Annu. Rev. Astron. Astrophys. 1998. 36: 599-654
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3.5. Internal Properties of Galaxies, Halos, or Clusters

The next set of statistics listed in Table 1 refers to the internal properties of galaxies or galaxy clusters. In cosmological simulations, galaxies must be identified according to some prescription in order to apply these statistics. Thus the first question is how to identify dense objects in simulations. When baryons are present with high resolution and cooling, this problem is greatly simplified (at the expense of a much costlier simulation) by the condensation of cold gas in dark matter potential wells.

In simulations with only dark matter, several algorithms have been proposed for identifying objects, including the friends-of-friends linking algorithm used by Davis et al (1985), extensions devised by Barnes & Efstathiou (1987), methods based on spherical overdensity (e.g. Warren et al 1992, Lacey & Cole 1994), and the DENMAX algorithm of Bertschinger & Gelb (1991) (and modified by Governato et al 1997, who have publicly released their code called SKID). The reader must exercise caution in "galaxy" or "halo" results from simulations without baryons because of the strong merging of dark matter halos and the dependence of this process on resolution and method of halo identification (e.g. Gelb & Bertschinger 1994a, Summers et al 1995).

Given a set of galaxies or clusters, all the particle statistics listed in Table 1 may be applied and compared with those applied to other classes of objects (e.g. galaxies versus mass) in order to deduce the relative bias. This issue is discussed further in Section 2.6. However, the distribution functions can also be measured for internal properties of the composite objects including mass (e.g. Press & Schechter 1974, Brainerd & Villumsen 1992) or, for clusters, the number of members (the multiplicity function of Bhavsar et al 1981 is a logarithmic number distribution). For objects with "isothermal" density profiles rho propto r-2, the total mass is divergent, but the circular speed Vc = (GM / r)1/2 is constant and provides an alternative to mass (Frenk et al 1988, Gelb & Bertschinger 1994a, Ueda et al 1994). For clusters of galaxies, the velocity dispersion, temperature, and luminosity provide alternative statistics whose distributions provide tests of theory against observations (Evrard 1989, Peebles et al 1989, Cen & Ostriker 1994a).

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