  We draw a quantitative comparison of the distribution of the galaxies and the
intra-cluster gas in the Virgo cluster by extending the morphological analysis
by Binggeli et al. (1987) to the intra-cluster gas. We use the Virgo Cluster
Catalog in combination with data from the ROSAT All-Sky Survey. The galaxy
distribution and the gas distribution are relatively similar. In both wavebands
the irregular structure of Virgo can be decomposed into three major subclusters
centred on M87, M49, and M86. A new statistical method of subcluster
decomposition is applied. Radial galaxy and X-ray density profiles of the three
subclusters are fitted with beta-models, allowing analytic deprojection.
Comparison of these profiles reveals, that there is no general luminosity
segregation. The gas density profile is steeper than the galaxy density profile
in the inner part, while this trend is reversed in the outer part. A comparison
among the subclusters shows the poorer the subcluster the steeper its radial
profile, i.e. the more compact it is, both in the optical and the X-rays. The
subcluster profiles for different Hubble types confirm the well-known result
that the distribution of the late-type galaxies is more extended than the early
types. Differential and integrated mass density profiles of the different
components in the M87 and M49 subclusters are presented. The total, gravitating
mass is inferred from the distribution of the X-ray gas. In the M87 subcluster
the gas mass is about three times the mass in galaxies, while it accounts only
for 8% to 14% of the total mass at 0.4 and 1 Mpc, respectively. In the M49
subcluster there is more mass in the galaxies than in the gas and the
gas-to-total mass fraction is only 1%, which is unusually low for a cluster.
The mass-to-light ratios show relatively constant values around 500Msol/Lsol.

Astrophysics