Inferring Gravitational Potentials From Mass Densities in Cluster-Sized Halos

Abstract

We use N-body simulations to quantify how the escape velocity in cluster-sized halos maps to the gravitational potential in a ΛCDM 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 < < M 1013 200 15 M  , 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 1σ 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 of velocity bias outside 0.4r 200 .

On Escaping a Galaxy Cluster in an Accelerating Universe

“…This ambiguity introduces a problem with the normalization of the potential that is used to calculate the escape velocity profile. In particular, as demonstrated in Miller et al (2016), this offset ends up overestimating the potential by ∼20%. Following Behroozi et al (2013), we define the equivalence radius to be the point at which the acceleration due to the gravitational potential of the cluster and the acceleration of the expanding universe are equivalent Setting the boundary condition such that the escape velocity must necessarily be zero at the equivalence radius, , and using Equation (1), we find This reproduces the result shown in Stark et al (2016) and Miller et al (2016).…”

“…Moreover, as is also demonstrated by Miller et al (2016), in contrast to the NFW model, once the cosmological term (Equation (5)) has been included, both the Gamma (Dehnen 1993) and Einasto (Einasto 1965) gravitational potential profiles can model the radial escape velocity profiles to better than 3% precision. In what follows, we utilize the Einasto profile.…”

“…We now derive the escape velocity profile that includes cosmology and which has been utilized and tested against both simulations of the ΛCDM universe (Behroozi et al 2013;Miller et al 2016) and extensions to general relativity such as Chameleon f (R) gravity . We then extend those derivations to include projection effects.…”

“…In this effort, we extend the work of Miller et al (2016) to include projection effects and also to test the theory and the algorithm on real data. We use projected synthetic data from the light-cone data of Henriques et al (2012) as well as archival data on 20 galaxy clusters with extensive spectroscopic data and weak-lensing mass profiles.…”

“…A recent analysis by Miller et al (2016) utilized threedimensional phase spaces from the Millennium simulation (Springel et al 2005) to demonstrate that the escape velocity edge (e.g., the three-dimensional caustic) can recover the true underlying escape velocity profile of galaxy clusters to high accuracy and precision. The true escape velocity profile is determined from the application of the Poisson equation to the measured cluster density profile.…”