Session 18. Cluster Surveys/Galaxies
Oral, Tuesday, November 7, 2000, 1:00-2:30pm, Pago Pago Ballroom

## [18.04] Precise Calibration of the Virial Theorem from Hubble Volume Cluster Catalogs

A.E. Evrard (University of Michigan, Departments of Physics & Astronomy), T. Horikawa (Osaka University, X-ray Astronomy Group), Virgo Consortium Collaboration

The Hubble Volume project of the Virgo Consortium has created 109 particle N-body simulations of large-scale structure formation in {\Lambda}CDM and {\tau}CDM cosmologies with resolution sufficient to define a virtual Coma cluster with 500 particles. Light-cone survey output from the simulations provide synthetic sky surveys of the dark matter distribution in very large cosmic volumes, ~ 1010 h-3 Mpc3. Cluster catalogs derived from the surveys contain 100,000 to 500,000 clusters with masses exceeding 5 \times 1013 h-1 {\rm M}\odot and redshifts extending to z ~2.

We analyse in detail the virial relation between dark matter mass M\Delta_c and velocity dispersion \sigma. We find a unified calibration of the relation in the form H(z) M\Delta_c = A \sigmap for which the amplitude A and slope p are independent of cosmology and/or epoch (H(z) is the Hubble parameter at redshift z). This holds for clusters whose properties are defined within a spherical region encompassing a fixed density contrast \Deltac (typically 200) with respect to the critical density. Other definitions of clusters require a redshift dependent amplitude A(z). The scatter in \sigma at fixed H(z) M about the mean relation is small (~6%) and positively skewed. Subdividing the population into two classes --- parents' and children' --- we identify the minority child component as the source of the skewness and infer that the children are merger debris that has not yet been fully incorporated into the parent population. For the parents alone, the probability distribution function of the velocity dispersion residuals is very well modeled by a Gaussian distribution, suggesting a central limit theorem interpretation.

The accuracy of the calibration will be addressed by examining Virgo simulations with higher mass resolution and smaller volumes. Connections to obervable measures --- cluster X-ray temperature and galaxy velocity dispersion --- will be briefly discussed.