**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 10^{13}*h* *M*_{} corresponds to plasma
mass fractions ranging from 0.004*h*^{-3/2} (H97) to
0.09*h*^{-3/2}
(NGC 4261).
The average is

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* > 10^{13}*h* *M*_{}, to systems with the mass
characteristic of
galaxies, *M* ~ 10^{12}*h* *M*_{}. The result of integrating this
mass function from *M* = 10^{12}*h* *M*_{} to *M* =
10^{14}*h* *M*_{} is

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 10*h*^{-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

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}*)

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

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 10*h*^{-1} Mpc is likely to be in the range

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,

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}
~ 0.056*h*^{-3/2} (*M*_{group} / 0.6 x
10^{14} *M*_{}) for
*M*_{group} < 0.6 x 10^{14} *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.