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With the occurrence of HI deficiency well established in some clusters and not in others, it is possible to examine the evidence for on-going sweeping in an attempt to identify the mechanism(s) that are responsible for the gas depletion. It is likely that several processes play a role, some more likely than others but all may occur in individual situations.

Gas removal mechanisms need not necessarily arise from external causes, driven by the environment. However, since the HI deficient spirals at least to a visual inspection show similar optical morphology to their HI rich counterparts outside clusters, it seems most likely that the cause of the deficiency is indeed governed by the peculiar circumstance of the galaxy's location within a cluster core. Thus we are led to examine the occurrence of HI deficiency in terms of the likely environment-dependent gas removal mechanisms generally divided into two categories: interactions among neighboring galaxies in the cluster and interactions between a galaxy and the intracluster medium (ICM) in which it is immersed.

In the environments of loose groups, tidal encounters are likely to remove gas from galaxies that come closer than a galaxy diameter (Toomre and Toomre 1972). There are many examples of such HI appendages and their explanations are, with few exceptions, quite straightforward in terms of tidal disruption (Haynes et al. 1984). In several cases, large fractions of the disk HI have been removed to larger radii. The ultimate fate of the disturbed HI is unclear. Cottrell (1978) would like to explain the occurrence of IrrII galaxies in terms of tidal disruption with subsequent gas infall and enhanced star formation. The likelihood that a galaxy will suffer a tidal collision depends on its cross section, the mean separation and the local velocity dispersion. The actual damage a galaxy suffers depends critically on parameters like the relative orientations of spin and orbital angular momentum, but can be examined, to first order, in terms of the separation and relative radial velocity of likely participants. In the impulse approximation, the "disruption damage" is just proportional to 1/a2v, where a is the separation and v is the relative velocity of the interacting galaxies. Hence, for the same perigalactic distance, a tidal encounter in a loose group will inflict more damage than will one in a cluster because the duration of the tidal pull will be longer where the velocity dispersion is lower. On the other hand, tidal encounters are more likely to occur in clusters where the cross section for an interaction is much larger.

Because of the high density of galaxies, it is also possible that direct collisions among galaxies might lead to the gas removal in clusters. Spitzer and Baade (1951) proposed that collisions could remove most of the interstellar medium from galaxies which suffer a head-on collision although the two stellar components would remain relatively intact albeit without their dust and gas. The stellar remnants would resemble S0 galaxies and the interstellar material, having been heated by the collisional shock to high temperatures, could expand and dissipate into the ICM. Direct collisions undoubtedly lead to dramatic events, and interpenetrating encounters are the likely cause of ring galaxies (Lynds and Toomre 1976). In clusters, the collisional cross section is higher, but it is not likely that it is high enough to lead to the observed deficiency seen in cluster spirals today, especially if orbits are preferentially radial. Sarazin (1979) has estimated a collision rate about 1000 times lower than that calculated by Spitzer and Baade.

Galaxy-ICM interactions have been the subject of a large number of papers many of which are referenced in Sarazin (1986). One of the most popular and simple treatments considers the ram pressure induced by the motion of a galaxy with a uniform velocity through a uniform ICM (Gunn and Gott 1972). In this picture, the pressure of the ICM felt by the cold interstellar gas competes with the gravitational force (per unit area) within the galaxy so that ram pressure sweeping is effective in the circumstance that

Equation 2

A typical spiral galaxy of total mass of 1011 Msun, radius of 10 kpc, gas density nH of 1 cm-3, and HI scale height of 100 pc has a surface mass density of stars sigma* of about 0.06 g cm-2 and of gas sigmag about 10-3 g cm-2, so that the restoring force created by its gravitational potential is 2 x 10-11 dyn cm-2. In rich clusters, the velocity dispersion yields an estimate of the three-dimension velocity of order 1700 kms-1 (although note that we actually need the component of the galaxy's orbital velocity normal to its disk). Therefore the ram pressure in a typical cluster can be written in terms of the local ICM density nICM, itself a function of the distance to the cluster center:

Equation 3

For the typical spiral then, stripping will occur when the ram pressure exceeds the restoring force, that is, when nICM > 5 x 10-4 cm-3.

