Cluster Radius

A Galaxy Cluster's radius (Cluster Radius) is measured according to various criteria, some based upon the extent of the extra Mass Density (more generally used for Dark Matter Halos). It is a Virial Radius. Some that are used:

• R_200m - radius covering a volume with mass density 200 times the average of the universe.
• R_200c (or just R₂₀₀)- radius covering a volume with mass density 200 times the Critical Density at the cluster's Redshift.
• R_500c (R₅₀₀)- similar for 500 times.
• R_sp - Splashback Radius, i.e., the radius to which matter that has fallen through the halo reaches.

Estimated proportions:

R500c:R200c:R200m:Rsp≈1:1.4:3:4

Distant galaxy clusters are often scaled in relation to the critical density at the redshift of the cluster, because there are galaxy cluster attributes that follow that scale. The commonly-used galaxy cluster radius value R₅₀₀ indicates the radius that surrounds a volume whose mean density is 500 times the critical density at that redshift. Radii within the cluster can be usefully scaled as R/R₅₀₀.

Values used, based, e.g., on R₅₀₀:

• M₅₀₀ - mass of the cluster within R₅₀₀.
• N₅₀₀ - galaxies within the same volume.
• Y₅₀₀ - Compton Scattering Y-Parameter integrated over the same volume.
• L₅₀₀ - Luminosity over the same volume.
• P₅₀₀ - a pressure scaled to R₅₀₀.

Other parameters can be defined similarly.