The probability distribution of cluster formation times and implied Einstein Radii

TL;DR

This paper assesses the probability distribution of galaxy cluster concentrations and Einstein radii within the standard Lambda CDM model, finding that observed high values are unlikely but could be explained by early structure formation or alternative cosmologies.

Contribution

It introduces a method combining the excursion set formalism and simulation-based scaling to evaluate cluster concentration and Einstein radius distributions.

Findings

Observed high cluster concentrations are unlikely in Lambda CDM.

Large Einstein radii, like in A1689, are improbable under standard model assumptions.

Early dark energy models can naturally produce larger Einstein radii in multiple clusters.

Abstract

We provide a quantitative assessment of the probability distribution function of the concentration parameter of galaxy clusters. We do so by using the probability distribution function of halo formation times, calculated by means of the excursion set formalism, and a formation redshift-concentration scaling derived from results of N-body simulations. Our results suggest that the observed high concentrations of several clusters are quite unlikely in the standard Lambda CDM cosmological model, but that due to various inherent uncertainties, the statistical range of the predicted distribution may be significantly wider than commonly acknowledged. In addition, the probability distribution function of the Einstein radius of A1689 is evaluated, confirming that the observed value of ~45" +/- 5" is very improbable in the currently favoured cosmological model. If, however, a variance of ~20% in the theoretically predicted value of the virial radius is assumed, than the discrepancy is much weaker. The measurement of similarly large Einstein radii in several other clusters would pose a difficulty to the standard model. If so, earlier formation of the large scale structure would be required, in accord with predictions of some quintessence models. We have indeed verified that in a viable early dark energy model large Einstein radii are predicted in as many as a few tens of high-mass clusters.