The X‐Ray Concentration–Virial Mass Relation

Abstract

We present the concentration (c)Yvirial mass (M ) relation of 39 galaxy systems ranging in mass from individual
\nearly-type galaxies up to the most massive galaxy clusters, (0:06Y20) ; 1014 M. We selected for analysis the most
\nrelaxed systems possessing the highest quality data currently available in the Chandra and XMM-Newton public data
\narchives. A power-law model fitted to the X-ray c-M relation requires at high significance (6.6 ) that c decreases with
\nincreasing M, which is a general feature of CDM models. The median and scatter of the c-M relation produced by the
\nflat, concordance CDM model (m 1⁄4 0:3, 8 1⁄4 0:9) agrees with the X-ray data, provided that the sample is comprised
\nof the most relaxed, early-forming systems, which is consistent with our selection criteria. When allowing only
\n8 to vary in the concordance model, the c-M relation requires 0:76 < 8 < 1:07 (99% confidence), assuming a 10%
\nupward bias in the concentrations for early-forming systems. The tilted, low-8 model suggested by a new WMAP
\nanalysis is rejected at 99.99% confidence, but a model with the same tilt and normalization can be reconciled with the
\nX-ray data by increasing the dark energy equation of state parameter to w 0:8. When imposing the additional constraint
\nof the tight relation between 8 and m from studies of cluster abundances, the X-ray c-M relation excludes
\n(>99% confidence) both open CDM models and flat CDM models with m 1. This result provides novel evidence for
\na flat, low-m universe with dark energy using observations only in the local (zT1) universe. Possible systematic errors
\nin the X-ray mass measurements of a magnitude 10% suggested by CDM simulations do not change our conclusions.