THE OVERDENSITY AND MASSES OF THE FRIENDS-OF-FRIENDS HALOS AND UNIVERSALITY OF HALO MASS FUNCTION

Journal Article · Fri Jul 01 04:00:00 EDT 2011 · Astrophysical Journal, Supplement Series

DOI:https://doi.org/10.1088/0067-0049/195/1/4· OSTI ID:21560356

More, Surhud; Kravtsov, Andrey V ^[1]; Dalal, Neal ^[2]; Gottloeber, Stefan ^[3]

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1. Kavli Institute for Cosmological Physics and Enrico Fermi Institute, University of Chicago, Chicago, IL 60637 (United States)
2. Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 3H8 (Canada)
3. Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam (Germany)

The friends-of-friends algorithm (hereafter FOF) is a percolation algorithm which is routinely used to identify dark matter halos from N-body simulations. We use results from percolation theory to show that the boundary of FOF halos does not correspond to a single density threshold but to a range of densities close to a critical value that depends upon the linking length parameter, b. We show that for the commonly used choice of b = 0.2, this critical density is equal to 81.62 times the mean matter density. Consequently, halos identified by the FOF algorithm enclose an average overdensity which depends on their density profile (concentration) and therefore changes with halo mass, contrary to the popular belief that the average overdensity is {approx}180. We derive an analytical expression for the overdensity as a function of the linking length parameter b and the concentration of the halo. Results of tests carried out using simulated and actual FOF halos identified in cosmological simulations show excellent agreement with our analytical prediction. We also find that the mass of the halo that the FOF algorithm selects crucially depends upon mass resolution. We find a percolation-theory-motivated formula that is able to accurately correct for the dependence on number of particles for the mock realizations of spherical and triaxial Navarro-Frenk-White halos. However, we show that this correction breaks down when applied to the real cosmological FOF halos due to the presence of substructures. Given that abundance of substructure depends on redshift and cosmology, we expect that the resolution effects due to substructure on the FOF mass and halo mass function will also depend on redshift and cosmology and will be difficult to correct for in general. Finally, we discuss the implications of our results for the universality of the mass function.

• OSTI ID: 21560356
• Journal Information: Astrophysical Journal, Supplement Series, Journal Name: Astrophysical Journal, Supplement Series Journal Issue: 1 Vol. 195; ISSN 0067-0049; ISSN APJSA2
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
ALGORITHMS
COSMOLOGY
DENSITY
MASS
MATHEMATICAL LOGIC
MATTER
NONLUMINOUS MATTER
PHYSICAL PROPERTIES
RED SHIFT
SIMULATION