On the Apparent Power Law in CDM Halo Pseudo Phase Space Density Profiles

Abstract

We investigate the apparent power-law scaling of the pseudo phase space density (PPSD) in CDM halos. We study fluid collapse, using the close analogy between the gas entropy and the PPSD in the fluid approximation. Our hydrodynamic calculations allow for a precise evaluation of logarithmic derivatives. For scale-free initial conditions, entropy is a power law in Lagrangian (mass) coordinates, but not in Eulerian (radial) coordinates. The deviation from a radial power law arises from incomplete hydrostatic equilibrium (HSE), linked to bulk inflow and mass accretion, and the convergence to the asymptotic central power-law slope is very slow. For more realistic collapse, entropy is not a power law with either radius or mass due to deviations from HSE and scale-dependent initial conditions. Instead, it is a slowly rolling power law that appears approximately linear on a log-log plot. Our fluid calculations recover PPSD power-law slopes and residual amplitudes similar to N-body simulations, indicating that deviations from a power law are not numerical artefacts. In addition, we find that realistic collapse is not self-similar: scale lengths such as the shock radius and the turnaround radius are not power-law functions of time. We therefore argue that the apparent power-law PPSD cannot be used to make detailed dynamical inferences or extrapolate halo profiles inward, and that it does not indicate any hidden integrals of motion. We also suggest that the apparent agreement between the PPSD and the asymptotic Bertschinger slope is purely coincidental.

13 pages, 11 figures; updated to match version accepted by MNRAS; conclusions unchanged

References in corpus (15)

• Power-law distributions in empirical data
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Intracluster Medium Entropy Profiles for a Chandra Archival Sample of Galaxy Clusters
• Dark matter and cosmic structure
• The Mass-Concentration-Redshift Relation of Cold and Warm Dark Matter Halos
• A universal density slope - velocity anisotropy relation for relaxed structures
• On the Origin of Cores in Simulated Galaxy Clusters
• On Universal Halos and the Radial Orbit Instability
• Self-Similar Solutions of Triaxial Dark Matter Halos
• Evolution of Phase-Space Density in Dark Matter Halos
• Orbital Instabilities in a Triaxial Cusp Potential
• Entropy of gas and dark matter in galaxy clusters
• Self-Similar Spherical Collapse with Tidal Torque
• Alas, the dark matter structures were not that trivial
• Phase-Space Density Profiles in Scale-Free Cosmologies

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• N-body simulations of dark matter-baryon interactions
• Structural and dynamical modeling of WINGS clusters. III. The pseudo phase-space density profile
• The Non-universal Pseudo Phase-Space Density Profiles of Symphony Host Halos