Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · astro-ph/9710128

The Multiplicity Function of Galaxies, Clusters and Voids

Patrick Valageas·Richard Schaeffer
View original source ↗Read source document ↗Export metadata ↓

Abstract

We calculate the multiplicity function of matter condensations by directly considering the actual, deeply non-linear density field, which we compare to the popular Press-Schechter approximation. We show the mass function is a function of a unique parameter that contains all the dependence on the mass and radius of the object. It enables us to derive the mass function of general astrophysical objects (in addition to just-virialized halos) which may be defined by any density threshold, that may even vary with the mass of the object. This is beyond the reach of usual formulations based on the initial gaussian field and gives a clear illustration of the advantages of our approach. We explain why numerical tests seem to favor both Press-Schechter and non-linear prescriptions even though the two approximations differ by their scaling as a function of mass as well as a function of redshift. The difference between the two is due to the fact that the Press-Schechter prescription assumes that present-day mass fluctuations can be recognized in the early linear universe, and that their number is conserved, while the non-linear approach takes into account their evolution which leads to an increase of the number of highly non-linear objects (very large or small masses). This difference is seen to be of the same magnitude as the difference obtained by varying the initial spectrum of density fluctuations. Earlier conclusions drawn about the relevance of the latter using analytical approximations to the mass function must thus be reexamined.

Explore related subjects

astro-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Patrick Valageas, Richard Schaeffer. 1997-10-13. The Multiplicity Function of Galaxies, Clusters and Voids. https://arxiv.org/abs/astro-ph/9710128

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2023

Dark Energy is the Cosmological Quantum Vacuum Energy of Light Particles-The Axion and the Lightest Neutrino

We uncover the general mechanism producing the dark energy(DE). This is only based on well known quantum physics and cosmology. We show that the observed DE originates from the cosmological quantum vacuum of light particles which provides a continuous energy distribution able to reproduce the data. Bosons give positive contributions to the DE while fermions yield negative contributions. As usual in field theory, ultraviolet divergences are subtracted from the physical quantities. The subtractions respect the symmetries of the theory and we normalize the physical quantities to be zero for the Minkowski vacuum. The resulting finite contributions to the energy density and the pressure from the quantum vacuum grow as log a(t) where a(t) is the scale factor, while the particle contributions dilute as 1/a^3(t), as it must be for massive particles. The DE equation of state P = w(z)H turns to be w(z)<-1 with w(z) asymptotically reaching the value -1 from below.A scalar particle can produce the observed DE through its quantum cosmological vacuum provided:(i)its mass is of the order of 10^{-3} eV = 1 meV,(ii) it is very weakly coupled and (iii) it is stable on the time scale of the age of the universe. The axion vacuum thus appears as a natural candidate. The neutrino vacuum (especially the lightest mass eigenstate) can give negative contributions to the DE. We find that w(z=0) is slightly below -1 by an amount ranging from [-1.5 10^{-3}] to [-8 10^{-3}] and we predict the axion mass to be in the range between 4 and 5 meV. We find that the universe will expand in the future faster than the de Sitter universe, as an exponential in the square of the cosmic time. DE arises from the quantum vacua of light particles in FRW cosmological space time in an analogous way to the Casimir effect in Minkowski spacetime with non trivial boundaries.

astro-ph↗
arXiv2023

Scaling of Black Hole Accretion Discs from Gamma-Ray Bursts and Black Hole X-Ray Binaries to Active Galactic Nuclei

I consider how physical processes scale over eight orders of magnitude in black hole mass, from stellar masses in gamma-ray bursts (GRB) and black-hole X-ray binaries (BHXRB) to supermassive active galactic nuclei (AGN). Accretion rates onto stellar mass black holes range over more than sixteen orders of magnitude, from the lower luminosity BHXRB to GRB. These enormous parameter ranges correspond to qualitative as well as quantitative differences in behavior. The fundamental questions involve the balance between nonequilibrium and thermalized plasmas. When energy fluxes exceed a critical value $\sim 10^{29}$ erg/cm$^2$s, as in GRB, a black-body equilibrium pair plasma forms. At the lower fluxes found in AGN, BHXRB and microquasars, accretion power electrodynamically accelerates a small number of very energetic particles, explaining their non-thermal spectra and the high energy gamma-ray emission of blazars. Ultra-high energy cosmic rays may be accelerated by massive black holes, otherwise undetectable, with very low thermal luminosities. New-born fast high-field pulsars may be in the black-body equilibrium regime, resembling SGR in permanent outburst. I also consider the question, significant for the acceleration of nonthermal particles in GRB outflows, of whether collisionless plasmas interpenetrate rather than forming hydrodynamic shocks, and propose this as an alternative to internal shock models of GRB. A new appendix attempts to explain why AGN are, proportionally, more efficient accelerators of energetic particles than stellar mass black holes.

astro-ph↗