Non-linear dynamics and mass function of cosmic structures: I. Analytical results

Edouard Audit, Romain Teyssier, Jean Michel Alimi

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63 Scopus citations


We investigate some modifications to the Press & Schechter (1974) (PS) prescription resulting from shear and tidal effects. These modifications rely on more realistic treatments of the collapse process than the standard approach based on the spherical model. First, we show that the mass function resulting from a new approximate Lagrangian dynamic (Audit & Alimi 1996), contains more objects at high mass, than the classical PS mass function and is well fitted by a PS-like function with a threshold density of δc ≃ 1.4. However, such a Lagrangian description can underestimate the epoch of structure formation since it defines it as the collapse of the first principal axis. We therefore suggest some analytical prescriptions, for computing the collapse time along the second and third principal axes, and we deduce the corresponding mass functions. The collapse along the third axis is delayed by the shear and the number of objects of high mass then decreases. Finally, we show that the shear also strongly affects the formation of low-mass halos. This dynamical effect implies a modification of the low-mass slope of the mass function and allows the reproduction of the observed luminosity function of field galaxies. In a companion paper, we present results of numerical simulations which complete this work.

Original languageEnglish (US)
Pages (from-to)439-449
Number of pages11
JournalAstronomy and Astrophysics
Issue number2
StatePublished - Sep 10 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • Cosmology: Theory
  • Gravitation
  • Large-scale structure of universe


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