Scale-invariant models of the galaxy and cluster luminosity functions.
Abstract
We take advantage of recent theoretical progresses made in the understanding of the matter clustering at the kpc to the Mpc scales to construct a model for the galaxy and cluster multiplicity functions. We check that the scaling law predicted by the theory, which relates the typical luminosity of a galaxy and of a rich cluster, and a similar rule relating the velocity dispersion are in agreement with the data. The theoretical predictions being relevant for the dark matter halos, we obtain explicit relations between the dark halo parameters (mass, radius) and the observed parameters within the radius where the luminosity is concentrated. We find that the halo radius behaves as R~M^0^0.3^ and that the mass multiplicity behaves as M^-2^, being nearly divergent, if the luminosity function is assumed to behave as L^-1.3^. It appears that most of the mass is contained in the smaller galaxies with (M/L)~L^0.6^ at the faint end. These estimates are new, and obtained by a method that differs from all the previous approaches, as they depend only on observed properties and do not require any assumption on the spectrum of initial fluctuations. These results turn out to be very similar to those obtained with a moderately diverging initial spectrum such as the one obtained for Cold Dark Matter initial conditions at M <= 10^12^M_sun_ scales. We finally construct explicitly the luminosity functions, from this scaling theory, for galaxies, for rich cluster, as well as for Turner- Gott groups. They are seen to agree very closely with the ones obtained from observations. We also obtain scaling rules for the 2-dimensional group multiciplicity function when the sample depth or the density constrast defining clusters varie. These scalings provide a specific test of our theory.
- Publication:
-
Astronomy and Astrophysics
- Pub Date:
- October 1991
- Bibcode:
- 1991A&A...250...23B
- Keywords:
-
- Astronomical Models;
- Dark Matter;
- Galactic Clusters;
- Galactic Radiation;
- Luminosity;
- Halos;
- Scaling;
- Astrophysics