Large scale bias and the peak background split

doi:10.1046/J.1365-8711.1999.02692.X

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Large scale bias and the peak background split

Journal Article•DOI•

Large scale bias and the peak background split

Ravi K. Sheth¹, Giuseppe Tormen¹•Institutions (1)

Max Planck Society¹

01 Sep 1999-Monthly Notices of the Royal Astronomical Society (Oxford University Press)-Vol. 308, Iss: 1, pp 119-126

TL;DR: In this paper, a simple model was proposed to estimate the bias of dark matter halos and their spatial distribution on large scales using the unconditional mass function, which was measured in numerical simulations of SCDM, OCDM and ΛCDM.

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Abstract: Dark matter haloes are biased tracers of the underlying dark matter distribution. We use a simple model to provide a relation between the abundance of dark matter haloes and their spatial distribution on large scales. Our model shows that knowledge of the unconditional mass function alone is sufficient to provide an accurate estimate of the large-scale bias factor. We then use the mass function measured in numerical simulations of SCDM, OCDM and ΛCDM to compute this bias. Comparison with these simulations shows that this simple way of estimating the bias relation and its evolution is accurate for less massive haloes as well as massive ones. In particular, we show that haloes that are less/more massive than typical M* haloes at the time they form are more/less strongly clustered than is predicted by formulae based on the standard Press–Schechter mass function.

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Journal Article•DOI•

First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Determination of cosmological parameters

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David N. Spergel¹, Licia Verde¹, Hiranya V. Peiris¹, Eiichiro Komatsu¹, M. R. Nolta¹, Charles L. Bennett², Mark Halpern³, Gary Hinshaw², N. Jarosik¹, Alan J. Kogut², Michele Limon⁴, Michele Limon², S. S. Meyer⁵, Lyman A. Page¹, Gregory S. Tucker⁴, Gregory S. Tucker², Gregory S. Tucker⁶, Janet L. Weiland, Edward J. Wollack², Edward L. Wright⁷ - Show less +16 more•Institutions (7)

Princeton University¹, Goddard Space Flight Center², University of British Columbia³, National Research Council⁴, University of Chicago⁵, Brown University⁶, University of California, Los Angeles⁷

01 Sep 2003-Astrophysical Journal Supplement Series

TL;DR: In this article, the authors find that the emerging standard model of cosmology, a flat -dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data.

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Abstract: WMAP precision data enable accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat � -dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data. For the WMAP data only, the best-fit parameters are h ¼ 0:72 � 0:05, � bh 2 ¼ 0:024 � 0:001, � mh 2 ¼ 0:14 � 0:02, � ¼ 0:166 þ0:076 � 0:071 , ns ¼ 0:99 � 0:04, and � 8 ¼ 0:9 � 0:1. With parameters fixed only by WMAP data, we can fit finer scale cosmic microwave background (CMB) measure- ments and measurements of large-scale structure (galaxy surveys and the Lyforest). This simple model is also consistent with a host of other astronomical measurements: its inferred age of the universe is consistent with stellar ages, the baryon/photon ratio is consistent with measurements of the (D/H) ratio, and the inferred Hubble constant is consistent with local observations of the expansion rate. We then fit the model parameters to a combination of WMAP data with other finer scale CMB experiments (ACBAR and CBI), 2dFGRS measurements, and Lyforest data to find the model's best-fit cosmological parameters: h ¼ 0:71 þ0:04 � 0:03 , � bh 2 ¼ 0:0224 � 0:0009, � mh 2 ¼ 0:135 þ0:008 � 0:009 , � ¼ 0:17 � 0:06, ns(0.05 Mpc � 1 )=0 :93 � 0:03, and � 8 ¼ 0:84 � 0:04. WMAP's best determination of � ¼ 0:17 � 0:04 arises directly from the temperature- polarization (TE) data and not from this model fit, but they are consistent. These parameters imply that the age of the universe is 13:7 � 0:2 Gyr. With the Lyforest data, the model favors but does not require a slowly varying spectral index. The significance of this running index is sensitive to the uncertainties in the Ly� forest. By combining WMAP data with other astronomical data, we constrain the geometry of the universe, � tot ¼ 1:02 � 0:02, and the equation of state of the dark energy, w < � 0:78 (95% confidence limit assuming w �� 1). The combination of WMAP and 2dFGRS data constrains the energy density in stable neutrinos: � � h 2 < 0:0072 (95% confidence limit). For three degenerate neutrino species, this limit implies that their mass is less than 0.23 eV (95% confidence limit). The WMAP detection of early reionization rules out warm dark matter. Subject headings: cosmic microwave background — cosmological parameters — cosmology: observations — early universe On-line material: color figure

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10,650 citations

Cites methods from "Large scale bias and the peak backg..."

