2.4.1. Warm Plasma in Groups

Some surveys are available from low energy X-ray observations with ROSAT (Mulchaey et al. 1996). The X-ray emission from 18 groups with total mass ranging from 1.2 to 8.3 x 10¹³h M corresponds to plasma mass fractions ranging from 0.004h^-3/2 (H97) to 0.09h^-3/2 (NGC 4261). The average is

(23)

significantly below the number for clusters (eq. [18]). In fact the baryon fraction shows a trend increasing with the group mass, approaching to the cluster value at the high mass end. This could be because groups are intrinsically poorer in plasma, or because much of the plasma is cooler and so escapes detection as an X-ray source. The latter is in line with the shallower gravitational potential wells in groups. The cool plasma clouds detected by Lyman- resonance absorption (Section 2.4.2) similarly are not detected as X-ray sources. Thus the plasma identifiable from its discrete X-ray emission might be considered a lower limit to the net plasma associated with groups of galaxies.

To convert equation (23) into a mean baryon density we need the mean gravitational mass associated with field galaxies (which almost always are in groups). The following measures may be compared. First, we can extrapolate the Bahcall-Cen (1993) mass function (eq. [15]), which they determined for M > 10¹³h M, to systems with the mass characteristic of galaxies, M ~ 10¹²h M. The result of integrating this mass function from M = 10¹²h M to M = 10¹⁴h M is

(24)

The cutoff is the characteristic mass of an L^* galaxy, the minimum for a group.

Second, we have dynamical mass measures from analyses of systems of galaxies on scales smaller than about 10h^-1 Mpc and outside the rich clusters. The survey of results of these analyses by Bahcall, Lubin & Dorman (1995) indicates M_grav/L (200⁺¹⁰⁰_-50)h. This with the mean luminosity density in equation (4) gives

(25)

Third, we can use the luminosity density, scaling from M/L calibrated in the great clusters by taking account of the difference in luminosities from the difference in morphological mixes (see also Carlberg et al. 1997). The small scatter in the color-magnitude relation for ellipticals and the spheroid components of spirals suggests these stars formed early, so it is reasonable to assume that the ratio of spheroid luminosity to gravitational mass is the same in clusters and the field. It would follow that the cosmic mean mass-to-spheroid-light ratio is (M/L_B)_cos = (M_grav/L_B)_cl f (sph, cos) / f (sph, cl) = (270 ± 60)h, where f (sph, cos) is the cosmic mean spheroid population luminosity fraction (eq. [3]), the value in clusters, f (sph, cl) = 0.64, follows from equation (21), and (M_grav/L_B)_cl is from equation (20). With equation (4) we have = 0.19^+0.07_-0.05. This however gives the cosmic mean including clusters; for comparison to equation (25) we ought to convert to the value outside rich clusters. The ratio of equation (16) to equation (20) is the mean luminosity density provided by the clusters, _cl = 0.09. The spheroid luminosity fraction in the field is

(26)

The assumption that the mass-to-spheroid-light ratio is universal thus indicates the density parameter in gravitational mass outside the Abell radii of the great clusters is

(27)

Despite the substantial uncertainties in each of these arguments we are encouraged by the consistency of equations (24), (25), and (27) to conclude that the density parameter in gravitational mass that clusters with galaxies on scales 10h^-1 Mpc is likely to be in the range

(28)

and that the spheroid-to-dark matter and baryon-to-dark matter ratios indeed do not vary widely between clusters and the field. As the evidence has indicated for some time (Peebles 1986) and has been widely noted in recent years, this low density parameter universe offers a natural interpretation of a variety of observations. Recent examples include the age/distance scale relation, the abundance of cluster baryons (White et al. 1993), the growth rate of correlation functions (Peacock 1997), the growth rate of the cluster mass function (Bahcall, Fan & Cen 1997), and preliminary indications from the distant supernova Hubble diagram (Garnavich et al. 1998, Perlmutter et al. 1998).

The product of equations (23) and (28) is the estimate of total plasma identified by X-ray emission in groups,

(29)

We remark that this estimate decreases only by 20% when we incorporate explicitly the trend that the baryon fraction increases as the group mass, (M_HII/M_grav)_group ~ 0.056h^-3/2 (M_group / 0.6 x 10¹⁴ M) for M_group < 0.6 x 10¹⁴ M. As we have noted, an alternative interpretation is that the trend is only apparent, a result of less efficient detection of plasma around cooler groups.