An excursion set model of hierarchical clustering: ellipsoidal collapse and the moving barrier

By R. Sheth, G. Tormen. 2001

827 citations recorded by the source corpus.

The excursion set approach allows one to estimate the abundance and spatial distribution of virialized dark matter haloes efficiently and accurately. The predictions of this approach depend on how the non-linear processes of collapse and virialization are modelled. We present simple analytic approximations that allow us to compare the excursion set predictions associated with spherical and ellipsoidal collapse. In particular, we present formulae for the universal unconditional mass function of bound objects and the conditional mass function which describes the mass function of the progenitors of haloes in a given mass range today. We show that the ellipsoidal collapse based moving barrier model provides a better description of what we measure in the numerical simulations than the spherical collapse based constant barrier model, although the agreement between model and simulations is better at large lookback times. Our results for the conditional mass function can be used to compute accurate approximations to the local-density mass function, which quantifies the tendency for massive haloes to populate denser regions than less massive haloes. This happens because low-density regions can be thought of as being collapsed haloes viewed at large lookback times, whereas high-density regions are collapsed haloes viewed at small lookback times. Although we have applied our analytic formulae only to two simple barrier shapes, we show that they are, in fact, accurate for a wide variety of moving barriers. We suggest how they can be used to study the case in which the initial dark matter distribution is not completely cold.

Subfields: Astronomy and Astrophysics, Ecology, Plant Science

View Paper: https://www.semanticscholar.org/paper/51b551dd39d6438c7319ae8922c63c7382bfc97d

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Citations in the corpus

Precision Determination of the Mass Function of Dark Matter Halos (2005, background): “This form is related to the multiplicity function resulting from the barrier-shape Ansatz of Sheth & Tormen (2002) but without an associated change of the exponential.”
Lensing and x-ray mass estimates of clusters (simulations) (2012, background): “Second, their mass function is highly sensitive to cosmology, since its evolution traces the growth of the linear density perturbations with exponential magnification (Press & Schechter 1974; Sheth & Tormen 2002; Jenkins et al. 2001; Warren et al. 2006).”
Constraining primordial non-Gaussianity with future galaxy surveys (2011, methodology): “Fitting formulae that improve agreement with Nbody simulations have also been presented (Sheth & Tormen 1999, 2002; Jenkins et al. 2001; Warren et al. 2006; Tinker et al. 2008; Pillepich et al. 2010).”
On the environmental dependence of halo formation (2004, background): “…for the conditional mass function of m haloes at t which are later (at T > t) in more massive haloes M > m (Bond et al. 1991; Lacey & Cole 1993; Sheth & Tormen 2002), for the abundance of haloes as a function of the larger scale environment (Mo & White 1996; Lemson & Kauffmann 1999; Sheth &…”
Formation of z~6 Quasars from Hierarchical Galaxy Mergers (2006, methodology): “It has been shown by previous numerical studies (e.g., Jenkins et al. 2001; Sheth & Tormen 2002; Springel &Hernquist 2003b) and more recently by the state-of-the-art Millennium Simulation by Springel et al. (2005c) that the PS formula underestimates the abundance of high-mass halos by up to an…”
The Growth of H II Regions During Reionization (2004, background): “The results are exactly analogous to the extended Press-Schechter formalism for calculating conditional halo mass functions (Lacey & Cole 1993; Sheth & Tormen 2002); the size distribution is m dn dm ∣ ∣ ∣ ∣ box = √ 2 π ρ̄ m ∣ ∣ ∣ ∣ d lnσ d lnm ∣ ∣ ∣ ∣ σ2(m) [σ2(m) −σ2box]3/2 ×B0exp [ −…”
Cosmic Dawn (CoDa): the first radiation-hydrodynamics simulation of reionization and galaxy formation in the Local Universe (2015, methodology): “Over-plotted are the theoretical mass function of Sheth & Tormen (2002) and the Watson et al. (2013) FoF universal fit (dotted and dashed lines, respectively).”
A Physical Model for the Coevolution of QSOs and Their Spheroidal Hosts (2003, methodology): “For the function νf(ν) we adopt the expression given by Sheth & Tormen (2002), which also takes into account the effect of ellipsoidal collapse: νf(ν) = A[1 + (aν)−p]( aν 2 )1/2 e−aν/2 π1/2 , (6) where A = 0.322, p = 0.3 and a = 0.707.”
Unusually Large Fluctuations in the Statistics of Galaxy Formation at High Redshift (2003, methodology): “The matching mass function is given by fST(δc(z),S) = A ′ ν S √ a′ 2π [ 1+ 1 (a′ν2)q′ ] exp [ − a′ν2 2 ] , (5) with best-fit parameters (Sheth & Tormen 2002)a′ = 0.75 and q′ = 0.3, and where normalization to unity is ensured by taking A′ = 0.322.”
A hierarchy of voids: much ado about nothing (2003, background): “For similar reasons, the clouds associated with the more massive halos should be more massive on average (this is also discussed more fully by Mo & White 1996; Sheth & Tormen 2002 and Gottlöber et al. 2003).”
HERSCHEL-ATLAS GALAXY COUNTS AND HIGH-REDSHIFT LUMINOSITY FUNCTIONS: THE FORMATION OF MASSIVE EARLY-TYPE GALAXIES (2011, background): “• The halo formation rate is given by the positive term of the derivative with respect to the cosmic time of the Sheth & Tormen (1999, 2002) cosmological mass function [eq.”
Concentration, spin and shape of dark matter haloes: Scatter and the dependence on mass and environment (2006, methodology): “1 we report the comparison of the halo mass functions of all our simulations with the analytical mass function of Sheth & Tormen (2002).”
LOCATING THE “MISSING” BARYONS WITH EXTRAGALACTIC DISPERSION MEASURE ESTIMATES (2013, result): “The calculations in this Letter assume a flat ΛCDM cosmological model, consistent with the recent determinations of Planck Collaboration et al. (2013), and the Sheth & Tormen (2002) halo mass function.”
The Halo Mass Function: High-Redshift Evolution and Universality (2007, background): “(Sheth & Tormen 2002 suggest a ¼ 0:75 as an improved value.)”