2.4.3. Scaling from Clusters to Groups

As an alternative to adding the previous two directly observed components (warm X-ray emitting gas and cool Lyman- absorbing gas), we can estimate the total plasma in groups from the assumption that it has the same ratio to dark matter as in the rich clusters. That is, the scaling used to arrive at the density parameter in gravitational mass in the field from spheroid luminosity (eq. [27) readily generalizes to a scaling estimate of the density parameter in plasma associated with groups. The product of equation (18) for the ratio of plasma to gravitational mass in clusters and equation (28) for the density parameter in the field yields

(32)

In a calculation along similar lines Carlberg et al. (1997) find a similar result, (_HII)_field = (0.01-0.014) h^-3/2. The central value in equation (32) agrees with the upper bound from the sum of the more direct estimates in equations (29) and (31).

Equation (32) assumes a fair sample of plasma relative to gravitational mass is assembled and preserved in the great clusters. If disks were less common in clusters because star formation has been suppressed, equation (32) would include baryons in disks in the field, but the correction is small because the baryon mass in disk stars is small. It is not thought that cluster cooling flows or winds have seriously depleted the cluster plasma mass. In a more direct argument Renzini (1997) finds that the iron and gas content of clusters and groups indicate the clusters indeed have close to the global star formation efficiency, and that the corresponding enriched gas from groups has been ejected into intergalactic space, presumably ending up in the form discussed in Section 2.4.1 and Section 2.4.2.