...We can evaluate this effect by first computing the fraction of collapsed objects, fDM , at a given redshift: fDM (z) = 1 ρ0 ∫ ∞ Mmin Φ(M, z)MdM, (2) where Φ(M, z) is the Sheth & Tormen (1999) mass function....
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Journal Article•DOI•

Modified Gravity and Cosmology

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Timothy Clifton¹, Pedro G. Ferreira¹, Antonio Padilla², Constantinos Skordis²•Institutions (2)

University of Oxford¹, University of Nottingham²

01 Mar 2012-Physics Reports

TL;DR: A comprehensive survey of recent work on modified theories of gravity and their cosmological consequences can be found in this article, where the authors provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a selfcontained, comprehensive and up-to-date introduction to the subject as a whole.

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3,674 citations

Cites methods from "Large scale bias and the peak backg..."

...To obtain the comoving number density of halos per logarithmic interval in the virial mass, and the linear bias, they use the Sheth-Tormen method [1137], while they use the Navarro-Frenk-White [946] form for halo profiles....
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Journal Article•DOI•

f(R) theories

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Antonio De Felice¹, Shinji Tsujikawa¹•Institutions (1)

Tokyo University of Science¹

26 Feb 2010-Living Reviews in Relativity

TL;DR: Various applications of f(R) theories to cosmology and gravity — such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds are reviewed.

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Abstract: Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

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3,375 citations

Cites methods from "Large scale bias and the peak backg..."

...The Sheth–Tormen mass function [535] and the Navarro–Frenk–White halo profile [449] are usually employed in GR....
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Journal Article•DOI•

Stable clustering, the halo model and non-linear cosmological power spectra

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Robert E. Smith¹, Robert E. Smith², John A. Peacock², Adrian Jenkins³, Simon D. M. White³, Carlos S. Frenk⁴, Frazer R. Pearce¹, Peter A. Thomas⁵, George Efstathiou⁶, Hugh M. P. Couchman⁷ - Show less +6 more•Institutions (7)

University of Nottingham¹, University of Edinburgh², Max Planck Society³, Durham University⁴, University of Sussex⁵, University of Cambridge⁶, McMaster University⁷

01 Jun 2003-Monthly Notices of the Royal Astronomical Society

TL;DR: In this paper, the authors present the results of a large library of cosmological N-body simulations, using power-law initial spectra, for the first order cosmologies.

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Abstract: We present the results of a large library of cosmological N-body simulations, using power-law initial spectra.

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2,072 citations

Cites background or methods from "Large scale bias and the peak backg..."

...As studies over many years have shown with increasing accuracy (Press & Schechter 1974; Sheth & Tormen 1999; Jenkins et al. 2001), the halo mass function appears to depend only on the dimensionless fluctuation amplitude ν ≡ δc/σ (R, t), (52) where δc is a constant of the order of unity, usually…...
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...…2000; Seljak 2000; Scoccimarro et al. 2001) resurrected the Neyman–Scott model with a modern mass function for dark haloes (Press & Schechter 1974; Sheth & Tormen 1999; Jenkins et al. 2001), plus realistic density profiles (Navarro, Frenk & White 1996, 1997; Moore et al. 1999), and a…...
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...In terms of the halo model, if one assumes = 0.4 in accord with Sheth & Tormen (1999), then a strong dependence of β0 on n is required in order to match the measured data....
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...Prescriptions for this clustering were given by Mo & White (1996), Mo, Jing & White (1997b), Sheth & Lemson (1999), Sheth & Tormen (1999), Sheth, Mo & Tormen (2000), and a recent example of their effectiveness is shown clearly in Colberg et al. (2000)....
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Journal Article•DOI•

Introducing the Illustris Project: simulating the coevolution of dark and visible matter in the Universe

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Mark Vogelsberger¹, Shy Genel², Volker Springel³, Volker Springel⁴, Paul Torrey², Debora Sijacki, Dandan Xu³, Gregory F. Snyder⁵, Dylan Nelson², Lars Hernquist² - Show less +6 more•Institutions (5)

Massachusetts Institute of Technology¹, Harvard University², Heidelberg Institute for Theoretical Studies³, Heidelberg University⁴, Space Telescope Science Institute⁵

12 May 2014-Monthly Notices of the Royal Astronomical Society

TL;DR: The Illustris Project as mentioned in this paper is a series of large-scale hydrodynamical simulations of galaxy formation, which includes primordial and metal-line cooling with self-shielding corrections, stellar evolution, stellar feedback, gas recycling, chemical enrichment, supermassive black hole growth, and feedback from active galactic nuclei.

