© CAMBRIDGE UNIVERSITY PRESS 1999

3.7. X-Ray-Optical Correlations of Cluster Properties

Some observed correlations between X-ray and optical properties are listed in Table 7 (Bahcall 1977a, b; Edge and Stewart 1991; David et al. 1993; Lubin and Bahcall 1993).

Table 7. Correlations Between X-Ray and Optical Properties. ^a

Properties	Correlation
r-T	r (km s-1) (332 ± 52)[kT (kev)]0.6 ± 0.1
T-N0.5	kT (keV) 0.3N0.50.95 ± 0.18
Lx-N0.5	Lx(bol) ~ 1.4 × 1040N0.53.16 ± 0.15h-2
Lx-fsp	Lx(bol) 0.6 × 1043fsp-2.16 ± 0.11h-2
fsp-T	fsp 1.2[kT (kev)]-0.94 ± 0.38
T-Lx	kT (keV) 0.3[Lx(bol) h2/1040]0.297 ± 0.004
a r is the galaxy line-of-sight velocity dispersion in the cluster (km s-1). T is the temperature of the intracluster gas [kT(keV)]. N0.5 is the central galaxy density in the cluster [number of galaxies brighter than m3 + 2m, within r 0.5h50-1 = 0.25 h-1 of the cluster center (Bahcall 1977a; Edge and Stewart 1991)]. Lx(bol) is the bolometric X-ray luminosity of the cluster (erg s-1). fsp is the fraction of spiral galaxies in the cluster ( 1.5h-1 Mpc) (Bahcall 1977b; Edge and Stewart 1991). Typical uncertainties of the coefficients are ~ 50% (see references).