Elliptical galaxies and their groups having the largest L _ { x } / L _ { B } lie close to the locus L _ { x } = 4.3 \times 10 ^ { 43 } ( L _ { B } / 10 ^ { 11 } ~ { } L _ { B \odot } ) ^ { 1.75 } expected for closed systems having baryon fractions equal to the cosmic mean value , f _ { b } \approx 0.16 .
The estimated baryon fractions for several of these galaxies/groups are also close to f _ { b } = 0.16 when the gas density is extrapolated to the virial radius .
Evidently they are the least massive baryonically closed systems .
Gas retention in these groups implies that non-gravitational heating can not exceed about 1 keV per particle , consistent with the heating required to produce the deviation of groups from the L _ { x } - T correlation for more massive clusters .
Isolated galaxies/groups with X-ray luminosities significantly lower than baryonically closed groups may have undermassive dark halos , overactive central AGNs , or higher star formation efficiencies .
The virial mass and hot gas temperatures of nearly or completely closed groups correlate with the group X-ray luminosities and the optical luminosities of the group-centered elliptical galaxy , i.e . M _ { vir } \propto L _ { B } ^ { 1.33 } , an expected consequence of their merging history .
The ratio of halo mass to the mass of the central galaxy for X-ray luminous galaxy/groups is M _ { vir } / M _ { * } \sim 80 .