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Register a new userThe Mass-Concentration-Redshift Relation of Cold Dark Matter Halos
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Aaron D. Ludlow
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We use the Millennium Simulation series to investigate the mass and redshift dependence of the concentration of equilibrium cold dark matter (CDM) halos. We extend earlier work on the relation between halo mass profiles and assembly histories to show how the latter may be used to predict concentrations for halos of all masses and at any redshift. Our results clarify the link between concentration and the ``collapse redshift of a halo as well as why concentration depends on mass and redshift solely through the dimensionless ``peak height mass parameter, $ u(M,z)=delta_{rm crit}(z)/sigma(M,z)$. We combine these results with analytic mass accretion histories to extrapolate the $c(M,z)$ relations to mass regimes difficult to reach through direct simulation. Our model predicts that, at given $z$, $c(M)$ should deviate systematically from a simple power law at high masses, where concentrations approach a constant value, and at low masses, where concentrations are substantially lower than expected from extrapolating published empirical fits. This correction may reduce the expected self-annihilation boost factor from substructure by about one order of magnitude. The model also reproduces the $c(M,z)$ dependence on cosmological parameters reported in earlier work, and thus provides a simple and robust account of the relation between cosmology and the mass-concentration-redshift relation of CDM halos.
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(Abriged) Assuming that the hydrostatic equilibrium holds between the intracluster medium and the gravitational potential, we constrain the NFW profiles in a sample of 44 X-ray luminous galaxy clusters observed with XMM-Newton in the redshift range 0.1-0.3. We evaluate several systematic uncertainties that affect our reconstruction of the X-ray masses. We measure the concentration c200, the dark mass M200 and the gas mass fraction within R500 in all the objects of our sample, providing the largest dataset of mass parameters for galaxy clusters in this redshift range. We confirm that a tight correlation between c200 and M200 is present and in good agreement with the predictions from numerical simulations and previous observations. When we consider a subsample of relaxed clusters that host a Low-Entropy-Core (LEC), we measure a flatter c-M relation with a total scatter that is lower by 40 per cent. From the distribution of the estimates of c200 and M200, with associated statistical (15-25%) and systematic (5-15%) errors, we use the predicted values from semi-analytic prescriptions calibrated through N-body numerical runs and measure sigma_8*Omega_m^(0.60+-0.03)= 0.45+-0.01 (at 2 sigma level, statistical only) for the subsample of the clusters where the mass reconstruction has been obtained more robustly, and sigma_8*Omega_m^(0.56+-0.04) = 0.39+-0.02 for the subsample of the 11 more relaxed LEC objects. With the further constraint from the fgas distribution in our sample, we break the degeneracy in the sigma_8-Omega_m plane and obtain the best-fit values sigma_8~1.0+-0.2 (0.75+-0.18 when the subsample of the more relaxed objects is considered) and Omega_m = 0.26+-0.01.
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