Other mechanisms also arise from galaxy-ICM interactions. Cowie and Songaila (1977) have investigated the case of thermal evaporation. Examining the simple stationary case, they find that heat conduction leads to subsequent evaporation of the interstellar HI gas. The evaporative mass loss rate is a sensitive function of the ICM temperature (largely uncertain) and less sensitively of the ICM density. In fact, if radiation from the interface between the hot and cold gas becomes important, material may actually condense onto the galaxy, causing an increase in the mass density and perhaps an enhancement of the star formation rate. In several papers, Nulsen and coworkers (Nulsen 1982; Takeda et al. 1984) have considered the more realistic case of a galaxy moving through the cluster on a radial orbit so that the ram pressure encountered varies greatly along its path. While in the outer regions of the cluster, the galaxy accumulates gas subsequently lost during its passage through the core. This treatment of turbulent viscosity predicts that some galaxies in low density, low dispersion clusters should retain their stripped interstellar gas as a hot X-ray halo. X-ray sources seen to be associated with individual galaxies in Virgo (Forman et al. 1979) and A1367 (Bechtold et al. 1983) might be identified as such objects. Rather more complicated two-dimensional codes which include hyrodynamical calculations have been examined by Gaetz et al. (1987) to study the effect of cluster passage on spherical galaxies. A real treatment of the problem for a disk of gas and stars requires added complexity and has yet to be fully solved. Sarazin (1986) discusses in more detail the various calculations that have been performed to investigate the stripping process.

Of the various mechanisms, several predict correlations that may lead to a variation in the observed degree of deficiency among clusters of different morphologies and properties. Based on the simple ram pressure sweeping model, we expect that galaxies travelling at high velocities through clusters with a dense ICM would be expected to be stripped. Thus the ram pressure scenario predicts greater stripping in clusters characterized by high velocity dispersion and higher ICM density. The efficiency of evaporative stripping is only weakly dependent on ICM density, but is strongly dependent on the ICM temperature. Therefore, it would be valuable for the comparison between ram pressure and evaporative stripping to discern any difference in the temperatures of the clusters with different degrees of deficiency. Note, however, that it is likely that high temperature clusters may also have a high velocity dispersion. A correlation is already noted between high X-ray luminosity and high velocity dispersion.

As part of their analysis, GH85 looked for correlations between the degree of HI deficiency and the X-ray properties of the cluster. A useful parameter derived by GH85 and presented in Table 1 is the "deficient fraction," d.f., the fraction of cluster galaxies in the observational sample that are HI deficient. Use of this fraction requires the assumption that there has been no particular bias introduced in choosing the observational sample, that is, that all candidate spirals have been observed. For the GH85 sample, Dressler (1986) has suggested that such is the case. GH85 find that d.f. correlates with the X-ray luminosity of the cluster: the clusters with the highest LX contain the greatest proportion of highly HI deficient objects.

There are two clusters that have been used in the direct comparison of the efficiency of galaxy-galaxy and galaxy-ICM interactions because they lie at the same distance and are close together on the sky: A2147 and A2151 (Giovanelli et al. 1981). In contrast to A2151 (the Hercules cluster), A2147 is more centrally concentrated, contains a greater elliptical fraction and has a stronger cluster X-ray source. A2151, however, contains a higher density of galaxies, so that the cross section for galaxy-galaxy interactions is expected to be higher in its core. While A2151 does contain some HI poor objects, the overall HI deficiency is significantly higher in A2147, thus supporting the relative importance of galaxy-ICM interactions. Furthermore, A2147 is characterized by a relatively low ICM temperature (Mushotzky 1984) so that ram pressure is more likely to be effective than evaporation. It should be noted, however, that this result depends on the comparison of only these two clusters which themselves are the most distant in the current sample, and hence should be considered supportive though not conclusive.

