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Sheth–Tormen approximation

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The Sheth–Tormen approximation is a halo mass function.

Background

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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: , where , , and .[1] The parameters were empirically obtained from the five-year release of WMAP.[2]

Discrepancies with simulations

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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.[3][2]

References

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  1. ^ AST541 Notes: Spherical Collapse, Press-Schechter Oct/Nov 2018
  2. ^ a b Physics 224 - Spring 2010 Origin and Evolution of the Universe
  3. ^ Klypin, Anatoly; et al. (2011). "Dark Matter Halos in the Standard Cosmological Model: Results from the Bolshoi simulation". The Astrophysical Journal. 740 (2): 102. arXiv:1002.3660. Bibcode:2011ApJ...740..102K. doi:10.1088/0004-637X/740/2/102. S2CID 16517863.