Inferring Gravitational Potentials from Mass Densities in Cluster-sized Halos

TL;DR

This study uses N-body simulations to accurately infer gravitational potentials from mass densities in cluster halos, emphasizing the importance of cosmological constants and specific density profiles for precise escape velocity predictions.

Contribution

It demonstrates that matter density profiles can predict escape velocities within a few percent accuracy, highlighting the effectiveness of Einasto and Gamma profiles over NFW in this context.

Findings

Density-inferred potential predicts escape velocity within a few percent.

Einasto and Gamma profiles outperform NFW in modeling potential.

Sub-halo escape velocities match dark matter profiles with minimal bias.

Abstract

We use N-body simulations to quantify how the escape velocity in cluster-sized halos maps to the gravitational potential in a LambdaCDM universe. Using spherical density-potential pairs and the Poisson equation, we find that the matter density inferred gravitational potential profile predicts the escape velocity profile to within a few percent accuracy for group and cluster-sized halos (10^13 < M_200 < 10^15 M_sun, with respect to the critical density). The accuracy holds from just outside the core to beyond the virial radius. We show the importance of explicitly incorporating a cosmological constant when inferring the potential from the Poisson equation. We consider three density models and find that the Einasto and Gamma profiles provide a better joint estimate of the density and potential profiles than the Navarro, Frenk and White profile, which fails to accurately represent the escape velocity. For individual halos, the 1 sigma scatter between the measured escape velocity and the density-inferred potential profile is small (<5%). Finally, while the sub-halos show 15% biases in their representation of the particle velocity dispersion profile, the sub-halo escape velocity profile matches the dark matter escape velocity profile to high accuracy with no evidence for velocity bias outside 0.4r_200.