How well do integral-of-motion distribution functions describe Milky Way-analogue halos?

Abstract

We study the dark-matter phase space distribution of Milky Way-mass halos in the Auriga simulations, considering both hydrodynamic and dark-matter-only runs. In a spherically averaged potential, we test whether the coarse-grained distribution function can be approximated as a function of the integrals of motion $E$ and $L$. We find that $f(E,L)$ provides a useful description of the simulated halos: although the deviations from this form are formally statistically significant, the median fractional residuals between radial shells are typically $\lesssim 15\%$, with 90th-percentile residuals of order tens of percent. An energy-only approximation, $f(E)$, gives similar median residuals but is systematically disfavored by ${\chi }^2$ tests, indicating that angular momentum dependence is statistically preferred. Ultimately we find that neither $f(E)$ nor $f(E,L)$ fully describes the particle data at high precision. The remaining residuals likely reflect departures from spherical equilibrium, including anisotropy, triaxiality, substructure, and baryonic effects.

arXiv comment11 pages, 4 figures, PDFLaTeX