The orbital PDF: the dynamical state of Milky Way sized haloes and the intrinsic uncertainty in the determination of their masses

Abstract

Using realistic cosmological simulations of Milky Way sized haloes, we study their dynamical state and the accuracy of inferring their mass profiles with steady-state models of dynamical tracers. We use a new method that describes the phase-space distribution of a steady-state tracer population in a spherical potential without any assumption regarding the distribution of their orbits. Applying the method to five haloes from the Aquarius Λ cold dark matter (ΛCDM) N-body simulation, we find that dark matter particles are an accurate tracer that enables the halo mass and concentration parameters to be recovered with an accuracy of 5 per cent. Assuming a potential profile of the Navarro, Frenk & White (NFW) form does not significantly affect the fits in most cases, except for halo A whose density profile differs significantly from the NFW form, leading to a 30 per cent bias in the dynamically fitted parameters. The existence of substructures in the dark matter tracers only affects the fits by ∼1 per cent. Applying the method to mock stellar haloes generated by a particle-tagging technique, we find the stars are farther from equilibrium than dark matter particles, yielding a systematic bias of ∼20 per cent in the inferred mass and concentration parameter. The level of systematic biases obtained from a conventional distribution function fit to stars is comparable to ours, while similar fits to dark matter tracers are significantly biased in contrast to our fits. In line with previous studies, the mass bias is much reduced near the tracer half-mass radius.