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Abstract: We introduce the Illustris Project, a series of large-scale hydrodynamical simulations of galaxy formation. The highest resolution simulation, Illustris-1, covers a volume of (106.5 Mpc)^3, has a dark mass resolution of 6.26 × 10^6 M_⊙, and an initial baryonic matter mass resolution of 1.26 × 10^6 M_⊙. At z = 0 gravitational forces are softened on scales of 710 pc, and the smallest hydrodynamical gas cells have an extent of 48 pc. We follow the dynamical evolution of 2 × 1820^3 resolution elements and in addition passively evolve 1820^3 Monte Carlo tracer particles reaching a total particle count of more than 18 billion. The galaxy formation model includes: primordial and metal-line cooling with self-shielding corrections, stellar evolution, stellar feedback, gas recycling, chemical enrichment, supermassive black hole growth, and feedback from active galactic nuclei. Here we describe the simulation suite, and contrast basic predictions of our model for the present-day galaxy population with observations of the local universe. At z = 0 our simulation volume contains about 40 000 well-resolved galaxies covering a diverse range of morphologies and colours including early-type, late-type and irregular galaxies. The simulation reproduces reasonably well the cosmic star formation rate density, the galaxy luminosity function, and baryon conversion efficiency at z = 0. It also qualitatively captures the impact of galaxy environment on the red fractions of galaxies. The internal velocity structure of selected well-resolved disc galaxies obeys the stellar and baryonic Tully–Fisher relation together with flat circular velocity curves. In the well-resolved regime, the simulation reproduces the observed mix of early-type and late-type galaxies. Our model predicts a halo mass dependent impact of baryonic effects on the halo mass function and the masses of haloes caused by feedback from supernova and active galactic nuclei.

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2,012 citations

Cites methods from "Large scale bias and the peak backg..."

...In Figure 6 we present the differential halo mass functions of Illustris-1 and Illustris-Dark-1 along with empirical fitting formulae (Sheth & Tormen 1999; Jenkins et al. 2001; Warren et al. 2006)....
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References

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Journal Article•DOI•

Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation

[...]

William H. Press, Paul L. Schechter

01 Feb 1974-The Astrophysical Journal

4,741 citations

"Large scale bias and the peak backg..." refers background in this paper

...The shape of the unconditional mass function is expected to depend on the initial fluctuation distribution (e.g. Press & Schechter 1974)....
[...]
...There has been considerable interest recently in developing models for the shape and evolution of the mass function of collapsed dark matter haloes (Press & Schechter 1974; Bond et al. 1991; Lacey & Cole 1993) as well as for the evolution of the spatial distribution of these haloes (Mo & White…...
[...]

Journal Article•DOI•

The statistics of peaks of Gaussian random fields

[...]

James M. Bardeen¹, J. R. Bond², Nick Kaiser³, Alexander S. Szalay⁴•Institutions (4)

University of Washington¹, Stanford University², University of Cambridge³, Fermilab⁴

01 May 1986-The Astrophysical Journal

TL;DR: In this paper, a set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed.

...read moreread less

Abstract: A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

...read moreread less

3,098 citations

Journal Article•DOI•

Merger rates in hierarchical models of galaxy formation

[...]

Cedric G. Lacey¹, Shaun Cole²•Institutions (2)

University of Oxford¹, Durham University²

01 Jun 1993-Monthly Notices of the Royal Astronomical Society

TL;DR: In this article, an analytical description of the merging of virialized haloes is presented, which is applicable to any hierarchical model in which structure grows via gravitational instability, and the dependence of the merger rate on halo mass, epoch, the spectrum of initial density fluctuations and the density parameter Ω 0 is explicitly quantified.

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Abstract: We present an analytical description of the merging of virialized haloes which is applicable to any hierarchical model in which structure grows via gravitational instability. The formulae are an extension of the Press-Schechter model. The dependence of the merger rate on halo mass, epoch, the spectrum of initial density fluctuations and the density parameter Ω0 is explicitly quantified. We calculate the distribution of halo formation times and survival times. We also describe a Monte Carlo method for constructing representative histories of merger events leading to formation of haloes of a prescribed mass. Applying these results to the age distribution of rich clusters of galaxies, we infer that a high value of the density parameter (Ω0 ≳ 0.5) is required to reproduce the substantial fraction of rich clusters that exhibit significant substructure, if such substructure only persists for a time 0.2t0 after a merger, where t0 is the present age of the universe. We also investigate the rate of infall of satellite galaxies into galactic discs, by combining our Monte Carlo technique for halo mergers with an estimate of the time required for dynamical friction to erode the orbits of the baryonic cores of the accreted galaxies. We find that, even for Ω0 = 1, the infall rate is low (provided that the satellite orbits are not too eccentric), and that we would expect only a modest fraction of stellar discs to be thickened or disrupted by this process.