In an attempt to pin down which one of the likely mechanisms was in fact responsible for the observed gas deficiency, Magri et al. (1988) have undertaken a detailed statistical analysis of the HI, optical and X-ray data available for galaxies in six clusters. They used maximum likelihood and non-parametric techniques to search for correlations between the observed HI deficiency in the galaxies and tracers of the likely stripping processes: (a) r, the distance to the cluster center, (b) r / rc, the same distance scaled to the cluster core radius, (c) nproj, the number density of galaxies projected locally, (d) V, the galaxy velocity relative to the cluster mean, (e) V2, the square of the velocity, (f) rhoICM, the local ICM density derived from fitting the X-ray surface brightness distribution, and (e) rhoICM V2, the intracluster ram pressure. Magri et al. find that HI deficiency is a monotonically decreasing function of distance from the cluster center. It is unclear whether the dependence is on the radius itself or on n or rho, since a linear dependence on density is almost equivalent to a dependence on r-3beta, with beta obtained from the fit to the surface brightness. As a mechanism, ram pressure should predict a correlation with rho, V2, or their product rhoV2, but no such dependence was observed. GH85 have employed Monte Carlo simulations to illustrate that the signature of the velocity dependence of ram pressure stripping would likely be masked by randomizing projection effects which reduce the sensitivity of the observational variable. For one problem, galaxies with normal HI contents but actually at large radii may be only projected on the core. In addition, the important vector in ram pressure is the component of the galaxy's orbital motion in the direction normal to the disk. Galaxies passing through the cluster edge-on will emerge relatively unscathed. In many galaxies, the surface mass density sigma* at the Holmberg radius is significantly lower than in the Milky Way (Bosma 1981) by as much as an order of magnitude. Since the simple ram pressure criterion described by Gunn and Gott (1972) balances the ram pressure force with the restoring force within the galaxy's disk, it is to be expected that dwarf galaxies, possessing smaller potential wells, should be preferentially stripped of the HI gas. However, such a dependence of HI deficiency on mass surface density has not been observed even among the Virgo dwarfs (Hoffman et al. 1985). Thus, while ram pressure sweeping is an often-invoked explanation for the gas removal, its direct predictions of velocity and mass dependence are not evident in the observational data.

While the effectiveness of ram pressure is highly dependent on galaxy orientation, the amount of gas lost through turbulent viscous stripping is comparable to the mass of hot ICM material encountered by the galaxy disk as it travels through the cluster and depends on the amount of time spent in the high density ICM core. As noted by Pryor and Geller (1984), a galaxy seen at a large projected distance must have a long period even if its orbit is highly radial. When in the outer portions of the cluster, such a galaxy has the opportunity to accumulate material lost by evolving stars. Several objects that are extremely HI deficient lie on the outskirts of the Virgo cluster and may be in the gas accumulation phase (Giovanelli and Haynes 1983). Based on the occurrence of HI deficiency relative to the X-ray emission seen in the center of Virgo, Haynes and Giovanelli (1986) argue that turbulent viscous stripping can account for the observed HI deficiency of galaxies within three degrees of M87.

The fact that the H2 component, as derived from the CO observations, remains intact argues again for an external gas sweeping mechanism, but may be easy to explain. Since the filling factor of molecular clouds in the ISM is much lower than that of HI clouds, collisions among the densest clouds during galaxy collisions will be unlikely, whereas the lower density clouds may be more susceptible. Numerical calculations by Kritsuk (1983) show that the molecular component will survive a sweeping event. What remains is our lack of understanding of the long-term effect of the removal of over ninety percent of a galaxy's HI mass. Surely its disk will fade.

As noted by Dressler (1986), the HI deficiency observed for spirals of types Sb and earlier is marked more severe than that observed for later types. He has examined the velocity distribution of deficient and HI-normal galaxies and concludes that this variation in the typical degree of HI depletion can be explained in terms of differences in the characteristic anisotropy of the orbits of different types. He suggests that early type spirals travel through the cluster on orbits that are preferentially more radial than the later spirals. A similar conclusion was reached for the HI-deficient galaxies in Virgo by Giraud (1986). Thus some fundamental fine-tuning of the orbital characteristics of the galaxies plays an important role in their likelihood of gas depletion and perhaps of the overall morphology as well. However, such kinematic differences are quite uncertain, and indeed, Pryor and Geller (1984) conclude that, based on current data, the most likely models are isotropic.

At the present time, the available data allow limited analysis of the three dimensional distribution of gas and galaxies in clusters. In several of the six clusters studied by Magri et al. , both the galaxy and X-ray surface densities show strong asymmetries in their azimuthal distributions and exhibit significant subclumping. Spatially resolved X-ray spectroscopy and imaging are needed in order to determine structure in both the temperature and density distributions of the intracluster gas.

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