Mathematics – Probability
Scientific paper
Oct 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000head....5.1804e&link_type=abstract
American Astronomical Society, HEAD Meeting #5, #18.04; Bulletin of the American Astronomical Society, Vol. 32, p.1209
Mathematics
Probability
Scientific paper
The Hubble Volume project of the Virgo Consortium has created 109 particle N-body simulations of large-scale structure formation in ΛCDM and τCDM 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 x 1013 h-1 Msun and redshifts extending to z ~ 2. We analyse in detail the virial relation between dark matter mass MΔ c and velocity dispersion σ . We find a unified calibration of the relation in the form H(z) MΔ c = A σ p 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 Δ c (typically 200) with respect to the critical density. Other definitions of clusters require a redshift dependent amplitude A(z). The scatter in σ 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.
Evrard August E.
Horikawa Takako
Virgo Consortium Collaboration
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