Journal Article

The probability distribution of cluster formation times and implied Einstein radii

Sharon Sadeh and Yoel Rephaeli

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 388, issue 4, pages 1759-1765
Published in print August 2008 | ISSN: 0035-8711
Published online August 2008 | e-ISSN: 1365-2966 | DOI:
The probability distribution of cluster formation times and implied Einstein radii

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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 Λ cold dark matter (ΛCDM) 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 arcsec is very improbable in the currently favoured cosmological model. If, however, a variance of ∼20 per cent in the theoretically predicted value of the virial radius is assumed, then 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.

Keywords: gravitational lensing; galaxies: clusters: general; large-scale structure of Universe

Journal Article.  4453 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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