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2,159 citations

Journal Article•DOI•

Excursion set mass functions for hierarchical Gaussian fluctuations

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J. R. Bond¹, Shaun Cole², George Efstathiou³, Nick Kaiser¹•Institutions (3)

University of Toronto¹, University of California, Berkeley², University of Oxford³

01 Oct 1991-The Astrophysical Journal

TL;DR: In this paper, the authors proposed a solution based on the theory of the excursion sets of F(r, R sub f), the four-dimensional initial density perturbation field smoothed with a continuous hierarchy of filters of radii.

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Abstract: It is pointed out that most schemes for determining the mass function of virialized objects from the statistics of the initial density perturbation field suffer from the cloud-in-cloud problem of miscounting the number of low-mass clumps, many of which would have been subsumed into larger objects. The paper proposes a solution based on the theory of the excursion sets of F(r, R sub f), the four-dimensional initial density perturbation field smoothed with a continuous hierarchy of filters of radii R sub f.

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1,826 citations

"Large scale bias and the peak backg..." refers background or methods in this paper

...…interest recently in developing models for the shape and evolution of the mass function of collapsed dark matter haloes (Press & Schechter 1974; Bond et al. 1991; Lacey & Cole 1993) as well as for the evolution of the spatial distribution of these haloes (Mo & White 1996; Catelan et al. 1997;…...
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...Bond et al. (1991) used a random walk barrier crossing model to derive the Press–Schechter unconditional mass function from the statistics of the initial fluctuation field....
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...Then, for initially scale free spectra in models with Ω0 = 1 and Λ0 = 0, ν f(ν) ≡ m2 n(m, z) ρ̄ d log m d log ν (9) has a universal shape (Press–Schechter 1974; Peebles 1980; Bond et al. 1991)....
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Journal Article•DOI•

An analytic model for the spatial clustering of dark matter haloes

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Houjun Mo¹, Houjun Mo², Simon D. M. White¹, Simon D. M. White²•Institutions (2)

Max Planck Society¹, University of California, Santa Barbara²

11 Sep 1996-Monthly Notices of the Royal Astronomical Society

TL;DR: In this article, the authors developed a simple analytic model for the gravitational clustering of dark matter halos to understand how their spatial distribution is biased relative to that of the mass, and showed that this bias function is sufficient to calculate the cross-correlation between dark haloes and mass.

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Abstract: We develop a simple analytic model for the gravitational clustering of dark matter haloes to understand how their spatial distribution is biased relative to that of the mass. The statistical distribution of dark haloes within the initial density field (assumed Gaussian) is determined by an extension of the Press-Schechter formalism. Modifications of this distribution caused by gravitationally induced motions are treated using a spherical collapse approximation. We test this model against results from a variety of N-body simulations, and find that it gives an accurate description of a bias function. This bias function is sufficient to calculate the cross-correlation between dark haloes and mass, and again we find excellent agreement between simulation results and analytic predictions. Because haloes are spatially exclusive, the variance in the count of objects within spheres of fixed radius and overdensity is significantly smaller than the Poisson value. This seriously complicates any analytic calculation of the autocorrelation function of dark halos. Our simulation results show that this autocorrelation function is proportional to that of the mass over a wide range in $R$, even including scales where both functions are significantly greater than unity. The constant of proportionality is very close to that predicted on large scales by the analytic model. This result permits an entirely analytic estimate of the autocorrelation function of dark haloes. We use our model to study how the distribution of galaxies may be biased with respect to that of the mass. In conjunction with other data these techniques should make it possible to measure the amplitude of cosmic mass fluctuations and the density of the Universe.

...read moreread less

1,555 citations

"Large scale bias and the peak backg..." refers background or methods in this paper

...(7) Furthermore, Mo & White (1996) argued that one can write 〈 ( δEh )2 〉 V ≈ b2Eul(m1, δ1) 〈 δ2 〉 V , (8) where the average is over cells of size V placed randomly in Eulerian space....
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...(4) This expression was first derived by Mo & White (1996)....
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...…in developing models for the shape and evolution of the mass function of collapsed dark matter haloes (Press & Schechter 1974; Bond et al. 1991; Lacey & Cole 1993) as well as for the evolution of the spatial distribution of these haloes (Mo & White 1996; Catelan et al. 1997; Sheth & Lemson 1999)....
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...When a = 1 and p = 0 the mass function has the Press–Schechter form, and this formula reduces to the one given by Cole & Kaiser (1989) and Mo & White (1996)....
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...The work of Mo & White (1996) shows that the exact form of this dependence can be computed provided that both the conditional and the unconditional mass functions are known (equation 4)....
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