Multifractality as a Link between Luminosity and Space Distribution of Visible Matter
Abstract
We discuss how luminosity and space distributions of galaxies are naturally linked in view of their multifractal properties. In particular, we show that the mass (luminosity) function corresponding to a multifractal distribution in a given observed volume consists of a power law followed by an exponential cutoff. This implies that the amplitude of the Schechter function scales with the sample depth; as confirmed by various observational data. This effect is analogous to the scaling of the space density due to the fractal nature of the space distribution. This has the important consequence that the luminosity function can be defined properly only in a volume-limited sample. Also, the so-called luminosity segregation and the concept of bias correspond to a natural consequence of multifractality. This implies, however, that they should be considered from a different perspective with respect to the usual one. Such a concept allows us to unify the space and luminosity distributions as being shaped by a single cause: multifractality, which should therefore claim a central stage in theoretical investigations.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- September 1996
- DOI:
- 10.1086/177754
- arXiv:
- arXiv:astro-ph/9605053
- Bibcode:
- 1996ApJ...469...26S
- Keywords:
-
- GALAXIES: CLUSTERS: GENERAL;
- COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE;
- GALAXIES: LUMINOSITY FUNCTION;
- MASS FUNCTION;
- METHODS: STATISTICAL;
- Astrophysics
- E-Print:
- 38 pages, Latex, 9 figures available under request at sylos@roma1.infn.it. To be published in the Astrophysical Journal, 1996, Vol.468 September 20