The Sheth–Tormen approximation is a

halo HALO, halo, halos or haloes may refer to: Most common meanings * Halo (optical phenomenon) * Halo (religious iconography), a ring of light around the image of a head * ''Halo'' (franchise), a sci-fi video game series (2001–2021) Arts and en ...

mass function.

Background

The Sheth–Tormen approximation extends the Press–Schechter formalism by assuming that halos are not necessarily spherical, but merely elliptical. The distribution of the density fluctuation is as follows:

frac\exp(-\frac)

, where

\delta_c=1.686

a=0.707

, and

A=0.3222

. The parameters were empirically obtained from the five-year release of

WMAP The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic mic ...

.Physics 224 - Spring 2010 Origin and Evolution of the Universe
/ref>

Discrepancies with simulations

In 2010, the Bolshoi cosmological simulation predicted that the Sheth–Tormen approximation is inaccurate for the most distant objects. Specifically, the Sheth–Tormen approximation overpredicts the abundance of haloes by a factor of

10

for objects with a

redshift In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and increase in frequency and e ...

z>10

, but is accurate at low redshifts.

References

Dark matter Equations of astronomy Astrophysics {{DEFAULTSORT:Sheth-Tormen approximation