THE LARGE-SCALE BIAS OF DARK MATTER HALOS: NUMERICAL CALIBRATION AND MODEL TESTS

By J. Tinker, Brant Robertson, Andrey V. Kravtsov, Anatoly Klypin, Michael S. Warren, G. Yepes, S. Gottlober. 2010

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We measure the clustering of dark matter halos in a large set of collisionless cosmological simulations of the flat ΛCDM cosmology. Halos are identified using the spherical overdensity algorithm, which finds the mass around isolated peaks in the density field such that the mean density is Δ times the background. We calibrate fitting functions for the large-scale bias that are adaptable to any value of Δ we examine. We find a ∼6% scatter about our best-fit bias relation. Our fitting functions couple to the halo mass functions of Tinker et al. such that the bias of all dark matter is normalized to unity. We demonstrate that the bias of massive, rare halos is higher than that predicted in the modified ellipsoidal collapse model of Sheth et al. and approaches the predictions of the spherical collapse model for the rarest halos. Halo bias results based on friends-of-friends halos identified with linking length 0.2 are systematically lower than for halos with the canonical Δ = 200 overdensity by ∼10%. In contrast to our previous results on the mass function, we find that the universal bias function evolves very weakly with redshift, if at all. We use our numerical results, both for the mass function and the bias relation, to test the peak-background split model for halo bias. We find that the peak-background split achieves a reasonable agreement with the numerical results, but ∼20% residuals remain, both at high and low masses.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/8dc6b6b6195437d1a7e55eb6b3980029df9d70fd

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Citations in the corpus

Mapping stellar content to dark matter haloes using galaxy clustering and galaxy–galaxy lensing in the SDSS DR7 (2015, background): “The halo mass function and the halo bias function are from Tinker et al. (2008) and Tinker et al. (2010), respectively.”
Galacticus: A Semi-Analytic Model of Galaxy Formation (2010, methodology): “Tinker: This method uses the functional form proposed by Tinker et al. (2010) to compute the halo mass function.”
DEPENDENCE OF THE OUTER DENSITY PROFILES OF HALOS ON THEIR MASS ACCRETION RATE (2014, methodology): “To explore this issue more generally, we have used fits in which we parameterize the outer profile as the 2-halo term with a power-law correction, ρouter = ρm [ be ( r 5 R200m )−se bh(ν)ξlin(r) + 1 ] , (A3) where we use the bias model of Tinker et al. (2010) to calculate bh(ν).”
GALAXY CLUSTERING IN THE NEWFIRM MEDIUM BAND SURVEY: THE RELATIONSHIP BETWEEN STELLAR MASS AND DARK MATTER HALO MASS AT 1 < z < 2 (2010, methodology): “(B2) Thus, the mean number of galaxies in halos of mass M is 〈N |M〉 = 〈Nc|M〉[1 + 〈Ns|M〉], (B3) and the predicted number density of galaxies is ng = ∫ dM n(M) 〈N |M〉, (B4) where n(M) is the halo mass function, for which we use the latest parameterization given by Tinker et al. (2010b).”
KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing (2016, methodology): “The connected trispectrum underlying this term is calculated via the halo model, using the halo mass function and halo bias of Tinker et al. (2010).”
Cosmological Parameters from Observations of Galaxy Clusters (2011, neutral): “Framed in terms of the normalized linear perturbation amplitude, ν∝σ(M)−1, Tinker et al. (2010) find a robust fit of the form b(ν) = 1−D νd νd + δdc + Eνe + Fνf , (14) with a single set of parameters {d, e, f,D,E, F} that are written only as functions of ∆.”
The VIMOS Public Extragalactic Redshift Survey (VIPERS) - Galaxy clustering and redshift-space distortions at z ≃ 0.8 in the first data release (2013, methodology): “We use the halo bias factor and mass function of Tinker et al. (2008) and Tinker et al. (2010) respectively, and assume that satellite galaxies trace the mass distribution within haloes.”
Cosmological constraints from a combination of galaxy clustering and lensing – I. Theoretical framework (2012, methodology): “(61) For our definition of halo mass (see §2.1), Tinker et al. (2010) find that η1 = 0.589(1 + z) 0.20, η2 = −0.729(1 + z)−0.08, η3 = −0.243(1 + z)0.27, and η4 = 0.864(1 + z)−0.01, while η0 = η0(z) is set by the normalization condition ∫ bh(ν) f(ν) dν = 1 , (62) with bh(ν) the halo bias function of…”
The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: analysis of potential systematics (2012, methodology): “Haloes from 2LPT runs are identified using a friends-offriends algorithm and are then mass-calibrated using the Tinker et al. (2010) mass function.”
Systematic Identification of LAEs for Visible Exploration and Reionization Research Using Subaru HSC (SILVERRUSH). I. Program strategy and clustering properties of ∼2000 Lyα emitters at z = 6–7 over the 0.3–0.5 Gpc2 survey area (2017, background): “…ic.oup.com /pasj/article-abstract/70/SP1/S13/4097647 by guest on 15 M arch 2020 bHODg = ∫ ∞ Mminh bNgndM∫ ∞ Mminh NgndM , (11) where n and b are the number density and the bias of dark-matter halos, respectively, with dark-matter halo mass Mh (Behroozi et al. 2013; Tinker et al. 2010).”
Clustering of intermediate redshift quasars using the final SDSS III-BOSS sample (2015, methodology): “The constraint on halo mass comes from the fact that more massive halos have higher clustering bias(Kai er 1984; Tinker et al. 2010), so the observed clustering of quasars determines the characteristic mass of their host halos.”
THE UV LUMINOSITY FUNCTION OF STAR-FORMING GALAXIES VIA DROPOUT SELECTION AT REDSHIFTS z ∼ 7 AND 8 FROM THE 2012 ULTRA DEEP FIELD CAMPAIGN (2012, methodology): “…redshifts, we simply match the abundance of galaxies from our luminosity functions with the abudance of dark matter halos provided by the Tinker et al. (2008) halo mass function, and then assign the clustering bias of the halos to the galaxies assuming the bias function of Tinker et al. (2010).”
First results from the IllustrisTNG simulations: matter and galaxy clustering (2017, methodology): “…results for the full physics (filled circles) and the DM-only (empty circles) simulations of TNG300, and compare to the analytic models of Mo & White (1996) and Sheth & Tormen (1999), as well as to the empirical fit of Tinker et al. (2010) calibrated on a suite of collisionless N-body simulations.”
Non-linear evolution of cosmological structures in warm dark matter models (2011, methodology): “This has been observed in the CDM framework by Tinker et al. (2010), and it seems to be the case for both our CDM and WDM simulations.”
CLASH: WEAK-LENSING SHEAR-AND-MAGNIFICATION ANALYSIS OF 20 GALAXY CLUSTERS (2014, methodology): “In fact, the two cluster samples have similar “peak heights” in the linear (primordial) density field (Tinker et al. 2010): ' 3.8σ for our X-ray-selected subsample and ' 4.1σ for the Umetsu et al. (2011a) sample.”
KiDS-450: The tomographic weak lensing power spectrum and constraints on cosmological parameters (2017, methodology): “The connected trispectrum required in this step is calculated in the halo model approach employing both the halo mass function and halo bias from Tinker et al. (2008, 2010).”