The X‐Ray Concentration–Virial Mass Relation

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Abstract
We present the concentration (c)-virial mass (M) relation of 39 galaxy systems ranging in mass from individual early-type galaxies up to the most massive galaxy clusters, (0.06-20) × 1014 M☉. We selected for analysis the most relaxed systems possessing the highest quality data currently available in the Chandra and XMM-Newton public data archives. A power-law model fitted to the X-ray c-M relation requires at high significance (6.6 σ) that c decreases with increasing M, which is a general feature of CDM models. The median and scatter of the c-M relation produced by the flat, concordance ΛCDM model (Ωm = 0.3, σ8 = 0.9) agrees with the X-ray data, provided that the sample is comprised of the most relaxed, early-forming systems, which is consistent with our selection criteria. When allowing only σ8 to vary in the concordance model, the c-M relation requires 0.76 < σ8 < 1.07 (99% confidence), assuming a 10% upward bias in the concentrations for early-forming systems. The tilted, low-σ8 model suggested by a new WMAP analysis is rejected at 99.99% confidence, but a model with the same tilt and normalization can be reconciled with the X-ray data by increasing the dark energy equation of state parameter to w ≈ -0.8. When imposing the additional constraint of the tight relation between σ8 and Ωm from studies of cluster abundances, the X-ray c-M relation excludes (>99% confidence) both open CDM models and flat CDM models with Ωm ≈ 1. This result provides novel evidence for a flat, low-Ωm universe with dark energy using observations only in the local (z 1) universe. Possible systematic errors in the X-ray mass measurements of a magnitude ≈10% suggested by CDM simulations do not change our conclusions.