The Halo Mass Function: High-Redshift Evolution and Universality

By Zarija Lukic, Katrin Heitmann, Salman Habib, S. Bashinsky, Paul M. Ricker. 2007

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We study the formation of dark matter halos in the concordance ΛCDM model over a wide range of redshifts, from z = 20 to the present. Our primary focus is the halo mass function, a key probe of cosmology. By performing a large suite of nested-box N-body simulations with careful convergence and error controls (60 simulations with box sizes from 4 to 256 h−1 Mpc), we determine the mass function and its evolution with excellent statistical and systematic errors, reaching a few percent over most of the considered redshift and mass range. Across the studied redshifts, the halo mass is probed over 6 orders of magnitude (107-1013.5 h−1 M☉). Historically, there has been considerable variation in the high-redshift mass function as obtained by different groups. We have made a concerted effort to identify and correct possible systematic errors in computing the mass function at high redshift and to explain the discrepancies between some of the previous results. We discuss convergence criteria for the required force resolution, simulation box size, halo mass range, initial and final redshifts, and time stepping. Because of conservative cuts on the mass range probed by individual boxes, our results are relatively insensitive to simulation volume, the remaining sensitivity being consistent with extended Press-Schechter theory. Previously obtained mass function fits near z = 0, when scaled by linear theory, are in good agreement with our results at all redshifts, although a mild redshift dependence consistent with that found by Reed et al. may exist at low redshifts. Overall, our results are consistent with a “universal” form for the mass function at high redshifts.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/7c36bf23bf2801d786f9505b7e820124c32b9111

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Citations in the corpus

Effects of scale-dependent non-Gaussianity on cosmological structures (2007, methodology): “Expressions for the halo mass function in the presence of non-Gaussian initial conditions have been derived as extensions of the Press–Schechter formula [72, 36, 73, 40, 74, 75].”
THE VELOCITY FUNCTION IN THE LOCAL ENVIRONMENT FROM ΛCDM AND ΛWDM CONSTRAINED SIMULATIONS (2009, methodology): “The statistical error bars presented in the figure are Poisson errors, employing the definition given in Lukić et al. (2007): σ± = √ N + 1/4 ± 1/2, where N is the number of halos per bin.”
DARK MATTER HALOS IN THE STANDARD COSMOLOGICAL MODEL: RESULTS FROM THE BOLSHOI SIMULATION (2010, result): “These results are at odds with those obtained with the Friends-Of-Friends (FOF) method (e.g. Lukić et al. 2007; Reed et al. 2007, 2009; Cohn & White 2008).”
Formation of Galaxy Clusters (2012, background): “…of halos canbe parameterized via a universal function of peak heightν (Bhattacharya et al. 2011, Courtin et al. 2011, Crocce et al. 2010, Evrard et al. 2002, Jenkins et al. 2001, Lukić et al. 2007, Reed et al. 2007, Sheth & Tormen 1999, Tinker et al. 2008, Warren et al. 2006, White 2002).”
DARK MATTER HALO PROFILES OF MASSIVE CLUSTERS: THEORY VERSUS OBSERVATIONS (2011, methodology): “We note that the simulations were carried out keeping in mind error control requirements on force-resolution, time-stepping errors, and mass resolution that have been spelled out in the literature (Tormen, Bouchet, & White 1997; Power et al. 2003; Heitmann et al. 2008; Lukić et al. 2007).”
MASS FUNCTION PREDICTIONS BEYOND ΛCDM (2010, methodology): “As has been emphasized earlier (Lukić et al. 2007), a possible solution is mass function emulation from a large, but finite set of simulations, using techniques that have been shown to be successful in high-dimensional regression problems (Habib et al. 2007).”
An accurate halo model for fitting non-linear cosmological power spectra and baryonic feedback models (2015, background): “Universality in the halo mass function is an approximation and theSheth & Tormen(1999) mass function is only accurate at the≃ 20 per cent level (e.g.,Warren et al. 2006; Reed et al. 2007; Lukić et al. 2007; Tinker et al. 2008; Courtin et al. 2011).”
FastPM: a new scheme for fast simulations of dark matter and haloes (2016, methodology): “This indicates that due to the low resolution, the density contrast in B = 1 is insufficient for detecting halos of M ≤ 1013h−1M , as also seen in Lukić et al. (2007).”
The Observed Growth of Massive Galaxy Clusters I: Statistical Methods and Cosmological Constraints (2009, background): “…some evolving w models (Klypin et al. 2003; Linder & Jenkins 2003; Łokas et al. 2004; Kuhlen et al. 2005).4 Other authors have studied the dependence of f (σ ) on redshift beyond that implicit in σ 2(M, z) (Lukić et al. 2007; Reed et al. 2007; Cohn & White 2008), replacing f (σ ) with f (σ , z).”
Toward a Halo Mass Function for Precision Cosmology: The Limits of Universality (2008, background): “More recent results quantify the evolution of the FOF at high redshift, z & 10, to be 5− 10% (Lukic et al. 2007; Reed et al. 2007; Cohn & White 2007).”
Resolving cosmic structure formation with the Millennium-II simulation (2009, unknown): “2007; Lukić et al. 2007; Cohn & White 2008; Tinker et al. 2008).”
FORMATION RATES OF POPULATION III STARS AND CHEMICAL ENRICHMENT OF HALOS DURING THE REIONIZATION ERA (2009, result): “However, the Sheth & Tormen (1999) and the Warren et al. (2006) formulae give very similar results in the range of halo masses of interest for Population III star formation (M 108 M —see Figure 3 in Lukić et al. 2007), thus we keep the Sheth & Tormen (1999) model as our reference.”
Halo mass function and scale-dependent bias from N-body simulations with non-Gaussian initial conditions (2008, result): “Overall our findings are in good agreement with Heitmann et al. (2006) and Lukić et al. (2007).”
THE COYOTE UNIVERSE. I. PRECISION DETERMINATION OF THE NONLINEAR MATTER POWER SPECTRUM (2008, background): “Note that this has nothing to do with the accuracy of the Zel’dovich or some other approximation (Lukić et al. 2007).”
The halo mass function through the cosmic ages (2012, methodology): “Lukic et al. (2007) note that a correction of this form has a dependence on the accuracy of the mass functions at redshifts greater than z = 5.”
A fundamental problem in our understanding of low-mass galaxy evolution (2012, unknown): “The resulting functional form is very similar to what has been found previously for dark matter-only simulations (Lukić et al. 2007).”
Simulating cosmic reionization: how large a volume is large enough? (2013, result): “The results confirmed the trend observed previously by us and others (Iliev et al. 2006; Reed et al. 2007; Lukić et al. 2007; Iliev et al. 2012), namely that at the high redshifts of interest here the halo mass functions differ significantly from both the Press-Schechter (Press & Schechter1974)…”
The MassiveBlack-II simulation: The evolution of haloes and galaxies to z ~ 0 (2014, methodology): “In this analysis, we choose the mass bin to be log M = 0.2 which is well within the recommended bin width (Lukić et al. 2007) to avoid any systematic error that may arise in the estimate of the MF due to large bins.”
Simulating the Universe with MICE: The abundance of massive clusters (2009, background): “Several potential sources of systematic errors must be considered and controlled when implementing an N-body run, with their relevance sometimes dictated by the regime in which one is interested (see Lukic et al. 2007 for a detailed analysis).”