturing the observed trend that many faint galaxies are more numerous than bright ones, while the number of extremely luminous galaxies declines rapidly. Mathematically, it is written as:

N(L) dL = φ* (L / L*)^α exp(-L / L*) d(L / L*)

where N(L) dL is the number of galaxies with luminosity between L and L + dL, φ* is a normalization constant indicating the overall density of galaxies, L* is the characteristic luminosity where the slope changes, and α is the faint-end slope determining how rapidly the number of faint galaxies increases.

This function is widely used in extragalactic astronomy and cosmology to analyze galaxy surveys, estimate luminosity functions, and understand galaxy formation and evolution. Its flexibility allows it to fit a variety of observational data across different wavelengths and environments.

Overall, the Schechter function remains a fundamental tool for quantifying the luminosity distribution of galaxies and exploring the properties of the universe's large-scale structure.