The Sheth–Tormen approximation is a halo mass function.
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:
σ
σ
δ
[1] The parameters were empirically obtained from the five-year release of WMAP.
[2] 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
for objects with a redshift
, but is accurate at low redshifts.