Limitations of the PressSchechter Formalism
Abstract
The PressSchechter (PS) formalism for mass functions of the collapsed objects is reanalyzed. The factor of 2 in the PressSchechter formalism is shown to be correct in the sharp kspace filter when we use the novel approach proposed by Jedamzik for the "cloudincloud" problem which was first discussed by Peacock & Heavens and Bond et al. The spatial correlation of the density fluctuations, however, was either neglected or treated in an approximate manner in the previous works dealing with the cloudincloud problem. In this paper the effect of spatial correlations is analyzed by using the Jedamzik formalism, taking explicitly into account the twopoint correlations of density fluctuations, and it is found that this effect alters the PS mass function on some mass scales. For example, in the case of the initial power index n = 0, the difference between the modified mass function and the PS mass function is a factor of 1.4 at M = 0.1M_*_ and is 3 orders of magnitude at M = 10M_*_. With our new derivation of the mass function, we find that the probability of the effective overlap of the collapsed objects can be neglected either on very small or on large mass scales (for example, in the case of the initial power index n = 0, M <~ 0.1M_*_ or M ~> 10M_*_, where M_*_ is the characteristic mass scale on which the variance of density fluctuations equals unity), while it cannot be neglected on intermediate mass scales.
 Publication:

The Astrophysical Journal
 Pub Date:
 July 1996
 DOI:
 10.1086/177488
 arXiv:
 arXiv:astroph/9504073
 Bibcode:
 1996ApJ...466....1Y
 Keywords:

 COSMOLOGY: THEORY;
 GALAXIES: FORMATION;
 GALAXIES: LUMINOSITY FUNCTION;
 MASS FUNCTION;
 COSMOLOGY: LARGESCALE STRUCTURE OF UNIVERSE;
 Astrophysics
 EPrint:
 23 pages, uuencoded compressed Postscript