The Luminosity Function of Galaxies as Modeled by a Left Truncated Beta Distribution

Author(s)
L. Zaninetti

ABSTRACT

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.

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.

Cite this paper

Zaninetti, L. (2014) The Luminosity Function of Galaxies as Modeled by a Left Truncated Beta Distribution.*International Journal of Astronomy and Astrophysics*, **4**, 145-154. doi: 10.4236/ijaa.2014.41013.

Zaninetti, L. (2014) The Luminosity Function of Galaxies as Modeled by a Left Truncated Beta Distribution.

References

[1] Schechter, P. (1976) An Analytic Expression for the Luminosity Function for Galaxies. Astrophysical Journal, 203, 297-306. http://dx.doi.org/10.1086/154079

[2] Zwicky, F. (1957) Morphological Astronomy. Springer, Berlin. http://dx.doi.org/10.1007/978-3-642-87544-1

[3] Kiang, T. (1961) The Galaxian Luminosity Function. Monthly Notices of the Royal Astronomical Society, 122, 263.

[4] Abell, G.O. (1965) Clustering of Galaxies. Annual Review of Astronomy and Astrophysics, 3, 1-22.

[5] Arakelyan, M.A. and Kalloglyan, A.T. (1970) The Luminosity Function of Field Galaxies. Soviet Astronomy, 13, 953.

[6] Driver, S.P. and Phillipps, S (1996) Is the Luminosity Distribution of Field Galaxies Really Flat? Astrophysical Journal, 469, 529. http://dx.doi.org/10.1086/177801

[7] 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.

[8] Tempel, E., Einasto, J., Einasto, M., Saar, E. and Tago, E. (2009) Anatomy of Luminosity Functions: The 2dFGRS Example. Astronomy & Astrophysics, 495, 37.

[9] Zaninetti, L. (2008) A New Luminosity Function for Galaxies as Given by the Mass-Luminosity Relationship. The Astronomical Journal, 135, 1264-1275.

[10] Zaninetti, L. (2010) The Luminosity Function of Galaxies as Modelled by the Generalized Gamma Distribution. Acta Physica Polonica B, 41, 729.

[11] Zaninetti, L. (2013) The Initial Mass Function Modeled by a Left Truncated Beta Distribution. Astrophysical Journal, 765, 128.

[12] 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.

http://dx.doi.org/10.1046/j.1365-8711.2003.06335.x

[13] 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. http://dx.doi.org/10.1046/j.1365-8711.2003.06254.x

[14] Cooray, A. and Cen, R. (2005) The Rise of Dwarfs and the Fall of Giants: Galaxy Formation Feedback Signatures in the Halo Satellite Luminosity Function. Astrophysical Journal, 633, L69.

[15] Cooray, A. and Milosavljevic, M. (2005) What is L*? Anatomy of the Galaxy Luminosity Function. Astrophysical Journal, 627, L89.

[16] Cooray, A. and Milosavljevic, M. (2005) Dissipationless Merging and the Assembly of Central Galaxies. Astrophysical Journal, 627, L85.

[17] Tinker, J.L., Weinberg, D.H., Zheng, Z. and Zehavi, I. (2005) On the Mass-to-Light Ratio of Large-Scale Structure. Astrophysical Journal, 631, 41.

[18] Tinker, J.L., Norberg, P., Weinberg, D.H. and Warren, M.S. (2007) On the Luminosity Dependence of the Galaxy Pairwise Velocity Dispersion. Astrophysical Journal, 659, 877.

[19] Abramowitz, M. and Stegun, I.A. (1965) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York.

[20] Von Seggern, D. (1992) CRC Standard Curves and Surfaces. CRC, New York.

[21] Thompson, W.J. (1997) Atlas for computing mathematical functions. Wiley-Interscience, New York.

[22] Gradshteyn, I.S. and Ryzhik, I.M. and Jeffrey, A. and Zwillinger, D. (2007) Table of Integrals, Series, and Products. Academic Press, New York.

[23] Olver, F.W.J., Lozier, D. W., Boisvert R.F. and Clark C.W. (2010) NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge.

[24] Zhang, S. and Jin, J. (1996) Computation of Special Functions. Wiley-Interscience, New York.

[25] Blanton, M.R., Hogg, D.W., Bahcall, N.A., Brinkmann, J. and Britton, M. (2003) The Galaxy Luminosity Function and Luminosity Density at Redshift z = 0.1. Astrophysical Journal, 592, 819.

[26] 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.

