Durham University

Department of Physics

Staff profile

Publication details for Prof Carlos Frenk

Evrard, A.E., Bialek, J., Busha, M., White, M., Habib, S., Heitmann, K., Warren, M., Rasia, E., Tormen, G., Moscardini, L., Power, C., Jenkins, A.R., Gao, L., Frenk, C.S., Springel, V., White, S.D.M. & Diemand, J. (2008). Virial Scaling of Massive Dark Matter Halos: Why Clusters Prefer a High Normalization Cosmology. The Astrophysical Journal 672(1): 122-137.

Author(s) from Durham


We present a precise estimate of the bulk virial scaling relation of halos formed via hierarchical clustering in
an ensemble of simulated cold dark matter cosmologies. The result is insensitive to cosmological parameters; the
presence of a trace, dissipationless gas component; and numerical resolution down to a limit of 1000 particles. The
dark matter velocity dispersion scales with total mass as log½ ¼ DM(M;z) log (1082:9 4:0 km s1) þ (0:3361
0:0026)log h(z)M200 /10 ½ 15 M , with h(z) being the dimensionless Hubble parameter. At fixed mass, the velocity dispersion
likelihood is nearly lognormal, with scatter ln  ¼ 0:0426 0:015, except for a tail with higher dispersions
containing 10% of the population that are merger transients. We combine this relation with the halo mass function in
CDM models and show that a low normalization condition, S8 ¼ 8(m /0:3)0:35 ¼ 0:69, favored by recent WMAP
and SDSS analysis requires that galaxy and gas-specific energies in rich clusters be 50% larger than that of the underlying
dark matter. Such large energetic biases are in conflict with the current generation of direct simulations of cluster
formation. A higher normalization, S8 ¼ 0:80, alleviates this tension and implies that the hot gas fraction within r500
is (0:71 0:09) h3=2
70 b /m, a value consistent with recent Sunyaev-Zel’dovich observations.