The distribution function of dark matter in massive haloes |
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| Authors: | Rados&#;aw Wojtak Ewa L &#;okas Gary A Mamon Stefan Gottlöber Anatoly Klypin Yehuda Hoffman |
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| Institution: | Nicolaus Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland;Institut d'Astrophysique de Paris (UMR 7095: CNRS and UniversitéPierre &Marie Curie), 98 bis Bd Arago, F-75014 Paris, France;GEPI (UMR 8111: CNRS and UniversitéDenis Diderot), Observatoire de Paris, F-92195 Meudon, France;Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany;Department of Astronomy, New Mexico State University, Box 30001, Departament 4500, Las Cruces, NM 880003, USA;Racah Institute of Physics, Hebrew University, Jerusalem 91904, Israel |
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| Abstract: | We study the distribution function (DF) of dark matter particles in haloes of mass range 1014–1015 M⊙ . In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard Λ cold dark matter (ΛCDM) model. The DF is expressed as a function of energy E and the absolute value of the angular momentum L , a form suitable for comparison with theoretical models. By proper scaling we obtain the results that do not depend on the virial mass of the haloes. We demonstrate that the DF can be separated into energy and angular momentum components and propose a phenomenological model of the DF in the form  . This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (β0 and β∞ ) and the scale of transition between them ( L 0). The energy part f E ( E ) is obtained via inversion of the integral for spatial density. We provide a straightforward numerical scheme for this procedure as well as a simple analytical approximation for a typical halo formed in the simulation. The DF model is extensively compared with the simulations: using the model parameters obtained from fitting the anisotropy profile, we recover the DF from the simulation as well as the profiles of the dispersion and kurtosis of radial and tangential velocities. Finally, we show that our DF model reproduces the power-law behaviour of phase-space density Q =ρ( r )/σ3( r ) . |
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| Keywords: | methods: analytical methods: N-body simulations galaxies: clusters: general galaxies: kinematics and dynamics dark matter |
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