Toward a Halo Mass Function for Precision Cosmology: The Limits of Universality

By J. Tinker, Andrey V. Kravtsov, Anatoly Klypin, K. Abazajian, Michael S. Warren, G. Yepes, S. Gottlober, D. Holz. 2008

1,526 citations recorded by the source corpus.

We measure the mass function of dark matter halos in a large set of collisionless cosmological simulations of flat ΛCDM cosmology and investigate its evolution at z≲ 2. Halos are identified as isolated density peaks, and their masses are measured within a series of radii enclosing specific overdensities. We argue that these spherical overdensity masses are more directly linked to cluster observables than masses measured using the friends-of-friends algorithm (FOF), and are therefore preferable for accurate forecasts of halo abundances. Our simulation set allows us to calibrate the mass function at z = 0 for virial masses in the range 1011 h−1 M☉ ⩽ M⩽ 1015 h−1 M☉ to ≲5%, improving on previous results by a factor of 2-3. We derive fitting functions for the halo mass function in this mass range for a wide range of overdensities, both at z = 0 and earlier epochs. Earlier studies have sought to calibrate a universal mass function, in the sense that the same functional form and parameters can be used for different cosmologies and redshifts when expressed in appropriate variables. In addition to our fitting formulae, our main finding is that the mass function cannot be represented by a universal function at this level or accuracy. The amplitude of the “universal” function decreases monotonically by ≈20%-50%, depending on the mass definition, from z = 0 to 2.5. We also find evidence for redshift evolution in the overall shape of the mass function.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/78db88210bb40279eebd670a614837e39d4b24cb

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Citations in the corpus

Halo mass function and scale-dependent bias from N-body simulations with non-Gaussian initial conditions (2008, methodology): “It is well known that the mass function of FOF haloes shows a more universal scaling even though other halo finders might be more directly linked to actual observables (Jenkins et al. 2001; Tinker et al. 2008).”
The Atacama Cosmology Telescope: A Catalog of >4000 Sunyaev–Zel’dovich Galaxy Clusters (2020, methodology): “…are extracted by computing the posterior probability µP M y z P y M z P M z, , , 6500c 0 0 500c 500c( ∣ ˜ ) ( ˜ ∣ ) ( ∣ ) ( ) where P(M500c|z) is the halo mass function at redshift z, for which we use the fitting formulae of Tinker et al. (2008), as implemented in the Core Cosmology Library v2.”
Weighing the Giants - I. Weak-lensing masses for 51 massive galaxy clusters: project overview, data analysis methods and cluster images (2012, background): “…different halo center definitions, such as center-ofmass (e.g. Lacey & Cole 1994), most bound particle or potential minimum (e.g. Meneghetti et al. 2010; Hilbert & White 2010), or highest density peak (Tinker et al. 2008; Becker & Kravtsov 2011) approximate different observational definitions.”
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 SUNYAEV–ZEL'DOVICH-SELECTED CLUSTERS WITH X-RAY OBSERVATIONS IN THE FIRST 178 deg2 OF THE SOUTH POLE TELESCOPE SURVEY (2011, methodology): “Tinker et al. (2008) claim an overall calibration of their mass function to simulations of 5%.”
Dark matter halo merger histories beyond cold dark matter – I. Methods and application to warm dark matter (2012, background): “It is now well known that this constant barrier does not result in a halo mass function that agrees well with that measured from N-body simulations of CDM (e.g. Tinker et al. 2008).”
A volumetric deep Convolutional Neural Network for simulation of dark matter halo catalogues (2018, methodology): “We chose to compare to the Tinker et al. (2008) mass function as it shares a similar definition of halo mass, measured by a spherical over-density calculation (SO) and not by friends-of-friends (FoF) as is common.”
The halo mass function through the cosmic ages (2012, methodology): “White (2002) highlighted that non-universality existed for most halo mass estimators; Tinker et al. (2008) present an SO mass function that includes redshift-dependent parameters for z ≤ 2.5; similarly Crocce et al. (2010) and Bhattacharya et al. (2011) present FOF mass functions with…”
THE CONNECTION BETWEEN GALAXIES AND DARK MATTER STRUCTURES IN THE LOCAL UNIVERSE (2012, methodology): “This matching is done with zero scatter, using the mass function of Tinker et al. (2008).”
Galaxy formation theory (2010, methodology): “Tinker et al. (2008) give values for these parameters as a function of the overdensity,∆, used to define what we consider to be a halo.”
Limits on dark matter annihilation signals from the Fermi LAT 4-year measurement of the isotropic gamma-ray background (2015, background): “, [42], but with the parameters deduced by [36] at redshift zero for the Planck cosmology.”
Planck 2013 results. XX. Cosmology from Sunyaev-Zeldovich cluster counts (2013, methodology): “The coefficients A, a, b and c are tabulated in Tinker et al. (2008) for different overdensities, ∆mean, with respect to the mean cosmic density, and depend on z.”