[27] Alcaniz, J.S. and Lima, J.A.S. (2004) Galaxy Luminosity Function: A New Analytic Expression. Brazilian Journal of Physics, 34, 455. http://dx.doi.org/10.1590/S0103-97332004000300026

[28] Taghizadeh-Popp, M., Ozogány, K., Rácz, Z., Regoes, E. and Szalay, A.S. (2012) Distribution of Maximal Luminosity of Galaxies in the Sloan Digital Sky Survey. Astrophysical Journal, 759, 100.

[1] Schechter, P. (1976) An Analytic Expression for the Luminosity Function for Galaxies. Astrophysical Journal, 203, 297-306. http://dx.doi.org/10.1086/154079

[2] Zwicky, F. (1957) Morphological Astronomy. Springer, Berlin. http://dx.doi.org/10.1007/978-3-642-87544-1

[3] Kiang, T. (1961) The Galaxian Luminosity Function. Monthly Notices of the Royal Astronomical Society, 122, 263.

[4] Abell, G.O. (1965) Clustering of Galaxies. Annual Review of Astronomy and Astrophysics, 3, 1-22.

[5] Arakelyan, M.A. and Kalloglyan, A.T. (1970) The Luminosity Function of Field Galaxies. Soviet Astronomy, 13, 953.

[6] Driver, S.P. and Phillipps, S (1996) Is the Luminosity Distribution of Field Galaxies Really Flat? Astrophysical Journal, 469, 529. http://dx.doi.org/10.1086/177801

[7] 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.

[8] Tempel, E., Einasto, J., Einasto, M., Saar, E. and Tago, E. (2009) Anatomy of Luminosity Functions: The 2dFGRS Example. Astronomy & Astrophysics, 495, 37.

[9] Zaninetti, L. (2008) A New Luminosity Function for Galaxies as Given by the Mass-Luminosity Relationship. The Astronomical Journal, 135, 1264-1275.

[10] Zaninetti, L. (2010) The Luminosity Function of Galaxies as Modelled by the Generalized Gamma Distribution. Acta Physica Polonica B, 41, 729.

[11] Zaninetti, L. (2013) The Initial Mass Function Modeled by a Left Truncated Beta Distribution. Astrophysical Journal, 765, 128.

[12] 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.

http://dx.doi.org/10.1046/j.1365-8711.2003.06335.x

[13] 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. http://dx.doi.org/10.1046/j.1365-8711.2003.06254.x

[14] Cooray, A. and Cen, R. (2005) The Rise of Dwarfs and the Fall of Giants: Galaxy Formation Feedback Signatures in the Halo Satellite Luminosity Function. Astrophysical Journal, 633, L69.

[15] Cooray, A. and Milosavljevic, M. (2005) What is L*? Anatomy of the Galaxy Luminosity Function. Astrophysical Journal, 627, L89.

[16] Cooray, A. and Milosavljevic, M. (2005) Dissipationless Merging and the Assembly of Central Galaxies. Astrophysical Journal, 627, L85.

[17] Tinker, J.L., Weinberg, D.H., Zheng, Z. and Zehavi, I. (2005) On the Mass-to-Light Ratio of Large-Scale Structure. Astrophysical Journal, 631, 41.

[18] Tinker, J.L., Norberg, P., Weinberg, D.H. and Warren, M.S. (2007) On the Luminosity Dependence of the Galaxy Pairwise Velocity Dispersion. Astrophysical Journal, 659, 877.

[19] Abramowitz, M. and Stegun, I.A. (1965) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York.

[20] Von Seggern, D. (1992) CRC Standard Curves and Surfaces. CRC, New York.

[21] Thompson, W.J. (1997) Atlas for computing mathematical functions. Wiley-Interscience, New York.

[22] Gradshteyn, I.S. and Ryzhik, I.M. and Jeffrey, A. and Zwillinger, D. (2007) Table of Integrals, Series, and Products. Academic Press, New York.

[23] Olver, F.W.J., Lozier, D. W., Boisvert R.F. and Clark C.W. (2010) NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge.

[24] Zhang, S. and Jin, J. (1996) Computation of Special Functions. Wiley-Interscience, New York.

[25] Blanton, M.R., Hogg, D.W., Bahcall, N.A., Brinkmann, J. and Britton, M. (2003) The Galaxy Luminosity Function and Luminosity Density at Redshift z = 0.1. Astrophysical Journal, 592, 819.

[26] 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.

[27] Alcaniz, J.S. and Lima, J.A.S. (2004) Galaxy Luminosity Function: A New Analytic Expression. Brazilian Journal of Physics, 34, 455. http://dx.doi.org/10.1590/S0103-97332004000300026

[28] Taghizadeh-Popp, M., Ozogány, K., Rácz, Z., Regoes, E. and Szalay, A.S. (2012) Distribution of Maximal Luminosity of Galaxies in the Sloan Digital Sky Survey. Astrophysical Journal, 759, 100.