A first new luminosity function of galaxies can be built starting from a left truncated beta probability density function, which is characterized by four parameters. In the astrophysical conversion, the number of parameters increases by one, due to the addition of the overall density of galaxies. A second new galaxy luminosity function is built starting from a left truncated beta probability for the mass of galaxies once a simple nonlinear relationship between mass and luminosity is assumed; in this case the number of parameters is six because the overall density of galaxies and a parameter that regulates mass and luminosity are added. The two new galaxy luminosity functions with finite boundaries were tested on the Sloan Digital Sky Survey (SDSS) in five different bands; the results produce a “better fit” than the Schechter luminosity function in two of the five bands considered. A modified Schechter luminosity function with four parameters has been also analyzed.
Blanton, M.R., Lupton, R.H., Schlegel, D.J., Strauss, M.A., Brinkmann, J., Fukugita, M. and Loveday, J. (2005)The Properties and Luminosity Function of Extremely Low Luminosity Galaxies. Astrophysical Journal, 631, 208.
Van den Bosch, F.C., Yang, X. and Mo, H.J. (2003) Linking Early- and Late-Type Galaxies to Their Dark Matter Haloes. Monthly Notices of the Royal Astronomical Society, 340, 771.
Yang, X., Mo, H.J. and van den Bosch, F.C. (2003) Constraining galaxy formation and cosmology with the conditional luminosity function of galaxies. Monthly Notices of the Royal Astronomical Society, 339, 1057.
Kauffmann, G., Heckman, T.M., White, S.D.M., Charlot, S. and Tremonti, C. (2003) Stellar masses and star formation histories for 105 galaxies from the Sloan Digital Sky Survey. Monthly Notices of the Royal Astronomical Society, 341, 33-53.