Arcs from a Universal Dark-Matter Halo Profile

TL;DR

This paper demonstrates that the universal dark-matter halo profile proposed by Navarro et al. can produce radial arcs in galaxy clusters despite its central singularity, challenging previous assumptions about core profiles.

Contribution

It shows how the Navarro et al. profile can explain radial arcs and provides a method to determine profile parameters from observed arcs in clusters.

Findings

The Navarro profile can produce radial arcs despite singularity.

Parameter ranges can predict unknown arc redshifts.

Radial magnification may cause thick tangential arcs.

Abstract

Navarro, Frenk, \& White have recently found numerically that the density profile of dark-matter halos can be described by a universal two-parameter function over a broad range of halo masses. The profile is singular, approaching the halo center with $\rho\propto r^{-1}$. It had been argued previously that radially distorted, gravitationally lensed images of background sources in galaxy clusters, so-called radial arcs, required a flat core in the cluster density profile. Such radial arcs have so far been detected in two galaxy clusters, in apparent contradiction with a singular density profile. I show here that the profile suggested by Navarro et al. can produce radial arcs despite its central singularity, and describe how the two parameters of the profile can be determined in clusters where radial and tangential arcs are observed. I then apply this analysis to the two clusters where radial arcs were detected. In both cases, the redshifts of the radial arcs are yet unknown, hence definitive conclusions on the profile parameters cannot yet be drawn. Numerically determined values for the parameters of cluster-sized halos can, however, be used to predict the range of the unknown arc redshifts, thus providing a direct observational test for the proposed density profile. A potential difficulty with the profile is that the radial magnification of tangential arcs is large, hence tangential arcs should be thick or their sources should be very thin in the radial direction.