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

TL;DR

This paper investigates the pseudo phase space density profiles in CDM halos, revealing that their apparent power-law behavior is a result of slow convergence and deviations from hydrostatic equilibrium, not indicative of underlying integrals of motion.

Contribution

The study demonstrates that the observed power-law PPSD profiles are due to slow convergence and deviations from equilibrium, challenging previous assumptions about their fundamental significance.

Findings

Power-law PPSD arises from slow convergence, not fundamental physics.

Deviations from hydrostatic equilibrium cause non-power-law behavior.

Realistic collapse is not self-similar, affecting halo profile interpretations.

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.